13th June 2022, 7:10 PM
(13th June 2022, 6:42 PM)Kribbles Wrote: Actually, visual representations of higher dimensional spaces are really important. I don't know anything about this astral projection things, but in signal processing, you've got principal component analysis that takes higher dimensional data and projects the data to a lower dimensional space. If you've reduced down to 3 dimensions, you can pan around it in MATLAB.
While it is important to have visual representations of higher dimensional spaces, these so-called principal component analysis are all based on scientific research and theory; MATLAB is the same way. I'll explain astral projection in the next thread. It's too complicated for some people to understand it, right now.
(13th June 2022, 6:42 PM)Kribbles Wrote: Machine learning methods really look into this a lot! If you've got a multidimensional tensor, there was non-linear principal component analysis using neural networks (autoencoders), but nowadays I hear UMAP and tSNE are the main visual representations of higher dimensional data. There's a lot of cool stuff with this all. Variational autoencoders are probably my favorite method for smearing between dimensions and understanding what the hyperplanes in your neural network are handling. I don't think VAEs are very... well, good, but it is really fun to look at your data with them.
I know this was kinda jokey, but I do love this stuff.
I didn't know they had UMAP and tSNE to try and narrow down the input features, variables, and columns of the 4th dimension; that's interesting to me. Well, it's great that they're putting in the effort to try and simplify the mysteries of the 4th dimension. However, even though they're using dimensionality reduction techniques... it has parameters, unfortunately.
This is why I mentioned dying or astral projecting. This higher dimension cannot be fully explained with science and technology because there's much more to visualize in that dimension. When you view it from a 3D perspective, you may not understand it as much, unless you die or astral project.
