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 ideas across several areas of mathematics. He succeeded brilliantly.
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 Limit?
-- Owen
On Aug 4, 2009, at 11:12 AM, Nicholas Thompson wrote:
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 Epping Forest," one may mean that this entire
manifold of some square miles is the forest; or else, that every
twig and leaf which one sees, in short, every least fragment of the
whole is Epping Forest. The former meaning is the true one; the
latter meaning is absolutely false. Everyone admits that while a
circle is a manifold of points, a single point is not a circle;
while a house is a manifold of bricks, boards and nails and any
single brick is not a house. "
I am interested in this concept of "manifold" . Can anybody make
the metaphor come alive for me? Is it like a shroud?
Nick
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