Flatness

[Timothy C. May]

Bonnie Surfus wrote:
> 
> I have mentioned this before and got little response.  Actually, there is 
> soemthing called an "eigenfunction" that has do with the non-differential 
> equations, attractors, and chaotica sytsems.  I am not yet sure what an 
> eigenfunction is--only saw it referenced in a book on strange attractors 
> and chaotic evolutions (by David Ruelle.)
...
> On Fri, 24 Feb 1995, James W. 
> Horton wrote:
...
> > This is something that might already be obvious to you if you are 
> > studying harmonic motion, (I haven't) but I understand there is such 
> > a thing as an Eigenvalue (as in the psychodontist) Number or Eigenvalue 
> > Equation which has to do with the oscillation of crystals.

Eigenvectors, eigenfunctions, and eigenvalues are just basic terms out
of "matrix" theory (matrix in this sense being the rectangular or n x
m arrays of values, a mathematical term--and matrices can be in n
dimensions, lest the quibblers correct my n x m example!).

The use in differential equations, quantum mechanics, chaos theory,
etc., etc., comes because matrices are the basic way _transformations_
(aka operators) are used. Cf. any encyclopedia article on matrices,
eigenvectors, etc.

I don't recally Pynchon's use...perhaps I saw it considered it
unremarkable. Pynchon, having worked for Boeing and obviously being
familiar with physics, was probably able to use it transparently.

In many transformations, such as distortions (squeezings,
compressions), one vector (direction) may get mapped into the same
direction, albeit of different length. (I could show this more
easily at a blackboard.) These vectors that maintain their direction
are called eigenvectors. (A German term, originally.) The coefficient
for their length is the eigenvalue.

About 5 minutes of explanation with pictures will burn this idea into
nearly anyone's mind forever.

Though this may not have been Pynchon's use, one could somewhat
obscurely use this as an allusion to the changes someone or some group
felt. Perhaps, "The Industrial Revolution changed many things, but the
aristocracy was an eigenvector of this transformation, maintaning its
position, though increased by a large eigenvalue."

(Well, I said it would be an obscure reach. Presumably Pynchon's use
was more subtle, though maybe even more obscure if eigenvectors and
eigenfunctions are an unknown concept.)

--Tim May




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