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Tony Orlow wrote:
> Randy Poe wrote:
> > Tony Orlow wrote:
> >> David Marcus wrote:
> >>> Tony Orlow wrote:
> >>>> David Marcus wrote:
> >>>>> Tony Orlow wrote:
> >>>>>> David Marcus wrote:
> >>>>>>> Tony Orlow wrote:
> >>>>>>>> David Marcus wrote:
> >>>>>>>>> Tony Orlow wrote:
> >>>>>>>>>> David Marcus wrote:
> >>>>>>>>>>> Tony Orlow wrote:
> >>>>>>>>>>>> Mike Kelly wrote:
> >>>>>>>>>>>>> Now correct me if I'm wrong, but I think you agreed that every
> >>>>>>>>>>>>> "specific" ball has been removed before noon. And indeed the
> >>>>>>>>>>>>> problem
> >>>>>>>>>>>>> statement doesn't mention any "non-specific" balls, so it seems
> >>>>>>>>>>>>> that
> >>>>>>>>>>>>> the vase must be empty. However, you believe that in order to
> >>>>>>>>>>>>> "reach
> >>>>>>>>>>>>> noon" one must have iterations where "non specific" balls
> >>>>>>>>>>>>> without
> >>>>>>>>>>>>> natural numbers are inserted into the vase and thus, if the
> >>>>>>>>>>>>> problem
> >>>>>>>>>>>>> makes sense and "noon" is meaningful, the vase is non-empty at
> >>>>>>>>>>>>> noon. Is
> >>>>>>>>>>>>> this a fair summary of your position?
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> If so, I'd like to make clear that I have no idea in the world
> >>>>>>>>>>>>> why you
> >>>>>>>>>>>>> hold such a notion. It seems utterly illogical to me and it
> >>>>>>>>>>>>> baffles me
> >>>>>>>>>>>>> why you hold to it so doggedly. So, I'd like to try and
> >>>>>>>>>>>>> understand why
> >>>>>>>>>>>>> you think that it is the case. If you can explain it cogently,
> >>>>>>>>>>>>> maybe
> >>>>>>>>>>>>> I'll be convinced that you make sense. And maybe if you can't
> >>>>>>>>>>>>> explain,
> >>>>>>>>>>>>> you'll admit that you might be wrong?
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> Let's start simply so there is less room for mutual
> >>>>>>>>>>>>> incomprehension.
> >>>>>>>>>>>>> Let's imagine a new experiment. In this experiment, we have the
> >>>>>>>>>>>>> same
> >>>>>>>>>>>>> infinite vase and the same infinite set of balls with natural
> >>>>>>>>>>>>> numbers
> >>>>>>>>>>>>> on them. Let's call the time one minute to noon -1 and noon 0.
> >>>>>>>>>>>>> Note
> >>>>>>>>>>>>> that time is a real-valued variable that can have any real
> >>>>>>>>>>>>> value. At
> >>>>>>>>>>>>> time -1/n we insert ball n into the vase.
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> My question : what do you think is in the vase at noon?
> >>>>>>>>>>>> A countable infinity of balls.
> >>>>>>>>>>> So, "noon exists" in this case, even though nothing happens at
> >>>>>>>>>>> noon.
> >>>>>>>>>> Not really, but there is a big difference between this and the
> >>>>>>>>>> original
> >>>>>>>>>> experiment. If noon did exist here as the time of any event
> >>>>>>>>>> (insertion),
> >>>>>>>>>> then you would have an UNcountably infinite set of balls.
> >>>>>>>>>> Presumably,
> >>>>>>>>>> given only naturals, such that nothing is inserted at noon, by
> >>>>>>>>>> noon all
> >>>>>>>>>> naturals have been inserted, for the countable infinity. Then
> >>>>>>>>>> insertions
> >>>>>>>>>> stop, and the vase has what it has. The issue with the original
> >>>>>>>>>> problem
> >>>>>>>>>> is that, if it empties, it has to have done it before noon, because
> >>>>>>>>>> nothing happens at noon. You conclude there is a change of state
> >>>>>>>>>> when
> >>>>>>>>>> nothing happens. I conclude there is not.
> >>>>>>>>> So, noon doesn't exist in this case either?
> >>>>>>>> Nothing happens at noon, and as long as there is no claim that
> >>>>>>>> anything
> >>>>>>>> happens at noon, then there is no problem. Before noon there was an
> >>>>>>>> unboundedly large but finite number of balls. At noon, it is the
> >>>>>>>> same.
> >>>>>>> So, noon does exist in this case?
> >>>>>> Since the existence of noon does not require any further events, it's a
> >>>>>> moot point. As I think about it, no, noon does not exist in this
> >>>>>> problem
> >>>>>> either, as the time of any event, since nothing is removed at noon. It
> >>>>>> is also not required for any conclusion, except perhaps that there are
> >>>>>> uncountably many balls, rather than only countably many. But, there are
> >>>>>> only countably many balls, so, no, noon is not part of the problem
> >>>>>> here.
> >>>>>> As we approach noon, the limit is 0. We don't reach noon.
> >>>>> To recap, we add ball n at time -1/n. We don't remove any balls. With
> >>>>> this setup, you conclude that noon does not exist. Is this correct?
> >>>> I conclude that nothing occurs at noon in the vase, and there are
> >>>> countably, that is, potentially but not actually, infinitely many balls
> >>>> in the vase. No n in N completes N.
> >>> Sorry, but I'm not sure what you are saying. Are you saying that what I
> >>> wrote is correct or are you saying it is not correct? I'll repeat the
> >>> question:
> >>>
> >>> We add ball n at time -1/n. We don't remove any balls. With
> >>> this setup, you conclude that noon does not exist. Is this correct?
> >>> Please answer "yes" or "no".
> >>>
> >> What do YOU mean by "exist"? Does anything happen which is proscribed if
> >> noon DOES arrive? No, not in this case. So, noon case "exist" or not.
> >
> > There is no event at noon. There is no "noon case". But you
> > seem to be saying that arrival of the actual time of noon, everywhere
> > in the world, is somehow controlled by how we define a certain set
> > of events.
> >
> > If you mean is there an event at noon, then say so. Don't say
> > "noon doesn't happen".
> >
> > There's an event at -60 seconds. The next event is at -30 seconds.
> > There's no event at -50 seconds. But would you really say
> > "-50 is proscribed in this experiment" or "-50 doesn't exist"?
> >
> >> In
> >> the other case, the vase also does not empty before noon, and nothing
> >> happens at noon. So, then, why do you conjecture that it's empty AT noon?
> >
> > In the absence of any events happening at noon, we need to
> > define what is meant by "number of balls in the vase at noon".
> >
> > We define that as "number of balls which have been inserted
> > at t<=noon and not removed".
> >
> > Forget calling this the "number of balls in the vase at noon". That
> > bothers you. Will you allow us to discuss "the set of balls which
> > have been inserted but not removed?"
> >
> > - Randy
> >
>
> I have seen and understood your argument. It "makes sense". It seems
> logical. All balls are inserted and removed before noon, the same set,
> it would seem. But the method of proof is not correct.
Why? What are you basing this assertion on? That you don't agree with
the conclusion?
--
mike.
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