# Can humans create random numbers? **URL:** \ **Category:** Factual Questions\ **Created:** [January 22, 2009, 9:55am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430 "2009-01-22T09:55:36Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 24, 2009, 10:09pm UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/41 "2009-01-24T22:09:59Z")
> [@tim314](#): > > But is the question “Is this sequence random” basically unanswerable if we don’t know where the sequence came from? Are you talking about looking at a particular finite sequence in itself and pronouncing it random or not? Or looking at a probability distribution of finite sequences and pronouncing it random or not? Or looking at the entirety of a particular infinite sequence, all at once, and pronouncing it random or not? Or looking at the digits output by some particular process one by one and coming to regard the process as random or not? Or looking at a probability distribution of infinite sequences? Or…? So far as I can tell, **ultrafilter** is saying “Given a particular infinite sequence, we call it ‘random’ if no algorithm can predict its bits with a limiting success rate better than chance”. He is giving a rule which defines particular infinite sequences as either random or not (same as one might define particular infinite sequences as computable or not). Whether this rule has applications to what you are concerned with depends on what you are concerned with. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 24, 2009, 10:17pm UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/42 "2009-01-24T22:17:36Z")
> [@Indistinguishable](#): > > It depends on what you mean by “random”. On some mathematical formalizations of this concept (e.g., the one **ultrafilter** is referring to), it will make sense to say of a particular sequence that it is or is not random; on other formalizations, it will not. As is often the case with concepts in ordinary language, “random” admits many related but non-identical mathematical interpretations… > > (Actually, if I understand **ultrafilter** correctly, the interpretation he is referring to will only allow us to say nontrivially of infinite sequences whether they are random or not; any finite sequence can, of course, be predicted perfectly by _some_ algorithm) If you want to be formal about it, the appropriate framework is something like the [PAC model](http://en.wikipedia.org/wiki/PAC_Learning) adapted to [online learning](http://en.wikipedia.org/wiki/Online_machine_learning). > [@tim314](#): > > I get that, but how do you _know_ if there exists an algorithm that can? I mean, the question “Is there an algorithm that can do X” isn’t always one we know the answer to. If it were, then we’d be able to answer questions like “Is there an algorithm that can solve this NP-Complete problem in Polynomial time?” > > I suppose if there’s no reason to expect any two numbers in the sequence to be related to each other (e.g., if it’s a sequence of die rolls or something), then we could say _of course_ there’s no algorithm that can do it. But is the question “Is this sequence random” basically unanswerable if we don’t know where the sequence came from? (I mean, unanswerable in the affirmative – clearly you could prove that it’s _not_ random just by exhibiting an algorithm that predicts the next number.) Yes, to show that a sequence is not random, you can simply exhibit an algorithm that learns it. Proving that a sequence is random is considerably harder. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [January 25, 2009, 12:13am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/43 "2009-01-25T00:13:54Z")
> [@Indistinguishable](#): > > Are you talking about looking at a particular finite sequence in itself and pronouncing it random or not? Or looking at a probability distribution of finite sequences and pronouncing it random or not? Or looking at the entirety of a particular infinite sequence, all at once, and pronouncing it random or not? Or looking at the digits output by some particular process one by one and coming to regard the process as random or not? Or looking at a probability distribution of infinite sequences? Or…? > > So far as I can tell, **ultrafilter** is saying “Given a particular infinite sequence, we call it ‘random’ if no algorithm can predict its bits with a limiting success rate better than chance”. He is giving a rule which defines particular infinite sequences as either random or not (same as one might define particular infinite sequences as computable or not). Whether this rule has applications to what you are concerned with depends on what you are concerned with. Well, what about the digits of the [fine-structure constant](http://en.wikipedia.org/wiki/Fine_structure_constant)? Are they random? Presumably not, since you can calculate the fine-structure constant from quantum field theory, so there’s certainly an algorithm that gives you each digit. But that doesn’t mean you can “work out the pattern” from the previous digits. You’re just saying “Hey, that looks like a particular number that I recognize and know how to calculate.” So is our ability to recognize the fine-structure constant as “not random” dependent on the fact that we have a theory of quantum electrodynamics? If that’s the case, it seems like proving a particular infinite sequence of numbers is random is not just difficult, but impossible. I mean, who is to say that number isn’t just some important fundamental constant of a physical theory that hasn’t been discovered yet, and when we _do_ discover that theory we’ll know just how to calculate it? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 12:16am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/44 "2009-01-25T00:16:03Z")
