## Wednesday, May 9, 2012

### Other Dimensions

I asked Stephanie what she thought about other dimensions.  Here is what she said.

Definitions:

Dimension - In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.

Physical theories that incorporate time, such as general relativity, are said to work in 4-dimensional "space-time", (defined as a Minkowski space). Modern theories tend to be "higher-dimensional" including quantum field and string theories. The state-space of quantum mechanics is an infinite-dimensional function space. A tesseract is an example of a four-dimensional object.

Manifolds
A connected topological manifold is locally homeomorphic to Euclidean n-space, and the number n is called the manifold's dimension. One can show that this yields a uniquely defined dimension for every connected topological manifold. For connected differential manifolds the dimension is also the dimension of the tangent vector space at any point.

*** Did you notice that the main character of the book is named Mannie Foldsky (get it?)

The best-known treatment of time as a dimension is Poincaré and Einstein's special relativity (and extended to general relativity), which treats perceived space and time as components of a four-dimensional manifold, known as spacetime, and in the special, flat case as Minkowski space.

Superstring theory, M-theory and Bosonic string theory respectively posit that physical space has 10, 11 and 24 dimensions. These extra dimensions are said to be spatial. However, we perceive only three spatial dimensions and, to date, no experimental or observational evidence is available to confirm the existence of these extra dimensions. A possible explanation that has been suggested is that space acts as if it were "curled up" in the extra dimensions on a subatomic scale, possibly at the quark/string level of scale or below.

** This is what I have to say about String Theory – “Hogwash!”
I don’t know enough about the math to make the call with 100% certainty, but 11 dimensions seems preposterous and hardly elegant.

A Calabi–Yau manifold is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold.

*** I liked the look of this thing, so I started to imagine what six dimensions was all about.  It was the Calabi-Yau manifold that inspired the topology of the Qualia Spectarum – the map of the Dreamscape.

The other manifold that got my attention was the Klein bottle (the form of the bongs that the glass blowing Wiccans, Teek and Voltar, make in the book).  A Klein bottle is a non-orientable surface, informally, a surface (a two-dimensional manifold) in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary. (For comparison, a sphere is an orientable surface with no boundary.)

*** What was the original question?... Thoughts on other dimensions
I think that there are theoretically infinite dimensions (I am a multi-dimensional database architect) and I can make an infinite number of dimensions which define a fact table.  However, the more dimensions you add, the larger the fact table will grow to accommodate all of the possible permutations until you need a computer the size of Texas to find out the answer to your question.

#### 1 comment:

1. What do you think about compactification of dimensions?