Date: Jan 1, 2013 8:18 PM
Author: Joe Niederberger
Subject: Re: A Point on Understanding

PT III says:
>To provide the reader with some context so that he or she can see Keith Devlin meant, to see that he is not confused at all, here is part of what Keith Devlin actually wrote:
>"What Exactly is Multiplication?"

This is pretty funny and I can't pass it up. Following the above ref. to one of Keithe's columns, we find:
Keith D. says:
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The MIRA fallacy becomes very apparent when you consider my second example, where I take an elastic band of length 7.5 inches and stretch it by a factor of 3.8. The final length of the band is 28.5 inches. But what are the units? What goes after the number 3.8 in the calculation

[3.8 - - -] x [7.5 INCHES] = 28.5 INCHES ?

The answer is nothing. It has no units. In this case, the 3.8 is a dimensionless scaling factor.
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He is writing far too fast here to consider his words. If no units are involved ("it has no units") then stretched inches of rubber band and un-stretched must be exactly the same to any commercial buyer. Same with puffed rice and uncooked rice. An inch is an inch. A cup is a cup. If I sell you 1000 yards stretched inches of rubber band you have no recourse if you expected 1000 yards UN-stretched. The very "nature of multiplication" declares you have no case!

Very funny indeed.

Joe N