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Kurt Gödel’s Brilliant Madness

59 points by DevilMadeMeDoIT 5y ago

kruxigt 5y ago
Paywall sux.
1cvmask 5y ago
Crazy to see that he was perpetually afraid of being poisoned and starved himself to death.
- bidirectional 5y ago
  I just find it bizarre that one of the greatest minds of the 20th century starved to death, weighing 65 lbs, in late 70s Princeton. I realise there's no easy way to counteract someone determined not to eat, but it just seems like such a slow, painful and irrational way to die that it's hard to fathom (obviously driven by severe mental illness).
  - de6u99er 5y ago
    Sounds completely insane, but from what I can see is that insanity and genius often go hand in hand.
- ProfHewitt 5y ago
  Seems to have been an occupational hazard. For example, Cantor, Boltzmann, and Turing ended similarly :-( For for more information, see the film "Dangerous Knowledge" by David Malone on BBC Two.
lqet 5y ago
Great read. > Kurt Gödel, only a year beyond his PhD, announced a result which would forever change the foundations of mathematics. He formalized the liar paradox, "This statement is false" to prove roughly that for any effectively axiomatized consistent extension T of number theory (Peano arithmetic) there is a sentence σ which asserts its own unprovability in T. John von Neumann, who was in the audience immediately understood the importance of Gödel's incompleteness theorem. [...] > In the next few weeks von Neumann realized that by arithmetizing the proof of Gödel's first theorem, one could prove an even better one, that no such formal system T could prove its own consistency. A few weeks later he brought his proof to Gödel, who thanked him and informed him politely that he had already submitted the second incompleteness theorem for publication.
- ProfHewitt 5y ago
  Actually, [Gödel 1931] claimed that the incompleteness result was for Russell's Principia Mathematica, which is much stronger than a first-order theory of the natural numbers. Also, Gödel's incompleteness result was not for the liar paradox. Instead, it was for the proposition I'mUnprovable, which [Gödel 1931] claimed to have constructed. However, [Wittgenstein 1937-1944] showed that I'mUnprovable leads to inconsistency in the foundations of mathematics. Fortunately, I'mUnprovable cannot be constructed in foundations because the attempted construction violates order on propositions. Furthermore, Gödel did not have a proof of the second incompleteness result at the time he wrote to von Neumann [von Plato 2018]. von Neumann never realized the deception by Gödel because it was discovered after both had died.
UncleOxidant 5y ago
As an anxious person who deals with hypochondria and germaphobia I could relate to some of this (I have in the past also kept journals of my temperature taken several times per day, for example). That he was able to achieve what he did in spite of all of these mental health obstacles is all the more amazing. > “you simply cannot […] find the concentration necessary for research if you read twice a day [about] things […] which touch the basis of the civilization of your country as well as your personal existence”. Kind of feels like the recent couple of years in the US. Only we don't just get news twice a day, we're constantly inundated with it. The same advice is given now, only it includes not just avoiding the news but also social media - in my experience it's pretty essential advice.
joe_the_user 5y ago
The thing about mathematics and logic is that logic went from being a branch of philosophy to a branch of mathematics and once logic was formalized it could then be described in terms of mechanical calculation. The proof of the halting problem took less than a page in my college text on Language, Automata and Machines and some version of the proof of Gödel's Incompleteness Theorem take little more space. But that's now that the properties of computation are well established and can be hand-waved away. So a lot of what Kurt Gödel did was follow a fairly inevitable progression before anyone else. And it is one of those ironies the result, that the-provable and the truth are far apart, did not please such a brilliant idealist. Edit: From wikipedia: "Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics (Ferreirós 2001, p. 443). "Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last [nineteenth] century with the aid of an artificial notation and a rigorously deductive method."[3] Before this emergence, logic was studied with rhetoric, with calculationes,[4] through the syllogism, and with philosophy. " https://en.wikipedia.org/wiki/Mathematical_logic#History https://en.wikipedia.org/wiki/Mathematical_logic#History
- stainforth 5y ago
  >before anyone else I read a tweet recently that seemed to summarize Kant as having done something similar for knowledge, and I immediately thought of Godel's incompleteness theorem. Obviously I don't claim to fully understand full threads of their works, but found the connection interesting (and Kant finally accessible perhaps) https://philosophy.stackexchange.com/questions/31633/was-kant-anticipating-g%C3%B6dels-incompleteness-in-his-antinomies https://philosophy.stackexchange.com/questions/31633/was-kan... https://www.cairn.info/revue-internationale-de-philosophie-2005-4-page-491.htm https://www.cairn.info/revue-internationale-de-philosophie-2...
nobodyandproud 5y ago
Adele Thusnelda Porkert: An absolute hero in the world of math and science. I remember reading some short bios that (with a wink and nod) mentioned Godel had a relationship with a cabaret dancer. I remember absolutely detesting it. Making a life with a genius, obsessive compulsive individual doesn’t seem very easy to say the least. Nevermind the importance of the individual to society, and the implied responsibility that came with it.
ProfHewitt 5y ago
Gödel did have some grounds for paranoia. Wittgenstein [1937-1944] had shown that Gödel failed to prove incompleteness of the foundations of mathematics. Gödel was aware of this failure but tried to bluff past it claiming that his incompleteness result was not for the foundations of mathematics. Contrary to [Gödel 1931], he claimed decades later that his result was for a limited first-order theory of the natural numbers [Wang 1987]. However, the failure may have secretly weighed on his mind. There is more information here: "Gödel failed to prove inferential undecidablity or incompleteness in foundations" https://professorhewitt.blogspot.com/2021/03/godel-failed-to-prove-inferential.html https://professorhewitt.blogspot.com/2021/03/godel-failed-to...

kruxigt 5y ago

Paywall sux.

