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You read the papers correctly, bc those are abstract dimensions, neither time nor space nor precise facial features. Adding another element to an array is changing it's arity, as arguments to a function (which nobody confuses as a function's dimensions). The chessboard case is an example of mixing disparate, concrete properties, and calling them all dimensions. But that is exactly the error in saying that time is the 4th dimension: mixing the concrete concept of dimension with the abstract one. Blame physicists, for they seem to really think time is our forth dimension, ergo fundamental, whereas time is an emergent property not of spatial dimensions alone, but motion in that space. Here is an example of purely abstract dimensions. When the researchers at OpenAI want to add the position of words in a sentence, they literally add time, in form of co/sines, to the data. They don't "add" as-in append/concat another dimension to the data, the add as-in sum the existing data with the co/sines, changing the data. They literally merge time into the dimensions of the input. Before and after are temporal, for clocks and words in a string (ie their relative position gives meaningful relativity to the concepts the words represent, or we are lost), but really ALL time is a position WITHIN the dimensions, and the changing of time is the change of position. Ergo time is not additional dimension to the space. We would not experience time if there was no motion, and objects moving faster experience faster time relative to a slow moving object, as Einstein proved. |
> whereas time is an emergent property not of spatial dimensions alone, but motion in that space.
Is that proven true generally? I have often really wondered this myself, but Ive not had anyone to ask for a fundamental proof of this. I appreciate your thorough answers could you please explain or point me in the right direction?