Absolute Zero

Date: 10/24/2001 at 12:18:11
From: Megan Garcia
Subject: Absolute zero

Our math teacher and our language arts teachers have been debating on 
if there is such thing as absolute zero. They are talking about 
absolute zero in math, but I would also like to know if there is
absolute zero in real life.

Megan

Date: 10/25/2001 at 10:11:57
From: Doctor Ian
Subject: Re: Absolute zero

Hi Megan,

Zero _is_ absolute, in the sense that a number is either zero, or it's 
not.  

Zero has properties that are not shared by any other number. For 
example, for any number x, it's true that 

  0 * x = 0

  0 + x = x

  x / 0 = undefined

These properties are not shared by any other number, even numbers that 
are 'close' to zero.  

But it's possible that your teachers are using 'absolute' in a 
different sense. For example, in the world, 'position' is not 
absolute, in the sense that it always has to be measured relative to 
some other position.  

If you have a GPS device, it might tell you that you're at latitude 
57 degrees, 27 minutes, 36.3 seconds north; longitude, 127 degrees, 
44 minutes, 29.1 seconds west; and elevation 147 feet above sea 
level... but that just tells you where you are relative to a 
particular coordinate system fixed to the earth. So, where is the 
earth? Well, an astronomer might give you some coordinates relative to 
the sun... but where is the sun? Well, it's in some location relative 
to the center of our galaxy. But where is our galaxy? It's in some 
location relative to a galactic cluster. But where is that cluster?  
Do you see the problem?    

In this sense, you could argue that zero is not 'absolute', in the 
sense that you can always shift a coordinate system (including a 
number line) to a new location; and the location of 'zero' in the old 
system would be somewhere other than at 'zero' in the new system.  

For example, the GPS device I mentioned earlier considers the center 
of the earth to be at the point (0,0,0). However, a different 
coordinate system would consider the center of the sun to be (0,0,0).  
Neither system is more 'correct' than the other. Each is useful for 
some calculations (for example, finding the distance between Chicago 
and Peoria), and not so useful for others (for example, finding the 
distance between two stars). 

But this has more to do with a particular way in which numbers can be 
_represented_, and not with numbers themselves. Numbers can be used to 
label points in a coordinate system, but they are _not_ points in a 
coordinate system. 

It turns out that in most conversations of this nature, the 
participants are talking nonsense without realizing it, largely 
because they haven't properly defined their terms. 

In _Surely You're Joking, Mr. Feynman_, Richard Feynman tells a 
wonderful story about a philosophy seminar that he attended, in which 
the participants were discussing Alfred North Whitehead's theory of 
'essential objects'.  After they'd been talking for a while, someone 
asked Feynman if he thought that an electron would be considered an 
'essential object', according to Whitehead's definition.  Feynman 
hadn't really been paying attention, so he decided to ask a question 
of his own, which would help him figure out what they'd been talking 
about.

He asked: "Is a brick an essential object?" He was going to ask a 
followup question - "Is the _inside_ of a brick an essential object?" 
- and then argue that an electron is like the inside of a brick, in 
the sense that we _know_ that they exist, but no one has ever really 
seen one. (You can't see the inside of a brick, because if you break 
the brick in two, you just have two new bricks, and you can only see 
their outsides!)

Anyway, he never got to ask the followup question, because it turned 
out that the philosophers at the seminar couldn't agree on whether a 
brick was an essential object! Some said yes, some said no, and they 
all had different explanations for their answers. In other words, 
they'd been tossing the phrase around without really understanding 
what they meant by it. 

(By the way, it's a very funny book, and you should probably read it 
if you get the chance.) 

People - not just philosophers! - do this quite a lot, when they talk 
about nebulous concepts like 'love' and 'justice' and 'fairness' and 
'peace'.  Without knowing anything else about the discussion that your 
teachers have been having, I'd guess that this is more or less what 
they're doing, too.  

There is a great scene in Kurt Vonnegut's book, _Cat's Cradle_, in
which a hard-core scientist is arguing with his secretary about truth.
He challenges her to say something that is absolutely true, and she
responds by saying "God is love." He looks at her and asks, "What is
'God'? What is 'love'?" 

This is the essence of philosophical exposition, as practiced in the
West. You choose two words whose definitions aren't agreed upon by
anyone, and then proceed to claim that there is some necessary
relationship between their referents:      

  Zero [is | is not] absolute.

What is 'zero'?  What is 'absolute'?

Does this help?  Write back if you'd like to talk about this some more 
(the more you can tell me about what they've said, the more light I'll 
be able to shed on this), or if you have any other questions. 

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