ionfish

8 ms·

31.
by ionfish 14y ago
Explanations are not justifications.
32.
by ionfish 14y ago
If it's a biography you want, you'd be better off with John Dawson's one (he is, of course, the author of the article linked at the root).
33.
by ionfish 14y ago
Knowing computer science stuff like regular languages is really not required to understand the incompleteness theorems; grasping first order logic, a little arithmetic and some elementary recursion theory is sufficient. I repeat my objectio
34.
by ionfish 14y ago
Do you have a decent understanding of first order logic? If not, sort that out first. Peter Smith has a good list of books to choose from: http://www.logicmatters.net/2012/05/teach-yourself-logic-1-f... Then get Smith's book An Introduct
35.
by ionfish 14y ago
One of the features of first order logic is that the provability relation is recursively enumerable : given any recursive first order theory, there is a Turing machine that can list every theorem of that theory (although of course it will
36.
by ionfish 14y ago
Right, but the point here is that we're not just talking about extensions of the system, we're talking about true but unprovable statements—that is, statements that are true in the standard model of arithmetic but not provable in PA (or wha
37.
by ionfish 14y ago
'Reducibility' in general is an informal notion, and as such there are many different technically precise ways of capturing aspects of it. Mutual interpretability and bi-interpretability are two of these, but they apply to formal systems wi
38.
by ionfish 14y ago
The Goldstein book is rubbish. Soloman Feferman destroys it in his LRB review. http://www.lrb.co.uk/v28/n03/solomon-feferman/provenly-unpro... http://math.stanford.edu/~feferman/papers/lrb.pdf (full text) "Those who are fascinated by Gö
39.
by ionfish 14y ago
The point must surely be that one can add the these true-but-unprovable statements to the original axioms without contradiction . They fit just fine: they're all elements of Th(N). It's a poor analogy because the natural way of thinking of
40.
by ionfish 14y ago
"I think the point is that if you try to add those unprovable theorems to the system to try to make it complete it becomes inconsistent." Eh? No it doesn't! If you add Con(PA) to the axioms of Peano arithmetic you obtain a stronger system.
41.
by ionfish 14y ago
"It's like an ill-designed jigsaw puzzle. No matter how you arrange the pieces, you'll always end up with some that won't fit in the end." I really don't understand this analogy. The first incompleteness theorem shows that there are stateme
42.
by ionfish 14y ago
Provability is relative to a formal system. Whether there are _absolutely undecidable_ statements is more controversial, and still an open question in the philosophy of mathematics. Gödel's disjunction is part of this literature: "Either …
43.
by ionfish 15y ago
> Last time I looked at Snap, it seemed like variables captured from the url, got mixed into the same environment as key/value pairs from the QUERY_STRING and POST data. This was fixed in the recent 0.8 release. http://snapframework.co
44.
by ionfish 15y ago
The rationale is closer to that behind dazzle camouflage, though—to confuse, rather than to conceal.
45.
by ionfish 15y ago
They do—yours looks unreadably compressed to me.
46.
by ionfish 15y ago
They did. http://en.wikipedia.org/wiki/Wings_of_Hope
47.
by ionfish 15y ago
I paid $10, so you can consider me as having paid for you if it makes you feel better.
48.
by ionfish 15y ago
Hindley and Seldin's Lambda-Calculus and Combinators: An Introduction is pretty solid. http://www.cambridge.org/gb/knowledge/isbn/item1175709/?site...
49.
by ionfish 15y ago
They could have just made a static version with wget.
50.
by ionfish 15y ago
> Don't let your fears and inhibitions turn you into a robot because some interview with Steve Jobs said not to put "powered by..." logos on stuff. Steve Jobs appeared happy enough to have "Designed by Apple in California" inscribed on
51.
by ionfish 15y ago
The position I'm attacking is the claim that it's just obvious that imperative programming is more intuitive, not that it is more intuitive. By exhibiting counterexamples to this supposedly obvious assertion, it's shown that it is not in
52.
by ionfish 15y ago
Another nail in the coffin of the claim that imperative programming is more intuitive, persistently asserted without good evidence. I submit that when people make claims of this sort, what they usually mean is actually "I'm used to doing it
53.
by ionfish 15y ago
"Would have". :)
54.
by ionfish 15y ago
Another sense in which it's not over is the question of what the weakest system is which will prove FLT. Various people have suggested that it should be provable in PA. Colin McLarty has been working on this and has managed to reduce the re
55.
by ionfish 15y ago
I should probably point out that snobbery is very far from the actual attitude towards Tennenbaum, at least as far as logicians are concerned. For example, in 2006 there was a conference organised to celebrate his contribution to mathematic
56.
by ionfish 15y ago
Bohm's theory is a (non-local) hidden-variable interpretation of quantum mechanics with the same empirical predictions. http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory
57.
by ionfish 15y ago
http://www.idlewords.com/2009/09/using_wordpress_to_generate...
58.
by ionfish 15y ago
I can't tell from the site itself, since it's non-responsive (back to WordPress?), but from the comments here it appears the author objects to Jekyll regenerating the entire site every time. If that's the case then I suggest he tries Hakyll
59.
by ionfish 15y ago
I recommend Graham Farmelo's 2009 biography of Dirac, The Strangest Man . http://www.guardian.co.uk/science/2009/apr/02/paul-dirac-str... I once started a physics degree at Bristol, where Dirac was born and raised, and the department mad
60.
My hero: Alan Turing, by Alan Garner(guardian.co.uk)
5 points by ionfish 15y ago|0 comments

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