To anybody following the Holt thread:
In an offline communication, Eric Charles has pointed out that I misspoke when
I wrote:
"So each mind is a kind of logical engine that generates a slice of the world
in much the same way that a tune is an engine that generates a pattern of
touches on a piano keyboard."
In Holt's view, "my" consciousness is the slice of the world implied by my
behavior. So mind is more like the manifold itself than it is like the
mechanism (the brain?) that generates the manifold.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
----- Original Message -----
From: ERIC P. CHARLES
To: Nicholas Thompson
Sent: 8/5/2009 9:48:04 PM
Subject: Re: [FRIAM] "manifold" in mathematics
Nick
I'm not sure this is relevant to the FRIAM list, but I think Holt is going
somewhere even bigger than you think. Not only is he going to claim that a
manifold results when the mind slices the world, he is going to claim that the
mind itself is a manifold. The mind is just one more type of describable
complexity. In case you want a preview, I am attaching what I consider to be
the main thesis of the book. It is found in the last chapter. (And I'm cc'ing
Jesse, because I am interested in any thoughts he might regarding the
attachment.)
Eric
P.S. The "punch line" was not at all what I expected, but it seemed strangely
modern and relevant. Based on having attended way too many talks by people who
study neuroscience, I can say with some certainty that as a field they have
still not overcome the problem Holt lays out.
P.P.S. I find the concentration of nervous response as opposed to a more
general notion of bodily response a bit unnerving. (ba dum bum, ching) I'm not
sure it is a necessary part of the thesis.
On Wed, Aug 5, 2009 12:37 PM, "Nicholas Thompson" <[email protected]>
wrote:
Clairborne,
Here is what I think Holt is up to. He is using a model of mathematical
induction for his understanding of mind. Mathematical induction is actually a
form of logical DEduction in which the combination of a principle with a single
case is used to generate a second case, and then a third, etc., ad infinitum.
(It is all strangely reminiscent of Rosen's Life Itself which tries to
understand life in terms of recursive sets.) In Holt's system, I think, a
mind is analogous to the principle in a mathematical induction and the cases
are "the world". So each mind is a kind of logical engine that generates a
slice of the world in much the same way that a tune is an engine that generates
a pattern of touches on a piano keyboard. (I am sorry; I didnt do that very
well, but I had to try!) Now, one might be tempted to simply say that a mind
is a function where the argument is facts about the world and the ! output is
behavior. But if calling it a function would limit the values that y can take
with respect to any given x (or vice versa, I can NEVER remember), then Holt
might be induced to call a mind a manifold (rather than a function) to free
himself of that constraint.
I dont think he speaks to the question of whether the leaves and twigs are
manifolds, only to the question of whether they are the forest. (They could,
after all, be manifolds WITHIN larger manifolds.) He seems to be arguing with
a very strange proposition, that he attributes to idealists, that the forest IS
each and every one of its parts. It sounds like an argument only a philosopher
could love, but he takes it very seriously and he is still banging on about it
a hundred pages later.
There is a topologist on the list (at least one) who, I am hoping, will offer
at least one more definition of manifold. I say hoping, because at present, I
dont understand why "set" or "metaset" is not a perfectly good definition of
the non-roger definitions of manifold so far offered.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
----- Original Message -----
From:
To: [email protected]
Sent: 8/5/2009 5:57:03 AM
Subject: Re: [FRIAM] "manifold" in mathematics
Let me add another inquiry to this - how do we reconcile this notion of
manifold with the idea of self-similarity? If Epping Forest is a manifold, but
the leaves and twigs are not, yet the leaves and twigs have some
self-similarity, is Holt truly thinking in terms of the mathematical definition
of manifold, as Roger gave us, or is the metaphor missing something (or am I)?
- Claiborne Booker -
-----Original Message-----
From: Nicholas Thompson <[email protected]>
To: [email protected]
Sent: Wed, Aug 5, 2009 12:39 am
Subject: Re: [FRIAM] "manifold" in mathematics
Is an organism a manifold?
