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  1. #1
    & Badger, Ratty and Toad Mole's Avatar
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    Smile The Beginning and End of Pure Mathematics

    Mathematics begins with an injunction - make a distinction.

    And ends with being unable to decide whether a problem is solvable or not.

    It's hard to believe I know, but mathematics has a beginning and an end.

    I have been touting mathematics as the language of God, but I was wrong.

    God, as we all know, is dead but some of us hoped we could hear his last whispers in mathematics. But no, mathematics itself teaches us that mathematics cannot describe the world.

    So we are left in the Universe, bereft children without God or logic. All we have left is ourselves.

    But alas the lust for Certainty remains in fundamentalism. Although we now know with mathematical certainty that the foundations are air.

    And as you note, this is a paradox that has driven four of our greatest mathematicians to madness and suicide, Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing.
    Last edited by Mole; 07-14-2010 at 05:35 AM.

  2. #2
    morose bourgeoisie
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    Looking for certainty is a form of looking for comfort.

    Looking for comfort is a form of fear.

    So what do you fear?

    Mathematics describe much of the universe, but not all. Is that sufficient reason to jettison it entirely? What in its incompleteness generates fear?

  3. #3
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    Quote Originally Posted by nebbykoo View Post
    Looking for certainty is a form of looking for comfort.

    Looking for comfort is a form of fear.

    So what do you fear?

    Mathematics describe much of the universe, but not all. Is that sufficient reason to jettison it entirely? What in its incompleteness generates fear?
    We first found certainty in God. And as God created the Universe, we thought that the Universe would display certainty.

    But all four mathematics, but particularly Kurt Gödel, have shown us with mathematical certainty that the Universe does not display certainty.

    This is of course a paradox. And the four mathematicians sought certainty while proving to their surprise and consternation that there is no certainty.

    This mathematical discovery has not reached the mind of the general public where is will also cause consternation and surprise. And it will be violently rejected by Fundamentalists.

    We can see on this site that new ideas are routinely met with ad hominem attacks, and in the world we can see that the Enlightenment of new ideas is met by global jihad.

    We can see the result of this discovery in the lives of the four mathematicians. They were rejected and hounded by their fellow mathematicians and by relentless ad hominem attacks which, combined with the paradox of their discovery, led to madness and suicide.

    Of course we know now that paradox or cognitive dissonance is emotionally painful and we can see our own members lashing out with ad hominem attacks in their pain. So we can expect this in the world as the Fundamentalists lash out with lethal, mass, ad hominem attacks in their emotional pain.

  4. #4
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    Quote Originally Posted by nebbykoo View Post
    Mathematics describe much of the universe, but not all. Is that sufficient reason to jettison it entirely? What in its incompleteness generates fear?
    We now know that mathematics does not describe any of the universe. But of course we still like to hang on to the erroneous idea that mathematics describes some of the universe but not all. And it is this erroneous belief that gives us comfort in our disorientation and fear.

  5. #5
    morose bourgeoisie
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    Copernicus said that the sun and not the earth, was the center of the solar system. This remains true.

  6. #6
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    Quote Originally Posted by nebbykoo View Post
    Copernicus said that the sun and not the earth, was the center of the solar system. This remains true.
    But we don't know which mathematical problems are solvable and which are not.

    And of course the whole point of mathematics is to solve mathematical problems and now we find we can't.

    And we won't ever be able to.

    So is God malicious or is God dead?

    Albert Einstein said that God is not malicious. But Albert also said that God does not play dice. But quantum mechanics shows Albert is wrong and God does play dice.

  7. #7
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    Complexity beyond our comprehension is not related directly to if something has certainty or not. The acknowledgement that the universe has no certainty though is admiting that its to complicated to understand...it is a turning point in a mans life when he accepts defeat.
    Im out, its been fun

  8. #8
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    Quote Originally Posted by poki View Post
    Complexity beyond our comprehension is not related directly to if something has certainty or not. The acknowledgement that the universe has no certainty though is admiting that its to complicated to understand...it is a turning point in a mans life when he accepts defeat.
    It's worse than that. It is not complexity that blocks our comprehension, but the very nature of mathematics.

    This is an extraordinary discovery and one that leads to a loop that if pursued leads to madness and suicide.

    One possible course of action is to become accustomed to paradox and cognitive dissonance. But this is too much for children to bear, and so we teach them fairy stories such as we understand the world through mathematics.

    But just as we wait until they are seven to tell them Santa doesn't exist, we may need to wait until twenty-two to tell them mathematics doesn't exist.

    It's hard to believe, isn't it?

  9. #9
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    Quote Originally Posted by Victor View Post
    Albert Einstein said that God is not malicious. But Albert also said that God does not play dice. But quantum mechanics shows Albert is wrong and God does play dice.
    This is why poor Al tried to recant some of his greatest work; he didn't like the outcome.

    Quote Originally Posted by Victor View Post
    But just as we wait until they are seven to tell them Santa doesn't exist, we may need to wait until twenty-two to tell them mathematics doesn't exist.

    It's hard to believe, isn't it?
    Newtonian physics didn't work perfectly -- so it wasn't Right -- but it was darn close enough for all practical purposes to satisfy the needs of the majority of people in the world.

    I don't think a lot of people will really be impacted by whatever fine-tuned issue this is. You're only going to get the higher elite and those whose work is impacted by it to care / be emotionally rocked, if that.
    "Hey Capa -- We're only stardust." ~ "Sunshine"

    “Pleasure to me is wonder—the unexplored, the unexpected, the thing that is hidden and the changeless thing that lurks behind superficial mutability. To trace the remote in the immediate; the eternal in the ephemeral; the past in the present; the infinite in the finite; these are to me the springs of delight and beauty.” ~ H.P. Lovecraft

  10. #10
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    Victor. Interesting topic, although I'm not sure I understand what's so earth-shattering.

    Mathematics does not describe existence perfectly, theories in general do not describe reality perfectly. Of course, we can approach reality/the world/the universe by viewing it from different angles, through different senses, perspectives, theories, etc., but we will always be gaining new information, adjusting the model appropriately. And each model is limited, though perhaps in different ways.

    Maybe I missed the whole point of it though...?
    Your kisses, sweeter than honey. But guess what, so is my money.

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