I thought my point would be pretty clear: if humans produce certain patterns when producing random numbers, that means that is how they are defining the word random.
The word pseudorandom is specifically defined in computer circles as having to do with preconceived tables. I see no indication that most humans have such a table, so they don’t fit that definition of pseudorandom. It you want to just use it to mean “false random”, and define random in the mathematical sense, that’s fine. But don’t assume someone else is doing the same.
I’d say that pseudorandom in the computer sense is more random in the mathematical sense than random in the colloquial sense.
Like many English words, there are different meanings for the word “random”. And, indeed, in some contexts we may mean “human-like random”.
For instance, if I ask someone to make a choice “at random”, I don’t expect them to become a RNG, I just mean “make a choice with little conscious thought”.
And sometimes we mean in the statistical sense where every number has an equal chance of being generated and there is (eventually) no pattern. Certainly we mean this definition when discussing gambling / lotteries / prize draws, for instance.
I think in the context of “generating random numbers”, the statistical sense is far more likely. The OP even discusses whether the distribution of human-generated numbers is truly random…so it’s pretty clear what meaning (s)he has in mind.
That’s going to depend on what you mean by “more random”. Random in the colloquial sense at least has some element of randomness in the mathematical sense. Pseudorandom, however, is deterministic.
Pseudorandom means using a deterministic algortihm (i.e. deterministic procedure) to produce a sequences of numbers with a probabilty distibution (usually uniform). For me though pseudorandom may very well fall under the colloquial defintion of random.
Humans when asked to produce sequences of random numbers try to produce sequences which follow a uniform distribution, but aqren’t as good at it as computers. Now the question of whether they are basically (poor) pseudorandom number generators (i.e. follow a deterministic procedure) or whether there is some elemnt of the procedure that can be defined in some way as non-deterministic is the whole crux of the OP.
Myself examing how I would choose a random number if asked (I am after all described as human in some circles) can’t see any elements in the procedure I use that are more non-deterministic (if 'more non-deterministic’isn’t an oxymoron) than the procedure that a pseudorandom number generator would use.
Think of it this way, if someone asked to to select three random numbers between one and ten, would you ever reply with three identical numbers? In other words, would you ever reply 5, 5, and 5? Math tells us the likelihood of that occurring should be 1 in 1000 if the human random number generation process was truly random. That being said, no one ever gives that reply.
There are a couple mathematical definitions of randomness, and neither of them has anything to do with stochastic models. A sequence of numbers is said to be random if it is either incompressible or hard to predict (both of which can be given much more precise meanings). Of course, the two notions are related in some non-trivial way, but there’s usually one that’s more appropriate for any given situation.
Do you have a reference for this? I’ve heard the same thing, but I haven’t been able to find any specifics.
Certainly computers can beat humans pretty consistently at paper-rock-scissors, even when the human is trying to play randomly. That effectively boils down to predicting random strings of numbers, though drawn from a very small alphabet.
And on a less serious note, I have found that there are ways to get humans to produce truly random numbers, like putting a physics test in front of them.
Funny you should mention – when I was at college, I remember seeing other students trying to put random values on multiple-choice homework assignments. But they’d say things like, “Hmm…three Bs in a row…can’t have that – I’d better mix it up a bit.”
Yes, the kind of randomness I’m curious about is that described by ultrafilter. Not computer-like pseudorandomness, and not “colloquial” randomness either.
No, I’m not referring to the multiple choice. I mean the kind of problem-solving that leads to answering questions like “what is the speed of the proton?” with answers like “3.210^-43 m/s", or "610^30”.
Your information is about 20 to 30 years out of date. The system pseudorandom number generators (/dev/random and /dev/urandom) on modern *nix operating systems, including Linux and Mac OS X, are seeded from several environmental sources, not just the system timer. The resulting numbers are sufficiently random to be used in cryptographically secure applications. I would be (mildly) surprised if recent versions of Microsoft Windows did not have similarly powerful PRNGs.