🚀 go-pugleaf

In <Cxo7oo.I8w@murdoch.acc.Virginia.EDU> smb3u@delton.psyc.virginia.edu (Steven M. Boker) writes:

>[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.

One should distinguish between two possible claims:

  The system must solve a problem which we would solve by integrating
  PDEs.

  The system actually integrates PDEs.

My skepticism was only of the second of these claims.  I have no
reason to disagree with the first claim.

>>Personally, I tend to doubt any argument which tries to make anything
>>important out of a difference between digital and analog.

>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.

I probably wrote my comment carelessly, and your interpretation is
not what I intended.  There is a question of fact, as to whether the
brain actually uses analog methods.  I would not be at all surprised
if the answer is yes.  I was discussing the different question, which
is a matter of principle.  Some people are arguing that, in
principle, cognition must be analog, and cannot be digital.  It is
this "in principle" argument which I suggested was bogus.