This document discusses curiosity, AI, and education. It talks about how western works were systematically translated into Chinese over hundreds of years. It mentions how Arthur Eddington introduced Einstein's theory of relativity into English during wartime. It discusses how studying nature can lead to breakthroughs through studying fields like mathematics and physics. It talks about the potential for AI progress in areas like protein folding, climate modeling, and pushing the boundaries of knowledge. Finally, it emphasizes values like curiosity, empathy, integrity, and responsibility.
This document discusses curiosity, AI, and education. It talks about how western works were systematically translated into Chinese over hundreds of years. It mentions how Arthur Eddington introduced Einstein's theory of relativity into English during wartime. It discusses how studying nature can lead to breakthroughs through studying fields like mathematics and physics. It talks about the potential for AI progress in areas like protein folding, climate modeling, and pushing the boundaries of knowledge. Finally, it emphasizes values like curiosity, empathy, integrity, and responsibility.
This document provides steps to solve a math problem involving trigonometric functions. It first lists cosine values for 84 and 44 degrees. It then adds and subtracts these angles. The next step uses these sums and differences in cosine functions, taking half the sum. This results in the value 0.075. Later steps multiply this by 75,000 and round up to get the final answer of 75,600. The document also mentions years related to prosthaphaeresis without providing additional context.
Knowledge Representation Systems From The Beginning 01- NumbersMingli Yuan
The document discusses the history of numerical representation systems from ancient times to their modern positional form. It describes early counting systems using tools like tally sticks and the Ishango bone that used markings to represent small quantities. Later, the Babylonians developed a positional numeral system in base-60 around 3000 BC and the Maya also used a positional system in base-20 around AD 400. The document then examines how positional systems establish soundness and completeness to represent all numbers and discusses early methods for multiplication problems using representations like in the Ahmes Papyrus.
This document introduces probabilistic topic modeling and discusses its applications to modeling social dynamics on social networks. It describes latent Dirichlet allocation and other topic modeling techniques like the dynamic topic model. It also discusses using topic models to analyze conversation graphs extracted from social media interactions and the need for new tools to model the interconnected structure of conversation graphs, referred to as topical social dynamics. Finally, it considers the possibility of ontological social dynamics but notes limitations due to current data and knowledge representation.
This document discusses an introduction to creative coding and shares several online resources. It describes creative coding as a form of artistic coding and lists examples of interactive simulations and games that can be created. These include simulations of orbits, weather, and plant growth. It also discusses physics engines, numerical modeling, and generative techniques that can be used. Links are provided to tutorials, documentation, code repositories, and forums for learning more about creative coding.
WSGI is a specification for connecting HTTP servers to web applications through a common interface. It defines an application as a callable object that receives environment variables from the server and returns a response. WSGI also supports middleware as callable objects that can process requests and responses between the server and application.
This document provides steps to solve a math problem involving trigonometric functions. It first lists cosine values for 84 and 44 degrees. It then adds and subtracts these angles. The next step uses these sums and differences in cosine functions, taking half the sum. This results in the value 0.075. Later steps multiply this by 75,000 and round up to get the final answer of 75,600. The document also mentions years related to prosthaphaeresis without providing additional context.
Knowledge Representation Systems From The Beginning 01- NumbersMingli Yuan
The document discusses the history of numerical representation systems from ancient times to their modern positional form. It describes early counting systems using tools like tally sticks and the Ishango bone that used markings to represent small quantities. Later, the Babylonians developed a positional numeral system in base-60 around 3000 BC and the Maya also used a positional system in base-20 around AD 400. The document then examines how positional systems establish soundness and completeness to represent all numbers and discusses early methods for multiplication problems using representations like in the Ahmes Papyrus.
This document introduces probabilistic topic modeling and discusses its applications to modeling social dynamics on social networks. It describes latent Dirichlet allocation and other topic modeling techniques like the dynamic topic model. It also discusses using topic models to analyze conversation graphs extracted from social media interactions and the need for new tools to model the interconnected structure of conversation graphs, referred to as topical social dynamics. Finally, it considers the possibility of ontological social dynamics but notes limitations due to current data and knowledge representation.
This document discusses an introduction to creative coding and shares several online resources. It describes creative coding as a form of artistic coding and lists examples of interactive simulations and games that can be created. These include simulations of orbits, weather, and plant growth. It also discusses physics engines, numerical modeling, and generative techniques that can be used. Links are provided to tutorials, documentation, code repositories, and forums for learning more about creative coding.
WSGI is a specification for connecting HTTP servers to web applications through a common interface. It defines an application as a callable object that receives environment variables from the server and returns a response. WSGI also supports middleware as callable objects that can process requests and responses between the server and application.
7. 延伸讨论
• 停机的程序-数据集合 HALT 半可判定
• 证明思路：利⽤用解释器 u，构造如下程序
read PD
V = u PD
write ‘true
• 推论：HALT的补集既不可判定也不半可判定
8. s-m-n 定理
• 特化器的存在性
• [[spec](p.s)](d) = [p](s.d)
• 构造思路：
• 特化时刻：
• 程序 spec 输⼊入的 s 转接给输出的程序 q，成为 q 内部的⼀一个赋值
• 程序 spec 输⼊入的 p 转接给输出的程序 q，使得 p 嵌⼊入到 q 内部
• 运⾏行时刻：
• q 有输⼊入 d，这样 q 可以把 s 和 d 合并，再转接给嵌⼊入其中的程序 p
9. Rice 定理
• ⼏几个定义：
• 属性 A 是⼀一个 While 程序的集合；
• 属性 A 是⾮非平凡的，当且仅当 A 不是空集或全集；
• 属性 A 是外延属性，当且仅当，对任意给定的语义等价的两个程
序 p 和 q， p 属于 A 等价于 q 属于 A；
• Rice 定理：
• 程序的任何⾮非平凡的外延属性都是不可判定的
10. Rice 定理的证明
• 证明思路：
• 若 Rice 定理不成⽴立，则存在⾮非平凡属性 R 可判定，即判定程序 is-R
可计算⼀一个程序 q 是否属于 R。
• 取程序 r 属于 R, 对任意程序 p 和任意⼀一个参数 d，可构造程序 q
read X; Y = p d; Z = r X; write Z;
• 另有程序 h ：
read pd; W = is-R q; write W;
• 易⻅见 h 可判定与停机定理⽭矛盾。
