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​論文

機械が,階層的な仕組みを作る.どんなとき,何が起こると,階層を作るかを示す.

機械が,自覚する始まりを示す.

機械は,何を保持していて,何がある / 起こると,5進法を作るなどを

やるか示す.

機械は,どんなときに,何か集まりに記号をつけるか.あるいは,どんなときに,集まりの要素を"たとえば"という記号で言おうとするか.

機械は,自分が何をやっているか言おうとするとき,総称を作り出し,自分がやったことを,相手にやらせようとするとき,記号"たとえば"を作り出す.

機械が,論証数学をはじめる過程をのべる.機械に,タレス,ピュタゴラス,パルメニデスらの思考展開を試みさせることで.

特に,何を得ると,機械は,量だけでなく量の間の関係(辺の長さが同じなど)で何かを説明するようになるのか,そして,量の間の関係を組み立てることで,説明を展開するようになるかを述べる.

このとき,感覚系が得ることと,謂とを区分けするようになることを述べる.

共通の解き方を求める

機械が,いくつかの課題を共通した解き方で解くことを始める.いくつかの課題は,比例中項,角を3等分する線,立方体の辺の長さ,そして,4次方程式の根を求めるものだ.

Say My Innnate Capabilities

in a Natural Language

A human uses a programming language and writes a program that will say what the program does, in strings that the program will acquire. The program does not see any program code written by the human but it says what the program code conducts while it gets input strings and makes output strings. It finds regularities in the input and output strings, stores the regularities, and later retrieves regularities that match new inputs, for applying them to generate strings that would follow the new inputs.

 

The program gets input strings through four channels, and it binds them together when it gets them at the same time. While the program finds many regularities and applies regularities to new inputs, it forms a way Wn of making regularities out of inputs as a new regularity. The program gives strings Sr to have another program Pa do Sr by applying a regularity Rr assuming that Pa has formed the regularity Rr. If the program Pa is not able to do it, the program tries to have the program Pa do the way Wn, namely make the regularity Rr so that the program Pa becomes able to apply the regularity Rr for doing Sr. The program binds the way Wn and strings Sw together, and gives Sw to have Pa do the way Wn. Here, the program has formed a regularity of having Pa do Wn to make Rr if the program Pa is not able to do Rr.

 

Since 1) the innate (or original) capability forms the way Wn, and 2) the program says the way Wn in strings Sw that the program aquires after it runs when the program tries to have the other program Pa do the way Wn, the program says its innate capability in strings Sw that it gets after it runs.

数学史に関することを,1つ,以下に述べる

バビロニア人は,等脚台形の広さ,斜辺の傾き,底辺の長さを与え,上辺の長さを求めよという問いをやる(右図参照).彼らは,図中の部分と部分の間にある関係を見出して使うことで,答えただろう.たとえば,等脚台形の底辺の長さを,4つの長方形の広さ(つまり台形の広さ),2つの正方形の広さの間にある関係を使って求めたのだろう.

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