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From: <Saved by Blink>
Snapshot-Content-Location: https://chatgpt.com/c/0a22c9fc-d493-4d65-8eb9-79ad92316ac7
Subject: Mantle Transferences
Date: Thu, 20 Jun 2024 19:42:19 -0300
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min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb213fe-3612-4013-88a6-97ca1a1b5ca0" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>JONATHAN A. CHEUNG, Ph.D.
Los Angeles, CA 90025 • [email protected] • github.com/jacheung • (415) 519-2029
Summary
• 9 years of experience using statistics and machine learning for data-driven discoveries
• 5 years of experience in client-facing roles leveraging analytics to deliver business solutions
• 4 peer-reviewed publications resulting from hypothesis-driven experimentation
Experience
Senior Data Scientist – Beyond Limits AI Nov ‘21 – Present
• Delivered 4 projects in the industrial sector – guiding clients from pain points to deployed solutions
• Facilitated user task completion rate by 18% through A/B testing and improving inference pipeline speed by 28%
on our flagship sand management product for British Petroleum
• Optimized 2 POCs for production through hardening codebase with MLflow, Optuna, and Kubeflow pipelines
• Collaborated cross-organizationally with the recruiting department to reduce time to hire from 45 to 36 days
leveraging our in-house hybrid AI technology, GPT-4, vector stores, and integration with Greenhouse API
• Devised and deployed a battery management solution – reducing cell testing time by 85%, from 70 to 10 days,
for 18650 and 21700 type batteries with 96% accuracy
• Recurring lecturer for 30+ student pods on problem discovery and data-science product building for Aramco’s
Global AI Corridor with Beyond Limits and Caltech
Data Scientist – Demand Forecasting and Rate Design, Southern California Gas Co. Aug ‘20 – Oct ‘21
• Improved forecasting accuracy of daily gas consumption by 29%, translating to cost-savings of $3-5M, via feature
engineering and XGBoost for forecasting
• Developed and deployed forecasting pipelines for data ingestion, forecast, and end-point monitoring of daily gas
consumption in PowerBI to address anomalies early and improve result visibility across the organization
• Founding member of SoCalGas’ Model Review Board- tasked with prioritizing data science applications from
end-to-end on dimensions of time and cost and providing a roadmap to deployment
Doctoral Researcher – Hires Laboratory, University of Southern California Sep ‘14 – Apr ‘20
• Resolved a decade-long debate on tactile search strategies through experimentation and predictive modeling using
16 uniquely extracted touch features – Cheung et al. 2019
• Produced key findings for 2 major grants, increasing funding from $1M to $4.5M over 4 years, by collaborating
with colleagues to author 4 manuscripts in high-impact peer reviewed journals
• Saved 2000+ work hours by automating touch frame detection using TensorFlow and the pre-trained base model,
ResNet50, to make fast and accurate image classification forces – Maire et al. 2023
Skills
• Tools: Python | SQL | GCP | AWS | Docker
• Non-Dev Tools: Figma Figjam | Miro | A/B Testing | Power BI
• Machine learning engineering: MLflow | Optuna | Kubernetes | Kubeflow
• Python libraries: pandas | NumPy | scikit-learn | TensorFlow | PyTorch | matplotlib | Langchain
• Supervised learning: linear and logistic regression | generalized linear models (GLM) | gradient boosting
regressors | time-series forecasting | convolutional neural networks (CNNs) | large language models (LLMs)
• Unsupervised learning: clustering (k-means, DBSCAN, OPTICS), dimensionality reduction (PCA, t-SNE)
Education
Ph.D. Neuroscience B.S. Human Biology
University of Southern California University of California, San Diego
Los Angeles, CA / 2020 San Diego, CA / 2013</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-3" 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11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="d5a1bc3e-8a37-4ac3-b4aa-097200e6e2f8" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Jonathan A. Cheung's resume showcases an impressive blend of expertise in data science and machine learning, with extensive experience in applying these skills to real-world business and scientific challenges. Here's a summary of his qualifications and achievements:</p><h3>Summary</h3><ul><li><strong>Experience:</strong> 9 years using statistics and machine learning for data-driven discoveries, with 5 years in client-facing roles.</li><li><strong>Publications:</strong> Contributed to 4 peer-reviewed publications.</li></ul><h3>Professional Experience</h3><h4>Beyond Limits AI (Nov 2021 – Present)</h4><ul><li><strong>Role:</strong> Senior Data Scientist</li><li><strong>Achievements:</strong><ul><li>Delivered multiple industrial projects, including an enhanced task completion rate for a sand management product and optimization of Proof of Concepts (POCs) using ML technologies.</li><li>Devised a battery management solution significantly reducing cell testing time.</li><li>Involved in academic collaborations and cross-functional organizational improvements.</li></ul></li></ul><h4>Southern California Gas Co. (Aug 2020 – Oct 2021)</h4><ul><li><strong>Role:</strong> Data Scientist</li><li><strong>Achievements:</strong><ul><li>Enhanced daily gas consumption forecasting, resulting in substantial cost savings.</li><li>Key member of the Model Review Board, overseeing the deployment of data science projects.</li></ul></li></ul><h4>University of Southern California (Sep 2014 – Apr 2020)</h4><ul><li><strong>Role:</strong> Doctoral Researcher</li><li><strong>Achievements:</strong><ul><li>Pioneered predictive models in tactile search strategies.</li><li>Increased grant funding through significant research contributions.</li></ul></li></ul><h3>Skills</h3><ul><li><strong>Programming and Tools:</strong> Python, SQL, GCP, AWS, Docker, Power BI.</li><li><strong>Machine Learning Engineering:</strong> MLflow, Optuna, Kubernetes, Kubeflow.</li><li><strong>Python Libraries:</strong> pandas, NumPy, scikit-learn, TensorFlow, PyTorch.</li><li><strong>Learning Techniques:</strong> Supervised and unsupervised learning, including advanced models and forecasting.</li></ul><h3>Education</h3><ul><li><strong>Ph.D. in Neuroscience</strong> from University of Southern California (2020).</li><li><strong>B.S. in Human Biology</strong> from University of California, San Diego (2013).</li></ul><p>Jonathan's diverse expertise not only spans technical skills but also reflects a strong ability to apply these skills in varied environments from corporate to academic, driving both innovation and efficiency.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" 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fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="2df51194-ca45-466a-9ffa-77020f61a57f" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Based on Jonathan A. Cheung's resume and professional experiences, he seems to have a strong interest in the application of machine learning and data science techniques to both industrial and academic challenges. Specific topics of interest include:</p><ol><li><p><strong>Industrial Applications of AI:</strong> Implementing machine learning solutions in the industrial sector, such as optimizing processes and improving product performance, as evidenced by his work on battery management and sand management solutions for large corporations like British Petroleum.</p></li><li><p><strong>Advanced Machine Learning Techniques:</strong> His technical skills and project roles suggest a deep interest in advanced machine learning methodologies, including supervised and unsupervised learning, as well as specific technologies like MLflow, Optuna, and Kubeflow for managing machine learning lifecycle.</p></li><li><p><strong>Data-Driven Business Solutions:</strong> He has demonstrated an ability to leverage analytics to deliver impactful business solutions, improving operational efficiencies and reducing costs, such as his work in forecasting gas consumption for Southern California Gas Co.</p></li><li><p><strong>Scientific Research and Experimentation:</strong> His doctoral research involved hypothesis-driven experimentation using predictive modeling, which indicates an interest in exploring and resolving scientific questions using data science.</p></li><li><p><strong>Educational Initiatives:</strong> His role as a lecturer for student pods and his involvement in the Global AI Corridor with Beyond Limits and Caltech show a commitment to education and mentoring in the field of data science and artificial intelligence.</p></li></ol><p>Overall, Jonathan is likely most interested in topics that merge the practical applications of AI and machine learning with impactful business and scientific outcomes.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span 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fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-6" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21b86-f730-4e92-9682-168c8e03471a" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Discovering Minimal Reinforcement Learning
Environments
Jarek Liesen ∗
BCCN Berlin
Chris Lu
University of Oxford
FLAIR
Andrei Lupu
University of Oxford
FLAIR
Jakob N. Foerster
University of Oxford
FLAIR
Henning Sprekeler
Technical University Berlin
Science of Intelligence
Robert T. Lange
Technical University Berlin
Science of Intelligence
Abstract
Reinforcement learning (RL) agents are commonly trained and evaluated in the
same environment. In contrast, humans often train in a specialized environment
before being evaluated, such as studying a book before taking an exam. The
potential of such specialized training environments is still vastly underexplored,
despite their capacity to dramatically speed up training.
The framework of synthetic environments takes a i rst step in this direction by meta-
learning neural network-based Markov decision processes (MDPs). The initial
approach was limited to toy problems and produced environments that did not
transfer to unseen RL algorithms. We extend this approach in three ways: Firstly,
we modify the meta-learning algorithm to discover environments invariant towards
hyperparameter conf i gurations and learning algorithms. Secondly, by leveraging
hardware parallelism and introducing a curriculum on an agent’s evaluation episode
horizon, we can achieve competitive results on several challenging continuous
control problems. Thirdly, we surprisingly i nd that contextual bandits enable
training RL agents that transfer well to their evaluation environment, even if it is
a complex MDP. Hence, we set up our experiments to train synthetic contextual
bandits, which perform on par with synthetic MDPs, yield additional insights into
the evaluation environment, and can speed up downstream applications.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="35d64f8b-9ca3-485e-b26e-7d13d57a70f8" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The abstract you've shared discusses a research paper focused on the development of minimal reinforcement learning (RL) environments. This study extends previous work on synthetic environments for training RL agents, which are typically designed as neural network-based Markov decision processes (MDPs). Here are the key points from the abstract:</p><ol><li><p><strong>Training vs. Evaluation Contexts</strong>: The study highlights a common practice in RL where agents are both trained and evaluated in the same environment. This contrasts with human learning behaviors, where training often occurs in specialized settings before performance is tested in a different context. The potential of creating specialized training environments to enhance learning efficiency in RL is emphasized.</p></li><li><p><strong>Limitations of Initial Approaches</strong>: Initially, the development of synthetic environments focused on simple, toy problems and faced issues with generalizability. These early environments often failed to transfer well to different, unseen RL algorithms.</p></li><li><p><strong>Proposed Extensions</strong>:</p><ul><li><strong>Meta-Learning Modifications</strong>: The research modifies the meta-learning algorithms to discover training environments that are invariant to changes in hyperparameters and learning algorithms. This is aimed at increasing the robustness and flexibility of the synthetic environments.</li><li><strong>Hardware Utilization and Curriculum Development</strong>: By leveraging hardware parallelism and introducing structured learning progressions (curricula) for RL agents, the study aims to improve outcomes on complex continuous control tasks.</li><li><strong>Contextual Bandits</strong>: A surprising finding from the research is that contextual bandits—simpler problems compared to full MDPs—can effectively train RL agents that perform well in more complex evaluation environments. This suggests that simpler models can be sufficient for training without losing the benefits of complex environments.</li></ul></li><li><p><strong>Experimental Setup and Results</strong>: The experiments focus on training synthetic contextual bandits alongside synthetic MDPs. Both types of environments provide comparable performance and yield valuable insights into the dynamics of the evaluation environments. Additionally, these synthetic environments demonstrate potential for accelerating the application of learned skills in downstream tasks.</p></li></ol><p>This paper appears to make significant strides in understanding and creating more effective training environments for RL agents, with potential broad implications for the speed and efficiency of training AI systems in various applications.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r98:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-8" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21339-a615-4da3-a691-59472e092a5a" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>1Introduction
Reinforcement learning (RL) agents are commonly trained and evaluated in precisely the same
environment. It is well known that this approach has several signif i cant disadvantages: RL agents are
brittle to minor changes in the environment dynamics, hyperparameter choices, or even the concrete
implementation of an algorithm [Henderson et al., 2018, Engstrom et al., 2019, Cobbe et al., 2020,
Agarwal et al., 2021]. Most recent research in RL has focused on improving RL algorithms to
alleviate these challenges. But what about the RL environment or the underlying Markov decision
process (MDP) itself? Unlike RL agents, professional athletes train under vastly different conditions
than their i nal competition settings. For example, long-distance runners do not repeatedly run the
target distance, but train shorter interval runs, progressively increase their pace, and occasionally
mix in long runs. Such specialized training environments have the potential to signif i cantly speed up
RL pipelines: They can be optimized to train agents rapidly, requiring several orders of magnitude
fewer environment steps. Additionally, when such environment proxies are parameterized by neural
networks, modern hardware accelerators enable rapid simulation of the environment. Thus, they can
∗Correspondence at [email protected]
Preprint. Under review.
arXiv:2406.12589v1
[cs.LG]
18
Jun
2024 Figure 1: (1) Training process for synthetic contextual bandits. Firstly, an agent is trained in an SCB
(blue), observing only an initial state and reward in each episode. After training, the agent is frozen
and transferred to an evaluation environment. The achieved episodic return is the training signal to
update the SCB (red). (2) Aggregated training results for challenging Brax environments. Training in
the SCB yields policies that are competitive with EE experts, sometimes even outperforming them.
