DIFFERENTIABILITY AND CONTINUITY

[Nick Thompson]

THERE YOU GO AGAIN!

So you BUY my notion that the algebra in the kingfisher example IS
simulation?

VERY interesting.   I never expected to get to first base with THAT one.

Nick

> [Original Message]
> From: <lrudolph at black.clarku.edu>
> To: <jkennison at clarku.edu>; <nickthompson at earthlink.net>
> Cc: David Joyce <djoyce at clarku.edu>; <friam at redfish.com>
> Date: 7/27/2007 4:15:38 AM
> Subject: RE: DIFFERENTIABILITY AND CONTINUITY
>
> Your original question was "In what way is algebra
> NOT a simulation?"  Pressed to give meaning to
> that question, you gave one example in which an
> algebraic formula was used in a simulation.  That
> was unresponsive and, dare I bullyingly say, really
> stupid.  I can give you millions of examples in
> which algebra is used where no "simulation" is
> apparent: for instance, the quadratic formula.
>
> In what way is the algebra in the quadratic
> formula "a simulation"?  If it is "a simulation",
> WHAT IS  BEING SIMULATED?
>
> To fix ideas, let me specify precisely what I
> mean, here, by "the quadratic formula".
> Let A, B, and C be three complex numbers,
> with A not equal to 0.  Then a complex
> number Z satisfies the equation
> AZ^2 + BZ + C = 0 if and only if
> Z = (sqrt(B^2-4AC))/2A, where the
> expression sqrt(B^2-4AC) signifies
> one of the at most two (and at least
> one) complex numbers W such that
> W^2 = B^2-4AC.  
>
> What is being simulated there?
> (Not, what *could be* simulated
> by a clever person; what *is*
> being simulated?)  And in what way?
>
>
> > 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.
> > > > >
> > > >
> > > >
> > >
> >
> >
>