An uncountable countable set
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From: Randy Poe on 27 Sep 2006 16:00 Tony Orlow wrote: > Randy Poe wrote: > > Tony Orlow wrote: > >> Randy Poe wrote: > >>> 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. > >>> > >> But, you do say it fills, > > > > Probably not. I wouldn't know how to describe "full" > > for an infinite vase. > > > >> or empties, right? > > > > It definitely empties, since every ball you put in is > > later taken out. > > So, it definitely empties...... Yes. > >> And, at the same time you > >> say it does not do so at noon, nor does it do so before noon. When does > >> this occur? > > > > It doesn't. > > ...but it doesn't! > > Wow, that's deep. Math is cool. Cool? Yes. Deep? I dunno. As I said, this is reasoning that I didn't have a major struggle with at the age of about 10. > > There is no last ball, so I wouldn't say there's > > a point where the nonexistent last ball goes in, nor > > would I say there's a full state corresponding to the > > nonexistent last ball. > > Oh definitely not. I mean, definitely. Or not. > > > > > So the reason I don't say it's full "an infinitesimal time > > before noon" or "some other time before noon" is that > > I don't say it's full. > > But, you do say it's full or empty, right? :| So your conclusion from my statement that I would never say it's full is that sometimes I would say it's full? Is this like when I say there's no last element of N, you agree, and then you say, "so at the last element of N..."? Let me try to make it more clear. I don't say it's full. Never, never, never. - Randy
From: Virgil on 27 Sep 2006 16:09 In article <451ad7e9(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451a891f(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> 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. > >> There is no science without mathematics, if that's what you mean. > > > > There are certainly areas of study which call themselves sciences which > > are at most peripherally mathematical, such as much of psychology. > > Psychology (and I've studied it a bit) is only a science to the extent > that it employs analysis. That depends on your definition of 'a science'. There is nothing in my definition of 'a science' that requires mathematics (or that bars it either). > Most cognitive science uses at least > statistics in order to establish any kind of certainty in its findings. > I don't consider Freudian Analysis to be science. Do you?
From: Randy Poe on 27 Sep 2006 16:10 On rereading this, I think there was some confusion. Whether through Tony deliberately misquoting, or a misunderstanding on my part or Tony's, I'm not sure which. But Tony seems to have conflated a statement I made about emptying with one about filling. Tony Orlow wrote: > Randy Poe wrote: This was about emptying: > > It definitely empties, since every ball you put in is > > later taken out. > > So, it definitely empties...... > > > > >> And, at the same time you > >> say it does not do so at noon, nor does it do so before noon. When does > >> this occur? > > This was about "filling" when I said it: > > It doesn't. > > ...but it doesn't! What I would say about emptying is that the vase is empty at noon, but there is no identifiable time before noon at which we can say "the last ball was taken out then". At any time before noon, there are balls in the vase. There is no time we can say "there goes the last ball out" since there is no last ball in. - Randy
From: Tony Orlow on 27 Sep 2006 22:17 Virgil wrote: > In article <451a8f41(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Virgil wrote: >>> In article <45193e6f(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>> Well, Han, I'm not sure I agree with the statement that reconciliation >>>> is hopeless. Is it hopeless to reconcile the wave nature of elementary >>>> entities with their particle nature? >>> >>> It is close to hopeless to expect those who reject the law of the >>> excluded middle (constructionists) and those who insist on it >>> (formalists) to agree. >>> >> If neither can appreciate the other's point, perhaps. Some christians >> get along quite well with some muslims. > > Only by agreeing to disagree. Or, by noting the many similarities and few differences between them. There's not much difference between a good christian and a good muslim. >> The question boils down to whether 0^0 is 1. > > 0^0 is, in any particular context, what it is defined to be. > There are contexts in which it is more useful to have it mean 1 and > others where it is more useful to have it mean 0. > > But...but...but how can you reconcile those two answers??? :o In which contexts do you find it more convenient for it to be 0? > > >>>> There is confusion about my "definition" of infinitesimals, because I >>>> can see the validity both in nilpotent infinitesimals and in those that >>>> are further infinitely divisible. >>> Until TO can come up with an axiom system which simultaneously allows >>> his infinitesimals to be both nilpotent and not, he is in trouble. >>> >> For purposes of measure on the finite scale, infinitesimals can be >> considered nilpotent. That's all. Do you disagree? > > I disagree that scale changes can convert between zero and non-zero. Infinite scale changes can. > > There are approximation methods is which products of small quantities > are regarded as negligible in comparison to the quantities themselves, > but they are always just approximations. Sure, but how negligible are those products? Like I said, there were terms in my infinitesimal sections of moving staircase which differed by a sub-infinitesimal from those in the original staircase. So, they could be considered to be two infinitesimally different objects in the limit. But, dropping just those terms, the two were identical. So, sure, they were "approximately" equal in the limit. By the same token, I think 0.999... is just an approximation of 1 as well. :) Tony
From: Tony Orlow on 27 Sep 2006 22:25
Randy Poe wrote: > Tony Orlow wrote: >> Randy Poe wrote: >>> Tony Orlow wrote: >>>> Randy Poe wrote: >>>>> 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. >>>>> >>>> But, you do say it fills, >>> Probably not. I wouldn't know how to describe "full" >>> for an infinite vase. >>> >>>> or empties, right? >>> It definitely empties, since every ball you put in is >>> later taken out. >> So, it definitely empties...... > > Yes. > >>>> And, at the same time you >>>> say it does not do so at noon, nor does it do so before noon. When does >>>> this occur? >>> It doesn't. >> ...but it doesn't! >> >> Wow, that's deep. Math is cool. > > Cool? Yes. > > Deep? I dunno. As I said, this is reasoning that I didn't > have a major struggle with at the age of about 10. Are you paying attention? You said it definitely empties, but it doesn't. If it does, it doesn't do it before noon, nor after noon, nor does it do it at noon. So, it doesn't empty? Do you even know what you're saying? You must have been a strange 10 year old, like that kid down the block that used to pull the legs off of roaches. > >>> There is no last ball, so I wouldn't say there's >>> a point where the nonexistent last ball goes in, nor >>> would I say there's a full state corresponding to the >>> nonexistent last ball. >> Oh definitely not. I mean, definitely. Or not. >> >>> So the reason I don't say it's full "an infinitesimal time >>> before noon" or "some other time before noon" is that >>> I don't say it's full. >> But, you do say it's full or empty, right? :| > > So your conclusion from my statement that I would never > say it's full is that sometimes I would say it's full? Uh, you would say it contains an infinite number of balls in some circumstances, as I understand it. If you say it empties, then you would agree that it either fills or it empties. When does it empty? You say, not before noon. You also say this does not occur at noon, but after noon there are no balls left. So when does this occur? > > Is this like when I say there's no last element of N, you > agree, and then you say, "so at the last element of N..."? > > Let me try to make it more clear. I don't say it's full. > Never, never, never. > > - Randy > Fine. When does it empty. At noon? Does the limit exist or not? |