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Cake day: June 30th, 2023

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  • It’s theoretically impossible to create a system to remember every human that doesn’t rely on external storage.

    I’ll explain: let’s say that for every human that dies, they will be remembered and live on in the heart of another, living human. Each living human can remember n dead humans.

    we can set up an equation

    pn >= r

    where p is the current population of live humans, r is the amount of dead humans that must be remembered.

    We can express the rate of deaths as a proportion of the current living population:

    d/dt[r] = pb

    Where t is time and b is the instantaneous death rate per captia with respect to time (generally a constant).

    Combined with the previous, we get the separable differential equation:

    d/dt[r] = pb >= (r/n)b

    dr/dt >= rb/n

    [1/r] rt >= [b/n] dt

    Integrated:

    ln|r| >= tb/n+C

    r >= e^(tb/n+C)

    pn >= r >= e^(tb/n+C)

    p >= e^(tb/n+C)/n

    So in order for this system to work, the living population must always be growing exponentially, which is not feasible for modern humanity.