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What is Randomness? (physics)

I have been thinking and have come to realize that there probably is no such thing as randomness. I mean if we create a computer program that's purpose is to generate 'random' numbers it will constantly use that algorithm hence it not really being random. Or maybe my understanding of how random is ,defined, is flawed. It seems to be deterministic to a degree.

Note by Johnson Adeleke
4 years, 7 months ago

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There are probably different ways to define random based upon the field you're studying. From a math perspective, here's a shot at it:

"An event is random if and only if it occurs with some underlying probability distribution - a distribution which we may (e.g. a coin flip) or may not (e.g. atmosphere noise) know. Until the event occurs, we can't be sure of the outcome."

More colloquially, something being random means it is unpredictable.

As for your comment about "physics behind randomness" - perhaps. Certainly, physical events such as atmospheric noise or a coin flipping through the air have an amount of randomness which human/computer-generated phenomenon have a hard time matching up to.

For a moment, let's throw that all out the window, and look at this from a totally different perspective - I have a feeling your remark about "deterministic" might have been getting at this. Let's consider the famous Monty Hall problem: there are 3 doors, behind one of which is a car and the other two conceal goats. You pick a door, and if you choose to "switch", one of the other doors will be opened which certainly contains a goat. It is said that the probability of switching gives you a 2/3 probability of getting the car. But really, you could argue that the probability is either 0 or 1: either the car isn't behind the door you're switching to, or it is -- you don't know which, but it's predetermined. Perhaps this is less true with a future event, such as flipping a coin, but depending on your personal/spiritual beliefs, you might even consider that predetermined.

In either case, I think probability/randomness is all about perspective. The question you're asking isn't actually "what is the probability of that happening", but rather "what is the probability of that happening GIVEN what I know now?". Sure, a string of bits isn't "truly random" - they're quite predetermined - but if you have no access to those bits and it's for a single trial, it's pretty random to you. Similarly, a meteorologist would say there's a 60% chance of rain tomorrow based on what he/she knows about the weather today. Eli Ross · 4 years, 7 months ago

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I agree with you. But your definition of an even being random I still do no understand. Because probability "is the chance of something happening". The outcome may be completely different from what we could determine from probability. I'm assuming random cannot really be defined. I think it is not an intrinsic property that would be necessary in a deterministic universe( I'm assuming our universe is deterministic). But then I was thinking of it in a non deterministic plane. So I don't know but maybe if we could this is a weird idea ( figure out how accurate is probability in the real world). The only problem with that is it would need us to take a lot of factors in consideration, Hence we would need a very powerful computer. :D In a non deterministic universe randomness would seem almost impossible to comprehend. Sorry if I haven't displayed my point very clearly. :) Johnson Adeleke · 4 years, 7 months ago

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Yes, thank you for the links. I'm not really sure how to define random. :) Is there physics behind randomness? Johnson Adeleke · 4 years, 7 months ago

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It depends what you mean by an "algorithm". Let's say I want to pick a random integer in \(\{0,1,2,\ldots,9\}\), so I write a program on my calculator that returns \(\lfloor10 r \rfloor \) where \(r\) is chosen uniformly on \((0,1)\). I would say this is random if and only if that \(r\) is chosen actually at random (so in that sense, an "algorithm" could be "truly random"). HOWEVER, you're on to something: a calculator doesn't actually choose truly at random -- instead, perhaps it will take a long string of bits and choose from it. We refer to this as pseudo-random, and you can read more about it here.

Now, let's suppose you want to actually have random numbers. Well, for that purpose, we turn to physical quantities that we believe to be "truly random". One example is atmospheric noise. This is what the random number generator random.org uses. Is it "truly random"? You could argue not. But it's quite certainly a better attempt at "truly random" than choosing from some predetermined bits.

This offers some good discussion. Eli Ross · 4 years, 7 months ago

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