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Instead of linear processing of all document vectors when searching for related content use: Lanczos methods OR a neural network -like approach.

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The uniquely defined dimension of every connected topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean n -space, in which the number n is the manifold's dimension.

The word "event" used in relativity should not be confused with the use of the word "event" in normal conversation, where it might refer to an "event" as something such as a concert, sporting event, or a battle. These are not mathematical "events" in the way the word is used in relativity, because they have finite durations and extents. Unlike the analogies used to explain events, such as firecrackers or lightning bolts, mathematical events have zero duration and represent a single point in spacetime.

Spread the LOVE! by Flemming Funch Have you ever wondered what lies beyond the 3rd dimension and how thoughts can become instant manifestations? This planet ...

The concept of time as the fourth dimension of space -- as a fundamental physical entity in which an experiment occurs -- can be falsified by an experiment in which time does not exist, according to the scientists. 

5. And last but not least as the idea of parallel universes. To go back to the idea that space-time is flat, the number of possible particle configurations in multiple universes would be limited to 10^10^122 distinct possibilities, to be exact. So, with an infinite number of cosmic patches, the particle arrangements within them must repeat — infinitely many times over. This means there are infinitely many "parallel universes": cosmic patches exactly the same as ours (containing someone exactly like you), as well as patches that differ by just one particle's position, patches that differ by two particles' positions, and so on down to patches that are totally different from ours.

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