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Subject: Re: Physicists and mathematicians

Author: Peter Fendrich

Date: 03:20:56 08/19/98

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On August 19, 1998 at 03:49:45, Tord Romstad wrote:

>>P.S.  Here is an interesting story about physists and mathematicians....
>>There was a famous physist (I can't remember his name) who claimed to be
>>able to tell a physist from a mathematician by how they answered the
>>following question:
>>  Two brothers live 10 miles apart.  They both leave their houses one day,
>>  at the same time, and walk on a straight line towards one another.  Each
>>  brother is walking at 4 miles an hour.  One brother has a dog who leaves
>>  his house with him.  The dog is running at 8 miles an hour.  When the dog
>>  reaches the other brother, he turns around and goes back to his owner.
>>  When he reaches his owner, he turns around again towards the other brother.
>>  The dog keeps up this back and forth travel between the brothers until they
>>  meet.  How far has the dog traveled?
>>The fellow found that physists will reply with the correct answer instantly,
>>while mathematicians will take several minutes to sum the series before
>>giving the correct answer.  He found this to be an excellent descriminator
>>between physists and mathematicians.
>Being a mathematician myself, I feel slightly offended by this one.  :-)
>I found the "physicist solution" instantly, and I am sure most other
>mathematicians would solve it equally fast.
>My personal experience is that mathematicians are generally much better than
>physicists at spotting "tricks" which solve mathematical problems without
>any calculations.  Most mathematicians I know also dislike calculataing.
>Faced with your problem, a mathematician would instantly see that the
>problem could be solved by summing a geometric series.  However, she would
>not want do go through the labor of actually summing the series, and would
>therefore spend a second looking for a simpler solution.  She would certainly
>be able to find the trick.
>Physicists are usually much better than mathematicians at making concrete
>calculations.  Like the mathematician, the physician would also quickly
>discover that the above problem could be solved by summing a geometric
>series.  The physician, however, having confidence in his abilities to
>calculate quickly and exactly, is much more likely to start summing
>whithout looking for a simpler solution.

I agree with you except I don't think anyone would start summing...

I think the typical physician solution is:
The brothers will meet in 1 1/4 hour.
The dog, runing back and forth, will during that time reach 8 miles/h * 1 1/4 h
= 10 miles

The mathematician approach is in a way more 'lazy' than the physician.
I think the typical mathematician answear would be:
The brothers are reachig each other with a speed of 8 miles/h which is the same
speed as the dog is running.
The dog must run the same distance as the brothers are walking, 10 miles.


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