🚀 go-pugleaf

	I am a medical student interested in obtaining information about the top rated teaching hospitals in the field of neurology and neurosurgery.  I would appreciate any information which can help me choose a place of residency in the near future.
		Much obliged,
				Christian

In article <37f794$ipf@portal.gmu.edu>, Harry Erwin <herwin@vanish> wrote:
>Here's the reason for the original 'turtles' post. It has
>to do with Searle, Pribram, and Penrose's argument that the brain can
>do computational things that a digital computer can't. If that is the
>case, then an AI will have to have 'analog' components similar to those
>in the brain, and the question of what those components are becomes
>interesting. Now, consider what processes could result in this. First,
>if the fourth derivatives of the underlying dynamics are bounded, then
>the system can be digitally simulated (using numerical PDE integration).
>Hence, for the SPP argument to hold, the fourth derivatives must be
>unbounded or undefined. That could be a result of significant structural
>discontinuities or possibly a lack of a smallest scale for significant
>structure ('turtles all the way down'). 
>
 Is it possible for you to briefly explain what is so special about
the fourth derivative as compared with, say, the fifth that effects
digital simulation?

>Note that I'm trying to avoid arguments from chaotic dynamics (weak
>based on the Grebogi and Ott results) and from computability (the brain
>as a Turing machine), since neither show the brain doing anything that a
>computer cannot do.
>
>--
>Harry Erwin

Andrzej
-- 
Andrzej Pindor                        The foolish reject what they see and 
University of Toronto                 not what they think; the wise reject
Instructional and Research Computing  what they think and not what they see.
pindor@gpu.utcc.utoronto.ca                           Huang Po

In article <37f794$ipf@portal.gmu.edu> herwin@vanish (Harry Erwin) writes:
>From: herwin@vanish (Harry Erwin)
>Subject: Turtles All the Way Down
>Date: 11 Oct 1994 23:31:48 GMT

>Here's the reason for the original 'turtles' post. It has
>to do with Searle, Pribram, and Penrose's argument that the brain can
>do computational things that a digital computer can't. If that is the
>case, then an AI will have to have 'analog' components similar to those
>in the brain, and the question of what those components are becomes
>interesting. Now, consider what processes could result in this. First,
>if the fourth derivatives of the underlying dynamics are bounded, then
>the system can be digitally simulated (using numerical PDE integration).
>Hence, for the SPP argument to hold, the fourth derivatives must be
>unbounded or undefined. That could be a result of significant structural
>discontinuities or possibly a lack of a smallest scale for significant
>structure ('turtles all the way down'). 

>Note that I'm trying to avoid arguments from chaotic dynamics (weak
>based on the Grebogi and Ott results) and from computability (the brain
>as a Turing machine), since neither show the brain doing anything that a
>computer cannot do.

Humans have a brain which can deliver (unbidden?) meaningful tangents to 
thoughts. Humans have a brain which can change its own programming without 
knowing the underlying linguistics which provide the programming fundamentals.

Are light based computers considered to be analog? They have the potential to 
be able to execute simultaneous non parallel instruction sets. 

In article <37f794$ipf@portal.gmu.edu>, Harry Erwin <herwin@vanish> wrote:
>Here's the reason for the original 'turtles' post. It has
>to do with Searle, Pribram, and Penrose's argument that the brain can
>do computational things that a digital computer can't. If that is the
>case, then an AI will have to have 'analog' components similar to those
>in the brain, and the question of what those components are becomes
>interesting. Now, consider what processes could result in this. First,
>if the fourth derivatives of the underlying dynamics are bounded, then
>the system can be digitally simulated (using numerical PDE integration).
>Hence, for the SPP argument to hold, the fourth derivatives must be
>unbounded or undefined. That could be a result of significant structural
>discontinuities or possibly a lack of a smallest scale for significant
>structure ('turtles all the way down'). 

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.

>
>Note that I'm trying to avoid arguments from chaotic dynamics (weak
>based on the Grebogi and Ott results) and from computability (the brain
>as a Turing machine), since neither show the brain doing anything that a
>computer cannot do.
>
>--
>Harry Erwin
>Internet: herwin@gmu.edu 
>Just a dumb graduate student working on Katchalsky network models....
>(And if you believe that, I have a ranch in California to sell you.)

Jeff Sieracki
== *

Andrzej Pindor (pindor@gpu.utcc.utoronto.ca) wrote:
: >
:  Is it possible for you to briefly explain what is so special about
: the fourth derivative as compared with, say, the fifth that effects
: digital simulation?

I've lost the track of the argument. It was something about second order RK
integration requiring bounded fourth spatial derivatives... 

--
Harry Erwin
Internet: herwin@gmu.edu 
Just a dumb graduate student working on Katchalsky network models....
(And if you believe that, I have a ranch in California to sell you.)

