From: Ronald Raygun 
Subject: Re: Like the Pig/Tattie but Bread instead
Newsgroups: uk.finance
Date: Mon, 13 Feb 2006 13:09:38 GMT

Tim wrote:

>> "Tim" wrote:
>> > Now if A is "100% thinner" than Q, then
>> > A is 100% x 100.0 = 100.0 less "thick",
>>
> "Ronald Raygun" wrote
>> No, it is twice as thin.
> 
> This is your mistake!
> Troy didn't say "twice as thin", he said "100% thinner".

No mistake, these two mean the same thing, in exactly the
same way as 100% thicker means twice as thick, and in the
same way as 100% Q-er means twice as Q for any Q, not just
for "positive" Qs like thick, big, and expensive, but also
for "negative" Qs like thin, small, and cheap, and of course
for things we don't tend to think of in positive and negative
terms, such as resistance and conductivity.

You have to think logarithmically.  Complementary positives
and negatives don't add and subtract, they multiply and divide.
Thin-ness, smallness, and cheapness are *reciprocals* of
thickness, bigness, and expensiveness, in the same way that
conductivity and resistance are reciprocals of each other.

> Now, the process of making something "thinner"
> is by reducing its thickness.

Correct.

> If you reduce its
> thickness by 100%, ie you "make it 100% thinner"
> (as Troy said), then the thickness becomes zero.

It is true that if you reduce its thickness by 100%
then the thickness becomes zero.  But the "ie" bit
inbetween is wrong.

Making something N% less thick is *not* the same thing as
making it N% thinner, not for N=100, nor for any N except N=0.

Making something N% less thick actually makes it M% thinner
where M = 100N/(100-N).  E&OE, but I think I've got the
arithmetic right:

It works for N=M=0, for N=50; M=100, and for, say, N=90; M=900:

Making something 90% less thick makes it 10% as thick, which is
therefore 1000% as thin, which is 900% thinner.

Of course, 100N/(100-N) is *approximately* equal to N, but only
for small N, so making something 1% less thick makes it
approximately 1% thinner.  So it's easy to understand why in
your little fantasy-world you assume that X% less thick means
the same as X% thinner for all X.  But that leads into a quagmire
from which the only way out is to define these things in terms of
reciprocals, and to accept that there is practically no such
thing as zero thin-ness.