Does True Randomness Actually Exist?
Idk if someone already said this but I think they made true randomness using quantum computers
It's already done using thermal noise. It is fundamentally unpredictable.
It’s like if you have a 1 million sided die. There’s a LOT of potential results, but it’s not an INFINITE amount.
A slot machine can only show a certain amount of slots. A roulette wheel can only have the ball land in a certain amount of spaces. Poker and Blackjack only has a certain amount of hands the player can get.
say for instance the candy bar called Mr. Goodbar which contains chocolate & peanuts made on an assembly line - what if a person buys a Mr. Goodbar and somehow there were no peanuts -
was the wrapping wrong and it should have been Hersey's or did the factory Not add the peanuts Randomly ?
I guess I should’ve said that it’s not the ONLY factor to “true randomness”. Something being completely unpredictable doesn’t mean much of anything if there’s not a lot of possible results. You’d have to have an INFINITE amount of possibilities.
I can be definitive and say you are talking about two different things. An infinite number of possibilities means you can have an infinite amount of randomness (measured in bits). By contrast a completely random coin flip is completely random, but it only requires one binary bit to represent that randomness.
Say for example you have a biased coin, and it comes up heads 2/3 of the time and tails 1/3 of the time. The results are still random, but the amount of randomness (technically called Shannon entropy) is lower than that for a fair coin. That is the sense it which it is "not as random" as a fair coin.
If you want a calculated number, the amount of randomness for a fair coin is:
-1/2 * log2(1/2) -1/2 * log2(1/2) = 1 bit
while for my biased coin it is -1/3 * log2(1/3) - 2/3 * log2(2/3) ~= 0.9183 bits
The latter is less (perhaps surprisingly only slightly less).
Mathematically inclined people may like this video. I hope it is not too bewildering to anyone. Do tell me. It's kind of university level, but doesn't involve particularly difficult concepts.
It's about infinite graphs, which are infinite sets of points, some (but not necessarily all) of which have an edge connecting them.
May imply recursivity in some way? Mind you, didn't watch the vid.
It's an excellent video about a fascinating mathematical fact. I am not sure the treatment of infinite objects would be in your wheelhouse, so to speak. But it could help your understanding if you watched it with the right attitude.
The wonderful central fact is that there is only one random graph (with a very general definition of what that is - something that could be made a tad clearer in the video, to be frank! To be fair, he does give two constructions and shows they are the same with probability 1).
The Rado Graph (also known as "the random graph")
[One more precise statement of the "there's only one random graph" theorem is as follows:
If you construct a graph by starting with a countable set of points and randomly connected each pair of points with some probability 0 < p < 1, then, with probability 1, you get the same graph to within isomorphism. For clarity, two graphs are isomorphic if there is a 1-1 mapping between their sets of vertices that preserves the property of two vertices being connected or not ].
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