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'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 think the
scaling has to go both directions, so larger scale patterns can set the
patterns at the smaller scale and so the smaller scale patterns can be
amplified to the larger scale. I see candidate amplification/reduction
processes involving stochastic resonance for the following scale levels:
synapse, dendrite, cell, cell assembly, large-scale network and up. The
main barrier seems to be sub-synaptic, although that's only an
information transfer barrier; the structure keeps on going. 

--
Harry Erwin
Internet: herwin@gmu.edu 
Just a dumb graduate student working on Katchalsky network models....
(And if you believe that, I have a ranch in California to sell you.)

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.

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.

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.

Neil Rickert (rickert@cs.niu.edu) wrote:
: 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.

: 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.

: 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.

Discrete in time, but continuous in space, and with active processes
using stochastic resonance to produce hyperacuity. 

If the arguments about analog components are bogus, the Strong AI
theorists win. Doesn't bother me, but it bugs the hell out of some
people I have to get along with.


--
Harry Erwin
Internet: herwin@gmu.edu 
Just a dumb graduate student working on Katchalsky network models....
(And if you believe that, I have a ranch in California to sell you.)

In article <37l2d0$hpr@mp.cs.niu.edu>, Neil Rickert <rickert@cs.niu.edu> wrote:
>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.

Whether fourth derivatives are meaningful or not is separate from the
issue of using PDEs (or ODEs) for modelling cellular and tissue-level
physical processes in the brain.  Since these processes are commonly
modeled using rates (e.g., of ion transport through the membrane), it
seems like ODEs, or possibly PDEs, are quite natural to use (and in
fact are used).  Besides that, what do you mean by "cells do not have
the high precision"?
---------
Chris Connolly   MIT Dept. of Brain and Cognitive Sciences
E25-616		 connolly@wccf.mit.edu

In <37mpe8$rec@senator-bedfellow.MIT.EDU> connolly@levanto.ai.mit.edu (Christopher Connolly) writes:

>In article <37l2d0$hpr@mp.cs.niu.edu>, Neil Rickert <rickert@cs.niu.edu> wrote:
>>The whole idea that the brain is doing something that requires
>>integrating PDEs seems very unlikely to me.

>Whether fourth derivatives are meaningful or not is separate from the
>issue of using PDEs (or ODEs) for modelling cellular and tissue-level
>physical processes in the brain.  Since these processes are commonly
>modeled using rates (e.g., of ion transport through the membrane), it
>seems like ODEs, or possibly PDEs, are quite natural to use (and in
>fact are used).

Differential equations might be very useful for us in modeling neural
systems.  But that is quite separate from the question of whether the
neural systems are actually solving differential equations.

Keep in mind that I was commenting on an argument which suggested
that digital approaches to AI were likely to fail because the fourth
derivative of the digital system is unbounded.

In article <37f794$ipf@portal.gmu.edu> herwin@vanish "Harry Erwin" writes:

 > .... Now, consider what processes could result in this. First,
 > if the fourth derivatives of the underlying dynamics are bounded, then
 > the system can be digitally simulated (using numerical PDE integration).

Eh? Wozzat? What has the fourth derivative of the dynamics got to do with the 
price  of cheese? 


_________________________________________________

  Oliver Sparrow
  ohgs@chatham.demon.co.uk

In article <782036878snz@chatham.demon.co.uk> ohgs@chatham.demon.co.uk (Oliver Sparrow) writes:
>From: ohgs@chatham.demon.co.uk (Oliver Sparrow)
>Subject: Re: Turtles All the Way Down
>Date: Mon, 17 Oct 1994 07:57:46 +0000

>In article <37f794$ipf@portal.gmu.edu> herwin@vanish "Harry Erwin" writes:

> > .... Now, consider what processes could result in this. First,
> > if the fourth derivatives of the underlying dynamics are bounded, then
> > the system can be digitally simulated (using numerical PDE integration).

>Eh? Wozzat? What has the fourth derivative of the dynamics got to do with the 
>price  of cheese? 


Blessed are the cheesemakers. -- Monty Python

Harry Erwin (herwin@vanish) wrote:

: Note that I'm trying to avoid arguments from chaotic dynamics (weak
: based on the Grebogi and Ott results) and from computability (the brain
: as a Turing machine), since neither show the brain doing anything that a
: computer cannot do.

: --
: Harry Erwin

Why do you avoid such chaotic arguments? I don't know how many reading 
this have seen the report by Hayes, Grebogi, Ott, and Mark in Phys Rev 
Letters 73, 1781 (1994). The letter describes the first experimental 
evidence of communication with chaos. One can easily imagine a situation 
where a "brain" uses an analagous method. In fact the "kicking" of the 
parameter as proposed by Ott, Grebogi, et el is something that a computer 
may not be able to do yet the system could still produce coherent 
communication. Secondly this kicking could be controlled by some complex 
indirect feedback similar to the way in which human consciousness does 
not have access to the rules which alter it.

Of course we have no evidence that this approach will be successful but 
it has potential.

Andrew Laska