An uncountable countable set
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From: Tony Orlow on 26 Sep 2006 10:54 Randy Poe wrote: > Tony Orlow wrote: >> Virgil wrote: >>> In article <45189d2a(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: >>> >>>> Virgil wrote: >>>>> In article <45187409(a)news2.lightlink.com>, >>>>> Tony Orlow <tony(a)lightlink.com> wrote: >>>> If so, then why do you say "There is no >>>> infinite case"? >>> Because there isn't any. >> There is no noon in the Zeno machine? > > There's no ball put in at noon in the Zeno machine. > > All cases, all Zeno balls, are put in before noon. > > - Randy > At any time finitely before noon, only a finite number of balls have been processed. Do you disagree? Are you suggesting that the vase fills at some *infinitesimal* amount of time before noon? How does that differ, in your view, from being *at* noon? Tony
From: Randy Poe on 26 Sep 2006 11:08 Tony Orlow wrote: > Randy Poe wrote: > > Tony Orlow wrote: > >> Virgil wrote: > >>> In article <45189d2a(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>>> Virgil wrote: > >>>>> In article <45187409(a)news2.lightlink.com>, > >>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>> If so, then why do you say "There is no > >>>> infinite case"? > >>> Because there isn't any. > >> There is no noon in the Zeno machine? > > > > There's no ball put in at noon in the Zeno machine. > > > > All cases, all Zeno balls, are put in before noon. > > > > - Randy > > > > At any time finitely before noon, only a finite number of balls have > been processed. Do you disagree? I agree. > Are you suggesting that the vase fills > at some *infinitesimal* amount of time before noon? No. There is no time before noon when the vase is full. Let t be any time before noon. Infinitely many balls will be inserted into the vase after t, but before noon. > How does that differ, in your view, from being *at* noon? Well since I also don't say "it fills at an infinitesimal time before noon", there is no need to distinguish one nonsensical statement from the other. - Randy
From: Virgil on 26 Sep 2006 14:23 In article <6e5c2$4518da26$82a1e228$6365(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Tony Orlow wrote: > > > Han de Bruijn wrote: > >> > >> I may be rude sometimes, but I never get _personal_ by calling somebody > >> an "idiot" or a "crank". Tony's "babbling" translates with Euroglot as > >> "babbelen" in Dutch, which is a word I can use here in the conversation > >> with my collegues without making them very angry (if I say "volgens mij > >> babbel je maar wat"). But, of course, I cannot judge the precise impact > >> of the word in English. Apologies if it is heavier than I thought. > > > > Do you have the saying, "Shallow brooks babble, and still waters run > > deep"? I figured you picked up the usage from this forum, actually. It's > > meant, in English, to mean you aren't making any sense. :) > > I have talked to my collegues and they have told me that "babbling" in > English indeed has a meaning which is somewhat different from "babbelen" > in Dutch. It is more like our "lallen", to be translated in English as > "talking while you are drunk". Is that correct ? > > "Babbelen" in Dutch is more like "having a nice chat". It's not that it > doesn't make any sense, but it's not very deep either. It's more social > than intellectual. > > > Math=Science? > > Definitely, yes! Only if science is a subset of mathematics.
From: Virgil on 26 Sep 2006 14:25 In article <93e90$4518db88$82a1e228$7258(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > Scientists, particularly those in the sciences most dependent on > > mathematics, tend to think that all mathematics is, or should be, a > > subservient to their particular fragment of science. > > > > Mathematicians know better. > > I have suggested a proper place for mathematics in: > > http://hdebruijn.soo.dto.tudelft.nl/QED/klassiek.htm > > What do you think, Virgil? I think that, despite the efforts of scientists to strangle the inependence of mathematics, it will survive independently.
From: Virgil on 26 Sep 2006 14:30
In article <8e5ca$4518e13e$82a1e228$9429(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Tony Orlow wrote: > > > Virgil wrote: > >> > >> Mathematicians know better. > > > > Define "better". Those that work in various areas of science share a > > notion which defines science. Theories which have no means of > > verification are not science, but philosophy. In mathematics, > > verification really consists of corroboration by other means, agreement > > between different approaches. In science, where you find a contradiction > > with your theory, it needs revision. So, the scientific approach to > > mathematics requires some criterion for universal consistency, as > > measured by the predictions of the various theories that comprise it. > > Where two theories collide, one or both is in error. I think that's better. > > Precisely ! In mathematics, there are contradictory approaches, such as > constructivism (Brouwer) against axiomatism (Hilbert). Its practicioners > are asked to be "nice" to each other and to "reconciliate" the different > points of view, which turns out to be a hopeless task. Such a situation > would be unthinkable if mathematics aimed to be a science. Therefore mathematics cannot ever be a science, or a part of science. In science, one must always pick one 'theory' over all others, but in mathematics, that is neither necessary nor necessarily desirable. |