The reason for this is that it is, in his opinion, too near to reality to be truely generalized. If we hadn't learnt plannar (is that correct?) geometry, but instead applied a different set of rules to a different symbolic universe, somewhat less similar to ours (like a two dimensional one that is actually shaped like a donut, for example), perhaps the tools we have acquired would have been more easily used against other aspects of life, having nothing to do with maths at all.
Yep, he's a mathematician alright. This is *exactly*
how mathematicians think: How can we generalize this
so that it is applicable to other things besides the
traditional applications? Let's define subtraction
entirely in terms of addition, so that if we redefine
addition we have subtraction too, for free. Then
let's develop a new class of numbers (or, if you
prefer, objects) that aren't remotely similar to
traditional natural or real numbers, and then let's
define an "addition" operation on them that's
isomorphic to standard arithmetic addition... we'll
do the same thing for multiplication, and then let's
generalize this whole process so that we can talk about
any given pair of addition/multiplication operatons on
any given set as a Group... then let's take these
Group concepts and apply them to electrical engineering,
art, philosophy, literature, ... anything *but*
arithmetic.
programming provided me with immensely useful tools of abstraction, perception and attitude towards many practical problems.
There are some very strong relationships between
programming and math. I've just been reading
Hofstadter's book <cite>Godel, Escher, Bach: an
Eternal Golden Braid</cite>, and the author (who
really wants to talk about Artificial Intelligence
but has to delve into other areas to make his points)
draws parallels (actually, a full-blown isomorphism)
betweem a formal system in math and a Turing-equivalent
programming language. (In particular, the chapter on
BlooP and FlooP and GlooP is of interest. See also the
notes on my scratchpad about this,
which may or may not eventually become a node.) In
other words, anything that can be done in the one can
be done in the other, though it may be more or less
convenient to do so. All of that to say, programming
and math have a great deal in common, and if one is
applicable to a problem you can expect the other to
be applicable as well. (Well, not quite; some forms
of modern math do not fit into formal systems and so
programming may not be able to handle them. But most
of the math you've probably had up to this point is
probably not in this category.)
Basically... Do you guys think that
programming has as much, or perhaps even more to give
to mind in need of general education, not specific
knowledge, than something like geometry?
You should study the geometry. If you have a mind
for programming, you should be able to enjoy the
geometry as well. If the teachers and textbooks
you've had haven't made it come alive for you, try
to find some other books on the subject that are
more suitable. Yes, the programming has as much
to offer, but the geometry is another way of
looking at things, and the added flexibility of
being able to think in terms of both will be very
beneficial. You should study both -- and if you
enjoy one, it should be possible to enjoy the other
as well, given the right approach. Like I said,
find a different book or a different tutor or
something, but don't give up on math. Math can be
very cool, if you find the right approach to it.