The sad history of Godels legacy, and the sad fate of Boltzmann, Turing and Cantor

[Zeuzzz]

[Note: Lengthy historical documentation I have gathered and put into a coherent prose here may seen like too long to read, but it gives the reason for why such great scientists such as Kurt Godel, Richard Turing and Ludwig Boltzmann committed suicide, and why George Cantor was also driven to the brink numerous times]


The greatest most intelligent minds that walked this earth in terms of understanding the machinery of the universe were likely Albert Einstein and Godel, I still think to this day. We would be wise to take a historical note of what Einsteins later years were spent doing and what conclusions he came to, as the scientific community ran off and made 'mainstream' with a set of his theories he himself was deeply uneasy with. Einstein and Godel seemed to reach similar conclusions, but seemingly one of them coped better with the implications of this than the other in the end.


The solid mathematical foundations that a lot of these modern day Nobels are awarded for, have a slightly darker and mirkier past in a historical context. And in fact, the whole materialist myopic view of linear maths as revealing deeper and deeper truths to us about the universe is fatally flawed from the get go.


It's a story of how some of our most intellectually stimulated minds untied the previously cosy relationship the universe seemed to have with the certainties of mathematics, and how these facts have been acknowledged but largely ignored. It's a story of how such deep questions being asked back then of such high importance resulted in the fact that when some of the greatest minds of the time engaged their mind with such questions their brain dare not look away from the evidence that perplexed them so much, and how pursuit of meaningful answers to these issues pushed them first to the brink of insanity, then over to madness and suicide.


But for all the humain tragedy of great minds lost due to seeking meaning from life from maths and logic, what they saw is still true - the intellectuals at the time that took over the consensus opinion, assigning Einsteins work greater credibility than the original creator himself did, whilst in the case of Godels work largely ignoring it; so to this date we have yet to inherit at large the conclusions they themselves made.


Now, the world that they saw, we still stand at the frontier of as much as they did over fifty years ago.


George Cantor (1845-1918) was a religious professor of maths who started a paradigm shift in the world of established maths and science, that maybe he did not appreciate at the time. The profundity of a brand new question, not based on previous knowledge or even a similar school of thought in maths at the time; he asked himself "how big is infinity"?


It’s just an incredible feat of imagination. It’s, to me, the equivalent of taking mind enhancing drugs for that era (1800-1900) Others before him, going back to the ancient Greeks at least, had asked the question but it was Cantor who made the journey no one else ever had, and found the answer. But he paid a price for his discovery. He died utterly alone in an insane asylum.


The question is what could the greatest mathematician of his century have seen that could drive him insane?


Cantor had auitary hullicinations from a little boy that he attributed to god as calling him to maths. So for Cantor, his mathematics of the nature of infinity had to be true, because God had revealed it to him.


Cantor soon discovered he could add and subtract infinities conceptually, and in fact discovered there was a vast new mathematics opening up infront of him - maths of the infinite. This out of the boxing thinking had revealed something special, and he could feel it as a sort of profound insight into the nature of maths he was previously blind to.


By 1884 Cantor has been working solidly on the Continuum Hypothesis for over 2 years. At the same time the personal and professional attacks on him for his heretical "maths of the infinites" had become more and more extreme. Due to this, the following may of that year he had a mental breakdown. His daughter describes how his whole personality is transformed. He would rant and rave and then fall completely and uncommunicatively silent. Eventually he is brought here to the NervenKlinik in Halle, which is an asylum.


Even after concerted further effort he could still not solve the Continuum Hypothesis, he came to describe the infinite as an abyss. A chasm perhaps between what he had seen and what he knew must be there but could never reach. He realised that there’s a way in which in order to understand something you have to look very hard at it but you also have to be able to sort of move away from it and kind of see it in a kind of wholistic context, and the person who stares too hard can often can lose that sense of context.


After the death of a close relative, Cantor went on to say that he "could no longer" even remember why he himself had left music in order to go into maths. That secret 'voice' which had once called him on to mathematics and given meaning to his life and work. The voice he identified with God. That voice too had left him.


Here I divert from Cantor, because if we treat Cantor’s story in isolation it does little to bridge the gap in the idea that Cantor had dislodged something was part of a much broader feeling of that time. That things once felt to be solid were slipping. A feeling seen more clearly in the story of his great contemporary- a man called Ludwig Boltzmann.


The physics of Boltzmann’s time was still the physics of certainty, of an ordered universe, determined from above by predictable and timeless God-given laws. Boltzmann suggested that the order of the world was not imposed from above by God, but emerged from below, from the random bumping of atoms. A radical idea, at odds with its times, but the foundation of ours. Ernest Marc one of the most influential er philosopher of science at that time stated: 'I cannot see, I don’t need it, they do not exist so why we should bring them in the game.'


Worse than insisting on the reality of something people could not see, to base physics on atoms meant to base it on things whose behaviour was too complex to predict. Which meant an entirely new kind of physics – one based on probabilities not certainties. Boltzman worked tirelessly at his idea irrespective, and as Boltzmann got older and more exhausted from the struggle, he'd get mood swings, mood swings that became more and more severe. More and more of Boltzmann’s energy was absorbed in trying to convince his opponents that his theory was correct. He wrote, “No sacrifice is too high for this goal, which represents the whole meaning of my life.”


The last year of Boltzmann he didn’t do any research at all, I’m talking about the last 10 years. He was fully immersed in a dispute, philosophical dispute, tried to make his point – writing books which were most of the time the same repeating the same concept and so on. So you can see he was in a loop that didn’t go ahead. By the beginning of the 1900’s the struggle was getting too hard him.


Boltzmann had discovered one of the fundamental equations, which makes the universe work and he had dedicated his life to it. The philosopher Bertrand Russell said that for any great thinker, “This discovery that everything flows from these fundamental laws… comes”, as he described it, “with the overwhelming force of a revelation: like a palace emerging from the autumn mist, as the traveller ascends an Italian hillside,”

And so it was for Boltzmann. But for him, that palace was at Duino in Italy, where he hung himself.


A new generation of mathematicians and philosophers, were convinced if only they could solve the problem of the nature of infinity Maths could be made perfect again.

Godel was born the year Boltzmann died 1906. He was an insatiably questioning boy, growing up in unstable times. His family called him Mr Why.


What Godel later showed in his Incompleteness Theorem is that no matter how large you make your basis of reasoning your axioms, your set of axioms in arithmatic there would always be statements that are true but cannot be proved. No matter how much data you have to build on, you will never prove all true statements.


There are no holes in Godels argument. It is, in a way, a perfect argument. Thus the present tense of this paragraph, it stands impeach-ably strong to this day. The argument is so crystal clear, and obvious.


To this day, very few want to face the consequences of Godel. People want to go ahead with formal systems, and Godel explodes that formalist view of mathematics that you can just mechanically grind away on a fixed set of concepts. There’s a very ambivalent attitude to Godel even now a century after his birth. On the one hand he’s the greatest logician of all time so logicians will claim him but on the other hand they don’t want people who are not logicians to talk about the consequences of Godel’s work because the obvious conclusion from Godel’s work is that logic is a failure - let’s move onto something else, as this will destroy the field.


