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RE: Fringe Math
February 1, 2012 at 1:28 am
(January 30, 2012 at 10:25 am)CliveStaples Wrote: I don't find constructivism very appealing. What would a constructivist make of the following argument:
n = 2 if the Goldbach conjecture is true, 3 otherwise
Is n prime?
I don't care. Can a computer AI (artificial Intelligence) find a structure it can make a decision with, your goldbach conjecture?
For this kind of programming, one needs constructionist tools. Infinity does not work on finite systems. You have to deal with reality sometimes, not hallucinations of god, and infinity.
When we remember we are all mad, the mysteries disappear and life stands explained.
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RE: Fringe Math
February 1, 2012 at 9:29 am
(February 1, 2012 at 1:28 am)Pendragon Wrote: I don't care. Can a computer AI (artificial Intelligence) find a structure it can make a decision with, your goldbach conjecture?
For this kind of programming, one needs constructionist tools. Infinity does not work on finite systems. You have to deal with reality sometimes, not hallucinations of god, and infinity.
So from this,
Does that mean math is only useful insofar that we can program with it?
From that infinity comment... Does that mean you're not a fan of real numbers, Hilbert spaces, Functional Analysis, Fourier analysis...
Draw lines plox.
So these philosophers were all like, "That Kant apply universally!" And then these mathematicians were all like, "Oh yes it Kan!"
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RE: Fringe Math
February 2, 2012 at 4:25 am
(February 1, 2012 at 1:28 am)Pendragon Wrote: I don't care. Can a computer AI (artificial Intelligence) find a structure it can make a decision with, your goldbach conjecture?
For this kind of programming, one needs constructionist tools. Infinity does not work on finite systems. You have to deal with reality sometimes, not hallucinations of god, and infinity.
"Infinity does not work on finite systems"...huh? It's quite easy to define transfinite arithmetic consistent with Cantor measures.
If you just disregarded infinity altogether, you'd never get anything like Wolfram Alpha, which can solve very sophisticated algebra and complex analysis problems that require a notion of infinity--in the case of complex analysis, it occasionally requires an action "point at infinity" to be described.
If you got rid of infinity, you'd get rid of most applications of computers to solving systems of differential equations; finding convergence or divergence requires a notion of what it means to "diverge to infinity".
“The truth of our faith becomes a matter of ridicule among the infidels if any Catholic, not gifted with the necessary scientific learning, presents as dogma what scientific scrutiny shows to be false.”
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RE: Fringe Math
February 5, 2012 at 4:15 am
to the main topic, whether the reals and integers are mappable,
that's something i've always wondered about. for example, we know the square root function generally produces irrational numbers. so what if we have the following set....
Code: 0 1 1/2 1/3
1 2 2/3
2/1 3/2
3/1
where each fraction is square rooted? you can even alternate between positive and negative results. this should, in my opinion, go over all the reals.
if you believe it doesn't, please give me a value that this function definitely won't hit.
(p.s. this a bit of a joke, please don't take it seriously. there are indeed irrational numbers this won't hit.)
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RE: Fringe Math
February 5, 2012 at 6:54 am
(February 5, 2012 at 4:15 am)phillip1882 Wrote: to the main topic, whether the reals and integers are mappable,
that's something i've always wondered about. for example, we know the square root function generally produces irrational numbers. so what if we have the following set....
Code: 0 1 1/2 1/3
1 2 2/3
2/1 3/2
3/1
if you believe it doesn't, please give me a value that this function definitely won't hit.
(p.s. this a bit of a joke, please don't take it seriously. there are indeed irrational numbers this won't hit.)
It won't hit the square root of pi, or the square root of e, or the square root of the square root of 2.
“The truth of our faith becomes a matter of ridicule among the infidels if any Catholic, not gifted with the necessary scientific learning, presents as dogma what scientific scrutiny shows to be false.”
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