mindpixel's Journal: Euclidean quantum gravity in seven dimensions

I wrote Jack Milnor today--kinda scary. I wonder if he will think my suggestion that the brain is a Milnor sphere generator, crazy. Afterall, the universe itself is giving hints of being a Milnor sphere too. Below is a an abstract very interesting paper I found today (Source):

Abstract. It is well known that in four or more dimensions, there exist exotic manifolds; manifolds that are homeomorphic but not diffeomorphic to each other. More precisely, exotic manifolds are the same topological manifold but have inequivalent differentiable structures. This situation is in contrast to the uniqueness of the differentiable structure on topological manifolds in one, two and three dimensions. As exotic manifolds are not diffeomorphic, one can argue that quantum amplitudes for gravity formulated as functional integrals should include a sum over not only physically distinct geometries and topologies but also inequivalent differentiable structures. However, can the inclusion of exotic manifolds in such sums make a significant contribution to these quantum amplitudes? This paper will demonstrate that it will. Simply connected exotic Einstein manifolds with positive curvature exist in seven dimensions. Their metrics are found numerically; they are shown to have volumes of the same order of magnitude. Their contribution to the semiclassical evaluation of the partition function for Euclidean quantum gravity in seven dimensions is evaluated and found to be nontrivial. Consequently, inequivalent differentiable structures should be included in the formulation of sums over histories for quantum gravity.

Maybe Einstein saw the universe as a hypergeometric object because he was looking at it through a hypergeometric object...and/or vice versa.

consciousness

[naoursla]

Not that it is directly related, but I thought you might find this paper interesting:

Consciousness: Drinking from the Firehose of Experience [utexas.edu]

All the right pieces

[mindpixel]

Yes, all the right pieces are in the paper...but I think you will find thinking of the mind in geometric terms to be easier than inventing new concepts like trackers...you see this clearly when you start talking about emotion. When your underlying structure is already dimensional, it is natural to think of emotion of just more dimensions.

Space, time and emotion are the primary invariants for mammals. The dimensions of which are compiled into out most ancient neural hardware. Again, I think it is no coincid

Re:All the right pieces

[naoursla]

I think the trackers idea is independent of the number of dimension of your data. There is no reason a tracker couldn't be written for 7-D data points or even a several hundred dimensional data points.

I had a conversation with a video conferencing guy about the specialized video compression he uses. He claimed that analysis of multiple faces reveals a few hundred primary dimensions in faces, and a feature vector of those components can be used to reconstruct the face (or recognize it).

Not that I'm saying

Re:All the right pieces

[mindpixel]

No doubt that if you look at a 7d thalamocortical vector you will find hundreds of statistical clusters embedded in it, but the brain is at any given point in time in a single 7d state. The state is global an unified and each state has maximum seperation from all other states because hypersurface is maximum at 7d. This makes for a map of all possible brain states. If you have the whole map you no longer have to "track" anything. Geometry does all your work for you. The problem with high dimensional maps is