Godel too felt the effects of his conclusion. As he worked out the true extent of what he had done, Incompleteness began to eat away at his own beliefs about the nature of Mathematics. His health began to deteriorate and he began to worry about the state of his mind. In 1934 he had his first breakdown. But it was after he recovered however, that his real troubles began, when he made a fateful decision.


Almost as soon as Godel has finished the Incompleteness Theorem, he decides to work on the great unsolved problem of modern mathematics, Cantor’s Continuum Hypothesis. Godel, like Cantor before him, could neither solve the problem nor put it down - even as it made him unwell. Again, the mind so engaged the brain dare not look away from the evidence that perplexed the mind so much. He calls this the worst year of his life. He has a massive nervous breakdown and ends up in a sanatoria, just like Cantor himself.


Alan Turing is the next person to enter this brief history. Turing was most well known for breaking the Enigma code; but he is also the man who made Gödel’s already devastating Incompleteness Theorem even more devastating.


Computers being logic machines was Turings predominant world view, and he showed that since they are logic machines incompleteness meant there would always be some problems they would never solve. A machine fed one of those problems, would never stop. And worse, Turing proved there was no way of telling beforehand which these problems were.


With Gödels work there was the hope that you could distinguish between the provable and the unprovable and simply leave the unprovable to one side. What Turing does, is prove that, in fact, there is no way of telling which will be the unprovable problems. So how do you know when to stop? You will never know whether the problem you’re working on is simply fundamentally unprovable or extraordinarily difficult. And that is Turing’s Halting Problem.


Startling as the Halting problem was, the really profound part of Incompleteness, for Turing, was not what it said about logic or computers, but what it said about us and our minds. Were we or weren’t we computers? It was the question that went to the heart of who Turing was.


This tension between the human and the computational was central to Turing’s life – and he lived with it until, the events which led to his death. After the war Turing increasingly found himself drawing the attention of the security services. In the cold war, homosexuality was seen as not only illegal and immoral, but also a security risk. So when in March 1952 he was arrested, charged and found guilty of engaging in a homosexual act, the authorities decided he was a problem that needed to be fixed.


They would chemically castrate him by injecting him with the female hormone, Oestrogen. Turing was being treated as no more than a machine (which in a sadly ironic way is what he was trying to prove himself). Chemically re-programmed to eliminate the uncertainty of his sexuality and the risk they felt it posed to security and order. To his horror he found the treatment affected his mind and his body .He grew breasts, his moods altered and he worried about his mind. For a man who had always been authentic and at one with himself, it was as if he had been injected with hypocrisy.


On the 7th June 1954, Turing was found dead. At his bedside an apple from which he had taken several bites. Turing had poisoned the apple with cyanide.
Turing had passed, but his question remained. Whether the mind was a computer and so limited by logic, or somehow able to transcend logic, was now the question that came to trouble the mind of Kurt Godel.


Having recovered from his time in the mentally unstable sanctum. But by the time he got here to the Insititute for Advanced Study in America he was a very peculiar man. One of the stories they tell about him is if he was caught in the commons with a crowd of other people he so hated physical contact, that he would stand very still, so as to plot the perfect course out so as not to have to actually touch anyone. He also felt he was being poisoned by what he called bad air, from heating systems and air conditioners. And most of all he thought his food was being poisoned.


Peculiar as Gödel was his genius was undimmed. Unlike Turing, Godel could not believe we were like computers. He wanted to show how the mind had a way of reaching truth outside logic. And what it would mean if it couldn’t.


So, why so convinced was Godel that humans had this spark of creativity? The key to his belief comes from a deep conviction he shared with one of the few close friends he ever had, that other Austrian genius who had settled at the Institute, Albert Einstein.


Einstein used to say that he came here to the Institute for Advanced Studies simply for the privilege of walking home with Kurt Godel. And what was it that held this most unlikely of couples together. On the one hand you’ve got the warm and avuncular Einstein and on the other the rather cold, wizened and withdrawn Kurt Godel. The answer for this strange companionship comes I think from something else that Einstein said.. He said that "God may be subtle but he’s not malicious." And what does that mean? Well, it means for Einstein is that however complicated the universe might be there will always be beautiful rules by which it works. Godel believed the same idea from his point of view to mean, that God would never have put us into a creation that we could not then understand.


The question is, how is it that Kurt Gödel can believe that God is not malicious? That it’s all understandable? Because Gödel is the man who has proved that some things cannot be proven logically and rationally. So surely God must be malicious? The way he gets out of it is that Gödel, like Einstein, believes deeply in Intuition - That we can know things outside of logic, maths and computation; because we just intuit them. And they both believed this, because they both felt it. They have both had their moments of intuition, moments of sudden conceptual realisation that were by far more than just chance.


Einstein talked about new principles that the mathematician should adopt closing their eyes, tuning out the real world you can try to perceive directly by your mathematical intuition, the platonic world of ideas and come up with new principles which you can then use to extend the current set of principles in mathematics. And he viewed this as a way of getting around the limitations of his own theorem. He no longer thought that there was a limit to the mathematics that human beings were capable of. But how could he prove such subjectives?


The interpretation that Gödel himself drew was that computers are limited. He certainly tried again and again to work out that the human mind transcends the computer. In the sense that he can’t understand things to be true that cannot be proved by a computer programme. Gödel also was wrestling with some finding means of knowledge which are not based on experience and on mathematical reasoning but on some sort of intuition. The frustration for Gödel was getting anyone to understand him.


Gödel was trying to show what one might call mathematical intuition of the kind we see in the brains of Synesthesia Savants such as Daniel Tammet in current times, and he was demonstrating that this is outside just following formal rules. What he had shown was that for any system that you adopt, which in a sense the mind has been removed from it because it's you that's used to lay down the system, but from there on mind takes over and you ask what’s it’s scope? And what Gödel showed is that it’s scope is always limited and that the mind can always go beyond it.


Here’s the man who has said, certain things cannot be proved within any rational and logical system. But he says that doesn’t matter, because the human mind isn’t limited that way. We have Intuition. But then of course, the one thing he really must prove to other people, is the existence of intuition. The one thing you'll never be able to prove. It would be synonymous in many regards to trying to prove the strong version of the gaia hypothesis.


Because he couldn’t prove a theorem about creativity or intuition it was just a gut feeling that he had and he wasn’t satisfied with that. And so Gödel had finally found a problem he desperately wanted to solve but could not. He was now caught in a loop, a logical paradox from which his mind could not escape. And at the same time he slowly starved himself to death.


Using mathematics to show the limits of mathematics is…is….is psychologically very contradictory. It’s clear in Gödel’s case that he appreciated this - his own life has this. What Gödel is, is the mind thinking about itself and what it can achieve at the deepest level.


