What are pseudo-random numbers? What’s wrong with them?
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Think of a coin toss. You can either get heads or tails a 0 or 1. Now true randomness means that exactly ½ of the times you get 0 and ½ of the times 1. But a coin toss isn’t random its just chaotic enough (heavily dependent on initial conditions) to be unpredictable. It isn’t truly random its pseudo-random.
A computer can generate you pseudo-random numbers in much the same way, the generation algorithm is chaotic. Much like a coin toss it is technically predictable like you can make a robot that always produces heads, but its practically random.
Now true randomness has no underlying mechanism so using algorithms cant produces truly random numbers. When it comes to science we often use random numbers for certain algorithms. Like you simulate a physical system and you want to know where random perturbations take that system, theoretically over time the system should settle in its lowest energy state, its most stabil state. So you can simulate this using random numbers. True randomness isn’t really required.
When it comes to quantum mechanics we find true randomness, and that can make simulating these systems difficult for just 1 or 2 particles. But when it comes to the mathematics we have the necessary mathematical tools to deal with this randomness.
So probably theory deals with truly random situations. Even treating pseudo-random ones as being truly random. Like a dice throw or a coin toss. But when it comes to simulating things we can only generate numbers that look random enough, now we can theoretically figure out these numbers by looking into the algorithm, but simulating is for practical purposes and for that pseudo-random numbers are perfectly random.
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