The Beginning and End of Pure Mathematics

[Mole]

Turing was harassed by the police. He did not kill himself because of mathematics.

Alan Turing was harassed by the police because they thought, as a homosexual he was security risk. And he was convicted of a homosexual offence and forced to take drugs to castrate him.

However at the same time he was also working on the death of pure mathematics, as bequeathed to him by Georg Cantor, Ludwig Boltzmann and Kurt Gödel.

And Alan's contribution was to try to avoid the incompleteness theorems on the computer he designed. Alan tried to make his computer conscious as a way of avoiding the death of pure mathematics. And this is where we get the Turing Test of 1950. But he failed, as everyone has failed since. He then injected an apple with cyanide and took a bite.

But what is interesting is that the four of them, Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing, all working on the same paradox, met a similar fate. They were rejected by their peers. They were subjected to ad hominem attacks and went mad or committed suicide or both.

This is the untold drama of pure mathematics.

This is Shakespearean in scope spanning two centuries with plenty of bodies on stage falling to a lethal paradox of pure mathematics.

 

[Mole]

A blind alley is not an end.

Of course this is what Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing thought. And it drove them mad. And it drove them to suicide.

But look around you - billions upon billions of people can't accept the death of God, so why would you think pure mathematicians would accept the death of pure mathematics? Far better to kill the messenger.

We killed our first messenger Socrates. And we killed our second messenger Jesus. And so how natural to kill our third messengers from pure mathematics.

 

[ygolo]

Mathematics is imaginary but useful...just like many other human constructs.

 

[Mole]

Mathematics is imaginary but useful...just like many other human constructs.

Yes, it is true that Applied Mathematics are useful but Pure Mathematics is useless and that is its glory.

Pure Mathematics is done for its own sake. Pure Mathematics is done for intrinsic reasons.

Pure Mathematics is like music or art. It's what makes us human and free.

No other animal does Pure Mathematics, just us.

Pure Mathematics enables the mind to fly, but sometimes like Icarus we fly too close to the sun and fall.

It would be sensible to confine ourselves to what is useful. It would be sensible to confine ourselves to what is safe. But then we would be confined.

But we don't have to worry, for hundreds of millions confine themselves to following Lindsay Lohan and almost no one follows the lives of Pure Mathematicians. In fact it is obvious that many on this site didn't even know Pure Mathematics existed and keep on confusing it with Applied Mathematics.

So we remain impoverished and confined with Lindsay Lohan and all we want to know is her type.

 

[ygolo]

Anything can be done for the pure joy of it, even so-called "applied" mathematics.

The line is not so clear. What used to be pure mathematics, often becomes applied.

The undecidability problems have become quite useful in compiler theory, for instance...and topology quite useful in applications of general relativity.

 

[stringstheory]

The line is not so clear. What used to be pure mathematics, often becomes applied.

that's why i'm a little skeptical of the word "useless" to describe theory. sometimes an idea leads to the means by which to apply the idea concretely; if that's so then it's pretty "useful". though i don't see why abstractions must become concrete in order to be useful.

 

[Mole]

Longing

The death of Pure Mathematics throws light on the death of God.

For although we take it for granted that believers want to hear the voice of God in the Bible or the Koran or in apparitions, we don't seem to acknowledge that agnostics, atheists and sceptics also want to hear the voice of God in Pure Mathematics.

And with God and Pure Mathematics dead, we have only one question left - why do we universally long for the voice of God?

And the answer is given in the book, "The Origin of Consciousness in the Breakdown of the Bicameral Mind", which says that we did actually and literally hear the voice of God in our bicameral mind, but with the breakdown of the bicameral mind, we had to seek the voice of God in holy books and pure mathematics.

So not so long ago God was as close to us as ourselves, as close as whiteness is to snow, and with the breakdown of the bicameral mind, God fell literally silent. But we long for intimacy with God. We long once again to hear the voice of God.

But all we are left with is our longing.

This was expressed by Robert Lax, a friend of the catholic contemplative, Thomas Merton, in his poem, "The Port Was Longing", from the early sixties -

The port
was longing

the port
was longing

not for
this ship

not for
that ship

not for
this ship

not for
that ship

the port
was longing

the port
was longing

not for
this sea

not for
that sea

not for
this sea

not for
that sea

the port
was longing

the port
was longing

not for
this &

not for
that

not for
this &

not for
that

the port
was longing

the port
was longing

not for
this &

not for
that

 

[Poki]

Pure Math is to NT as Idealism is to NF. Theres always something to learn from purity and idealism and the application is normally a middle ground. So the further you push the boundaries the further you extend the middle ground. The boundaries can seem to be a waste of time.

that's why i'm a little skeptical of the word "useless" to describe theory. sometimes an idea leads to the means by which to apply the idea concretely; if that's so then it's pretty "useful". though i don't see why abstractions must become concrete in order to be useful.

In my mind thats what concrete is. Concrete is application. Its what makes theory real.

 

[sculpting]

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.

Who needs certainty? (There could be NP bias here )

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.

Why does reading about cognitive dissonance and paradox make me happy? I mean, really I get quite excited by the thought of math not being completely understood.

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...?

Totally with Gromit. Agree perfectly. I guess I would be really bored if we ever actually understood everything about a topic. I would far rather find out a current model is flawed and there is still more stuff left to discover. Yeah!!! I get to play more!!! Victor this whole thread has actually brightened my day!

 

[uumlau]

Who needs certainty? (There could be NP bias here )

Certainty is useful, but nearly always boring.

