DIFFERENTIABILITY AND CONTINUITY

[Nick Thompson]

Nonsense!  I DID, Too.  See below.

the formula for the relationship between the angle of vision and the angle
of the optimal dive is a "simulation" of the process by which the
kingfisher determines the angle of its dive.  

You're SUCH a bully, Rudolph.  

Nick

> [Original Message]
> From: <lrudolph at black.clarku.edu>
> To: <nickthompson at earthlink.net>; <jkennison at clarku.edu>
> Cc: David Joyce <djoyce at clarku.edu>
> Date: 7/26/2007 5:02:46 PM
> Subject: RE: DIFFERENTIABILITY AND CONTINUITY
>
> You haven't answered my question: what do you
> suppose algebra to be a simulation, or model, OF?
>
> If you mean no more than the banal truth that algebra
> can be used as a generic tool in many different
> simulations, say so.  If you do mean something
> else, say WHAT.
>
> On 26 Jul 2007 at 15:59, Nicholas Thompson wrote:
>
> > 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.
> > >
> >
> >
>