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Did Poincaré anticipate Gödel? (mathpages.com)
83 points by sajid on Feb 18, 2015 | hide | past | web | favorite | 19 comments

In my (vane) attempt at reading Melville's Moby Dick I was struck at some point (Chapter 32: Cetology) by the following sentence, floating in a stormy and rather muddy sea of ramblings and jokes:

"Now the various species of whales need some sort of popular comprehensive classification, if only an easy outline one for the present, hereafter to be filled in all its departments by subsequent laborers. As no better man advances to take this matter in hand, I hereupon offer my own poor endeavors. I promise nothing complete; because any human thing supposed to be complete, must for that very reason infallibly be faulty."

I don't think this is quite analogous. For one, first-order arithmetic doesn't seem a uniquely human invention. Instead, it seems like it is mathematically universal in a certain way—induction is a thing that appears across all sorts of different logics, and is usually tied to a marked increase in logic strength.

And, there are plenty of logics that are complete, like presberger arithmetic; these logics just happen to be weaker than first-order arithmetic.

you mean, vain[1] attempt.

[1] http://public.wsu.edu/~brians/errors/vain.html

Oops. Embarassing, especially since I boasted a few days ago of never misspelling an English word :) Thanks!

And, I did it again :)

I don't know specifically why the article focuses on Poincare and anticipating Godel (it seems like a bit of a stretch).

But Poincare's writings on the philosophy of mathematics and science are really excellent.

link: http://www.gutenberg.org/files/37157/37157-pdf.pdf

English translations of Science and Hypothesis as well as The Measure of Time can be read here;



In French, most of Poincare's original works can be read here;


FYI, Your top two links fail since they're capturing the second quotation mark inside the markup.

Such a marvelous mind. From works quoted in the article, I read Poincaré's "Science et méthode" (in its Spanish translation "Ciencia y método") many years ago, being student. Got shocked, in similar way to when I found Bertrand Russell's works. Brilliant, sharp, elegant, kind, insightful, beautiful, and I'm still short in adjectives. I recommend it to everyone.

It was said that Poincare' was the last person who ever knew all of mathematics.

I don't know, but they both anticipated unicode.

I remember browsing this site before Unicode was even a vague plan. The march of charsets has not been kind to the site. But if you use that as an excuse to sneer and pass over it, you will be missing out on a true unsung gem. At least, if you like math. This is the sort of site that the web was created for in the first place.

I recommend "Reflections on Relativity" if you need a concrete starting place. Here on HN over the years I have wished it would be published at various times, but I am now happy to say I have a physical copy, despite having read it online at least three times before. It was worth it just to see it typeset properly.

UTF-8 is from 1992 (published in January 1993). ISO 8859-1 is from 1985.

Then perhaps rather I should say before anybody knew about it. Fair enough. The world was not running on Unicode until well after this site was established.

Windows NT's first release was 3.1 from 1993. Windows 2000 (which was really NT 5.0) was released in 2000.

I was fully able to write both Gödel and Poincaré with both 8859-1 and HTML entities and in both WordPerfect and Word back in the 90's (the current version of the page is generated by Microsoft Word 10).

The problem is not unicode but the fact that it was written by an American/someone who is rather sloppy with names. For example, he writes "Paul Von Hindenberg" when he means "Paul von Hindenburg". Things like that are trivial to get right unless one actually doesn't care.

If you're going to put the umlaut on the ö, you might as well put the acute accent on the é: Poincaré. Otherwise the e would be silent.

... or if you can't type ö on your keyboard, at least write “oe“ as in Goedel. Just a little hint from a German native here. (Same goes for ae and ue instead of ä and ü).

Interestingly that's getting less common in Scandinavia. It's the "proper" transliteration, but many people with names like Søren prefer to anglicize them as Soren rather than Soeren, if anglicization is needed. Not universally, but it's my impression of the trend.

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