### Are people capable of generating a random number?

• Let's say you tell me to produce randomly a number from 1-100, and I choose the number 47. Can it be said that there is a specific reason I chose the number 47, and that it is not completely random? By random I mean that there is absolutely no reason this number in particular was chosen.

It seems odd to me, since it seems like since I have applied conscious effort to produce or choose a number within that range, or even without range, that it can't be truly random, but there might be a reason why I chose that number amongst the many others I could have chosen.

I guess the general question, which I'm interested to know if any philosophers in the past have discussed, is whether our thoughts are necessarily based on prior thoughts, or if thoughts can be truly spontaneous and random?

You need to define what exactly you mean by "random", as this changes how we answer the question. It seems you are getting at causal determinism. If causal determinism is true, nothing is intrinsically random in that it could not have come about without a cause. However, if you define random as merely *unpredictable*, then causal determinism is irrelevant and obviously a man could generate an essentially random number (in that it would have low predictability).

If thoughts were spontaneous and random, your behavior would be completely erratic and insane. There is no way, short of the ole' monkeys writing Shakespeare, you could have posed this question.

@Justin: presumably if all our actions were random, yes, we would be ready for institutionalization. But the OP is just asking about a random number.

Very complex subject: http://en.wikipedia.org/wiki/Entropy_(information_theory)

Have a look at this question.

Humans are *terrible* at choosing random numbers, and at recognizing when other things are random. We see patterns everywhere, whether they are there or not. There's a reason Vegas casinos can build lavish hotels, and it's not the price of the room.

• Yes, many philosophers have discussed the question of free will vs determinism. Too many to mention here, in fact.

The notion of "randomness" (and the associated concepts of "choice" and "chance") are suprisingly difficult to pin down.

Jacques Derrida has a fascinating essay on the subject ("My Chances/Mes Chances"), but judging from the manner your question is posed, I imagine you are too unfamiliar with the underlying literature to glean much from it; I suggest instead you turn to some encyclopedias of philosophy to do some preliminary research on the subject.

Sure this is in the vein of free-will vs determinism but the OP has narrowed it down to a very very specific problem which might be assailable.

I don't see how it is assailable without solving the whole free will/determinism debate first; if there is free will, one can spontaneously "choose" (in an unmotivated fashion) some number; if determinism prevails, one cannot. It seems to me that this specific case reduces to the general case without loss of generality.

I'm just pursuing an argument.... I kinda agree with you. But I can imagine their might be a biological mechanism that'd be particularly specific to creating random numbers. Then there's still the separate idea that things may be deterministic but we can't ever know enough to practically distinguish high complexity from free will.

Can we imagine a "biological mechanism" which would not be deterministic, and yet does not involve free will? From what source of entropy would the random numbers arise? In practical terms, of course, you are correct-- there is no way to distinguish deterministic, random and freely chosen numbers from each other, so the whole exercise is moot.

I jeepnhearing that there is a physical mechanism, a Geiger counter recording the truly random decay rate of particles. So I could imagine a biological mechanism implementing something similar.

@Mitch: The strongest argument against randomness is that it is essentially undefined in any strict sense; you also can never infer that something is "truly random" *a posteriori*. It's is not even theoretically possible through mere observation to distinguish between that which is actually random and that which *appears* random. "Apparently" random processes could very well be determined ones we don't understand yet.

@stoicfury:randomness is very well-defined mathematically and there are physical theories of random atomic decay that are confirmed by experiment.

Randomness is very well defined in a mathematical sense, but not in a philosophical sense, and the physical theories of "random" atomic decay do not refute determinism. We have to be careful about crossing domains here.

Have a look at this. What are your thoughts?

@ThisIsNotAnId: My thoughts are that the procedure described by the thought experiment will *not* produce a random number if the universe is deterministic-- so, unless we can determine if the universe is deterministic (which we can't), we can't really define "random" from a philosophical perspective.

Ah, I see. The procedure outlined does not claim that it will produce random numbers. Rather, it makes a different claim. Have another look to see what I mean. At any rate, I think I should repost that answer here.

