What is a random number?

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This topic contains 11 replies, has 4 voices, and was last updated by  Autumn 1 month ago.

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  • #38059

    Unseen
    Participant

    You are in a study and a researcher asks you to enter a “random” six-digit number into a computer and you input “884477” or “222222.” Are these any less random than, say, “851904” or “781592.”? I assume the first set of numbers could show up in a truly random series. Rarely, perhaps, but nothing prevents them, does it?

    #38062

    If you get the computer to produce the sequence then it is not really a random number as it is based on a program written to generate the numbers.

    If you were to rearrange the numbers on the number pad ( The zero key could be anything from 1-9) and then allow your office cat to walk on the keyboard (as they do!) then is that number “more random” that your own one?

    #38063

    Unseen
    Participant

    If you get the computer to produce the sequence then it is not really a random number as it is based on a program written to generate the numbers.

    If you were to rearrange the numbers on the number pad ( The zero key could be anything from 1-9) and then allow your office cat to walk on the keyboard (as they do!) then is that number “more random” that your own one?

    I wonder if the coders who design pseudorandom number generators have included code that prevents such oddities as “000000,” “123456,” or “773366”?

    There are all kinds of ways, I imagine, to generate a truly random string. One thing that comes to mind is to take the first digit off license plates you pass/that pass you out on the road. Blindly picking numbers out of a jar with slips of paper or balls with equal numbers of all the first 10 digits (including “0,” of course).

    It seems that, however, if you’re in need of large quantities of random numbers, you’ll need a computer, possibly combined with some natural process that can generate them far faster than a cat.

    Imagine two computers working together, both generating pseudorandom strings but the second computer generating them at a variable clock rate, the rate depending upon readings of some constantly-changing natural process like the rate of airflow measured to the 10th decimal place, working off the digit in the 10th place. Something like that. And of course, there shouldn’t be any reason this can’t be replicated within a single computer with multiple CPU’s. (I say that not being a highly technical computer person.)

    #38064

    Autumn
    Participant

    I feel like this fits the same linguistic pattern as ‘free’. In the abstract, we can define them in absolute terms. But in practical application, we use these words in a relative sense. I play D&D with friends. A die roll or a digital roll generator are random with respect to our influence and predictive abilities. The roll is random in the context of the game. But with regard to physics for a physical die roll or math for digital, it’s a byproduct of a causal chain of events that are, hypothetically, predictable. They aren’t absolutely random.

    Likewise for a lotto draw. It’s random to the extent that no person influences the results, and the drawing mechanism is not predictable by the participants in the lotto.

    I’d entertain the possibility that absolute randomness may exist on some level, but I’m not one to invoke quantum witchfuckery in situations like this. My cursory knowledge doesn’t include anything that translates to a sort of randomness at the level humans can readily appreciate or convert to random number generation. But that’s not something I’ve ever spent much time reading up on.

    #38065

    _Robert_
    Participant

    When possible software random number generators often employ a “seed” input to help keep the result as random as possible. Sometimes the seed is something like a voltage noise measurement (good) or the current time and date (not as good).

    #38069

    Unseen
    Participant

    As long as deterministic physical laws are in control, is anything above the quantum scale ever totally, truly, and demonstrably random? (A lot seems to depend on whether the quantum level events ever intrude into the level above, where physical law applies.)

    Also, I’ll toss in Benford’s Law, a law applying to many sets of naturally occurring numbers.

    The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.[1] In sets that obey the law, the number 1 appears as the leading significant digit about 30 % of the time, while 9 appears as the leading significant digit less than 5 % of the time. If the digits were distributed uniformly, they would each occur about 11.1 % of the time.[2] Benford’s law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.

    The graph to the right (actually shown just below)

    shows Benford’s law for base 10, one of infinitely many cases of a generalized law regarding numbers expressed in arbitrary (integer) bases, which rules out the possibility that the phenomenon might be an artifact of the base 10 number system. Further generalizations were published in 1995[3] including analogous statements for both the nth leading digit as well as the joint distribution of the leading n digits, the latter of which leads to a corollary wherein the significant digits are shown to be a statistically dependent quantity.

