Re: Opinions on mathematics.

In article <4u5pcsF16pa00U1@xxxxxxxxxxxxxxxxxx>,
Bob Kolker <nowhere@xxxxxxxxxxx> wrote:

Michael Press wrote:


The notion of unicorns are not a mathematical
object. I
am very surprised to discover the notion in a
math
forum.

Alright. How about a one sided surface. That is
almost as fantastical as
a unicorn or a fire-breathing dragon. Or a bottle
with no inside or
outside.




I think that mathematical objects are mind
constructions developed from observation,
abstraction
from observation, mappings of mental processes,
and
striving for explication that leads to forming
new
mental paths.

How does anyone get a calbari-yao manifold from
observation?

How did anyone get it without observation? Not that I

know the definition of a cym, but manifolds are
abstractions from geometric surfaces such as spheres
and quadric surfaces.

The only mathematics we can do is what our
spatio-temporal apparatus allows, unless we receive
signals from another plane that gives us new
mathematics. When we do mathematics we are mapping
and
explicating that apparatus. Not that that is all we
are
doing.

--
Michael Press

Certainly, a Calabi-Yau manifold is not a product of
our "spatio temporal apparatus," nor can it be described
in terms of such an apparatus.

Tom
.

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