OK. I will bite. A sumulation is a model, i.e., a process or object that
stands in for another less well understood process or object in an attempt
to understand the latter. You know that drawing that has the king fisher
calculating the angle of refraction of the water to figure out how to dive
for the fish? That would be a simulation. It would also be algebra.
I think I know what you are going to say, but I will let you say it.
nick
> [Original Message]
> From: <lrudolph at black.clarku.edu>
> To: John F. Kennison <JKennison at clarku.edu>; <friam at redfish.com>;
<nickthompson at earthlink.net>
> Cc: Lee N. Rudolph <LRudolph at clarku.edu>; David Joyce <djoyce at clarku.edu>
> Date: 7/26/2007 3:01:37 PM
> Subject: RE: DIFFERENTIABILITY AND CONTINUITY
>
> > In what way is
> > algebra NOT a simulation?
>
> What do you suppose it to be a "simulation" *of*?
>
> Historically, perhaps, you could say it arose as a
> "simulation" of physical operations with physical
> objects. von Uexkull seemed to believe that counting
> is a simulation of one's own heartbeat, and then
> the natural numbers (which are an abstraction from
> counting) might be called a simulation of the heartbeat
> once removed. The first great strides in really
> popularizing what we'd now call "algebraic notation"
> (for arithmetic) arose out of *bookkeeping*, itself an
> abstraction of an abstraction, right? If you take
> simulation to be a type of abstraction (or vice versa,
> I suppose), then we could say that algebra originated
> in simulation. But that's irrelevant to either what it
> "is", or how it's actually used now. Of all the "pure
> and applied algebra" that appears in what may be
> John's favorite journal (which bears that name),
> that which is "applied" I would guess is 90%
> "applied" only to other mathematical concerns.
> It's true that physicists (who are a very strange
> bunch, with very odd ideas, and who really seem
> to have no better understanding of mathematics
> than psychologists, though they are usually much
> more confident about it and good at manipulations;
> Feynman, for instance, was a poor mathematician)
> often tend to adopt one mathematical thing or another
> (usually for a brief time), and that often those things
> are algebraic; for a decade now there's been quite a
> flush of applications of Dave Joyce's "quandles",
> some of which are allegedly to physics. But they
> still aren't SIMULATING anything, in any sense that
> I can see.
>
> Lee
>
> PS I'm keeping friam at redfish.com in the To: header,
> but I know that I'm not a subscriber so this won't
> get to them unless you make it get to them. Up
> to you.
>
Locked
