Re: Characteristics of multi-dimensional spaces?

On Apr 4, 6:09 pm, EskWI...@xxxxxxxxxxxxxxxxxxx wrote:
This is a vague sketch of an idea, ill-formed due to ignorance. But I'll
throw it out anyway, and I'll ask for your indulgence of a poor liberal
arts grad...

So anyway, I was thinking about a two-dimensional world, much like that
which is depicted in the book Flatland. The inhabitants of flatland exist
in a three dimensional context, but are only aware of two. They live on a
plane, extending in two of the available three dimensions. Anyone who is
familiar with the book knows what I mean.

I'm thinking that if their world is a plane, it extends to infinity in
each of the two dimensions into which it is extended. As such, it slices
the three dimensionsal world of which it is a part into two distinct
pieces. In the three dimensional context, a point cannot exist such that
it is on both sides of the plane, it must necessarily be on one side or
the other.

Ok, so this is trivial.

But - if our three dimensional world is in a four (spatial) dimensional
context (please remember I said "if" :), would we similarly slice the four
dimensional context into distinct spaces? Into three spaces? Another
number?

I suppose this is more a geometry question than a physics question, but
any insights would neertheless be appreciated.

Plato had an idea, that we see only shadows of the world outside the
cave (scull-cave?).
There exist geometry and topology. What, if the topology of our world
is multidimensional, and it must be embedded into three geometrical
dimensions as into the Procrustean bed?
kunzmilan


.

Relevant Pages

  • Characteristics of multi-dimensional spaces?
    ... in a three dimensional context, but are only aware of two. ... plane, extending in two of the available three dimensions. ...
    (sci.physics)
  • Re: Quantum Flux
    ... It's tricky in high dimensions because the data becomes too dense. ... But I don't even have an atomic geometry. ... I picture a generic point particle in spacetime. ... But that's a polysign interpretation. ...
    (sci.physics)
  • Re: the basis of relativity
    ... With regard to the theory of gravity as I described it. ... Take some solution to Einstein's equations, then perturb the geometry ... I see the space-time dimensions as simply the dimensions of a normal ... a firm foot in measureable reality. ...
    (sci.physics.relativity)
  • Re: the basis of relativity
    ... >>>one should say gravity is indistinguishable from geometry. ... > I see the space-time dimensions as simply the dimensions of a normal ... The unification of Spacetime by the Lorentz transform ...
    (sci.physics.relativity)
  • Non Abelian Universe?
    ... differs drastically from GR classical mechanics. ... geometry known as multisymplectic geometry. ... of discrete Planck units, not a continuous circle described by ... A closed path, or curve, C, in two dimensions, acquires a third ...
    (sci.physics.relativity)