The x-axis shows expert normalized performance as(R−Rrandom)/(Rexpert−Rrandom), whereRrandom
andRexpertare the episodic returns achieved in the EE by an expert and a random policy, respectively.
For full training results, see appendix 2. (3) Training curves for EE versus SCBs, saving orders of
magnitude of environment steps. A complete visualization is given in i gure 5. (4) Visualization of
observation feature importances for Pendulum-v1. For details refer to section 5.
be used in a myriad of applications including pretraining, neural architecture search, and downstream
meta-learning.
Here, we scale the framework of synthetic environments [SEs, Ferreira et al., 2022] to explore the
usefulness of synthetic training data for RL agent training. SEs are RL environments parameterized
by neural networks and optimized for transfer performance: After training an agent in an SE, the
agent achieves a high episodic return in a i xed evaluation environment (EE). A visualization of the
optimization algorithm is shown in i gure 1 (1). The initial approach parameterizes the SE using
a single network to represent the transition, reward, and termination functions. Combined with
the initial state distribution of the EE, the SE becomes a full MDP. During our experiments, we
found that extending the initial approach by additionally parameterizing the initial state distribution
leads to synthetic MDPs that terminate most episodes after a single time step. We propose that
this is not an artifact of meta-learning, but a discovered property that is benef i cial when training
agents. Therefore, we purposefully constrain our environment parameterization towards synthetic
contextual bandits (SCBs). SCBs perform competitively with synthetic MDPs, but have several
practical benef i ts including much smaller models and a high degree of interpretability. We make the
following contributions:
•We give analytical and empirical evidence that it is possible to transform MDPs into CBs. In
other words, we show that we can obtain a policy that performs well in an MDP by training
it in a CB. We demonstrate that SCBs arise naturally when parameterizing fully synthetic
MDPs (section 4.1).
•We show that our meta-learning algorithm discovers CBs invariant towards learning algo-
rithms and hyperparameters, and even generalize towards out-of-distribution agents and
training algorithms. Furthermore, we are the i rst to show that it is possible to discover syn-
thetic proxies for challenging control environments ((2) and (3) in i gure 1, and section 4.2).
•We demonstrate how the synthetic CBs can be analyzed to gain insights into their evaluation
environment, including a measure of feature importance ((4) in i gure 1, and section 5).
•We show how SCBs can be integrated into downstream meta-learning applications, such as
Learned Policy Optimization [Lu et al., 2022], speeding them up signif i cantly (section 6).
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11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="1f04d0e5-c294-45a4-a4c0-10e2a10c8719" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The introduction to the research paper on "Discovering Minimal Reinforcement Learning Environments" elaborates on the concept and necessity of creating more efficient and specialized training environments for reinforcement learning (RL) agents, akin to training methodologies in professional athletics. Here's an analysis of the key points detailed in the introduction:</p><h3>Current Challenges in RL Training:</h3><ul><li>RL agents are typically trained and evaluated in the same environment, which has been identified to lead to several drawbacks. These include the agents' susceptibility to minor variations in environment dynamics, hyperparameter settings, and algorithm implementations, making them brittle and less adaptable.</li></ul><h3>Concept of Specialized Training Environments:</h3><ul><li>Drawing parallels from how professional athletes train under varied conditions to enhance performance, the paper suggests that RL agents could benefit significantly from similar specialized training environments. These environments, distinct from the final evaluation settings, could potentially lead to faster training times and more robust agents.</li></ul><h3>Advantages of Synthetic Environments:</h3><ul><li><strong>Speed and Efficiency</strong>: Synthetic environments, especially when parameterized by neural networks, allow for rapid simulation thanks to modern hardware accelerators. This facilitates a much quicker training process, potentially reducing the required environmental steps by several orders of magnitude.</li><li><strong>Application Scope</strong>: These environments can be utilized in various applications including pretraining, neural architecture search, and downstream meta-learning tasks, enhancing overall efficiency and effectiveness.</li></ul><h3>Synthetic Contextual Bandits (SCBs):</h3><ul><li>The introduction discusses the novel approach of using synthetic contextual bandits (SCBs) instead of fully synthetic Markov decision processes (MDPs) for training RL agents. SCBs, which typically involve simpler setups where an agent interacts with an environment in a more limited context (i.e., observing only initial states and rewards), are found to be surprisingly effective.</li><li>SCBs are not only competitive with synthetic MDPs in terms of performance but also offer advantages like smaller model sizes and higher interpretability.</li></ul><h3>Contributions of the Paper:</h3><ol><li><strong>Transformation of MDPs into CBs</strong>: Empirical evidence and analytical insights show that it is feasible to train effective policies for MDPs using simpler CB environments.</li><li><strong>Meta-Learning Innovations</strong>: The paper’s meta-learning algorithm can discover SCBs that are invariant to different learning algorithms and hyperparameters and can generalize well even to out-of-distribution agents and training scenarios.</li><li><strong>Insightful Analytics</strong>: The ability to analyze SCBs to gain deeper insights into the evaluation environment, including assessing feature importance.</li><li><strong>Integration into Meta-Learning</strong>: Demonstrating how SCBs can be effectively integrated into downstream applications, significantly speeding up processes like Learned Policy Optimization.</li></ol><p>The introduction sets the stage for a detailed exploration of these concepts, aiming to prove that SCBs can not only match the training effectiveness of traditional synthetic MDPs but also offer additional practical benefits, thereby proposing a significant shift in how RL training environments are conceptualized and utilized.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span 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rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>•WeimplementseveralcommonRLalgorithmsinawaythatsupportsGPUparallelism, which
allows us to run experiments in a fraction of wall clock time compared to a multiprocessing-
based approach. Additionally, we release the synthetic environments using the gymnax
interface [Lange, 2022b], allowing for a drop-in replacement of the evaluation environment. 2Background
2.1Contextual Bandits are a Special Case of Markov Decision Processes
The most widely used formalism for RL environments is the Markov decision process (MDP), def i ned
as a tuple⟨S,A,P,R,η0,d⟩.
At the beginning of each episode, a states0∈ Sis
sampled from the
initial state distributions0∼ η0.
At each succeeding time stept, the agent samples an actionat∈ A
from its policya ∼ π(.|st).
The environment then generates the next state asst+1∼ P(.|st,at)and
issues a rewardrt∼ R(.|st,at).
As soon as the Boolean value of the termination functiond(st)
indicates it, the episode is terminated.
The basic reinforcement learning problem is to i nd a policyπ∗that maximizes the expected return
Eπ[P∞
t=0γ trt], where 0 < γ < 1is called discount factor. Alternatively, this can be stated in terms
of the Q-function as
π∗= argmax
π E
s0∼η0
a0∼π(.|s0)
[Qπ(s0,a0)],whereQπ(s,a) = Eπ "
∞ X
t=0
γtrt ? ? ? ? ?s0
= s,a0= a #
. (1)
Note that any optimal policy chooses actions greedily with respect to its Q-function, meaning
π∗(a|s) = 1 iff a = argmax˜ aQπ ∗(s,˜ a).
This work focuses on meta-learning a special case of MDPs, namely a contextual bandit (CB). In a
CB, the transition functionPis deterministic, and always points towards a statesdwithd(sd) = true.
From this constraint, it follows immediately that the Q-function of any policy is equal to the expected
immediate reward:
Qπ(s,a) = Eπ "
∞ X
t=0
γtrt ? ? ? ? ?s0
= s,a0= a #
= Eπ[γ0r0|s0= s,a0= a] = E[R(.|s,a)].(2)
Therefore in any contextual bandit, the optimal policy as def i ned in equation(1)greedily maximizes
the immediate reward, i.e. π∗(a|s) = 1 iff a = argmax
˜ a E[R(.|s,˜ a)].
2.2Meta-training Synthetic Environment and Parameterization
Algorithm 1 Bi-level optimization algorithm for meta-learning SEs
Require: number of generations G, population size N
Initialize population of SCBs via random neural network initialization
for g = 1,...,G do▷ Outer loop
for i = 1,...,N do▷ Inner loop
Train RL agent Aiin SCBi
Evaluate i tness of Aias episodic return in evaluation environment
Update population using meta-optimizer and performances of the agents Ai
Ferreira et al. [2022] introduce synthetic environments as RL environments parameterized by a
neural network. They parameterize parts of an MDP, namely the transition, reward, and termination
function, computed asst+1,rt,dt= fθ(st,at), wherefθrefers to the forward pass of a neural
network with parametersθ. The resulting networks are then optimized using a bi-level optimization
scheme consisting of two nested loops (see alg. 1). In the inner loop, an RL agent is trained in a
synthetic environment. After training it is frozen, and its i tness, the episodic return in an evaluation
3
environment, is calculated. At each generation (iteration) of the outer loop, the inner loop is executed
on a population (batch) of SEs. Afterward, the calculated i tness scores are used to generate the next
population, such that the expected return is increased. We use separable natural evolution strategies
[SNES, Wierstra et al., 2014, see appendix B] for outer loop optimization.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="91b83654-1a40-42dd-b731-c20910f5a457" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The provided text outlines the advancements in creating and utilizing synthetic environments for training reinforcement learning (RL) agents, focusing particularly on the development of contextual bandits (CBs) as a simplified form of Markov decision processes (MDPs). Here's a breakdown of the key points from the text:</p><h3>Section 2 Background</h3><h4>2.1 Contextual Bandits as a Special Case of MDPs</h4><ul><li><strong>Definition of MDPs</strong>: MDPs are defined as a tuple comprising states (S), actions (A), state transition probabilities (P), reward functions (R), initial state distributions (η0), and termination functions (d). In RL, the goal is to find a policy π* that maximizes the expected return, factoring in a discount factor γ which determines the weight of future rewards.</li><li><strong>Simplification to Contextual Bandits</strong>: In CBs, the transition function P is deterministic, typically leading to a terminal state after one action. This means the optimal policy in a CB scenario is solely focused on maximizing the immediate reward, simplifying the computational complexity compared to a full MDP where the policy must consider the entire sequence of potential rewards.</li></ul><h4>2.2 Meta-training Synthetic Environments and Parameterization</h4><ul><li><strong>Bi-level Optimization Algorithm</strong>: The approach uses a bi-level optimization algorithm to train RL agents in synthetic environments (SEs). These environments are parameterized by neural networks, allowing for the customization of the transition, reward, and termination functions. The algorithm operates in two nested loops:<ul><li><strong>Inner Loop</strong>: Each RL agent is trained in a synthetic contextual bandit. The agent's performance is assessed based on episodic returns in the evaluation environment.</li><li><strong>Outer Loop</strong>: After assessing the fitness of all agents, the population of synthetic environments is updated to maximize expected returns. This optimization uses techniques such as separable natural evolution strategies (SNES).</li></ul></li></ul><h3>Innovations and Techniques</h3><ul><li><strong>GPU Parallelism</strong>: Implementing RL algorithms to support GPU parallelism significantly reduces the wall clock time required for experiments, contrasting with more traditional multiprocessing approaches.</li><li><strong>Gymnax Interface</strong>: The environments are released using the "gymnax" interface, which facilitates easy replacement and integration into existing RL training pipelines.</li></ul><h3>Practical Applications</h3><p>The framework discussed not only streamlines the training process but also enhances the flexibility and adaptability of RL agents. By focusing on immediate rewards, contextual bandits provide a controlled yet effective training ground, suitable for complex real-world applications where training data might be scarce or expensive to simulate. This approach is particularly beneficial in situations where rapid decision-making based on limited data is critical.</p><p>Overall, the development of synthetic environments through advanced parameterization and optimization strategies represents a significant leap in training more efficient and robust RL agents, with direct implications for fields like autonomous driving, robotic control, and adaptive systems in fluctuating environments.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r9m:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-12" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb2156d-0225-422c-89fd-1168122372e7" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>3Methods: Improving the Discovery of Synthetic Environments by Sampling
Inner Loop Algorithms & Introducing an Outer Loop Curriculum
Meta-learning for generalization by sampling algorithms. The meta-learned CBs should not be
specif i c to certain RL algorithms. Instead, it should be possible for any RL algorithm to train a good
policy in the SCB, using a wide range of hyperparameters (HPs). To avoid overf i tting to specif i c
algorithms while meta-training, we extend the original optimization algorithm by sampling inner
loop tasks, each of which is represented by a random algorithm/HP combination. We use PPO, SAC,
DQN and DDQN [Schulman et al., 2017, Christodoulou, 2019, Mnih et al., 2015, van Hasselt et al.,
2015] for discrete, and PPO, SAC, DDPG and TD3 [Schulman et al., 2017, Haarnoja et al., 2018,
Lillicrap et al., 2015, Fujimoto et al., 2018] for continuous action spaces. HPs are sampled uniformly
from a broad range of sensible values (see appendix F.2).
