Random Is A (Useful) Fairy Tale

Albert Einstein said (many times) that ‘god doesn’t play dice’. For some reason I never thought it through. I always simply thought this was his opposition to Quantum Mechanics, which models certain properties as random events. But it goes much deeper. Is there really a ‘pure’ random event? My conclusion is that it seems like it does not exist, or at least, it is very hard to prove. ‘Random Theory’ is a mathematical tool/concept/abstraction that can be used to model aspects of the world. Most of the processes we perceive as random are just simulations of random processes.
A pure random event is an ideal concept; Just like ‘true love’, ‘fairy tales’ & a ‘Hollywood movie’.

The most common example of a random event is the result of a flip of a coin. For a ‘fair’ coin, we say the probability of heads equals that of tails:
P(flip result is heads) = P(flip result is tails) = 1/2
Or is it?
Given the law of physics, the flow of air, the environment in which the coin was tossed, the force that flipped the coin, and the hand that catches the coin- the result of the toss should be known. The fact we don’t know that, doesn’t mean it is an unknown random. However, it is a useful abstraction. One where we say that it is effectively random.

My ‘probability 101’ professor said that the probability of a random event is a peculiar thing; After you know the result, the probability collapses to either 0 or 1. If we let time pass, and we see the result of a flip of a coin is ‘heads’ we know for certain the probability for heads for that specific flip is/was 1:
P(flip result is heads given heads is the result) = 1
It sounds like I said nothing. Maybe I just did, who knows? Randomness describes uncertainty that can be resolved by time and/or observations.

Imagine 30 small balls in a vacuum (no, it’s not a physicist joke) that occupy the same place and they’re in a cube. Suddenly, there’s a bang! they got separated and they are flying around in this cube, hitting one another, hitting the cube walls. Can you know where ball no. 22 is after 2 billion years? Is it a ‘random’ place? maybe there was a sub bang and ball 22 turned into 100 smaller balls, maybe ball 22 merged with 27. You could describe the motion of the balls as a random process, and you would value from it more than I can express here. You might be able to calculate the probability balls would merge and even that some sort of equilibrium is bound to exist with high probability after the first million years. Which is to say — the fact you don’t have the whole information — you don’t have the positions & velocities of all the balls, or in a more compact representation, you don’t have the first “bang” information — doesn’t mean you cannot say useful things about the world. On the contrary.

There are places where probability theory is used without even pretending there is a random process involved. You can design elevators by working out the people using the elevators as some random process. Same true for designing roads. Is text a random process? Does it matter? if using random theory solves issues in natural language? Random is an abstraction, a tool, it reflects what we know and don’t know.

Let’s go back to Quantum Mechanics, which I really don’t have a clue about, I only took an introductory course. As far as I know, in some situations, you may say that a particle can have two possible energy levels. For example, in the first level it can be used as an instrument of electric current, and in the other it is cannot be part of this process. Is it really random? If we observe the particle actual energy level, we risk ‘changing’ it; But then the probability collapses to one of the probable energy levels. If you take a step away, and say to yourself — random is just a model, it’s just an abstraction of some details I don’t have and some that I have — you cannot possibly at least ponder, if this view of the world, where you “complect” (couple) the notion of random theory with the actual world hinders the way you perceive the problem and the world.

Random processes are great. The world is not black or white. And it’s not a fairy tale full of these ideal random particles. Just like Quantum Theory doesn’t change the way we perceive physical things (the phone I hold in my hand is in my hold with probability 1, especially due to the fact I continuously observe & hold it), what I say about the nature of randomness doesn’t change the fact a flip of a coin or a roll of a dice is effectively random. It is a simulation of a random event that we perceive because we can’t collect & process all the information needed to know the result.
Well, it seems like I said nothing. Or did I?