It's a paradox of self-reflection. The kind of madness that you find associated with modernism is a kind of madness that’s’ bound up with not only rationality but with all the paradoxes that arise from self-consciousness from the consciousness contemplating it’s own being as consciousness or from logic contemplating it’s own being as logic.


Even though he’d shown that logic has certain limitations he was still so drawn to the significance of the rational and the logical. That he desperately wants to prove whatever is most important logically even if it’s an alternative to logic. How strange and what a testimony to his inability to separate himself - to detach himself from the need for logical proof; Gödel all of all people.


Cantor originally had hoped that at its deepest level mathematics would rest on certainties, which, for him, were the mind of God. But instead, he had uncovered uncertainties. Which Turing and Godel then proved would never go away; they were an inescapable part of the very foundations of maths and logic. The almost religious belief that there was a perfect logic, which governed a world of certainties had unsurprisingly unravelled itself.


Logic had revealed the limitations of logic. The search for certainty had revealed uncertainty.


The notion of absolute certainty, is, there is no absolute certainty, in human life, in maths, in logic neither in science. The only certainty that has withstood the test of time to date is; that what we think is certain and true has a limited axiomatic scope, and the conscious mind is the only force in the universe that can transcend proclamations of truth by virtue of conceptualising and defining its limited scope, thus transcending certainties to higher values of truth it itself previously set the scope of. In this regard, focussed right by powerful minds, it's self transcendental in the fact that it's forever able to define the scope, lay it down, then re-analyse it and go beyond it.

Such realisations he said are only from becoming shut off from the outside world and looking fully internally, a sort of mathematical medication practise. It's the ability to see the full axiomatic scope of an internally self evolving mathematical framework; the message seeming to be that its always going to be expanded better by the internal mind, as long as no external influences of a social culture not open to questioning the scope and truth of the axioms it was predicated on, which was his current outside world over 50 years back. And, I feel, this culture largely remains so today, though certainly not to the extent it did 50 years back. The fact Godels Incompleteness Theorems still have a lot of applicability to many theories I think has been largely overlooked, or even rejected, by certain disciplines predicated on mathematical grounds and potentially spurious axioms, all of which can likely be viewed as a more wholistic viewpoint and expanded on with the power of the minds ability to always see the limits of the system.

But if consciousness in its normal form is indeed non computational, non algorithmic and not based on logic (incompleteness theorem) associated with turing machines then how are we ever going to try to understand it in terms of them without just tying ourselves up in knots made of the same paradoxes that drove the aforementioned geniuses mad?

To finish, applying Godels theorem more vigorously to current dominant paradigms could have such a catalysing effect in developing new, mathematically sound theories based on the more creative functions of human inspiration; whilst also pointing out certain unprovable assumptions that underly some.

I revel in scientific unknowns and theories being falsified and replaced by a better theory, personally. I have no pet theory I'm emotionally attached to.

The problem is that today, some knowledge still feels too dangerous.

Because our times are not so different to Cantor or Boltzmann or Gödel’s time.

We too feel things we thought were solid, being challenged, feel our certainties slipping away.

And so, as then, we still desperately want to cling to belief in certainty.
It makes us feel safe.

At the end of this journey the question, I think we are left with, is actually the same as it was in Cantor and Boltzmann’s time.

Are we grown up enough to live with uncertainties?

Or will we repeat the mistakes of the twentieth century and pledge blind allegiance to yet another certainty?

[and if there is anyone still reading, thanks

[fuelair]

Eventually, the mathmatics will prove each right or wrong. Not being a mathmatician myself, that's about as far as I can go. Based on the examples, the most I can say is it looks like the best of our mathmaticians are still limited - and even endangered at some point - where their concepts led far from currently accepted math limits (I suspect that goes for the mathmatically oriented realms of physice also). Shall we see!!

[Vermonter]

Soon we'll be applying sacred unguents in reverence to the machine, and only the red-hooded priests will know the secrets of technology...

[jsfisher]

Originally Posted by Zeuzzz

[Note: Lengthy historical documentation

...<snip>...

Lengthy, yes. Historical, not so much. Lot's of sweeping generalities and misrepresentations. More to the point, though, how does this colored history lead to question at the end?

What mistakes of the twentieth century would we be repeating and what dire consequences did they have?

[Gord_in_Toronto]

"There is a fine line between genius and madness."

[Chucky]

Originally Posted by Vermonter

Soon we'll be applying sacred unguents in reverence to the machine, and only the red-hooded priests will know the secrets of technology...

I can provide a pungent ungent made from the dust of the Grand Wazoo!

And such a deal for you!

Actually, per the OP directly, I've seen a documentary - BBC 4? - I don't remember - that looks at all of these gentlemen and if memory serves, and this subject of their mathematical pursuits and fates. It was quite interesting. I'm sure it can be found on the yoo-tubes. Sorry that I don't have time to look for it right now but it should be an easy search.

[Zeuzzz]

Originally Posted by Chucky

I can provide a pungent ungent made from the dust of the Grand Wazoo!

And such a deal for you!

Actually, per the OP directly, I've seen a documentary - BBC 4? - I don't remember - that looks at all of these gentlemen and if memory serves, and this subject of their mathematical pursuits and fates. It was quite interesting. I'm sure it can be found on the yoo-tubes. Sorry that I don't have time to look for it right now but it should be an easy search.

Heres your link enjoy.
http://www.google.co.uk/url?sa=t&rct...3M94z1U7FZIY1g

They are both there. Very well researched BBC documentaries. I wrote this text as I watched the documentaries and missed out the un-needed joining parts and largely scientifically irrelevant bits, but included my own literary take on the prose as it progressed. Think of the text here as succinct, rarely subjective (well I tried my best), way of referring to you lot in prose what would have been impossible to get across by demanding you watch the video series. I checked the copyright, and have emailed the owner. He was fine with me creating a 'down to the core elements' version. It's BBC anyway, I paid for it

[Zeuzzz]

Originally Posted by Gord_in_Toronto

"There is a fine line between genius and madness."

There is no line, no matter how fine.

The only line is the dominant paradigms polarising strength of influence on the thoughts of people who might indeed make such a distinction. Which is not science. But human nature; which in not a big fan of in the science area.

[Lowpro]

Originally Posted by Vermonter

Soon we'll be applying sacred unguents in reverence to the machine, and only the red-hooded priests will know the secrets of technology...

Warhammer 40k Reference?

[Zeuzzz]

BURSTING !!!

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[Kwalish Kid]

Originally Posted by Zeuzzz

What Godel later showed in his Incompleteness Theorem is that no matter how large you make your basis of reasoning your axioms, your set of axioms in arithmatic there would always be statements that are true but cannot be proved. No matter how much data you have to build on, you will never prove all true statements.

Unsurprisingly, you have this incorrect. What Godel showed was that within an axiomatic system of a certain kind that was strong enough to produce arithmetic, there are statements within that system that cannot be proven to be true and that cannot be proven to be false. These statements do not have to have a definite truth value.