Do the parts have to be heterogeneous? Dictionary definition would seem to
suggest so. Thus a regiment would not be a manifold (except insofar as it
contains soldiers of different ranks).
n
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
----- Original Message -----
From: Robert Cordingley
To: The Friday Morning Applied Complexity Coffee Group
Sent: 8/4/2009 8:03:00 PM
Subject: Re: [FRIAM] "manifold" in mathematics
So to return to the forest question... Sherwood Forest is I presume another
manifold. I know it is now discontiguous, separated by urban development and
such (perhaps Epping Forest is too). Is it still a manifold? I could ask the
same question about the British Isles: lots of little places, some bigger ones,
surrounded by water.
Also while the twig is in the forest it is part of the forest until someone
removes it. Does it's history keep it part of the manifold? Or can I declare
it as such and it is so?
Robert C.
russell standish wrote:
On Tue, Aug 04, 2009 at 03:51:38PM -0600, Nicholas Thompson wrote:
This is why I like to ask questions of PEOPLE: because when you getconflicting
answers, you have somewhere to go to try and resolve theconflict. So I have
three different definitions of a manifold: 1. A patchwork made of many
patches2. The structure of a manifold is encoded by a collection of charts
thatform an atlas. 3. a "function" that violates the usual function rule that
there can beonly y value for each x value. (or do I have that backwards).I can
map 1 or 2 on to one another, but not three. i think 3. is the mostlike
meaning that Holt has in mind because I think he thinks ofconsciousness as
analogous to a mathematical formula that generates outputs(responses) from
inputs(environments).
1 & 2 were different ways of saying the same thing - one does need adefinition
of patch or chart, though. I think (although I could bemistaken), each chart
(or patch) must be a diffeomorphism (aka smoothmap), although it may be
sufficient for them to be continuous. Thereason I say that, is that I don't
believe one could consider theCantor set to be a manifold.Most of my experience
of manifolds have been smooth manifolds (everypoint is surrounded by
neighbourhood with a diffeomorphicchart/patch), with the occasional nod to
piecewise smooth manifolds(has corners). The surface of a sphere is a smooth
manifold. Thesurface of a cube is not, but it is piecewise smooth.No 3 above
was just a way of saying that graphs of suitably smooth functions aremanifolds,
but not all manifolds are graphs of functions.
Thanks, everybody. Nick Nicholas S. ThompsonEmeritus Professor of Psychology
and Ethology, Clark University
([email protected])http://home.earthlink.net/~nickthompson/naturaldesigns/
[Original Message]From: Jochen Fromm <[email protected]>To: The Friday Morning
Applied Complexity Coffee Group <[email protected]>Date: 8/4/2009 6:31:57
PMSubject: Re: [FRIAM] "manifold" in mathematicsA manifold can be described as
a complex patchwork made of many patches.If we try to describe
self-consciousness as a manifold then we get- the patch of a strange loop
associated with insight in confusion(according to Douglas Hofstadter)- the
patch of an imaginary "center of narrative gravity" (according to Daniel
Dennett)- the patch of the theater of consciousness which represents the
audience itself(according to Bernard J. Baars)have I missed an important patch
?-J.=======================!
=====================================FRIAM Applied Complexity Group
listservMeets Fridays 9a-11:30 at cafe at St. John's Collegelectures, archives,
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============================================================FRIAM Applied
Complexity Group listservMeets Fridays 9a-11:30 at cafe at St. John's
Collegelectures, archives, unsubscribe, maps at http://www.friam.org
============================================================FRIAM Applied
Complexity Group listservMeets Fridays 9a-11:30 at cafe at St. John's
Collegelectures, archives, unsubscribe, maps at http://www.friam.org
============================================================FRIAM Applied
Complexity Group listservMeets Fridays 9a-11:30 at cafe at St. John's
Collegelectures, archives, unsubscribe, maps at http://www.friam.org
Eric Charles
Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601
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