Kinda a thought that pops into my head from time to time about if people that lived well before writing wanted to leave an eternal legacy and at best we see their remains dressed in ornaments.
It’s interesting to think that someone that lived 50k years ago paved a path for me in the sense that they probably exploded lands weren’t known to their tribe or human at the, found new edible plants, or maybe created a new tool.
Crazy to think that there’s billions of humans that I contributed to the life I have know and their names have long since been lost to time and that what I do today can still affect someone well into the future
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.
You could say that n would also have to increase with time. I’m thinking you have a tribe of 10 then 1 dies then 9 people to remember that person. We can say as time goes on the tribe stays at 10 but the original 10 die off then n = 1. So you could turn n into a function of it then solve the equations to see if it prevents a divergence