Quote:

There are no holes in Godels argument. It is, in a way, a perfect argument. Thus the present tense of this paragraph, it stands impeach-ably strong to this day. The argument is so crystal clear, and obvious.

Clearly it's not obvious, since you have it wrong.

Quote:

To this day, very few want to face the consequences of Godel. People want to go ahead with formal systems, and Godel explodes that formalist view of mathematics that you can just mechanically grind away on a fixed set of concepts.

Nobody anywhere wants to do this, nor have they ever wanted to do this.

Quote:

There’s a very ambivalent attitude to Godel even now a century after his birth. On the one hand he’s the greatest logician of all time so logicians will claim him but on the other hand they don’t want people who are not logicians to talk about the consequences of Godel’s work because the obvious conclusion from Godel’s work is that logic is a failure - let’s move onto something else, as this will destroy the field.

It is not a conclusion from anything that Godel did that logic is a failure. There is much, much more to logic that has been developed after Godel. I urge you to actually read Godel and related work in logic.

Just as you should apologize for your grand statements about cosmology made in almost complete ignorance, so too you should make an apology here.
[quote]

Quote:

To finish, applying Godels theorem more vigorously to current dominant paradigms could have such a catalysing effect in developing new, mathematically sound theories based on the more creative functions of human inspiration; whilst also pointing out certain unprovable assumptions that underly some.

This is clearly false. The reason for this is, primarily, that currently favoured theories are favoured because they can be compared to measurement results, there is no problem of the kind of provability that is relevant to Godel's mathematical results.

I know that you would prefer to castigate contemporary science based on an almost complete ignorance of the evidence for particular theories, but evidence is what drives science.

[Zeuzzz]

Originally Posted by jsfisher

More to the point, though, how does this colored history lead to question at the end?

The fact that Boltzmann and Turing died as the result of their belief in mechanistic formalities and truths being the mechanisms that governed them. Godel did not accept this, so lived on and spoke to Einstein about how open minded his theory had made his inner world of maths even though the outside world was sticking steadfast to its axioms. But he succumbed to the perils of the power of mind over maths in the end. For any mathematical system he created, his mind could always better it, and stuck in this never ending loop of intrigue into the power of the minds non logic based mathematical ability it drove him to death.

The nature of infinity being only an abstract concept that we can use mathematically to no end (Infinity is a perfectly concrete, reasonable concept which is accepted by mathematicians and many theoretical and classical scientists, but still is viewed with contempt by experimental scientists and engineers who have no evidence such things even exist apart from in the minds and hypostatisations of the people that make them up based on inference, for completeness of a model)

The experimental method vs the method(?) of inference.

I know where I would put my money.

[Zeuzzz]

dp

[Zeuzzz]

Originally Posted by Kwalish Kid

...

Could you word that whole post a bit more scientifically, or educationally, rather than confrontationaly? I don't wan't to argue.I don't want to engage with. I thought we were past ego battles and ad homs here, in the science section?

Out of interest, are you a cosmologist?

[jsfisher]

Originally Posted by Zeuzzz

The fact that Boltzmann and Turing died as the result of their belief in mechanistic formalities...

No, they didn't. You've built your house of cards on false premises. Try again.

...and you didn't address my question, either.

[tsig]

Originally Posted by Zeuzzz

[Note: Lengthy historical documentation I have gathered and put into a coherent prose here may seen like too long to read, but it gives the reason for why such great scientists such as Kurt Godel, Richard Turing and Ludwig Boltzmann committed suicide, and why George Cantor was also driven to the brink numerous times]


The greatest most intelligent minds that walked this earth in terms of understanding the machinery of the universe were likely Albert Einstein and Godel, I still think to this day. We would be wise to take a historical note of what Einsteins later years were spent doing and what conclusions he came to, as the scientific community ran off and made 'mainstream' with a set of his theories he himself was deeply uneasy with. Einstein and Godel seemed to reach similar conclusions, but seemingly one of them coped better with the implications of this than the other in the end.


The solid mathematical foundations that a lot of these modern day Nobels are awarded for, have a slightly darker and mirkier past in a historical context. And in fact, the whole materialist myopic view of linear maths as revealing deeper and deeper truths to us about the universe is fatally flawed from the get go.


It's a story of how some of our most intellectually stimulated minds untied the previously cosy relationship the universe seemed to have with the certainties of mathematics, and how these facts have been acknowledged but largely ignored. It's a story of how such deep questions being asked back then of such high importance resulted in the fact that when some of the greatest minds of the time engaged their mind with such questions their brain dare not look away from the evidence that perplexed them so much, and how pursuit of meaningful answers to these issues pushed them first to the brink of insanity, then over to madness and suicide.


But for all the humain tragedy of great minds lost due to seeking meaning from life from maths and logic, what they saw is still true - the intellectuals at the time that took over the consensus opinion, assigning Einsteins work greater credibility than the original creator himself did, whilst in the case of Godels work largely ignoring it; so to this date we have yet to inherit at large the conclusions they themselves made.


Now, the world that they saw, we still stand at the frontier of as much as they did over fifty years ago.


George Cantor (1845-1918) was a religious professor of maths who started a paradigm shift in the world of established maths and science, that maybe he did not appreciate at the time. The profundity of a brand new question, not based on previous knowledge or even a similar school of thought in maths at the time; he asked himself "how big is infinity"?


It’s just an incredible feat of imagination. It’s, to me, the equivalent of taking mind enhancing drugs for that era (1800-1900) Others before him, going back to the ancient Greeks at least, had asked the question but it was Cantor who made the journey no one else ever had, and found the answer. But he paid a price for his discovery. He died utterly alone in an insane asylum.


The question is what could the greatest mathematician of his century have seen that could drive him insane?


Cantor had auitary hullicinations from a little boy that he attributed to god as calling him to maths. So for Cantor, his mathematics of the nature of infinity had to be true, because God had revealed it to him.


Cantor soon discovered he could add and subtract infinities conceptually, and in fact discovered there was a vast new mathematics opening up infront of him - maths of the infinite. This out of the boxing thinking had revealed something special, and he could feel it as a sort of profound insight into the nature of maths he was previously blind to.


By 1884 Cantor has been working solidly on the Continuum Hypothesis for over 2 years. At the same time the personal and professional attacks on him for his heretical "maths of the infinites" had become more and more extreme. Due to this, the following may of that year he had a mental breakdown. His daughter describes how his whole personality is transformed. He would rant and rave and then fall completely and uncommunicatively silent. Eventually he is brought here to the NervenKlinik in Halle, which is an asylum.


Even after concerted further effort he could still not solve the Continuum Hypothesis, he came to describe the infinite as an abyss. A chasm perhaps between what he had seen and what he knew must be there but could never reach. He realised that there’s a way in which in order to understand something you have to look very hard at it but you also have to be able to sort of move away from it and kind of see it in a kind of wholistic context, and the person who stares too hard can often can lose that sense of context.