Scaling to locomotion environments using an outer loop curriculum. Many continuous control
problems in Brax [Freeman et al., 2021], like hopper or walker2d, require learning balance and
locomotion, and are truncated after 1000 steps. When evaluating SCB-trained agents for the full
1000 steps, SCBs quickly converge to balancing without forward movement. To address this, we
employ a curriculum on i tness evaluation rollout length: We start meta-training with short episodes
and gradually increase their length, shifting focus towards locomotion early in meta-training.
Leveraging automatic vectorization. To eff i ciently parallelize the training of agent populations,
we implement vectorizable versions of these algorithms in JAX [Bradbury et al., 2018]. This allows
for hardware-parallel training using different values of hyperparameters that don’t alter the memory
layout or sequence of executed operations. While this does not include model architecture or the
number of training steps, we i nd that the diversity in training algorithms allows for suff i cient
generalization (section 4.2). Additionally, we will publish the implementations as an open-source
library, available at https://github.com/keraJLi/rejax [Liesen et al., 2024].
4Results: Synthetic CBs are General & Scalable MDP Proxies
We i rst demonstrate that contextual bandits arise naturally from parameterizing fully synthetic MDPs
(section 4.1). Subsequently, we show that meta-learned synthetic contextual bandits generalize
out-of-distribution and scale towards challenging control environments (section 4.2).
4.1Contextual Bandits as a Discovered Property of Synthetic Environments
We begin our experiments by extending the setup of Ferreira et al. [2022] with a parameterized initial
state distribution of the forms0= fϕ(z), wherez ∈ RNis
a latent variable sampled from a diagonal
Gaussian distribution. After training these fully synthetic MDPs, we found that they often terminate
episodes after a single time step (see Figure 2, left). We interpret this as a discovered property of SEs,
and constrain our SEs to a single step, making them contextual bandits. Surprisingly, we i nd that this
has next to no negative impact on the performance of the synthetic environments, sometimes even
being benef i cial (see Figure 2, right). The usage of CBs has several practical advantages:
1.The number of parameters is signif i cantly lower. The transition function takesO(dim(S)2)
parameters, while the reward function only takesO(dim(S))when parameterizing with
fully connected networks, where S is the state space.
2.It avoids instabilities related to the recurrent application of the transition function. When
allowing for long episodes, we consistently encountered overf l owing state values (NaNs) in
the early stages of meta-training (for example, in the ablations in appendix D.2).
3.It signif i cantly simplif i es the meta-learning problem for sparse reward environments. Param-
eterizing the initial state distribution is necessary to obtain a well-performing SCB for the
MountainCar-v0 environment (appendix D.2). We hypothesize that this is because critical
4
0.000.250.500.751.00
Fraction of episodes
Acrobot-v1
CartPole-v1
MountainCar-v0
MountainCar
Continuous-v0
Pendulum-v1 1234
1
12
1
12 1
2
3
4 Number
of
steps 1
(SCB)
251050100max
(EE)
Max. #steps in synthetic MDP
0.4
0.6
0.8
1.0
1.2
Normalized
perf. Acrobot-v1
CartPole-v1
MountainCar-v0
MountainCar
Continuous-v0
Pendulum-v1
Figure 2: CBs are a discovered property of synthetic environments. Left: Fraction of episode
lengths in a synthetic MDP. In most environments, more than 80% of episodes are terminated after a
single time step. Episodes were generated using 50 episodes of agents trained with each algorithm.
Right: Normalized performance of synthetic MDPs with decreasing maximum episode length. “max”
refers to the maximum episode of the evaluation environment. Shown are the IQM scores and 95%
conf i dence intervals of 20 training runs, aggregated over all algorithms (see section 3). Performance
is normalized as(R−RSCB)/(R−Rrandom)for each algorithm individually, whereRSCBis the return
in the EE after training in the SCB, and Rrandomis the return of a random policy.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-13" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 1.94125 22.4257 1.36341C21.1295 0.785575 19.7249 0.491269 18.3058 0.500197C16.1708 0.495044 14.0893 1.16803 12.3614 2.42214C10.6335 3.67624 9.34853 5.44666 8.6917 7.47815C7.30085 7.76286 5.98686 8.3414 4.8377 9.17505C3.68854 10.0087 2.73073 11.0782 2.02839 12.312C0.956464 14.1591 0.498905 16.2988 0.721698 18.4228C0.944492 20.5467 1.83612 22.5449 3.268 24.1293C2.81966 25.4759 2.66413 26.9026 2.81182 28.3141C2.95951 29.7256 3.40701 31.0892 4.12437 32.3138C5.18791 34.1659 6.8123 35.6322 8.76321 36.5013C10.7141 37.3704 12.8907 37.5973 14.9789 37.1492C15.9208 38.2107 17.0786 39.0587 18.3747 39.6366C19.6709 40.2144 21.0755 40.5087 22.4946 40.4998C24.6307 40.5054 26.7133 39.8321 28.4418 38.5772C30.1704 37.3223 31.4556 35.5506 32.1119 33.5179C33.5027 33.2332 34.8167 32.6547 35.9659 31.821C37.115 30.9874 38.0728 29.9178 38.7752 28.684C39.8458 26.8371 40.3023 24.6979 40.0789 22.5748C39.8556 20.4517 38.9639 18.4544 37.5324 16.8707ZM22.4978 37.8849C20.7443 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="367fd1a2-4ede-4bba-ad1d-732b8f2eeb29" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The text discusses methodological enhancements for creating and optimizing synthetic environments (SEs) to train reinforcement learning (RL) agents, with a focus on synthetic contextual bandits (SCBs). Here’s a breakdown of the techniques and findings:</p><h3>3 Methods: Improving the Discovery of Synthetic Environments</h3><h4>Inner Loop Algorithms & Outer Loop Curriculum</h4><ul><li><p><strong>Meta-Learning for Generalization</strong>: The process is designed to ensure that synthetic contextual bandits (SCBs) are not specific to any one RL algorithm. This is achieved by introducing variability during training through sampling different algorithms and hyperparameters (HPs), including those for both discrete and continuous action spaces like PPO, SAC, DQN, and DDQN. This approach helps prevent overfitting to specific algorithms and ensures that the SCBs can support a variety of RL algorithms.</p></li><li><p><strong>Outer Loop Curriculum</strong>: For problems requiring balance and locomotion, such as those in the Brax environment, the authors introduce a curriculum in the fitness evaluation rollout length. This means starting with shorter episodes and gradually increasing their length, which helps shift the focus towards developing locomotion skills early in training.</p></li></ul><h4>Leveraging Automatic Vectorization</h4><ul><li><strong>Efficient Parallelization</strong>: The training of agent populations is parallelized using JAX, which allows for vectorization that does not alter the memory layout or sequence of operations. This approach ensures efficient hardware-parallel training and is claimed to be sufficient for generalization across diverse training algorithms.</li></ul><h4>Open-Source Library</h4><ul><li><strong>Publication of Code</strong>: The methods and implementations are made available as an open-source library, providing accessibility for further research and application.</li></ul><h3>4 Results: Synthetic CBs as General & Scalable MDP Proxies</h3><h4>4.1 Contextual Bandits as a Discovered Property of Synthetic Environments</h4><ul><li><strong>Experiment Setup and Findings</strong>: By parameterizing the initial state distribution and observing the behavior of fully synthetic MDPs, it was found that these often terminate after just one timestep. This led to the strategic constraining of SEs to single-step episodes, effectively turning them into SCBs. Surprisingly, this constraint did not negatively impact performance and sometimes even improved it.</li></ul><h4>Practical Advantages of Using SCBs:</h4><ol><li><strong>Reduced Complexity</strong>: SCBs significantly lower the number of parameters needed. For example, while the transition function in a typical MDP might require a quadratic number of parameters relative to the dimensionality of the state space, SCBs simplify this considerably.</li><li><strong>Stability</strong>: By limiting episodes to a single step, SCBs avoid issues like overflowing state values (NaNs) that occur in longer episodes due to recursive application of the transition function.</li><li><strong>Meta-Learning Simplification</strong>: SCBs simplify the meta-learning challenge, particularly in sparse reward environments, by focusing on parameterizing the initial state distribution to enhance performance.</li></ol><h3>Summary</h3><p>The methodological innovations presented focus on improving the robustness and applicability of SCBs as training environments for RL agents. By introducing diverse training conditions through algorithm and hyperparameter sampling, and by optimizing the rollout strategies, the researchers ensure that SCBs are capable of supporting generalized, efficient, and effective learning for a variety of RL tasks. These innovations not only advance the field of synthetic environment creation but also enhance the practicality and scalability of using SCBs in complex control tasks.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r9t:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-14" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21b0e-2a78-4b0a-801b-13fe158176e1" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Figure 3: Meta-learned SCBs generalize across hyperparameters and towards out-of-distribution RL
algorithms. Each column shows the return of a policy after training in either the SCB (blue) or the
EE directly (red), using sampled hyperparameters and 10,000 environment steps. Additionally, we
ablate the meta-training algorithm by using i xed hyperparameters in the inner loop. When sampling
hyperparameters during the evaluation, the ablated SCBs (green) perform worse. Additionally, the
SCBs generalize towards agents not used in the inner loop (right of dashed line). For more details,
refer to appenix C.
states can be shown to the agent immediately, instead of having to be reached via multiple
(meta-learned) transitions.
4.The synthetic reward function is well-interpretable since the episodic return is equal to
the immediate reward (eq.(2)). Neural parameterization allows differentiation and the
application of interpretability methods. We present two ways to interpret the CBs in
section 5.
Intuition suggests that being more general, MDPs have a richer class of solutions (i.e. optimal
policies) compared to CBs. Perhaps surprisingly, this is not the case:
Theorem 1. Given any Markov decision processM, there exists a contextual banditB, such that
every policy π∗that is optimal in B is also optimal in M. For a proof see appendix A.
Theorem 1 makes no statement about the training eff i ciency in practice. Thus, we dedicate the rest of
our experiments to empirically demonstrate that training in CBs is not only possible but benef i cial.
4.2Meta-Learning Synthetic Contextual Bandits
SCB generalization.Figure 3 demonstrates the generality of a meta-learned SCB for
ContinuousMountainCar-v0. It shows the performance of inner loop agents with random HPs,
5
010002000
Generation
250
500
750
1000
Evaluation
length
Curriculum 010002000
Generation
0
1000
2000
3000
Episodic
return
Fitness of SCB for hopper Curriculum
linear
fast
polynomial
none
Figure 4: Curriculum and training speed for Brax environments. Left: Visualization of different
curricula. Right: Inf l uence of curricula on the meta-training progress for the hopper environment.
For no curriculum, we show the IQM and 95% CIs over 9 seeds. One seed is shown per curriculum.
as well as the performance of several agents that were out-of-distribution, after training in the SCB
and evaluation environment directly. SCBs are universally much more robust to hyperparameter
changes than their respective evaluation environment. This is even the case when being meta-learned
using i xed hyperparameters in the inner loop, but the robustness can be increased further by sam-
pling them. Notably, SCBs enable consistently training PPO agents for MountainCar-v0, which
is not the case in the evaluation environment directly, even when using tuned HPs2. Due to the
technical constraints imposed by using JAX’s vectorization, SCBs were trained using both a i xed
set of gradient-based algorithms and a common i xed network architecture for each RL agent. Still,
the meta-learned SCBs generalize out-of-distribution. Replacing an RL agent’s activation function
or network architecture with one that was not used during meta-training does not hurt its perfor-
mance. Additionally, optimizing a policy network using SNES [Wierstra et al., 2014], an evolution
strategy instead of a gradient-based algorithm, works well across SCBs. Finally, we show that the
SCB-optimal policy performs well in the evaluation environment, meaning that SCBs should enable
training capable agents using any RL algorithm that i nds this policy.
Baselines and Ablations. Since CBs lack the temporal dynamics of an MDP, training in a CB can
be thought of as an (online) supervised learning problem. Instead of solving the temporal credit
assignment problem, the agent simply has to predict which action maximizes the immediate reward.
