Determinism

Determinism is the idea that a result is entirely fixed by its causes and its starting conditions. In a deterministic system, nothing is left to chance: the same initial conditions always lead, without exception, to the same result. It is, in this sense, the exact opposite of chance.

A simple image is to picture a perfectly tuned machine of gears. If you set the parts in the same position at the start and turn the crank, the machine reaches the same final state every time. To reproduce the starting conditions is to reproduce the outcome, identically and without surprise.

The behavior can be summed up thus: fully knowing the present state of a deterministic system is enough, in principle, to deduce the next state. A computation operation illustrates this trait well. Adding the same two numbers invariably gives the same total; no randomness slips in. Conversely, a truly random system remains unpredictable even when everything that precedes it is known.

The most instructive paradox concerns so-called "pseudo-random" generators. We spontaneously associate them with chance, whereas they are in reality perfectly deterministic: from the same seed, they always redo exactly the same sequence of numbers. This is precisely what justifies the prefix "pseudo": these sequences imitate chance without being it, since they flow from a reproducible computation.

This nuance illuminates how the site's tools work. Rolling a real physical die is not a deterministic act, since the conditions of the throw are impossible to reproduce. But the simulated chance that drives the coin flip, the dice, and the draws rests, for its part, on a deterministic mechanism: it is by making the seed unpredictable that we obtain, from a process that is nonetheless determined, results that are unpredictable in practice.