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There's an old book called "Flatland" ... google on it and the many essays that talk about it. Your idea reminds of the adage: "Its turtles all the way down."
Really... the idea of more dimensions than we "see" arrives when the data cannot be explained without resorting to extra dimensions in the mathematics. At the moment, we have truckloads of data (both at the quantum and at the galactic scales) that cannot be resolved with only 3 dimensions of space and 1 of time. However, the layering isn't necessarily infinite... you stop adding dimensions when there isn't any data that requires the addition of another.
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