We, therefore, investigate how the discovered reward function compares with several baselines. First,
we compare to online supervised learning of an expert policy, implemented by interacting with the
evaluation environment and taking steps to minimizeKL[π||πexpert]on
batches of states. We refer to
this setup as online behavioral cloning and interpret it as a replacement for the reward function of the
SCB. Alternatively, we can replace the reward function with one that was constructed using an expert
Q-function. We can construct it such that theorem 1 holds, thereby theoretically obtaining expert
policies from training in the SCB. Finally, we can replace the synthetic initial state distribution with
an expert state distribution, simulating the interaction of the evaluation environment and expert agent
in the background. We i nd that the synthetic initial state distribution is strictly required for successful
RL training, while the training speed of SCB training and online behavioral cloning is comparable
(appendix D.1). In appendix D.2 we additionally perform several ablations to the most important
design choices of our meta-training algorithm: A parameterized initial state distribution is needed for
sparse-reward environments, our method performs best with a continuous latent distribution for the
initial state, and meta-evolution is robust to the choice of meta-curriculum.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-15" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="c22e9f98-8a04-4032-9a9f-c29f541d9bbe" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The text dives deep into methods to enhance the creation and training of synthetic contextual bandits (SCBs) for reinforcement learning (RL), showcasing how these approaches enhance generalization and training efficiency. Here’s an exploration of key aspects discussed:</p><h3>4 Methods: Improving Synthetic Environment Discovery</h3><h4>Generalization Across Hyperparameters and Algorithms</h4><ul><li><strong>Meta-Learning SCBs</strong>: By varying hyperparameters and algorithms during the inner loop of meta-training, SCBs are developed to be robust and not overly specialized to any particular set-up. This includes using a variety of algorithms for discrete and continuous action spaces and ensuring that SCBs can adapt across out-of-distribution RL algorithms.</li><li><strong>Figure 3 Analysis</strong>: The meta-learned SCBs are shown to generalize well across different hyperparameters and to agents not used in the inner loop. SCBs demonstrate better performance compared to direct training in the evaluation environment (EE), indicating their robustness and utility.</li></ul><h4>Curriculum and Training Efficiency</h4><ul><li><strong>Outer Loop Curriculum</strong>: A progressive curriculum that extends episode lengths during meta-training enhances the agent's development of more complex skills like locomotion, crucial for environments such as those provided by Brax.</li><li><strong>Figure 4 Visualization</strong>: Different curricula strategies are visualized and analyzed for their impact on meta-training speed and effectiveness. The curriculum significantly influences how quickly and effectively SCBs can train RL agents.</li></ul><h3>4 Results: Empirical Validation and Theoretical Insights</h3><h4>Discovery and Practical Use of SCBs</h4><ul><li><strong>Robustness and Performance</strong>: SCBs, even when trained with fixed hyperparameters, demonstrate notable robustness and improved performance across various settings. They allow for consistent training outcomes, outperforming direct training in the EE in many cases.</li><li><strong>Baselines and Ablations</strong>: Training in SCBs is compared with online supervised learning strategies like behavioral cloning. It is found that synthetic initial state distributions are crucial for effective RL training, highlighting the unique advantage of SCBs in setting initial conditions conducive to learning.</li></ul><h3>Theoretical Insights</h3><ul><li><strong>Theorem 1</strong>: This theorem asserts that for any MDP, there exists a corresponding CB in which every optimal policy for the CB is also optimal for the MDP. This foundational theoretical backing supports the practical utility of training in SCBs even though they lack the temporal dynamics inherent in MDPs.</li></ul><h3>Practical Applications and Extensions</h3><ul><li><strong>Interpretation and Adaptation</strong>: The ability to interpret the reward functions in SCBs (as they directly equate to episodic returns) provides additional analytical leverage. Extensions of SCBs allow for the integration of RL training with other machine learning paradigms like online learning and policy optimization strategies.</li></ul><h4>Integration with Existing Systems</h4><ul><li><strong>Open Source Contributions</strong>: By making their implementations available on platforms like GitHub, the researchers encourage further exploration and adaptation of their methods in the broader RL community.</li></ul><p>Overall, the advancements detailed in the text not only enhance the meta-learning process by enabling the discovery of robust, generalizable SCBs but also provide empirical evidence and theoretical justifications for their effectiveness. These developments promise to significantly impact the efficiency and adaptability of RL agents trained in synthetic environments.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 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data-state="closed"><button type="button" id="radix-:ra4:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-16" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21845-2bca-4960-9767-b2f5762a0847" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Do you think you can come up with any analogies or metaphors to help explain it?</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-17" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex 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35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="4a519a71-80f6-4091-b6ce-b5678ea402e4" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Certainly! Explaining complex topics like synthetic contextual bandits (SCBs) and their role in reinforcement learning (RL) can be made clearer through analogies and metaphors. Here are a few that might help:</p><h3>1. <strong>Training Wheels on a Bicycle</strong></h3><p>Imagine learning to ride a bicycle. Initially, you might use training wheels (similar to SCBs) to get a feel for balancing and pedaling without the full complexity of keeping the bike upright. Once you're comfortable, the training wheels come off (akin to moving from SCBs to full MDPs), and you're ready to ride independently, applying the skills you've honed in a simplified environment.</p><h3>2. <strong>Cooking with a Recipe</strong></h3><p>Think of SCBs as following a simple recipe with clear, step-by-step instructions that guarantee a good meal if followed correctly (like maximizing immediate reward). This is easier and requires fewer decisions compared to cooking a gourmet meal (a full MDP) where timing, sequence, and preparation vary significantly and the outcome depends on a broader range of variables.</p><h3>3. <strong>Using a Map App in a Familiar Neighborhood</strong></h3><p>Using SCBs is like using a map application in a very familiar neighborhood. The app (SCB) suggests the quickest route from point A to B without needing to navigate the entire city (the full complexity of an MDP). It simplifies the process by focusing only on immediate decisions (turn left, turn right) rather than planning a complex journey across unknown areas.</p><h3>4. <strong>Gardening in a Controlled Environment</strong></h3><p>Growing plants in a greenhouse can be likened to training RL agents in SCBs. In a greenhouse (SCB), conditions such as temperature, light, and water are carefully controlled to optimize plant growth quickly and efficiently, similar to how SCBs control learning conditions to optimize the training of an RL agent. Once the plants are robust enough, they can be transferred to the outside garden (full MDP environment), where they are more likely to thrive even under less controlled conditions.</p><h3>5. <strong>Learning a Musical Instrument with Scales</strong></h3><p>When learning a musical instrument, one often starts by practicing scales and simple songs (SCBs). This focused practice helps you master the basics without the complexity of a full symphony (full MDP). Over time, these basic skills become second nature, allowing you to perform more complex compositions effectively.</p><p>These analogies help in visualizing how SCBs simplify the learning process by reducing complexity and focusing on the essentials, making it easier to generalize skills to more complex situations later on.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 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2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-18" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb2181c-cd37-4dc7-ae9d-2e9a8df5e9c2" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>So it sounds like it could be described as allowing them to play first?</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-19" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div 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6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="a54fcab9-a124-4c07-8a96-ba9289b237eb" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Exactly, that's a great way to put it! Using the metaphor of "allowing them to play first," SCBs can be seen as giving RL agents a simpler, more controlled "playground" to explore and learn the basics before they face the full complexity of the "real game" in more comprehensive environments like MDPs.</p><p>This approach helps the agents build confidence and learn effective strategies in a straightforward setting, which they can then apply to more complicated and less predictable scenarios. It ensures that the foundational skills are well-established, making the transition to more challenging tasks smoother and more successful.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 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data-state="closed"><button type="button" id="radix-:rai:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-20" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb2171f-0b79-45d6-bd98-5a7659ed8be3" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>What was the theme of the movie The Goat (1934)?</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-21" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 1.94125 22.4257 1.36341C21.1295 0.785575 19.7249 0.491269 18.3058 0.500197C16.1708 0.495044 14.0893 1.16803 12.3614 2.42214C10.6335 3.67624 9.34853 5.44666 8.6917 7.47815C7.30085 7.76286 5.98686 8.3414 4.8377 9.17505C3.68854 10.0087 2.73073 11.0782 2.02839 12.312C0.956464 14.1591 0.498905 16.2988 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20.0556L22.2312 14.4411L25.5976 12.4981C25.6142 12.4872 25.6333 12.4805 25.6531 12.4787C25.6729 12.4769 25.6928 12.4801 25.7111 12.4879L33.7631 17.1364C34.9967 17.849 36.0017 18.8982 36.6606 20.1613C37.3194 21.4244 37.6047 22.849 37.4832 24.2684C37.3617 25.6878 36.8382 27.0432 35.9743 28.1759C35.1103 29.3086 33.9415 30.1717 32.6047 30.6641C32.6047 30.5947 32.6047 30.4733 32.6047 30.3889V21.188C32.6066 20.9586 32.5474 20.7328 32.4332 20.5338C32.319 20.3348 32.154 20.1698 31.955 20.0556ZM35.3055 15.0128C35.2464 14.9765 35.1431 14.9142 35.069 14.8717L27.1045 10.2712C26.906 10.1554 26.6803 10.0943 26.4504 10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="fd333d1f-ead6-4036-9ede-c2c1ed946da8" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>"The Goat" from 1934 is a comedy film directed by Buster Keaton, who also stars as the main character. The film's central theme revolves around mistaken identity and the ensuing chaos and humorous situations that arise from it. Keaton's character is mistaken for a notorious criminal, leading to a series of slapstick chases and comedic encounters. This theme of mistaken identity is common in many of Keaton's films, where he often portrays an everyman caught up in extraordinary circumstances, highlighting the absurdity and unpredictability of life through physical comedy and clever visual gags.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 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m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21016-1e72-4b3d-a7df-313ec914f7bd" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Can you give a deeper analysis?</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex 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34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="0271aae9-a1bf-4074-ab64-ef599d725270" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Certainly! Buster Keaton's 1921 short film "The Goat" offers a rich tapestry for analysis, blending physical comedy with subtle social commentary. Here's a deeper look at the thematic elements and filmmaking techniques employed in the film:</p><h3>Theme of Mistaken Identity</h3><p>"The Goat" utilizes the theme of mistaken identity as a driving force for the narrative. Keaton's character, mistakenly identified as the criminal "Dead Shot Dan," finds himself relentlessly pursued by the police. This mistaken identity not only serves as a source of humor but also critiques societal and authoritative tendencies to judge individuals superficially, without understanding the true nature of their character. This theme resonates with the audience's fear of being wrongly accused and taps into the universal desire for personal justice and fairness.</p><h3>Commentary on Urban Life</h3><p>Keaton’s films often reflect on the challenges and absurdities of urban life. "The Goat" is no exception, depicting a bustling city where a simple misunderstanding can spiral into a chaotic, life-altering situation. The urban setting is integral, providing a backdrop that amplifies the comedic effect of Keaton's predicaments. The impersonal nature of the city, with its crowded streets and indifferent crowds, enhances the sense of isolation Keaton’s character feels, despite being constantly surrounded by people.</p><h3>Techniques of Physical Comedy</h3><p>Keaton was a master of physical comedy, and "The Goat" showcases his prowess in staging elaborate chase sequences and visual gags. His ability to use his body expressively, performing daring stunts without the aid of doubles or CGI, adds a layer of authenticity and charm that modern audiences still appreciate. Keaton's comedic style is characterized by his stoic expression amidst chaos, which contrasts sharply with the exaggerated behaviors typical of silent film acting, making his performances stand out as subtly sophisticated.</p><h3>Cinematic Innovation</h3><p>Keaton's work in "The Goat" also demonstrates his innovative use of cinematic techniques. The film features clever editing tricks, such as jump cuts and visual puns, that were groundbreaking at the time. For example, the sequence where Keaton's character sees his own wanted poster and manipulates his face to match the photo is not only funny but a clever use of the film medium to engage in self-referential humor.</p><h3>Underlying Pathos</h3><p>While "The Goat" is primarily a comedy, like much of Keaton’s work, it contains an undercurrent of pathos. Keaton’s character is a lonely figure, a drifter mistaken for a criminal, who navigates the indifferent city trying to clear his name. This blending of humor with a touch of sadness adds depth to the film, inviting the audience to empathize with Keaton's plight as an underdog fighting against a faceless society.</p><h3>Conclusion</h3><p>"The Goat" encapsulates Buster Keaton’s genius in blending slapstick comedy with deeper, more reflective themes. The film is not only a showcase of his physical comedic talent but also offers commentary on the absurdities of modern life and the often impersonal nature of urban society. Through innovative filmmaking techniques and a timeless comedic style, Keaton crafts a narrative that is both entertaining and thought-provoking.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rb0:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-24" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21079-55f5-40be-b9c3-a9f69f5afaed" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>You are right it was 1921. Is it a reference to scapegoat?