In what sense is there an algorithm which computes the digits of the fine-structure constant? Could you write an input-less computer program which output them sequentially? It doesn’t appear as though anyone knows how to calculate it to arbitrary precision without going out there and measuring things, which hardly counts. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 12:21am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/45 "2009-01-25T00:21:29Z")
_ignore this post_ ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [January 25, 2009, 12:26am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/46 "2009-01-25T00:26:47Z")
I guess that’s a bad example, since (if I remember right) what you’d do is calculate the fine-structure constant based on [g](http://en.wikipedia.org/wiki/Lande_g-factor), or vice versa. So you do have to measure something. I had thought about using pi for the point I was trying to make, but I’m not sure that’s the best example either . . . . I’ll have to think about it a bit. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 12:36am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/47 "2009-01-25T00:36:06Z")
So, yeah, as it happens, we don’t know how to compute the fine-structure constant; at least, not the same way we know how to compute, say, sqrt(2) or π. But sure… perhaps the fine-structure constant _is_ computable, even though we don’t realize it. Hell, perhaps, after the millionth digit, it’s all 0s. Or maybe it isn’t. I don’t know how to prove that either way. But the truth of the matter needn’t be tied to our ability to prove it. Anyway, maybe, it turns out that, on a certain computability-based account of what “randomness” is, the fine structure constant is “random”. Definitely, by a certain “is it describable from the physical laws of our universe?” based account, we would not call the fine structure constant “random”. By other definitions, we still would, and by yet other definitions, we would say it is meaningless to speak of the randomness of a particular number, and would only speak of randomness of probability distributions. Formalizations don’t have to be one-size-fits-all; the word “random” isn’t used in just one way. And, yes, many formalizations of “randomness” _will_ naturally be context-sensitive, in the sense that they will be relative to a particular language of description or knowledge base or what have you. (E.g., one natural notion of “randomness” of particular objects is taking “X is random” to mean “X satisfies every property which provably has probability 100% [in a certain proof system, modelling a certain probability distribution, using a certain language of description of properties]”. In this case, what is random depends highly on what proof system we are looking at. A very relative notion, yes, and yet still a useful one with clear ties to the intuitive concept of randomness (for example, in typical systems, we will end up being able to say things like “Every random real in [0, 1] is irrational, any random pair of such reals consists of two inequal random reals, any random sequence of coin flips has a 50-50 split of heads and tails in the long run, etc.”.) ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [January 25, 2009, 12:39am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/48 "2009-01-25T00:39:48Z")
I guess my point is, if a number _means_ something, you can calculate it (in principle). I mean, if I had no idea what pi was, I wouldn’t necessarily be able to answer the question “What’s the hundredth digit of pi?” based on the first 99 digits. But because I know it, I can calculate it. So were the digits of the [Euler-Mascheroni](http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant) constant random until Euler came up with it? Presumably the digits were always non-random (because the algorithm for them was always out there waiting to be discovered), but my point is who’s to say _any_ “random” sequence of digits couldn’t turn out to be some important constant in the mathematics of the 22nd century? It just seems that proving some sequence of numbers (of unknown origin) is “random” in this sense would be not just difficult, but impossible. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 12:44am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/49 "2009-01-25T00:44:43Z")
> [@tim314](#): > > I guess my point is, if a number _means_ something, you can calculate it (in principle). This isn’t really true (unless you’ve gerrymandered your definitions in such a way as to sap it of all significance). Are you familiar with the theory of computation, the unsolvability of the halting problem, etc.? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 12:58am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/50 "2009-01-25T00:58:59Z")
For example, here’s a definition of a quite significant number B: B’s n-th digit is 0 if the n-th program (in your favorite deterministic, input-less programming language) runs forever, and 9 otherwise. That number means something, right? And yet, I defy you to come up with a program which computes its digits, one by one. (Hint: it cannot be done). ---
