Godel's Theorem

My presentation on Godel's incompleteness theorem.

Category:

Entertainment

Tags:

• Godel
• theorem
• logic

[tseliottt]

what song is this?

[Frege100]

"Don't let go" by a 80's band from Liverpool called "Pink Industry". Too far ahead of their time to be very popular then and none of their material is available now except as very expensive collector's items or via the internet. They are very easily the best thing about a number of the presentations I've uploaded.

[agentredlum]

I am a bit confused. At 1:08 you say the cleverer computer has a program designed to test every OTHER program (my emphasis) then you have it testing itself. WHY?!?

[Frege100]

Sorry! I should have written "every other programme and itself."

Thanks for pointing it out.

[lovelplants]

nice video.. and i do love logic.. :)

[Idol2011no]

@FartsOutDust1901, I guess the dumb fuck operates under the assumption,"real" and "exist" are contextually equals. Thus, he cannot believe there is a mind, but only a brain. There are many of this kind.

[klimaxg]

Nice summary, thank you

[TheShankman]

why are the implications of this theorem so vast? it seems for a consistent system we've proved that the sentence G in question which reads "G is not provable" must be true, i.e. we've found a true but unprovable statement. in other words all we've shown is a trivial, self-referential statement is true but unprovable. what's the big deal?

[FartsOutDust1901]

@crossoldman actually there are many mathematical proofs of existence.

[crossoldman]

@hiestd Is that like the mathematical proof a bumble bee can't fly? How in the hell could math prove an existence? Math may suggest an existence but the proof must be in reality not math.

[vsaluki]

The only problem that can occur is in the creation of an endless recursion loop. If the program, while testing its own algorithm, decides that it must account for what happens when the algorithm tests itself, then it must test that situation by having the algorithm test itself while the algorithim being tested is also testing itself, and on, and on.

[vsaluki]

In other words, the program can never make a decision as long as it is testing a program that does not stop.

On the other hand, if the program is clever enough to decide if another program will stop simply by inspecting it's algorithm, then we have a different situation. It will then look at its own algorithm and decide that the algorithm is designed in such a way that it can stop. And so it will keep running.

[vsaluki]

Another problem. You say that the program stops when it finds a program that does not stop. How does it find a program that does not stop? If it finds it by running the program, then it would never stop because the program that it is running continues forever and the first program that is running it cannot stop because it can never know if the program that it is running will stop. This means that the testing program cannot do its job even without testing itself. (continued)

[vsaluki]

Your explanation doesn't make sense. On the one hand you say that the program is designed to find every program that does not stop, on the other hand you say that the program stops when it finds just one program that does not stop. If you are going to test every program, you cannot, by definition, stop after finding just one program that doesn't stop. There seem to be more explanation problems further down the line, but let's fix this one and then go from there.