    It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, and physical and mathematical constants.[4] Like other general principles about natural data—for example the fact that many data sets are well approximated by a normal distribution—there are illustrative examples and explanations that cover many of the cases where Benford’s law applies, though there are many other cases where Benford’s law applies that resist a simple explanation.[5] It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which is common in nature).

    (Source: https://en.wikipedia.org/wiki/Benford's_law)

    Go to the Wikipedia source if you wish to follow the footnotes.

    Anyway, the point is that even in naturally-occurring numbers, which you’d think are random, are not. Or, alternatively, that even numbers that ought to be random can embody an apparently nonrandom bias.

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    #38073

    Unseen
    Participant

    But, of course, a lot hangs on what you mean by “random.”

    #38076

    _Robert_
    Participant

    As long as deterministic physical laws are in control, is anything above the quantum scale ever totally, truly, and demonstrably random? Also, I’ll toss in Benford’s Law, a law applying to many sets of naturally occurring numbers. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.[1] In sets that obey the law, the number 1 appears as the leading significant digit about 30 % of the time, while 9 appears as the leading significant digit less than 5 % of the time. If the digits were distributed uniformly, they would each occur about 11.1 % of the time.[2] Benford’s law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on. The graph to the right (actually shown just below) shows Benford’s law for base 10, one of infinitely many cases of a generalized law regarding numbers expressed in arbitrary (integer) bases, which rules out the possibility that the phenomenon might be an artifact of the base 10 number system. Further generalizations were published in 1995[3] including analogous statements for both the nth leading digit as well as the joint distribution of the leading n digits, the latter of which leads to a corollary wherein the significant digits are shown to be a statistically dependent quantity. It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, and physical and mathematical constants.[4] Like other general principles about natural data—for example the fact that many data sets are well approximated by a normal distribution—there are illustrative examples and explanations that cover many of the cases where Benford’s law applies, though there are many other cases where Benford’s law applies that resist a simple explanation.[5] It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which is common in nature). (Source: https://en.wikipedia.org/wiki/Benford's_law) Go to the Wikipedia source if you wish to follow the footnotes. Anyway, the point is that even in naturally-occurring numbers, which you’d think are random, are not. Or, alternatively, that even numbers that ought to be random can embody an apparently nonrandom bias.

    “Randomness” is relative…it is “in the eye of the beholder” as they say. If you can’t find the pattern, well it is random to you. Of course, for an omniscient god, something like thermal noise (that exhibits ‘random to us’ gaussian frequencies) is not a problem.

    #38077

    I once told somebody that the odds of me winning the rollover lotto in Georgia are the same whether or not I buy a ticket 🙂

    #38078

    Autumn
    Participant

    But, of course, a lot hangs on what you mean by “random.”

    A definition that uses it in some absolute sense would be the outlier to standard usage. ‘True’ randomness is difficult to parse. I’d take it to mean an event that is intrinsically not predictable—something that can only be described as a statistical model, not as a deterministic model.

    #38081

    Unseen
    Participant

    But, of course, a lot hangs on what you mean by “random.”

    A definition that uses it in some absolute sense would be the outlier to standard usage. ‘True’ randomness is difficult to parse. I’d take it to mean an event that is intrinsically not predictable—something that can only be described as a statistical model, not as a deterministic model.

    Sort of like “Some random guy told me I looked like his friend’s stepsister” (random guy=weird dude), “I’m having random problems with my new computer” (random=intermittent, unexplainable).

    #38082

    Autumn
    Participant

    More or less, but to be clear, I’m not just talking colloquial usage.

    If we track historical definitions, it’s a word that’s been steadily shifting meaning. There was a time where it probably meant something more like haphazard or erratic. Over time it’s come to refer to a sort of disconnect between an event and any specific outcome. There is some sort of significant agnosticism between event and result.

    Sticking with a die roll, a D20 generates a result agnostic of what I want to do with that result. I make the roll agnostic of what the specific result will be outside of a 1 in 20 probability. that’s where the randomness is. That’s a practical and meaningful use of the term in line with how it’s evolved.

    The sort of randomness that falls entirely outside of determinism is also a logical progression of the term. It’s an extreme definition. I wouldn’t say it is ‘truer’. I think it starts to fall further away from the sorts of events we conventionally characterize as random.

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