@Michael: Do you know if that Derrida essay is available online somewhere? I spent a few minutes searching on Google, but didn't come up with anything that looked promising.

"Randomness" is actually a pretty simple concept mathematically: it's basically a formalization of "unpredictable". if there is any bet you could make on the outcome of the next sample whose expected value is > 0, then the sample isn't random.

In CS TRNG (Truly Random Number Generator) is one that cannot be simulated (in fact predicted, but if it can be predicted than it can be simulated) by TM. E.g. an RNG that returns n'th bit of irrational number is TRNG.

• Empirically, humans can't choose truly random numbers.

If our thoughts aren't based on our prior thoughts, what are they based on? If you don't have something to build off of it seems like you don't have anything.

By your argument, a newborn must either be "born" with thoughts or not be able to have *any* thoughts of his/her own, ever. Stimulus from the environment forms basis for "new" thought, yes?

@ThisIsNotAnId I can use the environment around me to generate a random number. For example, on my computer I always display the number of seconds so that I have a psuedo-random number generator to use when I want one. However, that is not me generating a random number. Taking in input from the environment is not generating.

@KellerScholl Aren't you falling in plain determinism? Not that I have a problem with it, but in that approach, there's no random at all.

• Ok - let's say I tell you a number between 1 and 100 inclusively, which is random - how could you prove it?

Of course, if I say 1, 100, 99, 42 or 13, most people will claim it wasn't random, because their first thoughts where about the same numbers, but if these numbers where excluded, then it wouldn't be a fair draw from 100 numbers, but from 95.

So from a single number, you can't distinguish a biased number from a random number. I can tell you a number, and you can't prove it isn't random, but you can't prove it is as well.

So I could tell you my technique, how to generate the number, and convince you. If most people could learn the technique, and you coulnd't tell before, what number the people are producing, and more: if the repeated usage of the technique would lead to an uniformly distribution over the numbers from 1 to 100, we would call this a 'Yes, we can'.

Ok. So I take a sheet of paper, write the numbers 1 to 100 on small pieces of it, put them in a bag, and pull a number - mission accomplished! :)

That is cheating!

Is it? Ok - we then need to see how to sharpen the rules, I guess? No tools allowed, like paper and bag, RNG and dices?

Ok - I pull a lot of hairs out of my head - much more than 100, let's say 500 to 1000 hairs, and then I count them, and take the modulo. :)

That is cheating!

Is it really? Well, of course the technique doesn't scale. It can't be repeated very often; not often enough to check, whether an equal distribution is reached. And you could tell, that the rules prohibit any material as tool.

Ok. Then I'm nearly to the end of my wisdom. For a random result, I need some unpredictable input, and of course, my brain isn't a good source for such an input. I could name a measurement, which would work for a small amount of small random numbers (1-10), and it works similar to the hair example:

I think about a song I know, and the first song which comes to my mind, I count the characters. I can't predict from the first song - "I am the walrus" how many characters it has. The number is pretty big, compared to the number range (1-10), and I take the modulo, and have a random result.

So this is a proof of concept, and the next time, I would, of course, have to choose a different song, and so the number of experiments is limited to the number of songs or poems I know, and it is a time consuming procedure.

If the rules say 'name a number spontaneusly - in 2 seconds', I'm pretty sure nobody can produce repeatedly random numbers. But given enough time, you can.

I quite like this response and the modulo was exactly what I was thinking: pick a huge number (random as you can), and mod it to be in the correct range (mod 100 + 1).

Computers commonly use the current time as their random seed. Humans could do likewise: use your best estimate of the current time to the second, modulo an odd number (to ensure that the part of the time that you're bad at estimating gets lost in the shuffle).

I'd argue that this would still be pseudorandom: It is seeded by the clock you're looking at, or by the state of your brain/memory in terms of which songs you can most easily recall. So it is deterministic, although the underlying factors would be extremely difficult to detect. Some hypothetical soulmate who would know your state of mind "infinitely well" might be able to guess the songs you'd pick and which modulo you'd prefer.

