• 0 Posts
  • 85 Comments
Joined 3 years ago
cake
Cake day: June 30th, 2023

help-circle






  • 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.










  • Unless the lorry was driving over the exact geographic north or south pole.

    Side note: the tallest lorry where the top doesn’t move faster than the speed of light at the equator is 3.8 light hours tall, which is weird to think about because the top doesn’t start moving until well after the bottom has reached it’s destination.





  • This is actually an issue caused by the hotel staff not allocating their rooms efficiently. When the first wave of infinite guests showed up, they should have assigned them to odd numbered rooms. Then theres still an infinite number of vacant even numbered rooms.

    Even if several more waves of infinite guests show up, you can assign them to rooms numbered 4n+2, 8n+4, 16n+8…

    That way, the hotel will always have rooms left over.