Is life possible in 4 dimensions?
In recent decades, physicists have explored this question by investigating the properties of other universes to see whether complex life could exist in them. Their conclusion is that it could not exist in a universe with four dimensions, nor in one with more than one dimension of time.
Do we dream in 4th Dimension?
A “dream” is a reality created within one’s mind. For us 3rd Dimensional (3D) humans, what we remember of our nightly dreams are 4th Dimension (4D) experiences. Some say we experience many higher dimensions in our dreams, but we only remember the 4D experience because it is closest to our 3D experience.
Do intuitions apply in high-dimensional worlds?
[O]ur intuitions, which come from a three-dimensional world, often do not apply in high-dimensional ones. In high dimensions, most of the mass of a multivariate Gaussian distribution is not near the mean, but in an increasingly distant “shell” around it; and most of the volume of a high-dimensional orange is in the skin, not the pulp.
What is the source of new behavior in high dimensional space?
Results like the Hales–Jewett theorem are another source of “new behavior” in sufficiently high-dimensional space. The Hales–Jewett theorem says, roughly speaking, that for any n there is a dimension d such that n -in-a-row tic-tac-toe on an n \imes n \imes \\dots \imes n board cannot be played to a draw.
Why does my data have a low intrinsic dimensionality?
Variance of distances becomes small compare to the average. So at some point, you run into trouble choosing thresholds, weights, ordering; and you may even get numerical precision problems, too. But if your data is sparse, it likely is of much lower intrinsicdimensionality.$\\endgroup$
Are examples distributed uniformly in a high-dimensional hypercube?
If a constant number of examples is distributed uniformly in a high-dimensional hypercube, beyond some dimensionality most examples are closer to a face of the hypercube than to their nearest neighbor.