• I think that this question has been answered to some degree outside of philosophy. There are several mathematical studies that have demonstrated that when humans are asked to provide strings of random numbers, they turn out not to be random at all, and that similar patterns may be found within the strings. The philisphical question is of course, are the patterns real? There is an occurrence of the same integer, and adjacent integers, and integers within specific sets of 10 from one ending in zero to the next,(10-20, 20-30,etc.) that greatly exceeds statistical probability of the occurrence. If given a choice from 1 to very large numbers, say a trillion, the strings are skewed toward lower numbers.

Any chance I might be able to persuade you to back your answer up with references to some of the studies you are talking about?

people are capable of generating random numbers.

it doesn't mean we're always acting in unpredictable ways. much to the opposite: the more conscious we are of our actions, the more predictable they are.

even if we could ever precisely pin out the reason why we choose a particular single number, that's not to say it wasn't random. reality can be both deterministic and completely unpredictable to every practical sense for the whole existence of life in it.

anyone can think of a completely unpredictable number for any practical purpose, specially if it's unconscious. our language tend to inflict a lot of bias in anything we do. but let's leave the discussion about randomness and free-will aside.

think of it this way...

despite what's shown in the movies, some amnesia cases turn people unable to remember anything, while maintaining the brain working seamlessly fine, having new thoughts normally, unrelated to previous thoughts.

those thoughts from a brain with amnesia couldn't be related to previous thoughts, since they simply don't exist. they are forgotten!

the hardest part between generating a random thought or action and making it into a number is actually verbalising it.

the best and most secure ways to generate entropy for random numbers in a computer will always use what we call noise. and it could be as simple as moving a mouse, typing the keyboard, or vocalising any sound.

the number a deterministic computer can generate with our human entropy is provably as real as any other seed that can be used to generate what we still call today real randomness.

• See, I believe that there is quite a confusion between 'randomness' and 'unpredictability'. Unpredictability is when WE can't pin down the outcome. We humans don't know everything so we aren't able to pin out the reason for the generation of that particular number, and the number, but, it(the reason) still exists.

Let's assume that there is a consciousness called 'Reality'. It knows everything and can analyze everything. This Reality has a brain. So, this Reality can pre-calculate every human action, or the string of random number(s) based on their experiences in this case. One can't permanently delete his experiences. Even if he/she is an amnesiac, they remain in the subconscious part of our brain, and based on his/her experiences we do everything. Also, forgotten means irretrievable. It's there, but you can't recollect it. It doesn't mean permanently erased.

Random is something that our friend Reality cannot pre-calculate. It has no roots, no origins, no subconscious reasons. It just is there. Nothing can generate random numbers. There always has to be something, or some reason to everything. Even computer random generation algorithms have a seed, i.e., the number starting from which the random generation algorithm is executed.

So, humans are incapable of producing a random number. We can make a unpredictable number, because our algorithms are unique and highly complex, but not a random one.

Source(s): Intellectual combat

i like the general story here. however, defining random as an unreal utopia is too far from the real use case of the word. rather say reality can also calculate randomness and the difference is that something unpredictable to us today might be predictable tomorrow... but randomness can only be predicted by "reality" alone. ever. also there's no need to evoke consciousness.

• Douglas Hofstadter has something to say about randomness in his book Godel, Escher, Bach. In chapter 19 he explores the complexities of mathematics and meaning as they could apply to Artificial Machine Intelligence. Its a daunting subject, and Hofstadter chooses to understand human intelligence as having the 'right stuff' to randomize. I should add he does not detail a specific human capacity for randomization. He recaps his thoughts on creativity itself within the general frame where machine and human processes, might, possibly intersect.

