What is "efficiency" in terms of represent things in a certain no of dimensions? Computer Science

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What is "efficiency" in terms of represent things in a certain no of dimensions? Posted: 31 Dec 2021 05:24 AM PST Little Context So I was reading this article in nature titled Information theory and dimensionality of space, I had 2 fundamental doubts upon reading this, first was regarding non-integer dimensions and the second one was the "efficiency in representing data in a certain no of dimensions". I thought that both of these are fundamental mathematical doubts hence I posted it in r/math, this is my post ( it was removed however citing some reasong but I still got some beneficial answers by that time ). One of the comments there pointed out that the second question of mine is related to "information theory" fundamentally so I thought of posting it here! Main question I do not get how the efficiency of representation of information in a dimensional space is related with the no.of dimensions of that space. First of all I do not get what one mean by "efficiency" here. For example in the article (mentioned above) it is written: The mathematical argument is that the e-dimensions are the most efficient representation of information and since Nature chooses optimality, as in physical laws such as the Principle of Least Action, the actual physical data should have this dimensionality. I do not get what any of this means. Any pointers on this will be helpful. If someone provides some resources on this it will be helpful :) submitted by /u/berzerker_x [link] [comments]

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