After the death of a close relative, Cantor went on to say that he "could no longer" even remember why he himself had left music in order to go into maths. That secret 'voice' which had once called him on to mathematics and given meaning to his life and work. The voice he identified with God. That voice too had left him.


Here I divert from Cantor, because if we treat Cantor’s story in isolation it does little to bridge the gap in the idea that Cantor had dislodged something was part of a much broader feeling of that time. That things once felt to be solid were slipping. A feeling seen more clearly in the story of his great contemporary- a man called Ludwig Boltzmann.


The physics of Boltzmann’s time was still the physics of certainty, of an ordered universe, determined from above by predictable and timeless God-given laws. Boltzmann suggested that the order of the world was not imposed from above by God, but emerged from below, from the random bumping of atoms. A radical idea, at odds with its times, but the foundation of ours. Ernest Marc one of the most influential er philosopher of science at that time stated: 'I cannot see, I don’t need it, they do not exist so why we should bring them in the game.'


Worse than insisting on the reality of something people could not see, to base physics on atoms meant to base it on things whose behaviour was too complex to predict. Which meant an entirely new kind of physics – one based on probabilities not certainties. Boltzman worked tirelessly at his idea irrespective, and as Boltzmann got older and more exhausted from the struggle, he'd get mood swings, mood swings that became more and more severe. More and more of Boltzmann’s energy was absorbed in trying to convince his opponents that his theory was correct. He wrote, “No sacrifice is too high for this goal, which represents the whole meaning of my life.”


The last year of Boltzmann he didn’t do any research at all, I’m talking about the last 10 years. He was fully immersed in a dispute, philosophical dispute, tried to make his point – writing books which were most of the time the same repeating the same concept and so on. So you can see he was in a loop that didn’t go ahead. By the beginning of the 1900’s the struggle was getting too hard him.


Boltzmann had discovered one of the fundamental equations, which makes the universe work and he had dedicated his life to it. The philosopher Bertrand Russell said that for any great thinker, “This discovery that everything flows from these fundamental laws… comes”, as he described it, “with the overwhelming force of a revelation: like a palace emerging from the autumn mist, as the traveller ascends an Italian hillside,”

And so it was for Boltzmann. But for him, that palace was at Duino in Italy, where he hung himself.


A new generation of mathematicians and philosophers, were convinced if only they could solve the problem of the nature of infinity Maths could be made perfect again.

Godel was born the year Boltzmann died 1906. He was an insatiably questioning boy, growing up in unstable times. His family called him Mr Why.


What Godel later showed in his Incompleteness Theorem is that no matter how large you make your basis of reasoning your axioms, your set of axioms in arithmatic there would always be statements that are true but cannot be proved. No matter how much data you have to build on, you will never prove all true statements.


There are no holes in Godels argument. It is, in a way, a perfect argument. Thus the present tense of this paragraph, it stands impeach-ably strong to this day. The argument is so crystal clear, and obvious.


To this day, very few want to face the consequences of Godel. People want to go ahead with formal systems, and Godel explodes that formalist view of mathematics that you can just mechanically grind away on a fixed set of concepts. There’s a very ambivalent attitude to Godel even now a century after his birth. On the one hand he’s the greatest logician of all time so logicians will claim him but on the other hand they don’t want people who are not logicians to talk about the consequences of Godel’s work because the obvious conclusion from Godel’s work is that logic is a failure - let’s move onto something else, as this will destroy the field.


Godel too felt the effects of his conclusion. As he worked out the true extent of what he had done, Incompleteness began to eat away at his own beliefs about the nature of Mathematics. His health began to deteriorate and he began to worry about the state of his mind. In 1934 he had his first breakdown. But it was after he recovered however, that his real troubles began, when he made a fateful decision.


Almost as soon as Godel has finished the Incompleteness Theorem, he decides to work on the great unsolved problem of modern mathematics, Cantor’s Continuum Hypothesis. Godel, like Cantor before him, could neither solve the problem nor put it down - even as it made him unwell. Again, the mind so engaged the brain dare not look away from the evidence that perplexed the mind so much. He calls this the worst year of his life. He has a massive nervous breakdown and ends up in a sanatoria, just like Cantor himself.


Alan Turing is the next person to enter this brief history. Turing was most well known for breaking the Enigma code; but he is also the man who made Gödel’s already devastating Incompleteness Theorem even more devastating.


Computers being logic machines was Turings predominant world view, and he showed that since they are logic machines incompleteness meant there would always be some problems they would never solve. A machine fed one of those problems, would never stop. And worse, Turing proved there was no way of telling beforehand which these problems were.


With Gödels work there was the hope that you could distinguish between the provable and the unprovable and simply leave the unprovable to one side. What Turing does, is prove that, in fact, there is no way of telling which will be the unprovable problems. So how do you know when to stop? You will never know whether the problem you’re working on is simply fundamentally unprovable or extraordinarily difficult. And that is Turing’s Halting Problem.


Startling as the Halting problem was, the really profound part of Incompleteness, for Turing, was not what it said about logic or computers, but what it said about us and our minds. Were we or weren’t we computers? It was the question that went to the heart of who Turing was.


This tension between the human and the computational was central to Turing’s life – and he lived with it until, the events which led to his death. After the war Turing increasingly found himself drawing the attention of the security services. In the cold war, homosexuality was seen as not only illegal and immoral, but also a security risk. So when in March 1952 he was arrested, charged and found guilty of engaging in a homosexual act, the authorities decided he was a problem that needed to be fixed.


They would chemically castrate him by injecting him with the female hormone, Oestrogen. Turing was being treated as no more than a machine (which in a sadly ironic way is what he was trying to prove himself). Chemically re-programmed to eliminate the uncertainty of his sexuality and the risk they felt it posed to security and order. To his horror he found the treatment affected his mind and his body .He grew breasts, his moods altered and he worried about his mind. For a man who had always been authentic and at one with himself, it was as if he had been injected with hypocrisy.


On the 7th June 1954, Turing was found dead. At his bedside an apple from which he had taken several bites. Turing had poisoned the apple with cyanide.
Turing had passed, but his question remained. Whether the mind was a computer and so limited by logic, or somehow able to transcend logic, was now the question that came to trouble the mind of Kurt Godel.


Having recovered from his time in the mentally unstable sanctum. But by the time he got here to the Insititute for Advanced Study in America he was a very peculiar man. One of the stories they tell about him is if he was caught in the commons with a crowd of other people he so hated physical contact, that he would stand very still, so as to plot the perfect course out so as not to have to actually touch anyone. He also felt he was being poisoned by what he called bad air, from heating systems and air conditioners. And most of all he thought his food was being poisoned.


Peculiar as Gödel was his genius was undimmed. Unlike Turing, Godel could not believe we were like computers. He wanted to show how the mind had a way of reaching truth outside logic. And what it would mean if it couldn’t.


