An uncountable countable set
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From: Tony Orlow on 22 Oct 2006 04:57 Virgil wrote: > In article <4539000e(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Virgil wrote: >>> In article <4535884c(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: >>> >>>> Virgil wrote: >>>>> One can separate the reals into everything before 0 as one set and 0 >>>>> and everything after it as the other. Does TO claim time is less >>>>> seperable? >>>>> >>>> Linear time? no. >>> Does TO claim that anything in the statement of the problem justifies an >>> assumption of non-linear time. >>> >> Yes, the fact that each event comes twice as fast as the last. > > Each event is instantaneous. It is only the intervals between events, > during which nothing is happening, that change. Uh, yeah. Should I have used "quickly" instead of "fast"? >>>> Yeah, noon doesn't exist in the description of the problem. It's like >>>> saying, "Everyone on Earth has 3 children which survive, for four >>>> generations, and then half the population of the planet dies. This >>>> happens an infinite number of times. What happens when there is no more >>>> planet?" The question is itself a non-sequitur. >>> One can claim that the vase problem cannot occur in any physical sense, >>> but if one accepts the statement of the problem, the only conclusion >>> which does not require assumptions not inherent in the problem itself is >>> that at noon the vase is empty. >>> >> Incorrect. > > Claimed but not justified. TO's usual technique! You didn't justify yours. It's clearly nonsensical. It pretends there's a time between noon and all times before noon. >>>>> One certainly starts with more balls. At what time do more balls become >>>>> less balls? And why? >>>> When the net addition of nine balls overtakes the mere subtraction of one. >>> Non sequitur. >>> >> Then you'll say I never answered the question.... > > Just so. And yet, I did. >>>> When ALL balls are added, and then balls are ONLY removed, to say that >>>> gives the same result as repeatedly adding more balls than you remove, >>>> that's what's idiotic, to borrow your obnoxious term. >>> When one starts with all infinitely many balls in the vase and then >>> balls are removed on the original schedule, there will be infinitely >>> many in the vase at all times from that group insertion up to but not >>> including noon. >> Yes, that is correct. You get a cookie. > > I delete cookies. I hope you remember all your passwords. >>>>>> You really >>>>>> don't understand the implications of the Zeno machine, do you? >>> As I am not using one, that is irrelevant. >> So, now you're doing it in linear time? Let me know when you're done.... > > It is the problem that uses linear time, 60 seconds to 1 minute, and so > on. The iterations do not occur in linear time. >>>>> I do not understand how having more balls in the vase for longer times >>>>> can produce less balls in the urn at any time. >>>> There is so much you fail to understand, or succeed in misunderstanding, >>>> that I don't even know where to begin with you. If you can't grasp the >>>> logic here, I really don't see any hope for you. >>> I can grasp logic well enough, but from TO I have not seen any. >> You have to step out of the cave to see it in the light, Virgil. They're >> only birds...... > > TO has obviously been standing under those birds at the wrong time too > often. heh heh. good one, Virge.
From: Tony Orlow on 22 Oct 2006 04:58 Virgil wrote: > In article <45390130(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Virgil wrote: >>> In article <453589db(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> As the only important part of that is that each nth ball, for n in N, >>> is inserted before being removed and removed before noon. >>> >>> Absolutely ANY arrangement of insertions and removals satisfying those >>> constraints will leave the vase empty at noon. >> In order for all the naturals to be removed, one has to actually reach >> noon, but reaching noon means adding infinite values to the pot. > > TO misses again. Every value "added to the pot" is finite. If TO meant > infinitely many values, he should have said so. Does anything occur in the vase at noon? If not, then it should have the same state as before noon.
