Posted by
Nick Thompson on
URL: http://friam.383.s1.nabble.com/manifold-in-mathematics-tp3385914p3387696.html
This is why I like to ask questions of PEOPLE: because when you get
conflicting answers, you have somewhere to go to try and resolve the
conflict.
So I have three different definitions of a manifold:
1. A patchwork made of many patches
2. The structure of a manifold is encoded by a collection of charts that
form an atlas.
3. a "function" that violates the usual function rule that there can be
only 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 most
like meaning that Holt has in mind because I think he thinks of
consciousness as analogous to a mathematical formula that generates outputs
(responses) from inputs(environments).
Thanks, everybody.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University (
[hidden email])
http://home.earthlink.net/~nickthompson/naturaldesigns/> [Original Message]
> From: Jochen Fromm <
[hidden email]>
> To: The Friday Morning Applied Complexity Coffee Group <
[hidden email]>
> Date: 8/4/2009 6:31:57 PM
> Subject: Re: [FRIAM] "manifold" in mathematics
>
> A 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.
>
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