Is Geometry 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?

Is there absolute zero in math? In real life?

Is there such a thing as a false equation?

Is math a science?

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