Re: Peano's space-filling curve

From: Daniel Grubb (grubb_at_lola.math.niu.edu)
Date: 06/09/04 

Date: 9 Jun 2004 18:16:04 GMT

>> Please note that I'm _not_ saying that you should
>> _believe_ us because we're Mathematicians! Simply
>> not believing the things we say is in some sense
>> a reasonable option. But if you simply didn't
>> believe us it's hard to see why you keep asking
>> us about these things...

>Ahh. There's the rub, and time for explanations. You
>of all people certainly deserve them.

>Primarily, because I want to understand. Because
>it (maths) fascinates me. The way its total non-worldliness,
>nevertheless, invades every aspect of the real world. Also
>it bugs me that there are things that I don't know about or
>can't comprehend. And the only kind of knowledge I can have
>any respect for is that which I understand.

This attitude is perhaps one of your best qualities. The desire
to understand is fundamental, in my mind. Unlike many other
areas, mathematics takes quite a bit of careful study and
awareness of subtleties to really understand what is going on.
Jargon is mainly important because it clarifies which particular
concept is being used. This is, possibly unfortunately, unavoidable
in an area where closely related concepts may have *very* different
properties. This will also be true of many of the 'hard' sciences.

Feynman told of a situation where someone claimed that she couldn't
talk about physics because nobody understands it. His reply was
that she couldn't talk about *because* some people understand it.
In areas that nobody really understands, everyone is able to say
something that sounds reasonable and get a following. But in areas
that *are* understood, the terminology has progressed to the point
that only those well-trained can use it correctly.

--Dan Grubb