Godel Incompleteness Theorum

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Escape_Artist
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Re: Godel Incompleteness Theorum

Post by Escape_Artist » Tue Aug 16, 2011 11:58 pm

Kat wrote:Image
I agree
Me gusta Capitalismo Anarquista!

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Kat
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Re: Godel Incompleteness Theorum

Post by Kat » Wed Aug 17, 2011 5:12 am

Image

Dual purpose complex theorem/Google Logo Of The Day submission.
If I could get any animal it would be a dolphin. I want one bad. Me and my mom went swimming with dolphins. I was like, 'How do we get one of those?' and she was like, 'You can't get a dolphin. What are you gonna do, put it in your pool?' Miley Cyrus

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Royal
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Re: Godel Incompleteness Theorum

Post by Royal » Wed Aug 17, 2011 5:22 am

I was looking into thermo dynamics today... If only I saw all the beauty to these equations years ago...

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Kat
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Re: Godel Incompleteness Theorum

Post by Kat » Wed Aug 17, 2011 8:28 am

If I could get any animal it would be a dolphin. I want one bad. Me and my mom went swimming with dolphins. I was like, 'How do we get one of those?' and she was like, 'You can't get a dolphin. What are you gonna do, put it in your pool?' Miley Cyrus

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Re: Godel Incompleteness Theorum

Post by Pigeon » Wed May 14, 2014 11:57 pm


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Re: Godel Incompleteness Theorum

Post by Pigeon » Thu May 15, 2014 9:15 pm

"Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel

Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory.

1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system.

2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers.

Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete.

Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent. "

What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent.

For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics.


"It's not that God is subject to the Freedom Proof or the Doubt Proof.
According to Gödel, He's not. But we have to be, or else we are not free. So
our truth game with God turns into something like Feynman had described.
Feynman's Gods, every time physicists think they have the rules of the game
figured out, throw in a new wrinkle. They let people like Feynman make
progress, but if the Feynmans of the world learn too much, physics will stop
being the joy and challenge that it is. The Gods don't let that happen.

Gödel's God has to be very careful about how he lets our universe unfold.
If the world becomes totally controllable and comprehensible, we'll be God.
God does not object to that. In fact, according to Gödel, that is our destiny.
But it is also the end of us as free human beings. And human freedom is an
essential part of the beauty of God's universe."


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Pigeon
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Re: Godel Incompleteness Theorum

Post by Pigeon » Thu May 15, 2014 11:59 pm


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Royal
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Re: Godel Incompleteness Theorum

Post by Royal » Fri May 16, 2014 1:51 am

Pigeon wrote:
Why negate it?

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Pigeon
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Re: Godel Incompleteness Theorum

Post by Pigeon » Fri May 16, 2014 2:31 am

I could see that coming.

I believe it is representing the info in the 2nd post of the thread.

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Royal
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Re: Godel Incompleteness Theorum

Post by Royal » Fri May 16, 2014 3:07 am

Pigeon wrote:I could see that coming.

I believe it is representing the info in the 2nd post of the thread.
It clears it up. Paradoxical statement basically.

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