So, why so convinced was Godel that humans had this spark of creativity? The key to his belief comes from a deep conviction he shared with one of the few close friends he ever had, that other Austrian genius who had settled at the Institute, Albert Einstein.


Einstein used to say that he came here to the Institute for Advanced Studies simply for the privilege of walking home with Kurt Godel. And what was it that held this most unlikely of couples together. On the one hand you’ve got the warm and avuncular Einstein and on the other the rather cold, wizened and withdrawn Kurt Godel. The answer for this strange companionship comes I think from something else that Einstein said.. He said that "God may be subtle but he’s not malicious." And what does that mean? Well, it means for Einstein is that however complicated the universe might be there will always be beautiful rules by which it works. Godel believed the same idea from his point of view to mean, that God would never have put us into a creation that we could not then understand.


The question is, how is it that Kurt Gödel can believe that God is not malicious? That it’s all understandable? Because Gödel is the man who has proved that some things cannot be proven logically and rationally. So surely God must be malicious? The way he gets out of it is that Gödel, like Einstein, believes deeply in Intuition - That we can know things outside of logic, maths and computation; because we just intuit them. And they both believed this, because they both felt it. They have both had their moments of intuition, moments of sudden conceptual realisation that were by far more than just chance.


Einstein talked about new principles that the mathematician should adopt closing their eyes, tuning out the real world you can try to perceive directly by your mathematical intuition, the platonic world of ideas and come up with new principles which you can then use to extend the current set of principles in mathematics. And he viewed this as a way of getting around the limitations of his own theorem. He no longer thought that there was a limit to the mathematics that human beings were capable of. But how could he prove such subjectives?


The interpretation that Gödel himself drew was that computers are limited. He certainly tried again and again to work out that the human mind transcends the computer. In the sense that he can’t understand things to be true that cannot be proved by a computer programme. Gödel also was wrestling with some finding means of knowledge which are not based on experience and on mathematical reasoning but on some sort of intuition. The frustration for Gödel was getting anyone to understand him.


Gödel was trying to show what one might call mathematical intuition of the kind we see in the brains of Synesthesia Savants such as Daniel Tammet in current times, and he was demonstrating that this is outside just following formal rules. What he had shown was that for any system that you adopt, which in a sense the mind has been removed from it because it's you that's used to lay down the system, but from there on mind takes over and you ask what’s it’s scope? And what Gödel showed is that it’s scope is always limited and that the mind can always go beyond it.


Here’s the man who has said, certain things cannot be proved within any rational and logical system. But he says that doesn’t matter, because the human mind isn’t limited that way. We have Intuition. But then of course, the one thing he really must prove to other people, is the existence of intuition. The one thing you'll never be able to prove. It would be synonymous in many regards to trying to prove the strong version of the gaia hypothesis.


Because he couldn’t prove a theorem about creativity or intuition it was just a gut feeling that he had and he wasn’t satisfied with that. And so Gödel had finally found a problem he desperately wanted to solve but could not. He was now caught in a loop, a logical paradox from which his mind could not escape. And at the same time he slowly starved himself to death.


Using mathematics to show the limits of mathematics is…is….is psychologically very contradictory. It’s clear in Gödel’s case that he appreciated this - his own life has this. What Gödel is, is the mind thinking about itself and what it can achieve at the deepest level.


It's a paradox of self-reflection. The kind of madness that you find associated with modernism is a kind of madness that’s’ bound up with not only rationality but with all the paradoxes that arise from self-consciousness from the consciousness contemplating it’s own being as consciousness or from logic contemplating it’s own being as logic.


Even though he’d shown that logic has certain limitations he was still so drawn to the significance of the rational and the logical. That he desperately wants to prove whatever is most important logically even if it’s an alternative to logic. How strange and what a testimony to his inability to separate himself - to detach himself from the need for logical proof; Gödel all of all people.


Cantor originally had hoped that at its deepest level mathematics would rest on certainties, which, for him, were the mind of God. But instead, he had uncovered uncertainties. Which Turing and Godel then proved would never go away; they were an inescapable part of the very foundations of maths and logic. The almost religious belief that there was a perfect logic, which governed a world of certainties had unsurprisingly unravelled itself.


Logic had revealed the limitations of logic. The search for certainty had revealed uncertainty.


The notion of absolute certainty, is, there is no absolute certainty, in human life, in maths, in logic neither in science. The only certainty that has withstood the test of time to date is; that what we think is certain and true has a limited axiomatic scope, and the conscious mind is the only force in the universe that can transcend proclamations of truth by virtue of conceptualising and defining its limited scope, thus transcending certainties to higher values of truth it itself previously set the scope of. In this regard, focussed right by powerful minds, it's self transcendental in the fact that it's forever able to define the scope, lay it down, then re-analyse it and go beyond it.

Such realisations he said are only from becoming shut off from the outside world and looking fully internally, a sort of mathematical medication practise. It's the ability to see the full axiomatic scope of an internally self evolving mathematical framework; the message seeming to be that its always going to be expanded better by the internal mind, as long as no external influences of a social culture not open to questioning the scope and truth of the axioms it was predicated on, which was his current outside world over 50 years back. And, I feel, this culture largely remains so today, though certainly not to the extent it did 50 years back. The fact Godels Incompleteness Theorems still have a lot of applicability to many theories I think has been largely overlooked, or even rejected, by certain disciplines predicated on mathematical grounds and potentially spurious axioms, all of which can likely be viewed as a more wholistic viewpoint and expanded on with the power of the minds ability to always see the limits of the system.

But if consciousness in its normal form is indeed non computational, non algorithmic and not based on logic (incompleteness theorem) associated with turing machines then how are we ever going to try to understand it in terms of them without just tying ourselves up in knots made of the same paradoxes that drove the aforementioned geniuses mad?

To finish, applying Godels theorem more vigorously to current dominant paradigms could have such a catalysing effect in developing new, mathematically sound theories based on the more creative functions of human inspiration; whilst also pointing out certain unprovable assumptions that underly some.

I revel in scientific unknowns and theories being falsified and replaced by a better theory, personally. I have no pet theory I'm emotionally attached to.

The problem is that today, some knowledge still feels too dangerous.

Because our times are not so different to Cantor or Boltzmann or Gödel’s time.

We too feel things we thought were solid, being challenged, feel our certainties slipping away.

And so, as then, we still desperately want to cling to belief in certainty.
It makes us feel safe.

At the end of this journey the question, I think we are left with, is actually the same as it was in Cantor and Boltzmann’s time.

Are we grown up enough to live with uncertainties?

Or will we repeat the mistakes of the twentieth century and pledge blind allegiance to yet another certainty?

[and if there is anyone still reading, thanks

Yes.

[tsig]

Originally Posted by Vermonter

Soon we'll be applying sacred unguents in reverence to the machine, and only the red-hooded priests will know the secrets of technology...

That would be the red robed priests of Isis.

