|
|
In article <45476529@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
> David R Tribble wrote:
> > David R Tribble wrote:
> >>> Each ball n is placed into the vase at time 2^int(n/10), and then later
> >>> removed at time n. This happens for every ball before noon. So every
> >>> ball is inserted and then later removed from the vase before noon.
> >>>
> >>> At any given time n before noon, ten balls are added to the vase and
> >>> then ball n (which was added to the vase in a previous step) is
> >>> removed. Your entire confusion results from assuming a "last" time
> >>> prior to noon, but there is no such time.
> >
> > Tony Orlow wrote:
> >> At no time prior to noon are all balls removed. Nor are any removed at
> >> noon. It cannot be empty, then.
> >
> > The problem states that every ball (every ball) is added to the vase
> > and then later removed from the vase.
>
> It states the specific times of those events, which imply that there are
> always more balls added than removed at any time.
Such a statement need not imply any such thing.
And there is no statement in the problem which denies that each ball
inserted before noon is also removed before noon.
>
> >
> > We conclude from this that every ball is removed (eventually).
>
> Yes, you conclude an end to the unending set by compressing events at a
> point in time so they cannot be distinguished and the difference between
> in and out is hidden. Whoopedy doo. It's a parlor trick.
That TO does not understand something may make it a parlor trick to him,
but need not make it so to anyone of greater comprehension.
>
> > You conclude that at no time are all balls removed.
>
> There is no finite t<0 when all balls have been removed. Agree?
>
> There are no balls removed at t=0. Agree?
Note how TO carefully avoids the point, which is whether there are any
balls which have not been removed by t = 0.
> > Obviously you think that there are balls left in the vase that never
> > got removed. In fact, you say that there are an infinitude of balls
> > left in the vase. Yet somehow you cannot name a single one of them.
> >
>
> I can, as soon as you tell me how many you inserted to begin with.
> Multiply that by 9/10 and you have an answer.
Since we claim that every ball inserted before noon has been removed by
noon, and the gedankenexperiment confirms this, the number of balls
inserted is irrelevant.
> Except that you can't,
> because what you're doing is not math, but Zeno-esque logic trick.
To those like TO, who do not understand math, most of math seems like
tricks. But their blissful ignorance is still ignorance.
|
|