I wonder if anybody has any comment to make on the following passage from EB
holt? (Remember, I am the guy who tends to ask questions of PEOPLE when he
should look them up, so feel free to ignore me here.)
Holt (1914) writes: "If one is walking in the woods, and remarks that "All
this is Epp
This is an interesting use of "manifold".
In mathematics, a manifold has a well-defined
meaning. The structure of a manifold
is encoded by a collection of charts that form
an atlas. A chart is a mapping between the
manifold and a simple (euclidean) space, see
http://en.wikipedia.org/wiki/Manifol
A manifold is something that can't be a function because it is multi-valued
where a function must be single-valued.
A circle, the set of points which satisfy the equation x^2 + y^2 = r^2, is a
manifold of points because there are two values of y that satisfy the
equation for each value of x, -r <
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 g
thlink.net/~nickthompson/naturaldesigns/
> [Original Message]
> From: Jochen Fromm
> To: The Friday Morning Applied Complexity Coffee Group
> Date: 8/4/2009 6:31:57 PM
> Subject: Re: [FRIAM] "manifold" in mathematics
>
> A manifold can be described as a
> complex pa
as S. Thompson
> Emeritus Professor of Psychology and Ethology,
> Clark University (nthomp...@clarku.edu)
> http://home.earthlink.net/~nickthompson/naturaldesigns/
>
>
>
>
> > [Original Message]
> > From: Jochen Fromm
> > To: The Friday Morning Applied C
> >
> > Nick
> >
> > Nicholas S. Thompson
> > Emeritus Professor of Psychology and Ethology,
> > Clark University (nthomp...@clarku.edu)
> > http://home.earthlink.net/~nickthompson/naturaldesigns/<http://home.earthlink.net/%7Enickthompson/naturaldesigns/>
kthompson/naturaldesigns/
[Original Message]
From: Jochen Fromm
To: The Friday Morning Applied Complexity Coffee Group
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
,
Clark University (nthomp...@clarku.edu)
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
definition
of manifold, as Roger gave us, or is the metaphor missing something (or am I)?
- Claiborne Booker -
-Original Message-
From: Nicholas Thompson
To: friam@redfish.com
Sent: Wed, Aug 5, 2009 12:39 am
Subject: Re: [FRIAM] "manifold" in mathematics
Is an
Of course, it would be unreasonable to expect Holt to conform to the modern
definition of "manifold", as formalized mathematics has changed quite a bit in
the last 100 years. While it is not quite as conceptually elaborate as it could
be, our friend wikipedia has a bit on the history of the term
(h
essor of Psychology and Ethology,
Clark University (nthomp...@clarku.edu)
http://home.earthlink.net/~nickthompson/naturaldesigns/
- Original Message -
From:
To: Friam@redfish.com
Sent: 8/5/2009 5:57:03 AM
Subject: Re: [FRIAM] "manifold" in mathematics
Let me add another in
q...@aol.com wrote:
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
Hi Nick.
This is an interesting discussion on the concept of Manifolds. But I
sense you have a wider interest than just this one word, right?
My guess is one of the most important books in this field is Spivak's
Calculus on Manifolds. Thus Spivak's interest was in the unification
of ide
Owen brings up an interesting (and important in it's relevance?) question...
Where is your interest? History/Philosophy of Mathematics?
Fascination with words and language? As a component of CAS? As a
core mathematical theme to be mastered, somewhat like the
epsilon/delta concept of the
On Wed, Aug 05, 2009 at 10:37:58AM -0600, Nicholas Thompson wrote:
> 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 def
f Psychology and Ethology,
Clark University (nthomp...@clarku.edu)
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'
Wednesday, August 05, 2009 12:49 PM
To: friam@redfish.com; nickthomp...@earthlink.net
Cc: John Kennison
Subject: Re: [FRIAM] "manifold" in mathematics
On 5 Aug 2009 at 10:37, Nicholas Thompson wrote:
> There is a topologist on the list (at least one)
Before attempting a substantive r
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