</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-25" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 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11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="8a0d6d5d-d89d-4bfa-9e08-2fa6692c5ce6" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>In Buster Keaton's "The Goat" (1921), while the title could potentially suggest a reference to a "scapegoat," there isn't a direct indication that this metaphor is intentionally employed as a major theme in the film. However, the concept does fit well with the plot, where Keaton's character is mistakenly pursued as a criminal, effectively making him a scapegoat for the actual villain's crimes. This misidentification leads to a series of humorous yet troublesome situations, reflecting the idea of an individual wrongly blamed for others' actions.</p><p>The term "scapegoat" itself has a rich historical and cultural background, originally referring to a ritual described in the Bible where a goat was symbolically burdened with the sins of the people and then sent away into the wilderness, symbolizing the removal of guilt. In Keaton’s film, while the term is not explicitly referenced, the protagonist does figuratively carry the burden of sins he did not commit, aligning with the concept of a scapegoat.</p><p>This interpretation adds an additional layer of meaning to the film, enhancing its depth beyond the immediate slapstick comedy. It allows audiences to contemplate the broader implications of mistaken identity and unjust accusation in society, themes that Buster Keaton subtly weaves into his comedic pursuits.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rb7:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-26" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21c22-1ca8-43b2-955e-96d4166f4143" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>I guess the part that struck me was when he was stopped by a police man and is given a lecture. He slips out of his coat and runs away only to look back and see that the police man has already left and is walking away.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-27" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 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10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="b1802f22-fbb8-477d-9e4b-78af57ef04ab" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>This scene from Buster Keaton's "The Goat" is a perfect example of his unique style of physical comedy mixed with subtle social commentary. The moment encapsulates several key aspects of Keaton's filmmaking:</p><ol><li><p><strong>Physical Comedy</strong>: Keaton's ability to slip out of his coat to escape, only to find that his frantic efforts were unnecessary because the policeman had already lost interest, highlights his mastery of visual gags and slapstick. This kind of physical humor, where the action unfolds in an unexpected yet visually logical manner, is typical of Keaton's approach to comedy.</p></li><li><p><strong>Subtle Social Commentary</strong>: The scene can be seen as a critique of authority—perhaps suggesting that the force and vigilance of law enforcement can be easily evaded, or might not be as formidable as it seems. The policeman’s disinterest once Keaton escapes could also imply a comment on the transient and sometimes superficial nature of such authority figures’ attention to actual issues.</p></li><li><p><strong>The Element of Surprise</strong>: Keaton’s films often use the element of surprise to subvert audience expectations. In this scene, the audience is led to anticipate a chase, only to be humorously let down when both characters nonchalantly part ways. This kind of anti-climax is a clever tool in Keaton’s comedic arsenal, often resulting in a bigger laugh because it is so unexpected.</p></li><li><p><strong>Loneliness and Isolation</strong>: This scene also subtly touches on themes of loneliness and the anonymity of urban life. Keaton's character is fundamentally alone, misunderstood by society and even when he is being chased, it’s more of a mechanical interaction than a meaningful human connection.</p></li></ol><p>This scene, like many others in Keaton’s work, demonstrates his ability to blend humor with poignant reflections on human nature and society, all without a word of dialogue. His films remain enduring not just for their innovative physical comedy but for their clever commentary and emotional depth, often encapsulated in brief, seemingly simple scenes.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 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0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" 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3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-28" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21b82-12ba-4fb6-b138-bc657880ed43" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>I guess I have to mention that it reminded me of the scene where a young man slipped away without his sheet, from the garden of gethsemene</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-29" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 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6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="3d8ab1bd-ae2a-4d97-9906-722baf035568" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The scene you're referring to from the Gospel of Mark in the New Testament describes a young man who, when seized during Jesus' arrest at Gethsemane, leaves his linen cloth behind and flees naked. This brief and somewhat enigmatic episode is rich with symbolic interpretations but fundamentally portrays vulnerability and desperate escape in the face of arrest or persecution.</p><p>Drawing a parallel between this biblical moment and the scene in Buster Keaton's "The Goat" where he slips out of his coat to evade the policeman adds a layer of historical and thematic depth to the analysis of the film. Here are a few connections and reflections on this comparison:</p><ol><li><p><strong>Vulnerability</strong>: Both scenes highlight the vulnerability of the characters—Keaton's character in a comedic light and the young man in a more dramatic, perhaps tragic context. In both cases, their quick thinking allows them to escape immediate capture, but they also leave behind something of themselves (a coat in Keaton's case, a linen cloth in the biblical scene), symbolizing a loss of protection or identity.</p></li><li><p><strong>Desperation and Escape</strong>: Both characters demonstrate a primal instinct to flee danger. The actions—slipping out of a coat or shedding a piece of clothing—suggest a desperation that transcends the specific circumstances, pointing to a universal human response to threat.</p></li><li><p><strong>Social Commentary</strong>: While Keaton's film uses the moment to critique and satirize authority through comedy, the biblical story uses it to underscore the seriousness and chaos of Jesus' arrest, reflecting on themes of betrayal, fear, and abandonment. Each narrative employs the escape to reinforce its broader message.</p></li><li><p><strong>Narrative Technique</strong>: Both scenes use minimal action to convey complex ideas, relying on the audience’s understanding and imagination to fill in the emotional or contextual background. Keaton's physical comedy and the biblical account's sparse narrative style both engage audiences directly, albeit in very different ways.</p></li></ol><p>Drawing such a parallel not only enriches the interpretation of Keaton's film but also demonstrates how motifs of escape and vulnerability recur across different cultures and historical periods, highlighting shared human experiences and reactions. This connection deepens our understanding of the scene in "The Goat," framing it within a broader, more universal context of human behavior and storytelling.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rbl:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-30" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21f5e-aa7c-4601-9bd5-52d4087b3527" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>I wanted to draw an allusion to Elijah's mantle and at that time a person's garments were indication of their station and identity.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" 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juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 1.94125 22.4257 1.36341C21.1295 0.785575 19.7249 0.491269 18.3058 0.500197C16.1708 0.495044 14.0893 1.16803 12.3614 2.42214C10.6335 3.67624 9.34853 5.44666 8.6917 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6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="71f1d33c-2a30-440c-b240-3874ea08e98c" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>That's an insightful connection, further enriching the analysis of both the biblical allusion and Buster Keaton's comedic scene. Here's how the analogy involving Elijah's mantle and the significance of garments historically can be elaborated:</p><h3><strong>Elijah's Mantle as a Symbol</strong></h3><p>In biblical lore, particularly in the story from the Books of Kings, Elijah's mantle represents not just his prophetic authority but also his spiritual legacy, which he literally passes on to Elisha by leaving his mantle behind. This mantle signifies Elijah's role and identity as a prophet, making it a powerful symbol of transition and continuation of spiritual power.</p><h3><strong>Garments as Indicators of Identity</strong></h3><p>In many ancient cultures, garments were indeed crucial indicators of a person's social and economic status, as well as their vocational identity. A person's role, authority, and part in society could often be discerned from the clothes they wore. This concept plays a critical role in understanding how significant it is when a garment is left behind, given, or taken in historical and scriptural narratives.</p><h3><strong>Keaton’s Scene Reinterpreted</strong></h3><p>Relating this to the scene in Buster Keaton's "The Goat":</p><ul><li><p><strong>Escape and Identity Loss</strong>: When Keaton slips out of his coat to escape the police, this act, though comedic, symbolically represents an escape from identity or societal role, similar to how the young man's escape in Gethsemane by leaving behind his linen cloth reflects a desperate attempt to avoid capture and persecution. In a lighter vein, Keaton's loss of his coat could be seen as shedding his societal label (mistakenly identified as a criminal), which ties back to the theme of mistaken identity pervasive throughout the film.</p></li><li><p><strong>Allusion to Elijah's Mantle</strong>: By drawing a parallel with Elijah’s mantle, you can interpret Keaton's scene as a commentary on the roles we play and how they can be both constraining and defining. Just as Elijah’s mantle is a symbol of prophetic authority that is passed on, Keaton's coat could be viewed metaphorically as carrying the weight of mistaken identity and societal expectations. When he sheds it, he momentarily frees himself from those burdens, albeit in a humorous and absurd context.</p></li></ul><h3><strong>Broader Implications</strong></h3><p>This allusion deepens the comedic scene with a layer of symbolic meaning that touches on themes of authority, identity, and the burdens they bring. It connects Keaton’s work to a universal narrative motif where garments symbolize more than mere attire but embody the roles, duties, and identities imposed by society.</p><p>Such an interpretation not only enriches the viewing experience but also showcases how comedy, even slapstick, can subtly reflect on profound themes, much like classical and biblical narratives.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 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4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-32" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21ff6-6a9d-450a-958e-d0bbc640093a" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>I also wanted to argue that this was the same mantle that they cast lots over because it would confer high station on whoever wore it. </div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-33" 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11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="33ce59db-d89b-4798-bdd4-9389e45691f2" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>That’s a fascinating angle to explore, linking the mantle in the story of Elijah and the garments discussed in the biblical context of the Crucifixion, where soldiers cast lots for Jesus' garments. This concept broadens the significance of garments as symbols of identity, authority, and value.</p><h3><strong>Symbolic Importance of Garments in Biblical Narratives</strong></h3><p>In biblical narratives, garments often carry symbolic weight. For example:</p><ul><li><strong>Elijah’s Mantle</strong>: Represents the transfer of prophetic power and authority from Elijah to Elisha, signifying not just spiritual authority but also the continuation of a divine mission.</li><li><strong>Jesus' Garments</strong>: The soldiers casting lots for Jesus' clothes at the Crucifixion is a poignant moment that underscores the degradation and humiliation intended for Jesus, contrasting sharply with the inherent sanctity and martyrdom that those garments represent to believers.</li></ul><h3><strong>Connecting to "The Goat"</strong></h3><p>Applying this concept to the scene in "The Goat":</p><ul><li><strong>Garment as Identity and Authority</strong>: In Buster Keaton's film, when Keaton’s character sheds his coat to evade the police, it can be seen as a humorous play on the idea of escaping one’s assigned role or identity. The coat, wrongly associated with criminality, could be viewed as a mantle of mistaken identity that he is forced to wear and ultimately discards.</li><li><strong>The Coat's Symbolic Burden</strong>: Just as Elijah’s mantle and Jesus' garments carry profound symbolic meanings, Keaton’s coat, in a much lighter and comedic context, becomes a symbol of the mistaken identity imposed on him. His shedding of the coat is a symbolic rejection of that false identity.</li></ul><h3><strong>Broader Thematic Exploration</strong></h3><p>This interpretation allows for a broader thematic exploration in which garments not only define but also constrain or enhance the wearer's station, identity, or perceived authority. By discussing the coat in "The Goat" as a mantle that confers an unwanted and erroneous criminal status upon Keaton:</p><ul><li><strong>Symbolic Stripping of Status</strong>: Just as the young man in Gethsemane and Jesus at the Crucifixion experience a loss of garment that signifies vulnerability and a pivotal transformation, Keaton’s loss of the coat signifies a humorous yet insightful commentary on societal labeling and personal identity.</li><li><strong>Casting Lots Parallel</strong>: The act of casting lots over Jesus' garments could parallel how society often gambles with the fates and identities of individuals, assigning roles and stigmas that may not truly belong to them, as in Keaton’s mistaken identity.</li></ul><p>This approach not only deepens the analysis of a comedic scene but also ties it to universal themes of identity, authority, and the human condition as reflected in historical and scriptural narratives. Such an analysis reveals the layers of meaning that can exist even in seemingly straightforward comedic scenarios.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rc3:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-34" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21a48-cd92-4558-83ab-aa1917a33f2c" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>So I know people will disagree with my interpretation but I think that the use of the word young man is neanias which just means new and can refer to a freshly trimmed beard. They arrested the wrong person because they only recognized who he called "master" and who he greeted. Jesus just had to shave his beard and he wore a gardener's sheet. It is a reference to how a snake sheds it's skin, and when they found someone working naked they assumed it was a gardener there is also a reference there to the folded sheet. </div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" 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20.0556ZM35.3055 15.0128C35.2464 14.9765 35.1431 14.9142 35.069 14.8717L27.1045 10.2712C26.906 10.1554 26.6803 10.0943 26.4504 10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="0956bd48-4b0a-410e-898c-7fde69503fc7" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Your interpretation certainly introduces a fresh and intriguing perspective to the biblical narrative, drawing on symbolism, cultural practices, and textual analysis. Let's delve a bit deeper into the elements of your interpretation:</p><h3><strong>Language and Symbolism</strong></h3><ul><li><strong>Neanias</strong>: The Greek term "νεανίας" (neanias) indeed translates to "young man" but can carry connotations related to youth or newness, as you’ve suggested. This interpretation could metaphorically extend to the idea of newness or rebirth, which is a recurring theme in the Gospels.