Universal behaviour of "linear" systems

[Penio Penev]

dhw at santafe.edu wrote:
| [..] The ``trick'' used to get such universal
| nonlinear behavior from a purely linear system is quite similar to the
| way nonlinear macroscopic physics arises from the purely linear
| microscopic physics of Schrodinger's equation. More precisely, the
| ``trick'' involves two parts. First, the kind of field computer
| studied in this paper is a continuum-limit threshold neural net. That

Thresholding is the most non-linear finite function.  In a sense, the
computer I'm writing this lines on is a finite linear machine with an
"IF" function, which is the same as thresholding. If I believe, that
my machine (given infinite disk space) is computationally universal, I
have no problems believing, that adding an infinite processor to it
would be universal also.

-- 
Penio Penev  x7423 (212)327-7423 (w) Internet: penev at venezia.rockefeller.edu