Timeline for Books that develop interest & critical thinking among high school students
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2012 at 9:02 | comment | added | Ron Maimon | The main difference is that the issues of self-reference are moved to the code and not to the logic, the logic is never even mentioned explicitly (except of course that it exists). There is also no Godel encoding, except the obvious encoding of computer programs into integers in step 2. Finally, the whole thing does not require a recursion theorem trick--- this is included in the first step "print your own code", which is the recursion theorem in a form obvious to all computer programmers. | |
| Apr 4, 2012 at 9:00 | comment | added | Ron Maimon | The proof is: given an axiomatic system which describes integers, it also describes computers. Write the program GODEL which 1. prints its code into a variable R. 2. Deduces all consequences of the axiom system, looking for the theorem "R does not halt". 3. If it finds this theorem, it halts. This is the construction of Godel's theorem, and it is obvious that GODEL will halt if and only if S proves it doesn't halt. The conclusions of Godel's theorem follow with only a few minutes of thinking. This is the correct proof, and I have presented it here and on math.overflow. | |
| Apr 4, 2012 at 4:18 | comment | added | Noldorin | Oh yeah... Godel's theorem... obvious. Rolls eyes. | |
| Apr 3, 2012 at 7:35 | history | edited | Nikolaj-K | CC BY-SA 3.0 |
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| Apr 3, 2012 at 7:31 | comment | added | Ron Maimon | While I read GEB in high school, and it was important, I find the discussion of Godel's theorem too long winded today. If you know how to program, it should be obvious. | |
| Nov 18, 2010 at 19:13 | history | made wiki | Post Made Community Wiki by Robert Cartaino | ||
| Nov 16, 2010 at 16:40 | history | answered | Noldorin | CC BY-SA 2.5 |