Is Geometry a Language?

Date: 01/28/2002 at 11:43:10
From: Jordan
Subject: Geometry is a language?

I'm doing a math unit on geometry in school, and I have to write an 
essay to defend or criticize the statement, "Geometry is a Language."  
I really don't understand what they're asking, and I don't know how to 
defend or criticize it. What would you say?  Is geometry a language?  
How would I explain whether or not geometry is a language?  

Thanks in advance for your help.

Sincerely,
Jordan

Date: 01/28/2002 at 12:33:42
From: Doctor Ian
Subject: Re: Geometry is a language?

Hi Jordan,

Suppose I wanted to investigate the question: Is a frying pan a 
vehicle? 

One way that I might go about that would be to make it very clear what 
I mean by 'frying pan' and 'vehicle', and then compare the definitions 
to see how much they overlap. 

For example, by 'vehicle' I might mean 'any agent of transmission', 
which would be a pretty broad definition. It would include viruses 
(which transmit diseases), books (which transmit ideas), and more 
traditional objects like cars and boats and planes. Or I might limit 
the definition to objects that are used to convey other physical 
objects.  

By 'frying pan', I might mean any metal pan in a certain range of 
sizes, with a flat bottom and a certain kind of handle, blah, blah, 
blah. 

Having done those two things, I would be in a much better position to 
consider the question: Is a frying pan a vehicle?  (Note that by 
limiting my definitions, I can avoid the need to consider questions 
like whether an image of a frying pan might be used to 'convey' some 
kind of metaphor. On the other hand, if one of my goals is to fill as 
many pages as possible, I would want to remove limits rather than 
adding them.) 

In considering that question, one of the first things that would occur 
to me is that a yes-or-no answer wouldn't be all that useful, which 
would suggest that I should rephrase the question slightly: To what 
extent is a frying pan a vehicle? 

Clearly, I can carry things in a frying pan, even if that's not the 
traditional use. On the other hand, if I cook an omelet and bring it 
to the table in the pan, it's not much of a stretch at all to say that 
I'm _using_ the frying pan as a vehicle, which isn't quite the same 
thing as saying that a frying pan _is_ a vehicle.  Do you see the 
difference?  

(It's a subtle difference, which is one of the reasons that there are 
so many comical stories making the rounds just now involving airport 
security. Is a ball-point pen a weapon? Not really, although it can 
certainly be _used_ as one in a pinch. What about a bottle? A broken 
piece of glass is sharper than many knives. Or a guitar string, which 
could be used as a garrote?)

Anyway, I would probably end up saying something like "A frying pan 
can be used as a vehicle in much the same way that _anything_ that can 
be used as a container can be used as a vehicle (since a vehicle is, 
in a sense, just a moving container), but it's not a particularly good 
example of a vehicle," inflating that answer to whatever size is 
necessary for the paper. 

You could go through these same kinds of steps to decide to what 
extent geometry is a language. What is geometry? What is a language?  
How much overlap is there? I would probably pay special attention to 
this question: What kinds of things is a language typically called 
upon to do that can't be done by geometry, and vice versa? 

For some examples of how to go about clarifying questions like 'Is 
geometry a language?', you might want to look at these items from our 
archive: 

  Was mathematics invented or discovered?
  http://mathforum.org/dr.math/problems/angela.1.1.01.html   

  Is there absolute zero in math?  In real life? 
  http://mathforum.org/dr.math/problems/megan2.10.24.01.html   

  Is there such a thing as a false equation? 
  http://mathforum.org/dr.math/problems/rheanna.2.12.01.html   

  Is math a science? 
  http://mathforum.org/dr.math/problems/rouzier.03.18.01.html   

I hope this helps.  Write back if you'd like to talk about this some 
more, or if you have any other questions. 

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