From: Tony Orlow on 22 Oct 2006 05:06 Virgil wrote: > In article <4539050f(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> imaginatorium(a)despammed.com wrote: > >>> Tony, which balls does "those balls" refer to here? >> Your supposed entire set of naturally-numbered balls. You have a >> diverging sum of them at every time before noon, and then at noon the >> sum is 0. > > Actually at every time before noon one only has a finite series or > operations. > Growing linearly without bound, yes. That's a diverging sum. >> So, this subtraction, or whatever, has to have occurred >> sometime between noon, and "before noon". > > It happens over the interval during which balls are being inserted AND > REMOVED. That would be before noon, then. However, at all times before noon, there are balls in the vase. So, it couldn't occur during that time interval. > > >>> You mention *any* time before noon, and we can work out what balls are >>> in the vase, and we can also work out exactly when those balls [refers >>> to the balls earlier in this sentence] will all have been removed, and >>> we know "in advance" that that time of removal will be before noon. So >>> at *no* time before noon will there be any balls in the vase with any >>> chance of lingering after noon. >> At every time before noon there are a growing number of balls in the >> vase. The only way to actually remove all naturally numbered balls from >> the vase is to actually reach noon, in which case you have extended the >> experiment and added infinitely-numbered balls to the vase. > > As WE do not have any infinitely-numbered balls and the problem does not > allow for any either, they must be inserted by TO, so exist only in his > private version. > If we cannot insert infinitely numbered balls, then the experiment cannot continue until time 0=1/2^n, otherwise known as noon. > > >> All >> naturally numbered balls will be gone at that point, but the vase will >> be far from empty. > > But it will be empty of all the balls which we are allowed to count. If we are only allowed to count the finite iterations, then we are not ALLOWED to get to noon. >>> Hmm. So your "those balls" must have been introduced into the vase in >>> this mysterious zone "between before noon and noon". But, see, in >>> mathematics, it's quite clear there is no such zone - here's a proof. >> If there is no such zone, and nothing changes AT noon, then the state >> must be the same as it was immediately BEFORE noon. > > That assumes an unwarranted "continuity". Since the number of balls as a > function of time is already endowed with infinitely many discontinuities > having noon as a cluster point, there is no reason to assume any better > behaviour at noon. Uh, are you saying time itself is not continuous? I suppose if you want to go there you can say anything you like..... > >> If at every time >> before noon there are balls in the vase, then there are still balls in >> the vase, because nothing happened, at noon. > > Assumes "continuity" at a point where continuity cannot occur. > > In time? You have a countably infinite number of balls disappearing in a moment, or even between moments. Can that "occur"? > > >> If something DID happen at >> noon, then it involved infinitely-numbered balls, and the vase has an >> uncountable number of balls. > > Only in TOland. Nowhere else do any such "infinitely-numbered balls" > exist. So, one can have a finitely numbered ball n such that 1/2^n=0? That's a fancy trick. >>> Let B = { t : t is a time, and t is before noon } // the set of all >>> times before noon >>> Let N = {noon} // the singleton set of noon >>> >>> I suggest that if there is a time _between_ before noon and noon, it >>> must be a member of the following set: >>> >>> Let Z = { t : t is a time, t is after b for all b in B, t is before n >>> for all n in N } >>> >>> Do you agree? >>> >>> Would you like to prove that Z is the empty set, just as a little >>> exercise? >>> >>> Brian Chandler >>> http://imaginatorium.org >>> >> Being obnoxious just kinda makes you look dumb, when you agree that the >> idea of "between before noon and noon" is stupid, but fail to see that >> it's a direct consequence of your conclusion regarding the vase. > > What seem to be "direct conclusions" in TO's dreamwold, exist only there. > > In the world as described by the problem, there is no need for any of > TO's dreams. No, just for time discontinuities and denial of the fact that it's a simple infinite series while obfuscating the situation with a Zeno machine, and for what? To sound magical and smart? Oy.
From: Tony Orlow on 22 Oct 2006 05:09 Randy Poe wrote: > Tony Orlow wrote: >> David Marcus wrote: >>> Tony Orlow wrote: >>>> You have agreed with everything so far. At every point before noon balls >>>> remain. You claim nothing changes at noon. Is there something between >>>> noon and "before noon", when those balls disappeared? If not, then they >>>> must still be in there. >>> I thought you just said that the vase doesn't exist at noon. If the vase >>> doesn't exist, how can the balls be in it? >>> >> Either the experiment goes until noon or it doesn't. If all moments are >> naturally indexed, then it doesn't. > > A set of moments is indexed. Those do not constitute > "all moments". The clock ticks between the first and second > insertion, for example, and we do not assign any index to > any moment in that interval. > > - Randy > So? Are you suggesting that something happens between all naturals having been processed, and noon? Is there such a time between x and less than x? All balls are processed at finite times BEFORE noon, at which times there are a growing but finite number of balls in the vase. What happens AT noon? Nothing.
From: Tony Orlow on 22 Oct 2006 05:12
Virgil wrote: > In article <45390fcc(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > >> Either the experiment goes until noon or it doesn't. If all moments are >> naturally indexed, then it doesn't. > > So that natural indexing won't work. The balls are NUMBERED WITH NATURALS! Are you daft? But time indexing with > discontinuous values at each transition and at noon does. Yeah, time discontinuities. No added assumptions there. That explains it all. Throw in Ross' golems and I'm starting to believe... |