Undercover in the Library- 3

Asli knows the end of the story, that's why she is so surprised!  :)

So here comes the sequel..(Click for Episode 1, Episode 2)

What  have we talked about so far? We said that Incompleteness Theorem showed that logic was not able to capture all the truths of mathematics and because of the relativity theory and since the solution of its equations fits to our model of universe the concept of an absolute time is not anymore valid. So my "now" and your "now" is different if we are travelling in different speeds...And logic was considered as the descriptive rules of thinking. Moreover, if you can prove that mathematics rest on logic solely, you would yell out to the whole world that mathematics is the most solid division in sciences... Well they still do--- And if you can apply this to the language, then artificial intelligence (AI) is a piece of cake. 

But in 1931 Godel showed that this was not possible. He liked to find inconsistencies in systems. He even find an inconsistency in American constitution that can lead to a dictatorship. That's a funny story which will wait for another post.. At the time (1950s) everybody thought that that was the end of  the AI. But now since cognitive scientists and computer programmers consider mind as a learning and predicting machine --not a logic machine--, they changed their set of codes. So they do not think that the AI is impossible...

Any theory, which analyzes itself as a whole with its own techniques is likely to fall into a paradox. So for example, in metamatematics; if you try to show with mathematics' own techniques that mathematics is complete, there arises a inconsistency. Which means if you can prove all the statements within the system (or their negations) -with its axioms and inference rules- then you will have a statement saying that "I am not provable" and it will be provable! Wha? :) Yes, you will be able to prove in a complete system, both an affirmation of a formula and its negation at the same time. It sounds like a biiig trouble isn't it? Escher's paintings have a similar idea in them! Beautiful paintings they are..

Next coming up:

What is Heisenberg Principle?
How much bigger I get if I travel in the speed of light?
But why offices in general set up so that we work 8 hours a day?
How could we make non communicable things communicable?
What is an intuition?
In which kind of universe time travel is possible?

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