Re: infinity

Jesse F. Hughes said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
>
> > Jesse F. Hughes said:
> >>
> >> I wonder if the following scenario is slightly more palatable to Tony
> >> and crew.
> >>
> >> 11:59 Put an unlabeled ball in.
> >> 12:00 - 2^(-n) min. Put balls 10*n - 9, 10 * 9 - 8, ..., 10 * n
> >> in. Take out ball n.
> >> 12:00 Take out the unlabeled ball.
> >>
> >> Claim: The vase is empty at 12:00:01. The last ball taken out was the
> >> only unlabeled ball put it.
> >>
> >> Proof of claim: One ball put in was unlabeled, but it was removed at
> >> 12:00.
> >>
> >> Each other ball put in was labeled with some number k. It was put in
> >> prior to 12:00 - 2^(-k) and was removed at 12:00 - 2^(-k). Thus,
> >> there are no labeled balls in the vase at noon.
> >>
> >> It is a trivial change to the problem, but it should take away the
> >> silly complaint that a vase can only be empty if the "last" ball is
> >> removed.
> >>
> >> Of course, the same could be done by a simpler fix:
> >>
> >> 12:00 - 2^(-n) min. Put balls 10*n - 9, 10 * 9 - 8, ..., 10 * n
> >> in. Take out ball n + 1.
> >> 12:00 Take out ball 1.
> >>
> > I'm sorry, but that really doesn't help any.
>
> What a remarkably utterly unthoughtful reply.
>
> Half the time, you claim that the vase can't be empty because we never
> remove a "last ball"[1]. So, I fix it so that we remove a last ball.
> How can you complain?
>
> Is it that we didn't remove a second-to-last? And third-to-last? No
> sweat. I'll fix it some more.
>
> 12:00 - 2^(-n) min. Put balls 10*n - 9, 10 * 9 - 8, ..., 10 * n
> in. Take out ball 2n.
> 12:00 + 2^(-n) min Take out ball 2n - 1.
>
> How about that? Now we remove a first, second, third ball...
> and at noon we start removing the ... fourth from last, third from
> last, second from last and last ball. Now surely the vase is empty.
>
> Right, Tony?
>
> Footnotes:
> [1] Of course, you say about another thought experiment that the vase
> *is* empty even though there is no last ball removed.
>
>
You can't demonstrate that the balls we started with originally are all gone
when you remove this "last" ball, so it's really a kludge, and an irrelevant
waste of time. Nice try.
--
Smiles,

Tony
.

Relevant Pages

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