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The whole left/right way of looking at things takes a very highdimensional space and compresses it into a single dimension.
Top Republican: I'd Rather Run Against Obama And His "NationalSecurity Deficit"

In summary, the idea was that a pair of parallel branes, floating in a highdimensional space triggered the Big Bang by “colliding” and bouncing apart.

And these patterns of points that I've shown for you actually represent symmetries of this highdimensional object that would be warping and moving and dancing over the space time that we experience.

In this model, perception and cognition are mathematically described as a continuous trajectory through a highdimensional mental space; the neural activation patterns flow back and forth to produce nonlinear, selforganized, emergent properties — like a biological organism.

Even in highdimensional space, where there exists a curve which is nondecreasing with respect to absolute fitness for the population to follow, feedback loops will cause its evolutionary trajectory to diverge from that curve to some degree, lowering its fitness from what it would be otherwise.

The role of the statistician is somewhat trivial in such cases; she simply calculates the projection of the highdimensional data onto the lowdimensional subspace the “model”.

In the late 70s, some researchers argued that the way to deal with these problems was to treat category representations as a collection or cluster in highdimensional space of all of the members of that category that we have encountered.

The solution, first proposed by Rosch, was to treat concepts as "clusters in a vast highdimensional similarity space that were devised to maximize the similarity within a cluster and minimize the similarity between clusters"4.

So to some extent, doing all of these activities is like working in a highdimensional space whose dimensionality keeps getting higher but we can handle it because we don't have to know of all of cultural history...we can just look at parts of it.

One idea is that our threedimensional universe may be embedded in a highdimensional space, just as you can imagine on these sheets of paper.
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