When you ask a human to generate random numbers, they’ll come up with a series of values.

Do we have any idea what mechanism in the brain is used for this?

I’ve heard somewhere, perhaps on here, that humans are terrible at generating randomness – for example, they fail to take into account that randomness is “clumpy”, and their values tend to be too well distributed.

Computers have trouble generating random values – some kind of “entropy” is required for the “seed” of the random number generate, such as a high-res timer or something provided by the user, such as mouse movements.

We don’t understand enough about the brain to say how it does much of anything that it does. There is no dedicated random number area of the brain though, and human generated random numbers tend to be anything but random. For example, if you ask a bunch of people to pick a random number between 1 and 100, they will avoid even numbers, powers of ten, and they will avoid both extremes of the scale as well as the middle (they’ll almost never pick 50). The number 67 shows up a lot. Instead of picking a truly random number, your brain tends to pick a number that it thinks conforms to its idea of what a random number should be.

Computers most often use the timer tick as a seed value into a pseudorandom sequence. On rare occasions you’ll see mouse movements and the like used, but most often they just get the current system timer value. There are some computers that have true random number generators in them, which are usually constructed out of white noise circuits, but you won’t find this sort of thing in a typical home computer.

Multiples of ten? Powers of ten from 1-100 are just 1 (10^0), 10 (10^1) and 100 (10^2). That is really interesting, though…I would expect people not to say the extremes of the scale or the number right square in the middle, but avoiding even numbers is the real surprise. Avoiding half of the possible numbers makes for a terrible random number generator. We are funny creatures sometimes.

I did a quick search, and I turned up abstracts of a couple papers that suggest that human-generated random numbers look a lot like a hidden Markov model. I’m not at school right now, so I can’t get to the full text, but I’ll take a look when I am to see how interpretable the models are.

There’s a difference between ‘random’ numbers, which humans are good at producing, and ‘pseudo-random’ numbers, which computers are good a producing. Computers need a seed so that they don’t produce the same sequence of numbers every time. It’s only used once at the start of the sequence, after that, the numbers aren’t truly random at all, they follow a known sequence, but the characteristics of that number set match the randomness found in nature.

Not a mathematician, so not saying any more on the subject.

Do you have a cite for this? Everything I’ve read (included the responses here) suggests the opposite – that humans are terrible at producing truly random numbers.

This is what I’m asking! Thanks. I’m also curious about the “mechanism”, the source of entropy the brain uses. I wonder what an fMRI of someone asked to generate random numbers would show.

I suppose you could argue that humans make random numbers, but not unweighted random numbers. That is, you can make statements that odd numbers are more likely than even numbers, 67 is disproportionally likely, 50 is disproportionally unlikely, etc., but there’s no script that you could discover that would tell you exactly what sequence of numbers is coming up, as is the case with a computer’s PRNG.

Colloquially, “random” numbers are as described. True random numbers don’t seem “random” for humans. For example, there’s a reason why the random feature of good MP3 players doesn’t just pick a random song, but keeps limited track of the previous song. The “random” we want does not have clumping.

I disagree. I think you are using a mathematical definition of random which can be assessed in terms of the characteristics of a sequence. For humans using the commonly understood definition, the only requirement is that there’s no intent to relate the numbers to each other, or something else.

I recall seeing a study that suggested that people could become very good at generating pseudorandom numbers with training.
This isn’t especially surprising since computers can generate good pseudorandom numbers using entirely deterministic processes.

It would be interesting whether such people would in a sense be better than standard RNGs, since they would (presumably) not require a seed value.

However, good cites are not forthcoming. I’m not going to link parapsychology.org for example.

It has been claimed in this thread that people, when asked to pick a random number from 1-100, pick some numbers more often than others. Are you disputing that?

Well you know you contrasted the pseudo-randomness of computer’s random number generators to the ‘randomness’ of human random number selcetion. So the defintion of random you’re using has gone beyond the colloquial.

Random here can only mean that it’s the result of some none deterministic procedure. However the evidence is that this is not the case, i.e. people will select a number that they think sounds random.
I know myself if someone asked me to select a radom number between 1-100 what would pop in to my head would be ‘56’ because that’s subconcious my pre-conceived notion of a random number, though I think I would probably adjust that slightly to ‘23’ as I’m aware of the tendency for people to select numbers lying in the middle of the range when asked to pick a random number (and ‘23’ would be my idea of a random nuber not lying in the middle of the range). I might even adjust it further to a ‘1’ as my perverse nature would want to select a number that I would expect the fewest people to select. Whether I selected ‘56’, ‘23’ or ‘1’ would just be related to the length of time I thought of it.

That doesn’t really seem like a truly random process to me.

First, what’s not random about the number 56? Or 23?

Second, what’s random about a single number?

Third, what non-deterministic process does a computer use to generate random numbers?

I can’t provide the mathematical definition of ‘random’. But that doesn’t have any effect on the definition of a word that existed before any computers or mathematical definitions. I don’t contend that humans are good at producing random numbers in a mathematical sense. But the sequences produced by computers are not random either in the sense of the random decay of a particle. I hoped that pointing this out would lead to mathematicians providing some good definitions for mathematical randomness.

Mathematics doesn’t have an absolute definition of random. The word usually means something along the lines of ‘stochastic’ i.e. modelled by probabilty theory. What’s more the distrbution is usually assumed (unless otherwise stated) to be uniform.

The funny thing is that non-random computers are actually pretty good at guessing what people will say when asked to give a random string of numbers.