**Author:** ![Kobal2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kobal2/32/20_2.png) [@Kobal2](https://boards.straightdope.com/u/Kobal2)\ **Post date:** [January 25, 2009, 1:10am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/51 "2009-01-25T01:10:13Z")
> [@Beware\_of\_Doug](#): > > Kornblutian Bistromathics is a method for generating random number sequences, based on Douglas Adams’ principle of [Bistromathics](http://www.earthstar.co.uk/bistro.htm), and determined through close observation of _Washington Post_ reporter [Anne Kornblut](http://media3.washingtonpost.com/wp-dyn/content/photo/2007/07/30/PH2007073001592.jpg). > > The researcher must first approach Ms. Kornblut for a lunch appointment. During said lunch, Ms. Kornblut (selected for her high observability quotient based on cuteness factor) is observed for such repetitive behaviors as blinking, using words such as “uh,” “um,” or “Obama,” tapping her salad fork on her plate, or toying with half-eaten chicken legs. The instances of each behavior are then tabulated; the result is a Kornblutian random number sequence. No need to even get into such specifics. An RPG group of mine came up with an ingenious yet perfectly fine way of generating D10 numbers without dice. Flip a book, read the page number, discard all but the last digit. There, random 1-10 number. No influence of prior results whatsoever (even if we assume players are going to aim for the general page cluster which yielded them their last critical success) ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [January 25, 2009, 1:18am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/52 "2009-01-25T01:18:34Z")
> [@Kobal2](#): > > No need to even get into such specifics. An RPG group of mine came up with an ingenious yet perfectly fine way of generating D10 numbers without dice. Flip a book, read the page number, discard all but the last digit. There, random 1-10 number. No influence of prior results whatsoever (even if we assume players are going to aim for the general page cluster which yielded them their last critical success) Don’t you have to choose left or right otherwise it’s all even or all odd? Seems like that choice would reduce it’s randomness. ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [January 25, 2009, 1:28am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/53 "2009-01-25T01:28:49Z")
Maybe you could do a system where you first half the page number, then use **Kobal2** ’s method? Hmm, it’s not a bad system for very casual use, but since some pages flip openly more readily than others, you’d notice after an hour or two that it’s not a great random number generator. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [January 25, 2009, 1:43am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/54 "2009-01-25T01:43:41Z")
> [@Indistinguishable](#): > > This isn’t really true (unless you’ve gerrymandered your definitions in such a way as to sap it of all significance). Are you familiar with the theory of computation, the unsolvability of the halting problem, etc.? Yeah, I realized as I was posting that that that wasn’t quite right. (\*) Really what I meant was “There are numbers that you can only calculate _because_ they mean something.” That is, it may be that the digits of pi are sufficiently random that you could never calculate the Nth digit based on the _pattern_ of the first N-1, _except_ if you recognize “Hey, this is pi, and I know how to calculate pi.” That is, maybe the digits are statistically random, so that no pattern _except_ being pi arises. No? If so, it seems our ability to create an algorithm to predict the Nth digit (for any N) is dependent on whether or not we’ve _discovered_ pi. But then, _any_ “random” sequence of digits could turn out to be the solution to some as yet unposed problem, one which is solvable by an algorithm – and thus, not random. No? (\*) Is this really a gramatically acceptable use of three consecutive "that"s? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 1:47am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/55 "2009-01-25T01:47:24Z")
> [@tim314](#): > > Really what I meant was “There are numbers that you can only calculate _because_ they mean something.” I’m not sure what you mean by this. Supposing we take a number to be calculatable just in case there’s some C++ code which outputs its digits in order. Then it doesn’t matter whether a number “means” anything or not; whether such a program exists or not is presumably independent of whether we know about it. > [@](#): > > But then, _any_ “random” sequence of digits could turn out to be the solution to some as yet unposed problem, one which is solvable by an algorithm – and thus, not random. No? No. I just gave an example of a number whose digits _provably_ can’t be computed by any computer program: a number whose digits encode the solution to the halting problem. > [@](#): > > (\*) Is this really a gramatically acceptable use of three consecutive "that"s? Yes, it’s perfectly acceptable. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [January 25, 2009, 2:15am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/56 "2009-01-25T02:15:03Z")
> [@Indistinguishable](#): > > I’m not sure what you mean by this. Supposing we take a number to be calculatable just in case there’s some C++ code which outputs its digits in order. Then it doesn’t matter whether a number “means” anything or not; whether such a program exists or not is presumably independent of whether we know about it. My point, though, is you’d never _know_ it was calculatable if it didn’t mean anything. I mean, there’s an infinite number of possible algorithms that _might_ produce the number, and you can’t possibly check all of them. So if you don’t _know_ “This number is the solution to such-and-such problem” and the number passes every statistical test for randomness, then how do you ever find out it wasn’t random. Incredibly lucky guess? My point is not “Whether a number is random is dependent on whether we know that number’s significance.” My point is “Whether we can _tell_ a number is random may depend on whether we know its significance.” Do you disagree? If I’m right on this point, it seems we can _never_ know for a fact that a particular numerical sequence is random. > [@](#): > > No. I just gave an example of a number whose digits _provably_ can’t be computed by any computer program: a number whose digits encode the solution to the halting problem. You gave a way of _defining_ a sequence of digits that provably can’t be computed. I’m not talking about that case, I’m talking about you giving me an explicit sequence of digits and asking me to test if it’s random. It seems like there’s no way to say “Yes, it’s random.” I can either say, “It’s not random because here’s the algorithm that generates it” or “I have no idea”. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 2:18am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/57 "2009-01-25T02:18:53Z")