1cvmask 5y ago

Crazy to see that he was perpetually afraid of being poisoned and starved himself to death.

bidirectional 5y ago
I just find it bizarre that one of the greatest minds of the 20th century starved to death, weighing 65 lbs, in late 70s Princeton. I realise there's no easy way to counteract someone determined not to eat, but it just seems like such a slow, painful and irrational way to die that it's hard to fathom (obviously driven by severe mental illness).
- de6u99er 5y ago
  Sounds completely insane, but from what I can see is that insanity and genius often go hand in hand.
ProfHewitt 5y ago
Seems to have been an occupational hazard. For example, Cantor, Boltzmann, and Turing ended similarly :-( For for more information, see the film "Dangerous Knowledge" by David Malone on BBC Two.

lqet 5y ago

Great read. > Kurt Gödel, only a year beyond his PhD, announced a result which would forever change the foundations of mathematics. He formalized the liar paradox, "This statement is false" to prove roughly that for any effectively axiomatized consistent extension T of number theory (Peano arithmetic) there is a sentence σ which asserts its own unprovability in T. John von Neumann, who was in the audience immediately understood the importance of Gödel's incompleteness theorem. [...] > In the next few weeks von Neumann realized that by arithmetizing the proof of Gödel's first theorem, one could prove an even better one, that no such formal system T could prove its own consistency. A few weeks later he brought his proof to Gödel, who thanked him and informed him politely that he had already submitted the second incompleteness theorem for publication.

ProfHewitt 5y ago
Actually, [Gödel 1931] claimed that the incompleteness result was for Russell's Principia Mathematica, which is much stronger than a first-order theory of the natural numbers. Also, Gödel's incompleteness result was not for the liar paradox. Instead, it was for the proposition I'mUnprovable, which [Gödel 1931] claimed to have constructed. However, [Wittgenstein 1937-1944] showed that I'mUnprovable leads to inconsistency in the foundations of mathematics. Fortunately, I'mUnprovable cannot be constructed in foundations because the attempted construction violates order on propositions. Furthermore, Gödel did not have a proof of the second incompleteness result at the time he wrote to von Neumann [von Plato 2018]. von Neumann never realized the deception by Gödel because it was discovered after both had died.

UncleOxidant 5y ago

As an anxious person who deals with hypochondria and germaphobia I could relate to some of this (I have in the past also kept journals of my temperature taken several times per day, for example). That he was able to achieve what he did in spite of all of these mental health obstacles is all the more amazing. > “you simply cannot […] find the concentration necessary for research if you read twice a day [about] things […] which touch the basis of the civilization of your country as well as your personal existence”. Kind of feels like the recent couple of years in the US. Only we don't just get news twice a day, we're constantly inundated with it. The same advice is given now, only it includes not just avoiding the news but also social media - in my experience it's pretty essential advice.

joe_the_user 5y ago

The thing about mathematics and logic is that logic went from being a branch of philosophy to a branch of mathematics and once logic was formalized it could then be described in terms of mechanical calculation. The proof of the halting problem took less than a page in my college text on Language, Automata and Machines and some version of the proof of Gödel's Incompleteness Theorem take little more space. But that's now that the properties of computation are well established and can be hand-waved away. So a lot of what Kurt Gödel did was follow a fairly inevitable progression before anyone else. And it is one of those ironies the result, that the-provable and the truth are far apart, did not please such a brilliant idealist. Edit: From wikipedia: "Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics (Ferreirós 2001, p. 443). "Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last [nineteenth] century with the aid of an artificial notation and a rigorously deductive method."[3] Before this emergence, logic was studied with rhetoric, with calculationes,[4] through the syllogism, and with philosophy. " https://en.wikipedia.org/wiki/Mathematical_logic#History https://en.wikipedia.org/wiki/Mathematical_logic#History

stainforth 5y ago
>before anyone else I read a tweet recently that seemed to summarize Kant as having done something similar for knowledge, and I immediately thought of Godel's incompleteness theorem. Obviously I don't claim to fully understand full threads of their works, but found the connection interesting (and Kant finally accessible perhaps) https://philosophy.stackexchange.com/questions/31633/was-kant-anticipating-g%C3%B6dels-incompleteness-in-his-antinomies https://philosophy.stackexchange.com/questions/31633/was-kan... https://www.cairn.info/revue-internationale-de-philosophie-2005-4-page-491.htm https://www.cairn.info/revue-internationale-de-philosophie-2...

nobodyandproud 5y ago

Adele Thusnelda Porkert: An absolute hero in the world of math and science. I remember reading some short bios that (with a wink and nod) mentioned Godel had a relationship with a cabaret dancer. I remember absolutely detesting it. Making a life with a genius, obsessive compulsive individual doesn’t seem very easy to say the least. Nevermind the importance of the individual to society, and the implied responsibility that came with it.

ProfHewitt 5y ago

Gödel did have some grounds for paranoia. Wittgenstein [1937-1944] had shown that Gödel failed to prove incompleteness of the foundations of mathematics. Gödel was aware of this failure but tried to bluff past it claiming that his incompleteness result was not for the foundations of mathematics. Contrary to [Gödel 1931], he claimed decades later that his result was for a limited first-order theory of the natural numbers [Wang 1987]. However, the failure may have secretly weighed on his mind. There is more information here: "Gödel failed to prove inferential undecidablity or incompleteness in foundations" https://professorhewitt.blogspot.com/2021/03/godel-failed-to-prove-inferential.html https://professorhewitt.blogspot.com/2021/03/godel-failed-to...