Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site pucc-i Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!inuxc!pur-ee!CS-Mordred!Pucc-H:Pucc-I:ags 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."