[Zeuzzz]

Originally Posted by jsfisher

No, they didn't. You've built your house of cards on false premises. Try again.

Ok. Attempt 2. (I've been up 24 hours now short term memory is going) Turing died inconsequentially to his actions in computation (wrong as they were when applied to Godels, ironically proved by him despite his admirable quest to keep trying).

Boltzmann hung himself in a martyrdom mannor as the larger intellects of the day refused to accept his immaterial atoms "I cannot see, I don’t need it, they do not exist so why we should bring them in the game."

I think many of the materialists arguing against consciousness in this thread as being purely a function of computation of brain chemistry could learn from that quote, dated as it is. As could neuroscientists possibly re-consider the order of cause and effect they have assumed in the brain > consciousness relationship.

Quote:

...and you didn't address my question, either.

To ignore things we can not currently see or detect by current means by saying they "do not exist so why we should bring them in the game." when the vast majority of the worlds population feels totally at odds with. There is some sort of feeling of qualia, of consciousness, of soul, spirit, spirituality and (even dare I say it) religion that some scientists seem to still be taking, the now quite frankly ancient view that religion is all bad and belief in 'god'* is stupid and not even worthy of scientific study.

Seems to be changing though: http://forums.randi.org/showpost.php...5&postcount=32

* whatever the hell that may subjectively be, a scientist with a doctorate in physics for example would describe it in totally different ways than your typical religious person would

[Zeuzzz]

Originally Posted by tsig

Yes.

I would tend to agree with this.

[Gord_in_Toronto]

And Gödel's Incompleteness Theorem (1931) so unnerved Alfred North Whitehead and Bertrand Russell by overturning their three-volume work, Principia Mathematica, that Whitehead only managed to stagger on for another 16 years to die at the age of 96 and Russell for 39 years to die at 98.

[ben m]

Originally Posted by Zeuzzz

But he paid a price for his discovery. He died utterly alone in an insane asylum.

The question is what could the greatest mathematician of his century have seen that could drive him insane?

Was that an all-mathematicians insane asylum? If not, maybe Cantor suffered from the same thing that thousands of nonmathematicians suffered from, then and today. He was a human being.

Quote:

The physics of Boltzmann’s time was still the physics of certainty, of an ordered universe, determined from above by predictable and timeless God-given laws. Boltzmann suggested that the order of the world was not imposed from above by God, but emerged from below, from the random bumping of atoms.

Worse than insisting on the reality of something people could not see, to base physics on atoms meant to base it on things whose behaviour was too complex to predict.

No. You forget to mention that, until 1900-ish, there was no evidence that atoms existed. They were a vague hypothetical idea, apparently consistent with some chemical data, but utterly invisible. Of course not everyone leapt to believe in them. You're making up the "too complex to predict" explanation.

Quote:

as Boltzmann got older and more exhausted from the struggle, he'd get mood swings, mood swings that became more and more severe.

... which happens to academics all the time. We had a poster here, once, defending a retired academic who had gone funny over a hypothesis about his bee dance theory.

Quote:

To this day, very few want to face the consequences of Godel. People want to go ahead with formal systems, ...

the obvious conclusion from Godel’s work is that logic is a failure - let’s move onto something else, as this will destroy the field.

Um. Not true. Godel's theorem is well known among mathematicians, who have indeed given up on the sort of formal systems Godel's theorem is relevant to, like Whitehead and Russell's. Where are you getting this stuff?

The beginning doesn't make me want to read to the end.

[Zeuzzz]

Uh oh the cosmologists are coming ...

[Zeuzzz]

Originally Posted by ben m

Was that an all-mathematicians insane asylum? If not, maybe Cantor suffered from the same thing that thousands of nonmathematicians suffered from, then and today. He was a human being.



No. You forget to mention that, until 1900-ish, there was no evidence that atoms existed. They were a vague hypothetical idea, apparently consistent with some chemical data, but utterly invisible. Of course not everyone leapt to believe in them. You're making up the "too complex to predict" explanation.



... which happens to academics all the time. We had a poster here, once, defending a retired academic who had gone funny over a hypothesis about his bee dance theory.



Um. Not true. Godel's theorem is well known among mathematicians, who have indeed given up on the sort of formal systems Godel's theorem is relevant to, like Whitehead and Russell's. Where are you getting this stuff?

The beginning doesn't make me want to read to the end.

Ben I hate to inform you now, belatedly, that you are not arguing with me, but paraphrases and odd quotes of significance from esteemed professors that know the history of these people probably better than most people ever have, which apart from a few additional comments I made along the way, to give a few more modern references every now and again, the OP is primarily the concise version of the vocal material in the aforementioned documentary.

In light of this is there a question you want to ask again or re-iterate?

[Zeuzzz]

Originally Posted by Gord_in_Toronto

And Gödel's Incompleteness Theorem (1931) so unnerved Alfred North Whitehead and Bertrand Russell by overturning their three-volume work, Principia Mathematica, that Whitehead only managed to stagger on for another 16 years to die at the age of 96 and Russell for 39 years to die at 98.

Did they reference and address Godels theorem? Do you have quotes as to what they said about it?

[PixyMisa]

Originally Posted by Zeuzzz

Ben I hate to inform you now, belatedly, that you are not arguing with me, but paraphrases and odd quotes of significance from esteemed professors that know the history of these people probably better than most people ever have, which apart from a few additional comments I made along the way, to give a few more modern references every now and again, the OP is primarily the concise version of the vocal material in the aforementioned documentary.

Then they are wrong, and it's time for another game of name that logical fallacy.

[Kwalish Kid]

Originally Posted by Zeuzzz

Could you word that whole post a bit more scientifically, or educationally, rather than confrontationaly? I don't wan't to argue.I don't want to engage with. I thought we were past ego battles and ad homs here, in the science section?

How is it a personal attack to point out that your claims about Godel's work are incorrect?

It may be a a personal attack to note, based on the large amount of evidence that you have provided in your posts, that you attack scientific claims in ignorance of the evidence for these claims. However, it would be nice for us and for you if you would end this pattern of behavior.

Quote:

Out of interest, are you a cosmologist?

The answer to that question is irrelevant to the disgust I feel seeing your baseless attacks in other threads. Your personal admission of ignorance in one of those threads was pleasing, but your failure to apologize and your dogmatic zeal that the evidence is going to be shown to be wrong are not.

Those would be issues for another thread, though your failure to address my direct points do not bode well for this thread and indicate that you would rather keep your personal dogmas about the foundations of contemporary mathematical logic.

[jsfisher]

Originally Posted by Zeuzzz

Ok. Attempt 2. (I've been up 24 hours now short term memory is going) Turing died inconsequentially to his actions in computation (wrong as they were when applied to Godels, ironically proved by him despite his admirable quest to keep trying).

What parts of Turing's work were "wrong as they were when applied to Godels"? Put your salad spinner away; we were expecting some meat.

Quote:

Boltzmann hung himself in a martyrdom mannor as the larger intellects of the day refused to accept his immaterial atoms "I cannot see, I don’t need it, they do not exist so why we should bring them in the game."