> [@tim314](#): > > You gave a way of _defining_ a sequence of digits that provably can’t be computed. I’m not talking about that case, I’m talking about you giving me an explicit sequence of digits and asking me to test if it’s random. It seems like there’s no way to say “Yes, it’s random.” I can either say, “It’s not random because here’s the algorithm that generates it” or “I have no idea”. How would you know that a particular algorithm generates it? That’s also an infinitary search (making sure each of infinitely many digits matches up). You’re right that this definition of “randomness” involves infinite quantification. I just don’t see what that has to do with whether the number “means” anything, or has any “significance”, unless “the meaning of X” is just another way to say “a program that generates X”. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 25, 2009, 2:42am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/58 "2009-01-25T02:42:12Z")
Let’s put it this way: how could we ever tell for a fact that a particular number was equal to π? That’s also a task which cannot be finitarily pulled off; even if you saw that the first million digits lined up with π, the number you’re looking at still _could_ differ later on. But with inductive reasoning, one might choose to conclude that it is likely equal to π all the same. Well, similarly, (iterated) inductive reasoning can, potentially, demonstrate that a particular number is uncomputable (or whatever else). Instead of inductively establishing that each of its digits matches that of π, we inductively demonstrate that each computer program misses one of its digits. Just the same sort of thing. ---
**Author:** ![Kobal2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kobal2/32/20_2.png) [@Kobal2](https://boards.straightdope.com/u/Kobal2)\ **Post date:** [January 25, 2009, 4:07am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/59 "2009-01-25T04:07:33Z")
> [@RaftPeople](#): > > Don’t you have to choose left or right otherwise it’s all even or all odd? Seems like that choice would reduce it’s randomness. I’ll admit it’s not a perfect system (although it was an elegant solution to a local problem), but it is an example of human random number generation. Nowadays, some crypto algorythms are based on similar random number generation, for example relying on the last digit of the exact time a number of keystrokes were made (down to microseconds, so a pattern doesn’t readily emerge), but the same could be roughly achieved with a basic chronometer. Start it, let it run while you do something else, stop it after a random time, jot down the seconds last digit, and repeat. During WW2, one-time-use random codes were generated by fishing playing cards out of a hat, or simple church-style bingo. The point is : there are lots of ways for humans to generate truly random numbers, even without using machines to do so. Or at least, numbers random enough that the chance elements which led to their choice can not be realistically infered from the numbers themselves (i.e. you can’t reverse-engineer the generation process from the string of numbers, no matter how many numbers are generated). The real trick is to design machines to do the same thing, without any human input nor a distinguishable pattern emerging over time. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [January 25, 2009, 4:14am UTC](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430/60 "2009-01-25T04:14:07Z")
> [@Indistinguishable](#): > > Let’s put it this way: how could we ever tell for a fact that a particular number was equal to π? That’s also a task which cannot be finitarily pulled off; even if you saw that the first million digits lined up with π, the number you’re looking at still _could_ differ later on. But with inductive reasoning, one might choose to conclude that it is likely equal to π all the same. > > Well, similarly, (iterated) inductive reasoning can, potentially, demonstrate that a particular number is uncomputable (or whatever else). Instead of inductively establishing that each of its digits matches that of π, we inductively demonstrate that each computer program misses one of its digits. Just the same sort of thing. But how do you inductively establish that _every possible_ computer program misses one digit of a number? It just seems like there’s no way to do this for any actual sequence of digits. I guess my point about “meaning” is this: Let’s say I wrote out the infinite sequence 3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,… (Setting aside the issue of how I would write an infinite sequence) And I asked you the question “Is this a random sequence of numbers?” If pi hadn’t turned out to “mean” something, so as to cause us to eventually discover those digits in the process of calculating the ratio of a circle’s circumference to its diameter, it seems highly unlikely we’d ever have discovered the algorithm for it. Doesn’t it? I mean, is there anything in the digits themselves that suggests any of the various formulas for calculating pi? It seems like if the digits are statistically random (which I’m guessing is true for pi), there’s no reason to pick the right algorithm out of the infinite space of algorithms . . . unless someone says “think circles” or something. [Previous page](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430.md?page=2) [Next page](https://boards.straightdope.com/t/can-humans-create-random-numbers/482430.md?page=4)