Give me ONE digit position of any real that isn't computable up to that digit position!
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From: Jesse F. Hughes on 9 Jun 2010 00:25 Transfer Principle <lwalke3(a)lausd.net> writes: > What I'd love to see is a poster who _fully_ > understands ZFC, perhaps as much or even more than > MoeBlee understands the theory -- yet still doesn't > believe that ZFC is the best theory. I don't know what "best theory" means, but... I think I have a passing familiarity with ZFC, but when I was an active mathematician, I much preferred to work with category theory. Not, mind you, because I thought that ZFC was "wrong" -- or even that such judgments make much sense. Just a matter of taste, really. So, do I count or not? Are you looking for someone with philosophical issues regarding ZFC? I'm not him -- but then the folks you defend rarely have anything properly called philosophical issues either. In any case, I'm sure there *are* some people out there who understand ZFC and yet believe that it is a "bad" theory for some (philosophical) reason. And those folks bear only the most superficial resemblance to the grate branes you defend here on sci.math. -- "If your community has been lying about my research hoping I'd never find a way to prove that with some super dramatic discovery that's almost yanked out of the clear blue because I am a great discoverer then yeah, maybe you should worry."--James S. Harris: great discoverer
From: Jesse F. Hughes on 9 Jun 2010 10:09 Marshall <marshall.spight(a)gmail.com> writes: > On Jun 8, 6:37 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: >> Marshall <marshall.spi...(a)gmail.com> writes: >> > That's right. Uninteresting. The TM is already too simple to be of >> > much interest to me. What is done with it could be done with any model >> > of computation; TMs are adequate for what we do with them but they are >> > horrifically awful by almost any metric I can think of. >> >> They are conceptual simple, a more-or-less straightforward idealised >> model of the way human computers go about computing stuff, as Turing >> clearly explains. This is important when discussing, say, the >> Church-Turing thesis. Other models of computation are better suited for >> other purposes. > > Just as I said. I don't understand your opinion. TMs are simple and flexible and are a model of human computation. They allow us to prove interesting theorems, such as that the Halting Problem is undecidable. I don't see how they can be called uninteresting. They don't do everything. They're not well-suited for modeling an interactive program, for instance, but so what? They are nonetheless interesting for other reasons. To each his own, I guess. -- "Destiny is a funny thing. Once I thought I was destined to become Emperor of Greenland, sole monarch over its 52,000 inhabitants. Then I thought I was destined to build a Polynesian longship in my garage. I was wrong then, but I've got it now." -- The Tick
From: Jesse F. Hughes on 9 Jun 2010 21:21 Transfer Principle <lwalke3(a)lausd.net> writes: > The closest that I've seen to such a poster is Nam > Nguyen, who does appear to be respected more than most > posters challenging standard theory. Nam's considerably more coherent than guys like Herc and AP, but I wouldn't say that he's respected in any reasonable sense of the word. -- "[Criticizing JSH's mathematics will result in] one of the worst debacles in the history of the world. It is foretold in most mythologies and religions. And yes, you are the ones, the cursed ones, who destroy the world." --James S. Harris reads from the Aztec Book of the Damned Mathematicians
From: Jesse F. Hughes on 10 Jun 2010 17:19 Transfer Principle <lwalke3(a)lausd.net> writes: > George Greene pointed out earlier that the idea of > having sets that aren't the same size as their set > of singleton subsets (which I admit is a very > counterintuitive concept) renders NF(U) not worth > considering except theoretically. > > But then again, there may be some posters who > consider Cantor's theorem to be even more > counterintuitive than card(P1(V)) < card(V), and > such posters should be given the choice of having > a set theory with non-Cantorian sets. Who could possibly take that choice away? Has anyone even been criticized for working in NFU? It's nice that you've dedicated your Usenet life to fighting oppression, but I think you ought to find some oppression first. -- Jesse F. Hughes "There are VERY FEW real mathematicians and I am one of them. Few of you can handle the pressure of real mathematics, like being wrong, while I demonstrably can." -- James S. Harris
From: Jesse F. Hughes on 10 Jun 2010 17:28
Transfer Principle <lwalke3(a)lausd.net> writes: > For one thing, the vast majority of posters who do > mention infinitesimals are criticized for doing so. No one is criticized for mentioning infinitesimals. They are criticized for making nonsensical and/or unsupported claims and the like. > MR is the most well-known infinitesimalist here on > sci.math (though currently, MR is posting against > negative numbers, rather in favor of nonzero > infinitesimals like his "smallest quantity"). AP > is another infinitesimalist. TO mentions such > numbers from time to time. RF has his "iota." Mitch does not have a theory *and you know it*. He has a few pronouncements. AP's "theory" is incompletely specified, hopelessly vague and changes every hour or so. Tony has no theory of infinitesimals. He has a few syntactic constructions and that's about it. And Ross has no theory either. > Would any of these posters be open to the smooth > infinitesimals described by McInnes? I can't be > sure of this. For one thing, these infinitesimals > are said to be nilpotent. It's hard to say whether > RF, TO, MR would accept them. AP is unlikely to > accept any infinitesimals that don't have digits, > unless there's way to define digits for these > smooth infinitesimals. Also, I'm not sure whether > any of them want to give up Excluded Middle. > > Still, McInnes has started the type of discussion > that I'd like to see. The response I'd like to > see is one which defends classical analysis > against these smooth infinitesimals -- and I mean > something more like "Smooth infinitesimals are bad > because they contradict LEM" than "There are no > nonzero infinitesimals, and anyone who thinks so > is a --" (five-letter insult). *Neither* of those responses are very sensible. So what if smooth infinitesimals contradict LEM? Why should anyone think that this is by itself a bad thing? And I cannot imagine *any* of the usual posters on this group claiming that every theory involving infinitesimals is crankish. This is just your usual straw man, but he's looking a bit ragged. -- Jesse F. Hughes "He was still there, shiny and blue green and full of sin." -- Philip Marlowe stalks a bluebottle fly in Raymond Chandler's /The Little Sister/ |