What were Einstein and Gödel talking about? (2005)(newyorker.com) |
What were Einstein and Gödel talking about? (2005)(newyorker.com) |
[Article] > He believed in ghosts; he had a morbid dread of being poisoned by refrigerator gases; he refused to go out when certain distinguished mathematicians were in town, apparently out of concern that they might try to kill him. “Every chaos is a wrong appearance,” he insisted—the paranoiac’s first axiom.
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[Book] > Gödel believed in ghosts; he had a morbid dread of being poisoned by refrigerator gases; he refused to go out when certain distinguished mathematicians were in town, apparently because he feared that they would try to kill him. Gödel said, "Every chaos is a wrong appearance."
This is kind of a bummer too, because the article was a wonderful read, and it actually flows a lot better than the text in the book. However, it does appear that a lot of the article is a re-wording of what's in the book, just weaved together into a better flow.
EDIT: Based on the other replies, I may have things reversed. It may be that the book is ripping off the article.
Hey, AI, who was the first author of those words? Email me, when you wake up. Thanks.
After his wife couldn't make his food anymore, because he trusted only her.
Somehow I find that both sweet and tragic at the same time. That a man can be that paranoid and yet trust someone so completely.
It seems like this ordinary world is not enough for the genius, so their brains make new worlds and new scenarios (like "you get poisoned if you eat other people's food.")
Sounds to me like Einstein suffered from a bit of imposter syndrome.
I can't believe the New Yorker can't typeset superscripts. The equation might be the most famous of all, but sometimes it's also the most misinterpreted and mistyped.
I wonder how this relates to the refrigerator design Einstein worked on, "motivated by contemporary newspaper reports of a Berlin family who had been killed when a seal in their refrigerator failed and leaked toxic fumes into their home":
https://en.m.wikipedia.org/wiki/Einstein_refrigerator#Histor...
It's not nearly as clear-cut. It's not the trendy theory du jour, of course, but it's an idea that perennially re-emerges in Physics circles. For a famous modern proponent (whose view is arguably even more radical), see Max Tegmark.
> When you are famous it is hard to work on small problems.
> The Institute for Advanced Study in Princeton, in my opinion, has ruined more good scientists than any institution has created, judged by what they did before they came and judged by what they did after. Not that they weren't good afterwards, but they were superb before they got there and were only good afterwards.
tl;dr Gödel came up with an alternate model of the Universe but Einstein didn't like it. Gödel starved himself to death after Einstein died.
In typical New Yorker fashion it assumes you have never heard of platonism, formal logic or 20th century physics but assumes you remember the future conjugations of regular latin verbs.
"If time travel is possible, he submitted, then time itself is impossible. A past that can be revisited has not really passed. And the fact that the actual universe is expanding, rather than rotating, is irrelevant. Time, like God, is either necessary or nothing; if it disappears in one possible universe, it is undermined in every possible universe, including our own."
For a much more intuitive explanation as to why consciousness is not algorithmic, I recommend "The Neural Basis of Free Will" by Tse. His argument is that neurons and neuronal circuits (and more) harness randomness to provide inputs to "criterial detectors" which are satisfied when the right combinations of inputs (spatiotemporal patterns) arrive at the detector at the right time. This can't be algorithmic, because of the requisite noise in the inputs and because the brain realizes true parallel processing. As a further note, he posits that free will is realized in the resetting of the input weights, so "current" actions set up the criteria for future actions avoiding the issue of causa sui in free will.
A simulation of a brain or some set of neurons is an algorithm, as are algorithms that use nondeterminism or that simulate parallelism.
Perhaps this is a Turing test for consciousness. "I can't prove this, but I've been thinking about these theorems [inserts true but unprovable list of theorems] and I think they're true".
A lazily evaluated, natively parallelized stochastic lambda calculus with Church-like query operators is still merely probabilistic-Turing-complete.
Arrrrrgh now you've got my CS401 knowledge screaming that someone is wrong on the internet.
You could write a computer program to generate random propositions, and test those logically against known truths. After enough testing, the program could assert that propositions not disproven are true. Voila! You have a computer program that has "arrived" at truths outside of a logical system. Some of those truths will be wrong, and some will be right, much like humans and their "truths" that are not based on logical reasoning.
If you've never encountered a human claim to "see" the truth of something that turns out to be false, well, it happens... a lot.
The topic of Einstein and Godel seems to have been in the air in 2005. (Edit: 100 year anniversary of SR publication?)
A "true but unprovable" Goedel statement is true in standard models of arithmetic but untrue in certain nonstandard models. The "incompleteness" is syntactic, not semantic. The real and complex numbers, AFAIK, only have one model, up to isomorphism.
And sometimes statements are difficult to prove because they're actually independent of the foundational system. Or because a counterexample exists somewhere.
"This problem is unresolved, therefore it's a Goedel Statement within our current foundational system" is extraordinarily unlikely. For one thing, that would imply that we could figure out the axiom we're missing and pass to the stronger system capable of resolving the conjecture straightaway, or that starting from some stronger foundation like homotopy type theory would resolve the conjecture right-away. Most unresolved conjectures are not unresolved for lack of proof-theoretic strength in our foundations.
A test requires that you be able to produce an artifact which is witness to the results -- what could you produce as the result of the test to distinguish between a true, but unprovable theorem and a nearly true theorem with a single (very, very, VERY) large counter-example?
So true and so well put - And I love the New Yorker. If I use this phrase in the future should I attribute it to you (although "according to gumby" might not fly so well with my other New Yorker aficionados).
[+] The referenced Kliban cartoon seems quintessentially New Yorker Magazine material but as far as I know he never appeared in it.