what is computer math?

[kirby urner]

In a thread here recently the discussion turned

to the = operator ("equals"), and the role it plays

in computer languages to "assign a name to"
as in Let x = 3.  This is in contradistinction to

comparing or equating values, an operation
with a True or False outcome (unless the very
act of comparing is somehow verboten).  For
such comparison, == may be used, as in x==y.

In algebra we get to ask:  what would x have to
be to make this equation true?  x is asked to

"satisfy" some equation.  Later, a whole cast
may be asked to bring satisfaction to a whole

"system of equations".  This is where our concept
of "algorithm" enters in i.e. if there's a way to
squeeze actual solutions from this puzzle, by

turning some wheels as it were, we want to
know about it.

Here I'd say computer math does not substitute
for human genius in actually discovering some
algorithms.  The computer becomes the recording
device for recording the step-by-step routines,

once the beginning inputs are known, the para-
meters of a given equation.  The computer is
the new executor for the algorithm, not someone
paid "to compute" i.e. we no longer hirer based
on mental arithmetic skills as a spreadsheet or

other electronic computing context is assumed.
We have been relieved of that responsibility, as
far as business is concerned.

Another distinction I think computer math brings,
is a sense of being in a location yourself, as a

user or participant.  You have an avatar or a
footprint as a "self" in this picture.  One might
object that simple programs of the type y = F(x)
are not "place aware", but when we go to "save"
a "piece of code" the idea of "storage" appears,
and we have a "current directory" in that "storage
space".

The two points link together: x = 3 as "assigning"
and living in a "you are here" geography for "saving"
or "storing" the creations of your mathematics. 

In mathematics, there's no economy of "memory"
or "saving" a thing.  The "real number" are just
"there" (where?) and don't need to be regarded
as persisting in some medium, along with character
strings. 

In computer mathematics, to say x = 3 is to allocate

memory for some new fact in the world and the
language itself has concern for this memory and
its eventual limitations.  Memory "goes away"
when the computer turns off and so "permanent
storage" becomes an issue.  All concerns these
concerns are alien to non-computer mathematics,

which has library science at its beck and call.

Very similarly, when rendering an XYZ coordinate

system in terms of a scene description language
such as POVray's, one must define the position
of the camera i.e. the viewpoint from which the
scene is seen. 

In contrast, non-computer mathematics pays

no attention to any "observer" of its content in
a rather general sense.  Storage / retrieval of

mathematical writings is considered the domain
of "library science" not math itself.  Computer
programs, on the other hand, may be intimately
involved with matters of their own storage,

including what encoding should be used -- all

alien to mathematics, which takes place in this
science fiction "no energy / no observer" realm

of the Platonic imagination.

Kirby