You are ignoring the actually sequence of events. He died some years after his theories were finally accepted. Boltzmann hanged himself because of a bipolar disorder with episodes of deep, deep depression.

So, where's the beef?


By the way, as for Gödel's death, it cannot be classified as suicide (which you did) nor due to being consumed by his work (which you did). And you have still not answered my question. It requested specifics; here it is for your reference:

Quote:

What mistakes of the twentieth century would we be repeating and what dire consequences did they have?

[Gord_in_Toronto]

Originally Posted by Zeuzzz

Did they reference and address Godels theorem? Do you have quotes as to what they said about it?

Yes. Of course they did. They thought they had a complete theory of Mathematics. Gödel proved they were wrong. All three were among the leading mathematicians of the time.

No. In my earlier life I did a fair bit of reading in the history of Mathematics but I am not prepared at this time to go searching the Internet for quotes.

If someone more current on Russell and Gödel wants to chime in, I say go ahead, but otherwise you are on your own.

[Pup]

Originally Posted by ben m

Was that an all-mathematicians insane asylum? If not, maybe Cantor suffered from the same thing that thousands of nonmathematicians suffered from, then and today. He was a human being.

I notice that people have a tendancy to assume all else is normal, unless proven otherwise. It's practical and probably good for survival, but it does make people look for causes in odd places.

So people tend to assume that outlying famous people were otherwise normal, or would have been normal--if not for the one thing that made them famous.

Yet, as you note, the rate of insanity in a population of non-famous people is greater than zero.

I wonder if this tendency is due to the comfort of cause and effect. It's comforting, when one encounters a madman, to be able to think: that won't happen to me, because... and to be able to articulate that cause so clearly. He went mad because he looked into the abyss. If I don't look into the abyss like he did, I won't go mad.

And yet the very reason that one can choose not to look into the abyss, may be because the "madness" isn't already there: there are no demanding voices of schizophrenia, no obsession with patterns and numbers of autism, no drive to work day and night during manic times, no need to keep the mind constantly focussed to kill the mental pain that would otherwise require drugs.

[Kwalish Kid]

I suspect that the causal relationship that many internet crackpots look for is the opposite: they would like to believe that they are mentally ill because they are brilliant.

There really needs to be much greater support for mental illness. It is all too common and all too ignored.

[Perpetual Student]

So, here is the Hollywood version of the history of Gödel, Boltzmann, Turing and Cantor. Zuezzzzzzz, get George Lucas, a screen play writer and John Williams for the music -- this could be your legacy. Perhaps you might grow a beard and audition for the role of Boltzmann. The audiences would be -- well -- zzzzzzzzzzzzz.

[ddt]

Originally Posted by ben m

Was that an all-mathematicians insane asylum?

And it always had room for one more mathematician. Run by David Hilbert.

[ben m]

Originally Posted by Zeuzzz

Ben I hate to inform you now, belatedly, that you are not arguing with me, but paraphrases and odd quotes of significance from esteemed professors that know the history of these people probably better than most people ever have, which apart from a few additional comments I made along the way, to give a few more modern references every now and again, the OP is primarily the concise version of the vocal material in the aforementioned documentary.

If you're quoting them correctly, apparently I disagree with your unnamed experts.

On the other hand, you got this from a documentary? Documentaries often edit together a bunch of soundbites to make an exciting story that runs close to the truth, not to report a sober-but-accurate picture of what the experts believe. "Cantor looked into the abyss of infinity, and was changed forever" or whatever, is a nice stinger quote to pull into your promo, without being an important historical fact to build a thesis statement around and defend using argument-by-authority.

I happen to know the history of Boltzmann and early atomic/kinetic theory fairly well. I know enough about Godel's Theorem (but not his biography) to recognize problems in your use of it.

I am not a cosmologist.

[ben m]

Originally Posted by Perpetual Student

So, here is the Hollywood version of the history of Gödel, Boltzmann, Turing and Cantor. Zuezzzzzzz, get George Lucas, a screen play writer and John Williams for the music -- this could be your legacy. Perhaps you might grow a beard and audition for the role of Boltzmann. The audiences would be -- well -- zzzzzzzzzzzzz.

Hey, they pulled it off for John Nash. Play up the generic interpersonal drama, invent an external, film-able manifestation of the inner turmoil, and you've got a biopic about a mentally ill person. Add ten lines of deep-sound pop-science exposition to establish that your character is brilliant, that makes the whole thing feel highbrow. Whammo! "I'd like to thank the Academy."

Boltzmann? It practically writes itself. Frame story: an elderly Walther Nernst and some Nazis; the rest of the story is flashbacks. Mach as the villain, scheming in smoke-filled rooms. Invent a base motive---jealousy of Henriette. There's a key anagnoresis scene: the camera zooms into Boltzmann's eye, like Anton Ego in Ratattouille, and we see molecules whizzing about.

[Beerina]

Originally Posted by Gord_in_Toronto

"There is a fine line between genius and madness."

IIRC, in Psych 101, they went through a list of common misconceptions, and this was one of them.

[Gord_in_Toronto]

Originally Posted by Beerina

IIRC, in Psych 101, they went through a list of common misconceptions, and this was one of them.

How disappointing.

I'll have to do some more Googling to find the source of the quote. And then have the Time Police go back in time to erase the author.

[Zeuzzz]

Originally Posted by Perpetual Student

So, here is the Hollywood version of the history of Gödel, Boltzmann, Turing and Cantor. Zuezzzzzzz, get George Lucas, a screen play writer and John Williams for the music -- this could be your legacy. Perhaps you might grow a beard and audition for the role of Boltzmann. The audiences would be -- well -- zzzzzzzzzzzzz.

I am sorry for taking the time to post this here then

[Myriad]

Originally Posted by Kwalish Kid

Unsurprisingly, you have this incorrect. What Godel showed was that within an axiomatic system of a certain kind that was strong enough to produce arithmetic, there are statements within that system that cannot be proven to be true and that cannot be proven to be false. These statements do not have to have a definite truth value.

To clarify: Godel's incompleteness proof involves constructing statements that are well-formed within the system in question, and cannot be proven true within the system, but can be proven true via analysis outside the system.

Mere undecidable statements (that cannot be proven true or false at all) are far easier to construct and do not render a formal system incomplete.

Respectfully,
Myriad

[xtifr]

BTW, Turing should really be taken off the list, since his suicide (if it was a suicide--that's probably a question more suited for the CT thread, and not directly relevant here) was attributed to his treatment as a homosexual by the British Government, and had nothing to do with his mathematical prowess.

[Perpetual Student]

Originally Posted by Zeuzzz

I am sorry for taking the time to post this here then

Posting a long winded, unsubstantiated, emotionally laden, collection of sweeping generalities about four important figures in the history of mathematics and physics isn't the best approach to creating a fruitful dialog -- in this forum or elsewhere.