An uncountable countable set
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From: Virgil on 20 Oct 2006 13:50 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. > > >> 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! > > > > >>> 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. > > >> 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. > > >>>> 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. > > >>> 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.
From: Tony Orlow on 20 Oct 2006 13:52 cbrown(a)cbrownsystems.com wrote: > Tony Orlow wrote: >> cbrown(a)cbrownsystems.com wrote: >>> Tony Orlow wrote: >>>> cbrown(a)cbrownsystems.com wrote: >>>>> Tony Orlow wrote: >>>>>> cbrown(a)cbrownsystems.com wrote: >>>>>>> Tony Orlow wrote: >>>>>>>> cbrown(a)cbrownsystems.com wrote: >>>>>>>>> Tony Orlow wrote: >>>>>>>>>> cbrown(a)cbrownsystems.com wrote: >>>>>>>>>>> Tony Orlow wrote: >>>>>>>>>>>> cbrown(a)cbrownsystems.com wrote: >>>>>>> <snip> >>> <snipitty-snip> >>> >>>>> Do you accept the above statements, or do you still claim that there is >>>>> /no/ valid proof that ball 15 is not in the vase at t=0? >>>>> >>>> 15 is a specific finite number for which we can state its times of entry >>>> and exit. >>> Agreed, >>> >>>> At its time of exit, balls 16 through 150 reside in the vase. >>> Agreed. >>> >>>> For every finite n in N, upon its removal, 9n balls remain. >>> "upon its removal" = "at the time of ball n's removal"; Agreed. >>> >>>> For every n >>>> e N, there is a finite nonzero number of balls in the vase. >>> "For every n e N, there is a finite non-zero number of balls in the >>> vase at t = -1/n". Agreed. >>> >>>> Every >>>> iteration in the sequence is indexed with an n in N. >>> "Balls are only added or removed at a time t = -1/n for some natual n." >>> Agreed. >>> >>>> Therefore, nowhere >>>> in the sequence... >>> ..., i.e, at no time t such that t = -1/n for some natural n, ... >>> >>>> is there anything other than a finite nonzero number of >>>> balls in the vase. >>> Agreed. >>> >>>> Now, where, specifically, in the fallacy in that argument? >>>> >>> Well, what do you state is the conclusion of this argument? >> You have agreed with everything so far. At every point before noon balls >> remain. > > To be precise, the assertions above all imply that at every time t = > -1/n, where n is a natural number, there are balls in the vase. > > But that *alone* does not even include every time t before noon; let > alone every time t. For example, notice that nowhere above do you or I > /explicitly/ assert: "at t=-2/3, the number of balls in the vase is a > positive finite number". > > We assert something specific about t = -2/4, and something specific > about t = -1/3, but nowhere do we directly state somthing about t = > -2/3. > > On the other hand, given the problem statement, I think we would both > /agree/ that there "should be" an obvious (perhaps even unique) > well-defined answer to the question : "what is the number of balls in > the vase at time t = -1/pi?" > > Assuming in the remaining statements that one agrees with the previous > statement, this leads us to the question: what are the unstated > assumptons that allow to agree that this must be the case? > > I attempted to describe those assumptions in my previoius post. Did you > read those assumptions? If so, do you agree with those assumptions? At this point I don't recall your previous post. I've been off a bit. But, it's obvious that at each point from the first insertion until noon, there are balls in vase, even if the number of balls is not changing at that moment. They accumulate. > >> You claim nothing changes at noon. > > Where, exactly, above do I claim that "nothing changes at noon"? Do you disagree with the other standard-bearers, and claim that something DOES occur at noon? What can happen at noon, when all -1/2^n's occur before noon? > >> Is there something between >> noon and "before noon", when those balls disappeared? If not, then they >> must still be in there. > > In the statements I made to which you are referring, I am responding to > the argument you gave in my previous post; which I naturally assumed > (as it directly followed) was a response to my question: > >>>>> Do you accept the above statements, or do you still claim that there is >>>>> /no/ valid proof that ball 15 is not in the vase at t=0? I said that any specific ball was obviously out of the vase at noon. > > At this point in the post, you had not stated your "nothing changes, so > how can something change?" argument; so it is not surprising that I did > not, at this point in the post, refute it, or even comment in any way > upon it. > > I refuted your identical statement, in the section you snipped. Did you > read it? > I read every post in the thread, when I get to the computer. I don't care to hash over the history of it, but I responded to what you quote above. >>> If the conclusion of this argument is "we cannot therefore state that >>> ball 15 is not in the vase at t=0", I really don't see how you have >>> addressed the issue. You agree that ball 15 is removed, and not put >>> back in the vase at any time before or at noon; and I think you would >>> agree that if if a ball is not put in the vase, it cannot be in the >>> vase. Therefore ball 15 is not in the vase at noon; and nothing you >>> said above challenges the logic of this conclusion. >> Of course not. Ball 15 is gone. >> > > You say here, "of course not", but you previously stated that it is > "not in my purview" to claim /anything at all/ about the state of > affairs at noon; because "noon does not occur". Therefore, we can > conclude that you now retract these statements, is that correct? > The state of affairs with regard to the VASE. Ball 15 is obviously out of the vase. All finitely numbered balls are out. But not before noon. And if the experiment continues UNTIL noon, infinitely-numbered balls are added. There's no way around that. There's nothing in between. >>> If your conclusion is "therefore, at t=0, there must be a finite >>> nonzero number of balls in the vase", then the fallacy is called non >>> sequituur - it doesn't logically follow. >> There must be a nonzero number, unless soemthing occured between "before >> noon" and noon. Is there something between those two? >> > > In light of my observations, why won't you directly address the > validity of your argument as you /actually stated it/ in your previous > post, instead of haring off on some new and unrelated argument? It's all the same argument, with many different disproofs of the standard conclusion. Just answer the question. > > I addressed the question you ask above in the previous post. It does > not provide a well-defined property "change happened to (something) at > some time t". Change in the sta
From: Virgil on 20 Oct 2006 13:53 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.
From: Tony Orlow on 20 Oct 2006 14:05 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.
From: Virgil on 20 Oct 2006 14:08
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. >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. > > > > 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. > 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. > > > > > 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. > 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. > 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. > > > > > 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. |