The Beginning and End of Pure Mathematics

[Mole]

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.

 

[Stanton Moore]

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?

 

[Mole]

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.

 

[Mole]

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.

 

[Stanton Moore]

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

 

[Mole]

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.

 

[Poki]

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.

 

[Mole]

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?

 

[Totenkindly]

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.

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.

 

[gromit]

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...?

 

[Polaris]

It isn't that there's no certainty; it's that to be certain of something is to raise it up as a hypothesis that awaits confirmation. You can take the simplest, most indisputable statement--I'm certain there's a chair over there--and the moment you say it, you get the feeling you're somehow on trial. Maybe that isn't a chair after all, or maybe someone will challenge me and I'll have to defend myself. Certainty is always in question, always vulnerable to correction, and the first thing we've got is certainty (and I question that).

 

[Mole]

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.

God died in 1859 with the publication of, "The Origin of Species", but we have those on this site whose whole life revolves around God.

So just as there are those who don't believe God is dead, so there are those who don't believe mathematics are dead. I mean it's unimaginable. But read Kurt Gödel to find it true.

But even Kurt couldn't believe it and devoted his life to proving it wasn't true by a mathematical description of intuition. Kurt failed. He went mad and starved himself to death.

 

[Mole]

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.

It's that we can't tell in advance which mathematical problems are soluble. So all we can do is try to solve them and see if there is a solution.

This is devastating for mathematics which purported to tell us which problems were soluble, but now it can't.

A problem may or may not be soluble but we don't know and will never know unless we solve it first.

So the whole edifice of mathematics is unknowable forever.

 

[Mondo]

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?

Are you arguing mathematics is an illusion equivalent to Santa??

 

[Mole]

Are you arguing mathematics is an illusion equivalent to Santa??

Yes.

Preposterous, you say. Well, even Kurt Gödel thought is was preposterous, and tried to prove it wrong but he failed and starved himself to death.

I hope, though, I haven't spoiled your appetite.

 

[Pixelholic]

You should just argue from semiotics and deconstruction. You'll make a bit more sense.

 

[Mole]

You should just argue from semiotics and deconstruction. You'll make a bit more sense.

I had my first encounter with mathematics at the age of seven. But even then it was obvious to me that what I was being shown had no basis.

I mentioned this to my father and he told me not to worry about it but just do the maths. And naturally I followed my father's advice. But it still niggled at me until I read George Spencer Brown's book, "The Laws of Form", and discovered the beginning of all mathematics in the injunction, "Make a distinction".

And having discovered the beginning, I was primed to discover the end which I did in Kurt Gödel's Incompleteness Theorems in his 1931 work, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. Monatshefte für Mathematik und Physik".

I may well make no sense to you but Albert Einstein would walk Kurt Gödel home from work every day because he publicly recognised Kurt made sense and was a mathematical genius.

 

[jixmixfix]

God died in 1859 with the publication of, "The Origin of Species", but we have those on this site whose whole life revolves around God.

So just as there are those who don't believe God is dead, so there are those who don't believe mathematics are dead. I mean it's unimaginable. But read Kurt Gödel to find it true.

But even Kurt couldn't believe it and devoted his life to proving it wasn't true by a mathematical description of intuition. Kurt failed. He went mad and starved himself to death.

How did God die with darwins theory? that's a fallacy, if you look at it from a different angle his theory explains God's work within the universe, and our connection with other living creatures.

 

[jixmixfix]

Mathematics is only useful when it is put into practice as a tool to construct things, when there is just theory it is unlimited and useless.

 

[Mole]

How did God die with darwins theory that makes no sense what so ever, if you look at it from a different angel his theory explains God's work within the universe, and our connection with other living creatures.

I understand you are as reluctant to let go of God as letting go of mathematics.

You are certainly not alone.