"It is common notion that randomness is an indispensable ingredient of creative acts. [...] This world is a giant heap of randomness; when you mirror some of it inside your head, your head's interior absorbs a little of that randomness. The triggering patterns of symbols, therefore, can lead you down the most random-seeming paths, simply because they came from your interactions with a crazy, random world. So it can be with a computer program, too. Randomness is an intrinsic feature of thought, not something which has to be 'artificially inseminated' whether through dice, decaying nuclei, random number tables, or what-have-you. It is an insult to human creativity to imply that it relies on such arbitrary sources." (p.673)

• I don't believe a single person could generate a truly random number, but two people can (with the same premise that a person will randomly win, draw, or lose when playing Rock, Paper, Scissors).

1. Between you and your friend, establish who will be "initial", who will be "final" (must pick different ones); e.g. Adam is initial, Bill is final.

2. Establish the integer range; e.g. -5 to 18.

3. After a synchronized count down, both people simultaneously call out a number within the range; e.g. Adam: "-2", Bill: "9".

4. Take the positive difference of the two numbers; e.g. |-2 - 9| = 11.

5. If initial <= final, then add the difference to the minimum; e.g. -5 + 11 = 6 (6 is your randomly generated number).

6. If initial > final, then take the positive difference, subtract it from the maximum, then add 1; e.g. initial = 15, final = 8, |15 - 8| = 7, 18 - 7 = 11, 11 + 1 = 12 (12 is your randomly generated number).

Step 6 makes sense if you imagine that you may only count up, and that the number immediately after the maximum is the minimum; e.g. 16, 17, 18, -5, -4, -3 (that is where the extra 1 comes from).

Flaws: Just like in Rock, Paper, Scissors, players don't pick all choices with equal tendency; people use this knowledge to their advantage by anticipating what the other person may pick; e.g. Adam tends to pick odd numbers more often than even numbers, Bill knows this and wants an even number, therefore Bill would pick a low odd number, or a high even number.

Very interesting. This might get more random the more participants there are. But even then, if you had a hundred participants, the resulting number would be random from each individual perspective, but as a whole, I wonder if there is non-randomness in the result, whatever that means.

if 1 person can't generate randomness, N people also can't. same thing with computers. your proposal is just pseudo at best, meaning it's just adding complexity to the predictable end event, not making it unpredictable by adding more predictable seeds.

• I appreciate the well thought out answers, but I think this topic could benefit from some objective statistical analysis, e.g. one subjects responses to several random number queries plotted over time, a large group's individual responses ranked by volume of occurrence of each number in the range, etc.. Would we see that most answers are bunched up in the middle or in the upper half of the range? Would we see that very few people pick numbers at the extreme top and bottom of the range? In essence, can we make "random" human response more predictable, and what do the observed patterns say about human nature?

This is an interesting point, but only shows whether humans can be pseudorandom number generators. I had a professor once who asked everyone in the class for two random integers. He then told us about a theorem in which (two random integers are coprime with probability 6/pi^2)[http://en.wikipedia.org/wiki/Coprime_integers#Probabilities]. Sure enough,the numbers that we had "generated" were a pretty close approximation. So, that would seem to satisfy your point, but it doesn't address whether some deterministic but seemingly-random process generated those numbers in the first place.

• My \$0.10 of wisdom is this: if you try to apply philosophy to the question, you'll end up with either a physics conundrum whose empirical testability is provably indeterminable, or you will begin doubting in the soundness of the foundations of mathematics and/or mathematics' suitability to model anything other than perhaps itself. On the other hand, my personal experience with life points to man's freedom to choose good or evil (that's what I'd call the axiom of choice :).

Have you, in a painfully related vein, ever heard of this tragic Guinness Book record: https://en.wikipedia.org/wiki/Roy_Sullivan. I must admit that this particular instance of a sequence of "random" events has a distinctly more gruesome dimension than my flipping 10 tails followed by 10 heads just 3 days after I had attempted to define mathematically an ideal "fair coin" while pondering some "baby probability" problems. You can deduce what my definition was (50/50 every time). OK, granted, this sequence was a subsequence of slightly longer string of flips, however, even so, the "probability" of getting that event was theoretically less than 1 in 300,000. Even Roy's wife was hit by a thunderbolt. The man survived 7 lightning strikes only to commit a suicide. I mean, is this a random act of nature? 7 random acts of nature?

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