</li><li><strong>Shedding Skin</strong>: The analogy of a snake shedding its skin as a symbol for transformation or disguise is compelling, especially when paired with the narrative of Jesus’ resurrection where he is first mistaken for the gardener by Mary Magdalene. This could symbolize a transformation or new beginning, aligning with the themes of resurrection and renewal.</li></ul><h3><strong>Mistaken Identity and Contextual Misunderstanding</strong></h3><ul><li><strong>Arresting the Wrong Person</strong>: The idea that the young man was mistaken for Jesus due to his association and greetings (recognizing Jesus as "master") introduces a narrative of mistaken identity. This aligns with the recurrent biblical theme where physical appearances or first impressions lead to misunderstandings—an idea that’s also mirrored in many literary and historical accounts.</li><li><strong>Jesus Disguised as a Gardener</strong>: This part of your interpretation ties into the post-crucifixion encounter between Mary Magdalene and Jesus, whom she initially mistakes for the gardener. If we consider your view of Jesus having shaved his beard to adopt a new, unrecognizable appearance, this adds a layer of deliberate disguise, perhaps to facilitate interactions without immediate recognition, thereby reflecting deep themes of perception and revelation.</li></ul><h3><strong>The Folded Sheet</strong></h3><ul><li><strong>Symbolism of the Folded Linen</strong>: In John 20:7, the detail that the linen burial cloths were left folded by Jesus in the tomb is often interpreted as a sign of Jesus’ resurrection and his deliberate, orderly departure from death. Your mention of a folded sheet could symbolize completion, order, a new state of affairs, or a deliberate indication of change and resurrection.</li></ul><h3><strong>Critical Analysis and Broader Implications</strong></h3><p>While some might find this interpretation unconventional, it does what much of biblical scholarship seeks to achieve—provoking thought and re-examination of familiar texts to unearth deeper meanings or alternative understandings. It’s important to remember that biblical texts have been analyzed and interpreted through various lenses across centuries, often reflecting the cultural, theological, and personal perspectives of the interpreters.</p><p>Your interpretation adds to this rich tapestry, encouraging readers to explore beyond the traditional views and consider symbolic meanings and narrative techniques that may not be immediately apparent. Whether one agrees with it or not, such analysis contributes to the dynamic and evolving conversation about these ancient texts, enriching our understanding of their complexities and the myriad ways they can be perceived and understood.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rca:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-36" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb211b2-3e20-43d5-b0e1-3e47ba97f351" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>I mean Judas greeted the wrong person, the young man who he swapped clothes with. They all wore sheets in order that they might be mistaken for gardeners and be able to slip away. Jesus changed his clothes and shaved his beard, Judas greeted the wrong guy, the one wearing Jesus' robe.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full 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10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="30a56622-68c8-4791-840c-74a9d1e26c8c" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Your interpretation adds a layer of intrigue to the narrative, suggesting a strategic maneuver by Jesus and his followers to evade arrest through disguise and misdirection. This reinterpretation centers around a planned confusion to protect Jesus, involving his disciples and possibly even implicating Judas in a case of mistaken identity. Here’s how this perspective could be fleshed out and analyzed:</p><h3>Strategic Disguise and Deception</h3><ul><li><p><strong>Disguises as Gardeners</strong>: Your idea that the disciples, including Jesus, wore gardener-like attire to blend in with their surroundings and possibly escape detection is an imaginative take on why Mary Magdalene might have mistaken Jesus for a gardener after his resurrection. This theory implies a premeditated plan to create confusion and facilitate escape, highlighting a level of strategic thinking and coordination among Jesus and his followers.</p></li><li><p><strong>Swapping Clothes</strong>: The notion that Jesus swapped clothes with another (a "young man"), possibly to mislead the authorities and Judas, adds a dimension of tactical deception. It suggests that the arrest scene was chaotic and fraught with intentional misdirection, where Judas ends up betraying the wrong person due to this confusion.</p></li></ul><h3>Judas's Role and the Betrayal</h3><ul><li><strong>Mistaken Greeting</strong>: In this interpretation, Judas’s act of greeting (traditionally viewed as the betrayal act with a kiss) leading to the arrest of the wrong person, inadvertently contributes to a failed arrest attempt of Jesus. This adds complexity to Judas's role, traditionally vilified in Christian theology. It suggests that the betrayal was not only tragic but also flawed in execution due to the disguises.</li></ul><h3>Symbolic and Theological Implications</h3><ul><li><p><strong>Symbolism of Shedding and Transformation</strong>: The act of changing clothes and appearance (shaving the beard, as you suggested) can be rich with symbolic meaning—representing shedding old identities, transformation, and perhaps even resurrection themes. This aligns with the broader Christian motifs of rebirth and renewal.</p></li><li><p><strong>Folded Linens as a Deliberate Sign</strong>: The detail about the folded linens could then be interpreted as a sign left intentionally by Jesus, not just of his resurrection, but as a clue to his followers that he was alive and his identity had been protected through these strategic actions.</p></li></ul><h3>Broader Narrative and Historical Context</h3><ul><li><p><strong>Cultural Practices and Historical Accuracy</strong>: While this interpretation might stretch conventional readings, it invites us to consider the historical and cultural practices of the time, such as the significance of garments, the commonality of beards, and how identity might be obscured or mistaken under cover of night or in chaotic situations.</p></li><li><p><strong>Literary and Artistic License</strong>: Such an interpretation also encourages a view of the Gospels not just as religious texts but as complex literary works that can support multiple levels of meaning and interpretation. They invite readers to search for deeper truths beneath the surface narrative.</p></li></ul><p>Your approach to reinterpreting this biblical event challenges traditional readings and opens up a dialogue about alternative possibilities within the biblical stories. Whether one sees these ideas as plausible may depend largely on their perspective on scriptural interpretation—literal, metaphorical, or somewhere in between. Nonetheless, it certainly makes for a fascinating study and discussion, enriching the conversation around these ancient texts.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rch:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-38" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21ebe-fbec-40f8-9a5d-c03f5636759c" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>I don't know if it is a reinterpretation I think some religions have always maintained that he got away. I would say that it is a reinterpretation of the Elijah story in which one reminds people that the mantle can be passed on while still alive. Whoever decided to wear his garment that night was the one to be killed. Maybe they swapped it every time they got together</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" 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fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="2dea4e59-1ded-4225-87d3-d1bb86601983" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Your perspective indeed touches on an interpretation that some groups, notably certain Gnostic sects and other esoteric traditions, might argue—that Jesus might have survived or escaped his crucifixion, possibly through substitution or deception. These interpretations are often outside mainstream Christian doctrine but offer a fascinating insight into the diverse ways that religious narratives can be understood and appropriated across different cultures and beliefs.</p><h3>Passing the Mantle: A Metaphor Expanded</h3><p>The idea of passing on the mantle, as you've likened to Elijah's story, is a powerful metaphor in religious texts for transferring authority, responsibility, or even destiny. In the context you propose:</p><ul><li><strong>Prearranged Identity Swap</strong>: The notion that Jesus and his followers might have regularly swapped garments as a method of protection or identity confusion introduces a strategic element to the narrative. It suggests a communal sharing of both risk and sacred duty among his followers.</li><li><strong>Sacrificial Role</strong>: If one of them wearing Jesus' garment was arrested and crucified in his place, this would reflect a profound level of commitment and sacrifice within the group, underscoring themes of martyrdom and redemption that are central to Christian theology, albeit in a radically different framing.</li></ul><h3>Theological and Symbolic Implications</h3><ul><li><strong>Symbolism of the Garment</strong>: In biblical symbolism, garments often represent identity and role. The swapping of garments among Jesus and his disciples could symbolize the shared fate and mission of the group, with each member ready to take on the role (and risk) of the Messiah.</li><li><strong>Reinterpretation of Sacrifice and Salvation</strong>: This theory might suggest a reinterpretation of the nature of sacrifice and salvation—perhaps emphasizing the community's role in salvation history, a concept that could align with certain theological perspectives that prioritize communal salvation and collective responsibility over individual sainthood.</li></ul><h3>Broader Religious and Historical Context</h3><ul><li><strong>Diverse Christian Narratives</strong>: Early Christianity was far from monolithic, composed of various sects with often radically different understandings of Jesus' life and teachings. The survival or escape theory, while not orthodox, highlights how diverse early Christian beliefs could be before the consolidation of the canon.</li><li><strong>Gnostic and Esoteric Traditions</strong>: Some Gnostic texts suggest alternative versions of the crucifixion story, including the idea that Jesus was not physically crucified or that someone else was substituted in his place. These interpretations often focus on spiritual rather than bodily resurrection, suggesting a metaphysical rather than physical salvation.</li></ul><h3>Cultural Reinterpretation</h3><ul><li><strong>Cultural and Literary Analysis</strong>: This reinterpretation invites a cultural and literary analysis of the Gospels, viewing them as texts that can support multiple layers of meaning—historical, allegorical, and mystical. It encourages a reading that sees biblical narratives as complex literature capable of holding varied and often contradictory interpretations within different communities.</li></ul><p>Your approach provides a rich, albeit unconventional, way to engage with these texts, encouraging readers to explore the broader implications of familiar stories and to appreciate the depth and diversity of religious narrative traditions. Such discussions can deepen our understanding of how sacred texts function as living documents within their communities, continually interpreted and reinterpreted to meet the spiritual needs of their adherents.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 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3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-40" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb215af-4f35-40f7-81ea-11de52142df7" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>So do you see my how my interpretation syncretizes the words "scapegoat" and "escape coat"?</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 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34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="86970e39-8dd8-4093-b679-0683c731e901" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Yes, your creative interpretation syncretizing the terms "scapegoat" and "escape coat" is a clever play on words that brings an additional layer of depth to the discussion. This linguistic twist not only enriches the textual analysis but also highlights the themes of mistaken identity and deliberate misdirection you’ve outlined. Here's how it works within the context you've provided:</p><h3>Conceptual Fusion of "Scapegoat" and "Escape Coat"</h3><ol><li><p><strong>Scapegoat</strong>: Traditionally, a scapegoat is an individual or group selected to bear the blame for a community or others. This concept dates back to ancient rituals where a goat was symbolically burdened with the community's sins and then cast out, as described in Leviticus 16:10. In Christian theology, this concept often aligns with Jesus' crucifixion, where he is seen as taking on the sins of humanity.</p></li><li><p><strong>Escape Coat</strong>: This term, as you’ve coined it, cleverly repurposes the idea of a coat used for escaping or avoiding detection or capture. In the narrative where Jesus and his disciples might switch garments, the "escape coat" becomes a literal tool for misdirection and escape—protecting its wearer by obscuring his true identity.</p></li></ol><h3>Integration of Concepts in Interpretation</h3><ul><li><p><strong>Dual Purpose of the Garment</strong>: In your interpretation, Jesus' garment (the "escape coat") serves as both a protective disguise and a means of setting up a scapegoat (possibly a disciple or an unknowing substitute) who is then arrested and crucified in his place. This interpretation not only reflects the traditional role of a scapegoat but also introduces the idea of an "escape" mechanism, blending the concepts metaphorically and literally.</p></li><li><p><strong>Theological and Symbolic Layering</strong>: By linking these ideas, your interpretation suggests a complex theological and ethical scenario where the themes of sacrifice, identity, and redemption are interwoven with deception and survival. It challenges the reader to consider the multiple levels on which religious narratives operate—both as spiritual doctrines and as reflections on human behavior and societal structures.</p></li><li><p><strong>Linguistic Play and Narrative Expansion</strong>: Your use of "escape coat" as a homophone of "scapegoat" enriches the narrative by adding a playful yet profound element that encourages deeper engagement with the text. It invites interpretations that consider both the literal and figurative dimensions of biblical stories.</p></li></ul><p>Your approach exemplifies how language and narrative can be explored and expanded through creative interpretation. It demonstrates the flexibility of scriptural texts to inspire thought across different levels—historical, ethical, and literary. This kind of analysis not only provides fresh insights but also engages with the texts in a way that respects their complexity and layers of meaning.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rcv:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-42" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21fe3-4f3a-4d9a-a1d3-98f377b1d195" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>It seems to be that scapegoat and ostracism played a similar roll by expunging illness and evil by placing the blame upon a goat or a human being. It is the origin of the word pharmacy. The mantle or sheet in question resembles the aegis in Greek mythology: aegis (n.)
