OK, I had a hard time coming up with a single sentence title, so please bear with me.
Let’s assume I have a computer with a perfect random number generator. I want to draw from a (electronic) deck of cards that have been shuffled. I can see two distinct algorithms to accomplish this:
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Fill a list with the 52 cards in random order, and then pull cards from the list in sequence. That is, defining the (random) sequence of cards before getting them. This is analogous to flipping over cards from a the top of a well-shuffled deck.
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Generate a random card from the set that hasn’t been selected yet. In other words, you don’t keep track of what card is going to come up next, you do a random select each time.
Programattically I can see advantages to both systems, but I’m wondering if there’s any mathematical or statistical difference between them.
The lava lamps are not true random though. For something to be truly random, it must be non-deterministic (no seed at all). The only way for a computer to accomplish this is to read from a source of true randomness in nature. The lava lamps are random enough, but not truly random.
At the moment, the only source thought of being non-deterministic is quantum mechanics.
So if you make a computer generate random numbers out of the randomness of quantum mechanics, you would have truly random numbers.
And even then, if you look at quantum mechanics through the right lens, its apparent randomness is only an illusion of perspective. If you flip the quantum coin, then with 100% certainty, perfectly deterministically, it will come up heads in one timeline and tails in the other. It’s only because your two future selves can’t interact with each other that they can’t have an argument about what the result “really” was, so one says, “it actually came up heads, and the result was completely random,” and the other says, “it actually came up tails, and the result was completely random.”