Sometimes, however, such "boring" things are what let us sleep quietly at night.

Why does reading about cognitive dissonance and paradox make me happy? I mean, really I get quite excited by the thought of math not being completely understood.

Heh, just read about how math slowly became to be what it is, today. There will always be aspects which are not very well understood, because there are an infinity of ways to expand the topic. Just make up a rule about how numbers behave, and explore the rule. It doesn't have to be "true" or "real," just self-consistent and logical. E.g., "What if we could take the square root of a negative number? What would happen?"

Totally with Gromit. Agree perfectly. I guess I would be really bored if we ever actually understood everything about a topic. I would far rather find out a current model is flawed and there is still more stuff left to discover. Yeah!!! I get to play more!!! Victor this whole thread has actually brightened my day!

Of course our current models are flawed. If they weren't, then the models would be identical to reality. A model which is identical to reality turns out not to be very useful.

No, such models, whether mathematical or otherwise, don't describe the world, precisely, though it is tempting to think so.

But they do describe the world.

I used to tell my students that Newton's "Laws" were better thought of as "descriptions." They aren't edicts. They aren't "true," necessarily. But they are very close to the truth, even after dealing with Einstein and Maxwell.

A description doesn't have to be 100% accurate. It merely has to be useful.

 

[Mole]

Incomplete

Of course our current models are flawed.

It's not that Pure Mathematics is flawed, for we have known beyond doubt since 1931 that Pure Mathematics is incomplete. It is inherently incomplete and forever incomplete.

It is analogous to knowing that an all powerful, all knowing and all good God is incomplete.

 

[Blank]

Has anyone considered that somewhere, beyond basic 'rithmetic, that maybe we got something wrong?

 

[Mole]

Has anyone considered that somewhere, beyond basic 'rithmetic, that maybe we got something wrong?

Basic 'rithmetic is both Applied Mathematics and Pure Mathematics, for Bertrand Russell spent great swarths of his, "Principia Mathematica", in three volumes (1910-1913), to proving 1+1=2, in order to show that Pure Mathematics was complete.

But all to no avail, for in 1931 Kurt Gödel proved with his two incompleteness theorems that Pure Mathematics was incomplete.

Its not that Pure Mathematics is flawed or that there are flawed models, no, its that Pure Mathematics at its highest level is inherently and forever incomplete.

We now know there are some things we don't know.

But worse, we now know there are some things we can't know.

 

[gromit]

We now know there are some things we don't know.

But worse, we now know there are some things we can't know.

I still don't understand what is so bad about it all, though...

 

[Oberon]

It appears that Victor is preaching again. Today it's a variation on his usual theme, Existentialism.

And you're in good form today, Victor. Well done.

 

[Mole]

I still don't understand what is so bad about it all, though...

Well, some think the death of God in 1856 is bad, and no doubt those same people would think the death of Pure Mathematics in 1931 is also bad.

Unfortunately most did not notice that God or Pure Mathematics were ill. And so far they have not been apprised of their respective deaths.

We have spent millennia worshipping God and to find He is dead without even knowing He was ill, is a bit of a shock.

And for millennia we have practised Pure Mathematics mainly to worship the astrological Gods. And to find that Pure Mathematics has died behind our backs, and died in 1931 when no one was looking, is a bit hard to take.

 

[gromit]

Hm. I follow you somewhat but I disagree with your conclusions.

I don't think God is dead. I think God is a mystery. God IS mystery, in a way. As such we can never fully comprehend him/her/it/them/us. God. That part of ourselves, the universe which is beautiful, terrifying, filled with love and meaning, but not fully understood. Just because something is not fully comprehensible doesn't mean it is dead. In fact, the opposite. Our conceptions and understandings of things are constantly evolving, collectively and individually. If growth, transformation, is not the essence of life, I do not know what is.

Mathematics is a language. It is an attempt to describe the mystery that is the universe. All languages have their limitations. The language is not dead if it continues to convey meaning and to unite people with those ideas, that meaning... if it continues to have relevance.

 

[Mole]

Dangerous Knowledge

Hm. I follow you somewhat but I disagree with your conclusions.

I don't think God is dead. I think God is a mystery. God IS mystery, in a way. As such we can never fully comprehend him/her/it/them/us. God. That part of ourselves, the universe which is beautiful, terrifying, filled with love and meaning, but not fully understood. Just because something is not fully comprehensible doesn't mean it is dead. In fact, the opposite. Our conceptions and understandings of things are constantly evolving, collectively and individually. If growth, transformation, is not the essence of life, I do not know what is.

Mathematics is a language. It is an attempt to describe the mystery that is the universe. All languages have their limitations. The language is not dead if it continues to convey meaning and to unite people with those ideas, that meaning... if it continues to have relevance.

I hesitate to put dangerous ideas into young hands, for who knows what they might do. But I feel my hand is being forced and reluctantly I hand my dangerous idea over to you.

Just click on -

YouTube - BBC-Dangerous Knowledge (Part 1-10)

 

[gromit]

I will have to watch it when I'm not at work. Is it terribly long? Does make many points that you haven't already said in your posts?

Out of curiosity, how old do you think my hands are?

 

[Oberon]

I knew a fellow once... his name was Willard... who was working on a novel. In his novel, he wrote a character who made disturbing scientific discoveries... discoveries that led inevitably to the conclusion that there could be no such thing as an Author.

Willard's funeral was last spring, and since then the characters in the novel have been stuck in an existential wasteland, victims of inevitable ennui.