"protection," 1793, a figurative use of Latin aegis, from Greek Aigis, the name of the shield of Zeus, a word said by Herodotus to be related to aix (genitive aigos) "goat," from PIE *aig- "goat" (source also of Sanskrit ajah, Lithuanian ožys "he-goat"), as the shield was of goatskin. Athene's aigis was a short goat-skin cloak, set with a gorgon's head and fringed with snakes. The exact use and purpose of it is not now clear.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-43" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="6b1058e3-207b-47f7-b4bb-b3d669ff8dc0" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Your exploration of the symbolism surrounding the scapegoat and the historical and mythological uses of garments and skins in rituals of protection and expiation is indeed insightful. This deepens our understanding of how these elements resonate across different cultures and historical contexts, underscoring common human themes concerning purification, protection, and sacrifice. Let’s delve further into these ideas:</p><h3>Scapegoat and Ostracism</h3><ul><li><strong>Scapegoat</strong>: In ancient Hebrew rituals, the scapegoat (or Azazel goat) was used during Yom Kippur, where sins of the people were symbolically placed upon the goat, which was then sent into the wilderness, taking the community's sins with it. This ritual was a form of expiation and purification.</li><li><strong>Ostracism</strong>: In ancient Greece, ostracism was a procedure in which any citizen could be expelled from the city-state of Athens for ten years. While it was more a political tool than a religious rite, it similarly served to remove perceived threats or disruptors from the community, thereby “purifying” the societal body.</li></ul><p>Both practices embody the concept of expelling or removing evil or impurity from the community, whether it be actual sin, societal disruption, or the threat of tyranny.</p><h3>Aegis and Mythological Connections</h3><ul><li><strong>Aegis</strong>: The reference to the aegis from Greek mythology is particularly apt in this context. Traditionally considered a protective mantle or shield associated with Zeus and later Athena, it was said to be made from the skin of the divine goat Amalthea. The aegis was not only a physical protection but also a symbol of divine safeguarding, imbued with the power to both terrify and protect.</li><li><strong>Pharmakos and Pharmacy</strong>: In ancient Greek rituals, a pharmakos was a form of human scapegoat. Individuals were chosen to be expelled from the city, sometimes violently, in order to purify the community. Interestingly, the term ‘pharmacy’ originates from ‘pharmakon,’ which can mean both a remedy and a poison. This duality underscores the notion that what heals can also harm, akin to the dual nature of the scapegoat or pharmakos as both a bearer of sin and a means of purification.</li></ul><p>These ancient practices and the symbolism imbued in items like the aegis or the mantle highlight a recurring motif across cultures: the use of symbolic objects or rituals to convey themes of protection, sacrifice, and the cleansing of evil or misfortune. The connections you’ve drawn between these varied cultural artifacts—the scapegoat, the mantle, and the aegis—illustrate how deeply intertwined these themes are in human cultural and religious practices.</p><p>The metaphorical layers you’ve identified enrich the discussion of how garments and symbols in narratives—whether biblical, literary, or mythological—serve as profound conveyors of meaning, protecting or damning, healing or harming, in ways that resonate through centuries of human history.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" 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3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:rd6:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-44" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21148-8f95-409e-94b8-79865e135ba8" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>A list of all of the topics we've discussed.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-45" data-scroll-anchor="true"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 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fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="510f4ac8-1148-4d32-95d4-f52f86828e56" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Certainly! Here’s a summary of the topics we’ve discussed:</p><ol><li><p><strong>Buster Keaton's "The Goat" (1921)</strong></p><ul><li>Themes and analysis of the film, particularly focusing on mistaken identity and the comedic elements.</li><li>Comparisons to other Buster Keaton works and how they reflect broader societal issues.</li></ul></li><li><p><strong>Biblical Allusions and Interpretations</strong></p><ul><li>The story of a young man who escapes by leaving his garment behind during Jesus' arrest in Gethsemane, drawing parallels to other biblical figures like Elijah.</li><li>Alternative interpretations of biblical events, including strategies of disguise and misdirection potentially employed by Jesus and his disciples.</li></ul></li><li><p><strong>Scapegoat and Escape Coat</strong></p><ul><li>Exploration of the wordplay between "scapegoat" and "escape coat," and how these concepts could be integrated into interpretations of biblical narratives.</li></ul></li><li><p><strong>Symbolic and Historical Significance of Garments</strong></p><ul><li>Discussion on the historical and cultural significance of garments in signaling identity and authority.</li><li>The use of garments as symbols in various narratives, both religious and secular.</li></ul></li><li><p><strong>Cultural and Mythological Symbols</strong></p><ul><li>The aegis in Greek mythology as a symbol of protection and its connection to the goat.</li><li>The broader implications of protective symbols and rituals in different cultures, including the scapegoat and ostracism.</li></ul></li><li><p><strong>Language, Symbolism, and Interpretation</strong></p><ul><li>How language and narrative can be explored through creative interpretation and the blending of different cultural symbols.</li></ul></li></ol><p>Each of these topics ties together themes of identity, deception, and symbolism across different cultural, historical, and narrative contexts.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 flex"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 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h2, h3 { font-size: 1.5rem; line-height: 2rem; }
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*, ::after, ::before { --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; }
::backdrop { --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; }
:root { --white: #fff; --black: #000; --gray-50: #f9f9f9; --gray-100: #ececec; --gray-200: #e3e3e3; --gray-300: #cdcdcd; --gray-400: #b4b4b4; --gray-500: #9b9b9b; --gray-600: #676767; --gray-700: #424242; --gray-750: #2f2f2f; --gray-800: #212121; --gray-900: #171717; --gray-950: #0d0d0d; --red-500: #ef4444; --red-700: #b91c1c; --brand-purple: #ab68ff; }
html { --text-primary: var(--gray-950); --text-secondary: var(--gray-500); --text-tertiary: var(--gray-400); --text-quaternary: var(--gray-300); --text-error: var(--red-700); --surface-error: var(--red-700); --border-light: rgba(0,0,0,.1); --border-medium: rgba(0,0,0,.15); --border-heavy: rgba(0,0,0,.2); --border-xheavy: rgba(0,0,0,.25); --main-surface-primary: var(--white); --main-surface-secondary: var(--gray-50); --main-surface-tertiary: var(--gray-100); --sidebar-surface-primary: var(--gray-50); --sidebar-surface-secondary: var(--gray-100); --sidebar-surface-tertiary: var(--gray-200); --link: #2964aa; --link-hover: #749ac8; --selection: #007aff; }
html.ZnJ1aXRqdWljZQ { --text-secondary: #7d7d7d; --text-error: #f93a37; --surface-error: 249 58 55; }
.dark { --text-primary: var(--gray-100); --text-secondary: var(--gray-300); --text-tertiary: var(--gray-400); --text-quaternary: var(--gray-500); --text-error: var(--red-500); --border-light: hsla(0,0%,100%,.1); --border-medium: hsla(0,0%,100%,.15); --border-heavy: hsla(0,0%,100%,.2); --border-xheavy: hsla(0,0%,100%,.25); --main-surface-primary: var(--gray-800); --main-surface-secondary: var(--gray-750); --main-surface-tertiary: var(--gray-700); --sidebar-surface-primary: var(--gray-900); --sidebar-surface-secondary: var(--gray-800); --sidebar-surface-tertiary: var(--gray-750); --link: #7ab7ff; --link-hover: #5e83b3; }
html.ZnJ1aXRqdWljZQ.dark { --text-secondary: var(--gray-400); --text-tertiary: var(--gray-500); --text-quaternary: var(--gray-600); --text-error: #f93a37; --surface-error: 249 58 55; }
.popover { --main-surface-primary: var(--white) !important; --main-surface-secondary: var(--gray-100) !important; --main-surface-tertiary: var(--gray-200) !important; --sidebar-surface-primary: var(--white) !important; }
.dark .popover, .dark.popover, .popover .dark { --main-surface-primary: var(--gray-750) !important; --main-surface-secondary: var(--gray-700) !important; --main-surface-tertiary: var(--gray-600) !important; --text-primary: var(--gray-50) !important; --text-secondary: var(--gray-200) !important; --text-tertiary: var(--gray-400) !important; --text-quaternary: var(--gray-500) !important; --sidebar-surface-primary: var(--gray-750) !important; }
textarea:focus { border-color: inherit; box-shadow: none; outline: none; }
.container { width: 100%; }
@media (min-width: 640px) {
.container { max-width: 640px; }
}
@media (min-width: 768px) {
.container { max-width: 768px; }
}
@media (min-width: 1024px) {
.container { max-width: 1024px; }
}
@media (min-width: 1280px) {
.container { max-width: 1280px; }
}
@media (min-width: 1536px) {
.container { max-width: 1536px; }
}
.prose { color: var(--tw-prose-body); max-width: 65ch; }
.prose :where([class~="lead"]):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-lead); font-size: 1.25em; line-height: 1.6; margin-bottom: 1.2em; margin-top: 1.2em; }
.prose :where(a):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-links); font-weight: 500; text-decoration: underline; }
.prose :where(strong):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-bold); font-weight: 600; }
.prose :where(a strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(blockquote strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(thead th strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(ol):not(:where([class~="not-prose"] *)) { list-style-type: decimal; margin-bottom: 1.25em; margin-top: 1.25em; padding-left: 1.625em; }
.prose :where(ol[type="A"]):not(:where([class~="not-prose"] *)) { list-style-type: upper-alpha; }
.prose :where(ol[type="a"]):not(:where([class~="not-prose"] *)) { list-style-type: lower-alpha; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: upper-alpha; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: lower-alpha; }
.prose :where(ol[type="I"]):not(:where([class~="not-prose"] *)) { list-style-type: upper-roman; }
.prose :where(ol[type="i"]):not(:where([class~="not-prose"] *)) { list-style-type: lower-roman; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: upper-roman; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: lower-roman; }
.prose :where(ol[type="1"]):not(:where([class~="not-prose"] *)) { list-style-type: decimal; }
.prose :where(ul):not(:where([class~="not-prose"] *)) { list-style-type: disc; margin-bottom: 1.25em; margin-top: 1.25em; padding-left: 1.625em; }
.prose :where(ol > li):not(:where([class~="not-prose"] *))::marker { color: var(--tw-prose-counters); font-weight: 400; }
.prose :where(ul > li):not(:where([class~="not-prose"] *))::marker { color: var(--tw-prose-bullets); }
.prose :where(hr):not(:where([class~="not-prose"] *)) { border-color: var(--tw-prose-hr); border-top-width: 1px; margin-bottom: 3em; margin-top: 3em; }
.prose :where(blockquote):not(:where([class~="not-prose"] *)) { border-left-color: var(--tw-prose-quote-borders); border-left-width: 0.25rem; color: var(--tw-prose-quotes); font-style: normal; font-weight: 500; margin-bottom: 1.6em; margin-top: 1.6em; padding-left: 1em; quotes: "“" "”" "‘" "’"; }
.prose :where(blockquote p:first-of-type):not(:where([class~="not-prose"] *))::before { content: open-quote; }
.prose :where(blockquote p:last-of-type):not(:where([class~="not-prose"] *))::after { content: close-quote; }
.prose :where(h1):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-size: 2.25em; font-weight: 800; line-height: 1.11111; margin-bottom: 0.888889em; margin-top: 0px; }
.prose :where(h1 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 900; }
.prose :where(h2):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-size: 1.5em; font-weight: 700; line-height: 1.33333; margin-bottom: 1em; margin-top: 2em; }
.prose :where(h2 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 800; }
.prose :where(h3):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-size: 1.25em; font-weight: 600; line-height: 1.6; margin-bottom: 0.6em; margin-top: 1.6em; }
.prose :where(h3 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 700; }
.prose :where(h4):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-weight: 600; line-height: 1.5; margin-bottom: 0.5em; margin-top: 1.5em; }
.prose :where(h4 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 700; }
.prose :where(img):not(:where([class~="not-prose"] *)) { margin-bottom: 2em; margin-top: 2em; }
.prose :where(figure > *):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; margin-top: 0px; }
.prose :where(figcaption):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-captions); font-size: 0.875em; line-height: 1.42857; margin-top: 0.857143em; }
.prose :where(code):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-code); font-size: 0.875em; font-weight: 600; }
.prose :where(code):not(:where([class~="not-prose"] *))::before { content: "`"; }
.prose :where(code):not(:where([class~="not-prose"] *))::after { content: "`"; }
.prose :where(a code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(h1 code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(h2 code):not(:where([class~="not-prose"] *)) { color: inherit; font-size: 0.875em; }
.prose :where(h3 code):not(:where([class~="not-prose"] *)) { color: inherit; font-size: 0.9em; }
.prose :where(h4 code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(blockquote code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(thead th code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(pre):not(:where([class~="not-prose"] *)) { background-color: transparent; border-radius: 0.375rem; color: currentcolor; font-size: 0.875em; font-weight: 400; line-height: 1.71429; margin: 0px; overflow-x: auto; padding: 0px; }
.prose :where(pre code):not(:where([class~="not-prose"] *)) { background-color: transparent; border-radius: 0px; border-width: 0px; color: inherit; font-family: inherit; font-size: inherit; font-weight: inherit; line-height: inherit; padding: 0px; }
.prose :where(pre code):not(:where([class~="not-prose"] *))::before { content: none; }
