Re: 3rd Experiment |OR| Infinity
- From: "Joubin Houshyar" <Sun_of_27@xxxxxxxxx>
- Date: 4 Oct 2005 07:38:03 -0700
pfntjux@xxxxxxxxx wrote:
> >Suppose you have a giant vase and a bunch of ping pong balls with an integer written on each one, e.g. just like the lottery, so the balls are numbered 1, 2, 3, ... and so on. At one minute to noon you put balls 1 to 10 in the vase and take out number 1. At half a minute to noon you put balls 11 - 20 in the vase and take out number 2. At one quarter minute to noon you put balls 21 - 30 in the vase and take out number 3. Continue in this fashion. Obviously this is physically impossible, but you get the idea. Now the question is this: At noon, how many ping pong balls are in the vase?
>
> At every step you are adding 10 balls and removing 1. This is the same
> as saying that you are adding 9 balls at every step. If you repeat this
> ad infinitum you end up with an infinite amount of balls in the vase.
> Simple as pie.
>
> The corresponding mathematical expression to find the number of balls
> after the nth step is
>
> 10*n - 1*n
>
> which is obviously the same as 9*n. To find how many balls are there in
> the vase at infinity (or as we approach infinity, as you prefer) we
> take the following limit:
>
> lim n->oo (10*n-1*n)
>
> Well, if you don't simplify 10*n-1*n, you get with an expression oo-oo
> which as we know is *indeterminate*, and which I believe to be the
> hidden cause of the debate.
>
> In the other hand, if we simplify the limit to
>
> limit n->oo 9*n
>
> the answer should be obvious.
>
> Oh, and please carry out the experiment with transparent vases. That
> should help make evident that we are not getting any closer to
> emptiness the more steps we take, and it should help with your friend's
> phobia too (full reference:
> http://groups.google.com/group/sci.math/browse_frm/thread/2ffb3c24245d7803/a80c935e2d7b1c40#a80c935e2d7b1c40
> ).
>
> Cheers,
> --Tech
You are analyzing the original experiments #1 and #2.
The problem at hand is the 3rd experiment as outlined.
I claim my Giant Vase will be found empty on, or, at any time after,
noon. And I have 100 years of unassailable mathematics to "prove" it.
To anyone who claims my Giant Vase contains even a single ball, I
challange you to Name that 'n'! For any 'n' that you can 'Name', I can
pick it out from the pile in front of me.
He has 'demonstrated' that his Giant Vase is NOT empty. And of course
it isn't 'Magic'! He never removed anything from his Giant Vase. Now
what he is claiming is that *my* Giant Vase is not empty and is being
very (very) aggressive about wanting to shake my Giant Vase (which I
refuse on 'Principle'!)
So this is where we are stuck:
If he challanges me to shake my Giant Vase (to prove there are balls in
there) I tell him, "Nonsense! 'Name' the 'n' that you propose is in my
Giant Vase!". And he can't.
If *I* challange him that we did NOT perform the same task afterall,
*he* challanges me "Oh yeah? Then 'Name' the 'n' that you claim is in
your pile in front of you that is NOT in my pile!" And this is where I
am stuck: FOR ANY 'n' that I can 'Name', it is found BOTH in his pile
and my pile!
We both agree that we did NOT perform the 'exact' 'same' operations,
but that they are equivelant.
I've tried to use the *fact* that he does NOT 'Mark' every ball whereas
I do -- obviously NONE of the balls in his Giant Vase are 'Marked' --
but then he smirks and says "Mysticism doesn't suite you. Lets just
stick to math, shall we?"
I've also tried to use the *fact* that his 'partitioning' of the
unit-set -- you know, the 10 un-Marked balls we take out of the Giant
Bag of Balls -- at each step occurs 'Outside' of the Giant Vase (given
his alleged 'phobia' (which now I suspect is just a ruse)), whereas I
do this 'Inside' the Giant Vase. But when I point that out to him, he
starts shaking his head and says "Oh dear! Are we doing Math or
Meta-Physics?"
Finally, I grab at the *last* difference in the situation and tell him
"Ok, since the balls inside of your Giant Vase are not 'Marked', how
would you 'Name' them uniquely given that the pile in front of you is
N?" And that is when he starts laughing like a mad man and says
"HAHAHAH ... Oooh I could 'Name' them, but you wouldn't like it!"
So there we are:
We have taken 'similar' but not identical actions. For any
(arbitrarily large) number of steps 'n', it can be demonstrated that
both our Giant Vases contains the *exact* same number of balls, and, we
both have an *identical* pile of balls marked '1', '2', ..., 'n'.
Then, AFTER the expermient is finished, we have:
2 Giant Vases: one 'demonstrated' to be apparently full of un-Marked
balls; one 'asserted' to be empty.
2 Giant Bags of Balls: both now completely empty.
2 big pile of 'Named' balls: These appear to be 'identical'. (At
least no one has been able to Name an 'n' that is in my pile that is
also NOT in his pile. Further no one (including myself) can come up
with any function that would produce a 'n' that is in my pile but NOT
in his. (Try it.))
So, this guy wears a shirt with a picture of Poincare on the front and
a cryptic "Wot's in 'Name'?" on the back ... just to give you an idea
what I'm dealing with here ... and he has written the following letter
[1] on his Giant Vase. He points to his Giant Vase and says "There is
my Tauf-Nut!" and then start to laugh!
Its very annoying.
/R
Joubin Houshyar
[1]: http://www.njop.org/jsAlephbet/ltr29.gif
.
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- 3rd Experiment |OR| Infinity
- From: Joubin Houshyar
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