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> while the natural rate of growth of a biological system is O(e^t).

The theoretical growth rate; in practice this is impossible to keep up due to biological resource limitations.

> The universal speed limit dictates how much of the Universe humans (or whatever comes after us) can ever visit, because of the Hubble constant.

So unless every point in space was an "agar plate for humans", ready to serve us and house our breeding, we'd run into resource limitations far before any theoretical maximum due to finite c and expansion.



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