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From: ags@pucc-i (Seaman)
Newsgroups: net.puzzle
Subject: Re: Balls in the bowl: Final word.
Message-ID: <227@pucc-i>
Date: Wed, 29-Feb-84 11:48:43 EST
Article-I.D.: pucc-i.227
Posted: Wed Feb 29 11:48:43 1984
Date-Received: Fri, 2-Mar-84 06:24:08 EST
References: <220@pucc-i> <178@hou2g.UUCP>, <224@pucc-i> <181@hou2g.UUCP>
Organization: Purdue University Computing Center
Lines: 56

>> Your arguments show quite convincingly that the limit of the number of balls
>> in the bowl, as time-->noon, is infinity.
>> 
>> What makes you think the ACTUAL number of balls in the bowl at noon has
>> anything to do with the limit?  ...
>
>Well, because the limit is the only meaningfull way of getting a unique answer.
>Dave's technique of numbering terms in the series can be used to generate any
>final result you want because it is an invalid operation.
----------------------------------------------------------------------------

You can't choose a method simply because it is the only way to get an
answer you like.  The method also has to make sense.  Your approach sounds
rather like a creationist trying to defend his religious beliefs.

(Flames to net.religion, please -- where I won't see them.)

Your suggested modification of the problem (one ball in and one ball out
each time) DOES give a unique answer of zero balls in the bowl at noon,
despite the fact that the LIMIT is undefined  -- more evidence that the
limit is irrelevant here.  Please explain to me how the numbered-balls 
argument can be used to arrive at any answer other than zero for this 
version of the problem:  If the first ball in is numbered "1", then the 
first ball out is also numbered "1", simply because no other balls are 
available.

The numbered-balls argument gives an ambiguous answer to the (100 in, 1 out)
problem because the PROBLEM is faulty, not because the ANALYSIS is faulty.

Consider the following variation on the (100 in, 1 out) problem:  The balls
are not numbered, but ONE of the first group of balls is green.  All other
balls are red.

Question:  Is the green ball still in the bowl at noon?

Question:  Does it make a difference if the green ball is not known to
	   be one of the first 100 to go in?

Question:  Suppose there are N green balls.  How many of them are in the
	   bowl at noon?

Question:  Suppose one of each group of 100 balls is green.  How many green
	   balls are in the bowl at noon?

***

Dudley Moore:  "But those questions don't make any sense!"
Questioner:    "Correct."
		- NOVA program "It's About Time" (PBS)
-- 

Dave Seaman
..!pur-ee!pucc-i:ags

"Against people who give vent to their loquacity 
by extraneous bombastic circumlocution."