Doubling Zero?

Date: 02/13/2007 at 06:19:07
From: Claire
Subject: (no subject)

I have a student who asked, "What is twice as cold as zero?"

Date: 02/13/2007 at 09:29:46
From: Doctor Ian
Subject: Re: 

Hi Claire,

It's not really a sensible concept, because temperature is a relative
measurement, not an absolute one (like length, or mass).  

What you CAN sensibly ask is something like:

  In the _____ scale, what temperature is twice as 
  far from zero degrees as _____ degrees?

For example, it makes sense to say that 

  In the Celsius scale, 48 degrees is twice as far 
  from 0 degrees as 24 degrees.  

But that doesn't make it "twice as hot".  When asked this way, you can
say that

  In the Celsius scale, 0 degrees is twice as far 
  from 0 degrees as 0 degrees.  

But this doesn't mean that 0 is "twice as cold" as zero.

The real lesson here is that just because you can form a question that
is grammatical, that doesn't mean the question makes sense, or has an
answer.  

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 02/14/2007 at 00:36:26
From: Claire
Subject: Thank you ((no subject))

Thank you - that makes sense!!!