representation theory with chatGPT, medicine and representation theory

• chatGPTと一緒に数学を勉強していく。
• chatGPTの活用方法についての動画があった。
• リンクはこちら。
• 大事なコツがあるらしい
•  トークン数（長すぎたらダメ、4000 トークン（日本語なら1000字）
• 検索の代わりに使わない
• 無茶振りをする
• 人間にできないことをさせる。
• 人間の創造性と、chatGPTの創造性の違いに由来
• しつこく聞く
• 人に聞けないこと（デリカシー、体裁などの、妨げるものがない）
• 英語でまとめる
• OK
• ここまでの話を踏まえて、数学の勉強をしていく。
• 表現論について勉強している。
• 表現論と医学の共通点について無茶振り質問をした。
• すると、このような答えが返ってきた。

One similarity between medicine and representation theory is that both fields involve the analysis and understanding of complex systems. In medicine, complex biological systems are studied, including the human body and its various organs, tissues, and cells, as well as the interactions between them. In representation theory, complex algebraic structures, such as groups, rings, and algebras, are studied, along with the various ways in which these structures can be represented by linear transformations of vector spaces.

Both fields also involve the use of mathematical tools and methods. In medicine, mathematical models and statistical analysis are used to analyze and understand complex biological systems, as well as to develop new diagnostic and treatment approaches. In representation theory, mathematical methods are used to study algebraic structures and their properties, as well as to develop new representation theories and techniques.

Another similarity between medicine and representation theory is the importance of pattern recognition. In medicine, doctors and researchers often look for patterns in medical data, such as symptoms, test results, and imaging studies, in order to diagnose diseases and develop new treatments. Similarly, in representation theory, mathematicians look for patterns and symmetries in algebraic structures, which can provide important insights into their properties and behavior.

Overall, while medicine and representation theory are very different fields, they share some important similarities, including the analysis of complex systems, the use of mathematical tools and methods, and the importance of pattern recognition.

• 面白い
• 両方とも、複雑な構造物を取り扱う手法であり、かつ、構造物に潜むパターン（や対称性）を取り出すことが重要である、ということか。
• 表現論で扱う複雑さと、人体の複雑さの違い・共通点が気になる。
• まず、違いについて聞いてみる。

The complexity of medicine and the complexity of representation theory are difficult to compare directly, as they involve very different types of complexity.

In medicine, the complexity often arises from the biological systems being studied. The human body, for example, is a highly complex system with many interacting parts, from individual cells to entire organs and organ systems. These systems are influenced by a wide range of factors, including genetics, environmental factors, and lifestyle choices, and they can exhibit complex behaviors and patterns of disease that are not fully understood.

In representation theory, the complexity typically arises from the algebraic structures being studied. These structures can be highly abstract and can involve a large number of elements and relationships between them. For example, a group can have many different subgroups, each with their own properties and relationships with the rest of the group. These relationships can be highly complex and difficult to understand, and they can have important implications for the behavior of the group as a whole.

Overall, both medicine and representation theory involve complex systems with their own unique forms of complexity. The complexity in medicine often arises from the biological systems being studied, while the complexity in representation theory often arises from the algebraic structures being studied.

• なるほど。
• 医学は、階層構造のそれぞれおよび階層間において、多くの要素と関係性があり、それがシステムの振る舞いの予測・理解を困難にしている。
• 一方で、表現論においては、代数的構造に起因する。それはつまり、要素の多さと、部分構造の性質や、部分構造間の関係性が原因となっている。
• ふんわりと理解は出来ている。
• 続いて、類似性について聞いてみる。
• One similarity between the complexity of medicine and the complexity of representation theory is that both involve dealing with complex systems that can exhibit emergent behavior.

In medicine, emergent behavior refers to the unexpected behavior that can arise from complex biological systems. For example, the behavior of an organ system may not be fully understood until all of the individual cells and biochemical processes are taken into account. This emergent behavior can be difficult to predict and understand.

Similarly, in representation theory, the behavior of a group or algebraic structure can exhibit emergent properties that are not immediately obvious from its individual elements and relationships. For example, the behavior of a Lie group can be highly complex and can exhibit emergent properties related to its symmetry and geometry.

Both medicine and representation theory also involve dealing with uncertainty and incompleteness of information. In medicine, incomplete or uncertain data may make it difficult to diagnose and treat diseases, while in representation theory, incomplete or uncertain information about an algebraic structure may make it difficult to understand its properties and behavior.

Overall, the complexity of medicine and the complexity of representation theory share some similarities in terms of dealing with emergent behavior and uncertainty, despite their very different domains.

• ほんとにそうなのか、という答えが返ってきた。
• 医学の方はわかる。予測困難さ、不確実性を扱うこと。
• それが、表現論においても成り立っているか、私はまだ不勉強なのでわからない。
• 引き続き学習を進める。