🚀 go-pugleaf

[Copied in from several postings in this thread]

J. Sieracki (elf@universe.digex.net) wrote:
>
>: Fourth order?  I'd guess you're limiting your thinking to canned Runge-Kutta
>: routines.  One can generate numerical integrators to any order you like.
>: Realistically the order must be finite, as is the numerical precision.  You
>: can escape this with analog circuits but then you've just swapped finite
>: precision error for an analog noise floor.
>

I would consider this to be an interesting swap.  At the smallest
scaling you have a extremely high dimensional process decoupling
you from numeric artifactual basins of attraction.  A thermal noise
floor can be useful.

In <37kln5$nh3@portal.gmu.edu> herwin@vanish (Harry Erwin) writes:
>I'm new to this aspect of the field, and I think I got it garbled. In
>order to get around a digital model of the brain using PDE integration
>techniques, I need arbitrarily small significant features.

I really doubt that you need arbitrarily small significant features.
Certainly there is a limit beyond which the differences are trivial
within the range of time scales that are meaningful within the
nervous system.

In article <37l2d0$hpr@mp.cs.niu.edu> rickert@cs.niu.edu (Neil Rickert) writes:
>The whole idea that the brain is doing something that requires
>integrating PDEs seems very unlikely to me.  The brain is made of
>biological cells, and cells do not have the high precision where the
>boundedness of 4th derivatives would have any particular relevance.
>
Actually, researchers studying such mundane behavior as postural
stability (how does the nervous system maintain the stability of
the inverted pendulum that comprises a human standing in one spot)
and reaching behavior (how does the nervous system solve the problem
of smoothly reaching for and grasping an object) have observed that
the brain must be solving a problem which involves integrating PDEs
and have further observed that optimization of derivatives up to
the fourth appear to be involved.  I'm afraid that integrating PDEs
is necessary, however the nervous system manages to accomplish it.

>Personally, I tend to doubt any argument which tries to make anything
>important out of a difference between digital and analog.  It is
>worth remembering that movie theaters have long been delivering
>discrete shows, with the picture image switching 24 times per second,
>and except for the occasional backward turning wagon wheels, it all
>looks continuous to us.  This should caution us that arguments about
>the importance of analog components are bogus.
>
Whether or not there is a difference between analog and digital
representation of information in the brain has nothing to with the
phenomena of flicker fusion and apparent motion, two highly
interesting cognitive probes in their own right.

Steve


-- 
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 #  Steven M. Boker            #       "Two's bifurcation         #
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