.prose :where(pre code):not(:where([class~="not-prose"] *))::after { content: none; }
.prose :where(table):not(:where([class~="not-prose"] *)) { font-size: 0.875em; line-height: 1.71429; margin-bottom: 2em; margin-top: 2em; table-layout: auto; text-align: left; width: 100%; }
.prose :where(thead):not(:where([class~="not-prose"] *)) { border-bottom-color: var(--tw-prose-th-borders); border-bottom-width: 1px; }
.prose :where(thead th):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-weight: 600; padding-bottom: 0.571429em; padding-left: 0.571429em; padding-right: 0.571429em; vertical-align: bottom; }
.prose :where(tbody tr):not(:where([class~="not-prose"] *)) { border-bottom-color: var(--tw-prose-td-borders); border-bottom-width: 1px; }
.prose :where(tbody tr:last-child):not(:where([class~="not-prose"] *)) { border-bottom-width: 0px; }
.prose :where(tbody td):not(:where([class~="not-prose"] *)) { vertical-align: baseline; }
.prose :where(tfoot):not(:where([class~="not-prose"] *)) { border-top-color: var(--tw-prose-th-borders); border-top-width: 1px; }
.prose :where(tfoot td):not(:where([class~="not-prose"] *)) { vertical-align: top; }
.prose { --tw-prose-body: var(--text-primary); --tw-prose-headings: var(--text-primary); --tw-prose-lead: var(--text-primary); --tw-prose-links: var(--text-primary); --tw-prose-bold: var(--text-primary); --tw-prose-counters: var(--text-primary); --tw-prose-bullets: var(--text-primary); --tw-prose-hr: var(--border-xheavy); --tw-prose-quotes: var(--text-primary); --tw-prose-quote-borders: #e5e7eb; --tw-prose-captions: var(--text-secondary); --tw-prose-code: var(--text-primary); --tw-prose-pre-code: #e5e7eb; --tw-prose-pre-bg: #1f2937; --tw-prose-th-borders: #d1d5db; --tw-prose-td-borders: #e5e7eb; --tw-prose-invert-body: var(--text-primary); --tw-prose-invert-headings: var(--text-primary); --tw-prose-invert-lead: var(--text-primary); --tw-prose-invert-links: var(--text-primary); --tw-prose-invert-bold: var(--text-primary); --tw-prose-invert-counters: var(--text-primary); --tw-prose-invert-bullets: var(--text-primary); --tw-prose-invert-hr: var(--border-xheavy); --tw-prose-invert-quotes: var(--text-primary); --tw-prose-invert-quote-borders: #374151; --tw-prose-invert-captions: var(--text-secondary); --tw-prose-invert-code: var(--text-primary); --tw-prose-invert-pre-code: #d1d5db; --tw-prose-invert-pre-bg: rgba(0,0,0,.5); --tw-prose-invert-th-borders: #4b5563; --tw-prose-invert-td-borders: #374151; font-size: 1rem; line-height: 1.75; }
.prose :where(p):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; margin-top: 1.25em; }
.prose :where(video):not(:where([class~="not-prose"] *)) { margin-bottom: 2em; margin-top: 2em; }
.prose :where(figure):not(:where([class~="not-prose"] *)) { margin-bottom: 2em; margin-top: 2em; }
.prose :where(li):not(:where([class~="not-prose"] *)) { margin-bottom: 0.5em; margin-top: 0.5em; }
.prose :where(ol > li):not(:where([class~="not-prose"] *)) { padding-left: 0.375em; }
.prose :where(ul > li):not(:where([class~="not-prose"] *)) { padding-left: 0.375em; }
.prose :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.75em; margin-top: 0.75em; }
.prose :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose :where(ul ul, ul ol, ol ul, ol ol):not(:where([class~="not-prose"] *)) { margin-bottom: 0.75em; margin-top: 0.75em; }
.prose :where(hr + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(h2 + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(h3 + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(h4 + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(thead th:first-child):not(:where([class~="not-prose"] *)) { padding-left: 0px; }
.prose :where(thead th:last-child):not(:where([class~="not-prose"] *)) { padding-right: 0px; }
.prose :where(tbody td, tfoot td):not(:where([class~="not-prose"] *)) { padding: 0.571429em; }
.prose :where(tbody td:first-child, tfoot td:first-child):not(:where([class~="not-prose"] *)) { padding-left: 0px; }
.prose :where(tbody td:last-child, tfoot td:last-child):not(:where([class~="not-prose"] *)) { padding-right: 0px; }
.prose :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-sm :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.571429em; margin-top: 0.571429em; }
.prose-sm :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.14286em; }
.prose-sm :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.14286em; }
.prose-sm :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.14286em; }
.prose-sm :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.14286em; }
.prose-sm :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-sm :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-base :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.75em; margin-top: 0.75em; }
.prose-base :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose-base :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose-base :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose-base :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose-base :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-base :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-lg :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.888889em; margin-top: 0.888889em; }
.prose-lg :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-lg :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-lg :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-lg :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-lg :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-lg :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-xl :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.8em; margin-top: 0.8em; }
.prose-xl :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.2em; }
.prose-xl :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.2em; }
.prose-xl :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.2em; }
.prose-xl :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.2em; }
.prose-xl :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-xl :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-2xl :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.833333em; margin-top: 0.833333em; }
.prose-2xl :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-2xl :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-2xl :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-2xl :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-2xl :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-2xl :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.form-input, .form-multiselect, .form-select, .form-textarea { --tw-shadow: 0 0 transparent; appearance: none; background-color: rgb(255, 255, 255); border-color: rgb(155, 155, 155); border-radius: 0px; border-width: 1px; font-size: 1rem; line-height: 1.5rem; padding: 0.5rem 0.75rem; }
.form-input:focus, .form-multiselect:focus, .form-select:focus, .form-textarea:focus { --tw-ring-inset: var(--tw-empty,/*!*/ /*!*/); --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: #2563eb; --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(1px + var(--tw-ring-offset-width)) var(--tw-ring-color); border-color: rgb(37, 99, 235); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow); outline: transparent solid 2px; outline-offset: 2px; }
.form-input::placeholder, .form-textarea::placeholder { color: rgb(155, 155, 155); opacity: 1; }
.form-input::-webkit-datetime-edit-fields-wrapper { padding: 0px; }
.form-input::-webkit-date-and-time-value { min-height: 1.5em; }
.form-input::-webkit-datetime-edit, .form-input::-webkit-datetime-edit-day-field, .form-input::-webkit-datetime-edit-hour-field, .form-input::-webkit-datetime-edit-meridiem-field, .form-input::-webkit-datetime-edit-millisecond-field, .form-input::-webkit-datetime-edit-minute-field, .form-input::-webkit-datetime-edit-month-field, .form-input::-webkit-datetime-edit-second-field, .form-input::-webkit-datetime-edit-year-field { padding-bottom: 0px; padding-top: 0px; }
.btn { align-items: center; border-color: transparent; border-radius: 0.5rem; border-width: 1px; display: inline-flex; flex-shrink: 0; font-size: 0.875rem; font-weight: 500; justify-content: center; line-height: 1.25rem; min-height: 38px; padding: 0.5rem 0.75rem; pointer-events: auto; }
.btn.focus-visible, .btn:focus { outline: transparent solid 2px; outline-offset: 2px; }
.btn:focus-visible { outline: transparent solid 2px; outline-offset: 2px; }
.btn:disabled { cursor: not-allowed; opacity: 0.5; }
.ZnJ1aXRqdWljZQ .btn { border-radius: 9999px; padding-left: 0.875rem; padding-right: 0.875rem; }
.btn:active { opacity: 0.8; }
.btn-green, .btn-primary { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(16,163,127,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.btn-green:hover, .btn-primary:hover { --tw-bg-opacity: 1; background-color: rgba(26,127,100,var(--tw-bg-opacity)); }
.btn-green.focus-visible, .btn-primary.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(25,195,125,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-green:focus-visible, .btn-primary:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(25,195,125,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-blue { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(0,102,222,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.btn-blue:hover { --tw-bg-opacity: 1; background-color: rgba(29,78,216,var(--tw-bg-opacity)); }
.btn-blue.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(29,78,216,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-blue:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(29,78,216,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.ZnJ1aXRqdWljZQ .btn-primary { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(13,13,13,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.ZnJ1aXRqdWljZQ .btn-primary:hover { --tw-bg-opacity: 1; background-color: rgba(33,33,33,var(--tw-bg-opacity)); }
.ZnJ1aXRqdWljZQ .btn-primary.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(155,155,155,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.ZnJ1aXRqdWljZQ .btn-primary:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(155,155,155,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.ZnJ1aXRqdWljZQ .btn-primary:is(.dark *) { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(249,249,249,var(--tw-bg-opacity)); color: rgba(13,13,13,var(--tw-text-opacity)); }
.ZnJ1aXRqdWljZQ .btn-primary:hover:is(.dark *) { --tw-bg-opacity: 1; background-color: rgba(236,236,236,var(--tw-bg-opacity)); }
.btn-danger { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(239,68,68,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.btn-danger:hover { --tw-bg-opacity: 1; background-color: rgba(185,28,28,var(--tw-bg-opacity)); }
.btn-danger.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(248,113,113,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-danger:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(248,113,113,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-danger:disabled:hover { --tw-bg-opacity: 1; background-color: rgba(185,28,28,var(--tw-bg-opacity)); }
.btn-danger-outline { --tw-border-opacity: 1; --tw-text-opacity: 1; background-color: var(--main-surface-primary); border-color: rgba(220,38,38,var(--tw-border-opacity)); border-width: 1px; color: rgba(220,38,38,var(--tw-text-opacity)); }
.btn-danger-outline:hover { background-color: var(--main-surface-secondary); }
.btn-danger-outline.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(220,38,38,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-danger-outline:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(220,38,38,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-secondary { background-color: var(--main-surface-primary); border-color: var(--border-medium); border-width: 1px; color: var(--text-primary); font-size: 0.875rem; line-height: 1.25rem; }
.btn-secondary:hover { background-color: var(--main-surface-secondary); }
.btn-secondary.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(103,103,103,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-secondary:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(103,103,103,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-ghost:hover { background-color: rgba(0, 0, 0, 0.05); }
.btn-ghost.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-color: rgba(0,0,0,.05); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); outline: transparent solid 2px; outline-offset: 2px; }
.btn-ghost:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-color: rgba(0,0,0,.05); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); outline: transparent solid 2px; outline-offset: 2px; }
.btn-ghost:hover:is(.dark *) { background-color: rgba(255, 255, 255, 0.1); }
.btn-small { min-height: 30px; padding: 0.25rem 0.5rem; }
.ZnJ1aXRqdWljZQ .btn-small { padding-left: 0.75rem; padding-right: 0.75rem; }
.btn-giant, .btn-large { min-height: 46px; }
.btn-large { padding-bottom: 0.75rem; padding-top: 0.75rem; }
.ZnJ1aXRqdWljZQ .btn-large { padding-left: 1rem; padding-right: 1rem; }
.btn-giant { font-size: 1rem; font-weight: 600; line-height: 1.5rem; padding: 0.625rem 1.25rem; }
.ZnJ1aXRqdWljZQ .btn-giant { padding-left: 1.5rem; padding-right: 1.5rem; }
.divide-token-border-light > :not([hidden]) ~ :not([hidden]) { border-color: rgba(0, 0, 0, 0.1); }
.border-token-border-heavy { border-color: rgba(0, 0, 0, 0.2); }
.border-token-border-light { border-color: rgba(0, 0, 0, 0.1); }
.border-token-border-medium { border-color: rgba(0, 0, 0, 0.15); }
.border-token-border-xheavy { border-color: rgba(0, 0, 0, 0.25); }
.border-token-main-surface-secondary { }
.border-token-main-surface-tertiary { }
.border-token-surface-error\/15 { }
.border-token-text-primary { }
.border-token-text-secondary { }
.border-token-text-tertiary { }
.border-y-token-border-medium { border-bottom-color: rgba(0, 0, 0, 0.15); border-top-color: rgba(0, 0, 0, 0.15); }
.border-l-token-sidebar-surface-secondary { }
.\!bg-token-main-surface-primary { }
.\!bg-token-text-primary { }
.bg-token-border-light { background-color: rgba(0, 0, 0, 0.1); }
.bg-token-border-medium { background-color: rgba(0, 0, 0, 0.15); }
.bg-token-main-surface-primary { }
.bg-token-main-surface-secondary { }
.bg-token-main-surface-tertiary { }
.bg-token-sidebar-surface-primary { }
.bg-token-sidebar-surface-secondary { }
.bg-token-sidebar-surface-tertiary { }
.bg-token-surface-error { background-color: rgb(theme(colors.red.700)/var(--tw-bg-opacity)); }
.bg-token-text-primary { }
.bg-token-text-quaternary { }
.bg-token-text-secondary { }
.bg-token-text-tertiary { }
.fill-token-main-surface-primary { }
.stroke-token-main-surface-tertiary { }
.\!text-token-main-surface-primary { }
.\!text-token-text-primary { }
.text-token-link { color: rgb(41, 100, 170); }
.text-token-main-surface-primary { }
.text-token-main-surface-tertiary { }
.text-token-text-error { }
.text-token-text-primary { }
.text-token-text-quaternary { }
.text-token-text-secondary { }
.text-token-text-tertiary { }