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Comment by DeathArrow | Hacker News Reader

Picking a random integer between 1 and 1 million.

That depends on the quality of your randomness. If it's a person picking the number that definitely isn't a 1 in a million chance for most numbers. You need to get pretty specialized hardware before you can confidently say it's definitely an equal chance for every number every time.

No, you don’t need specialized hardware. The output of a modern hash for crypto absolutely needs to produce a uniform distribution across a million.

But how do you pick the input for the hash?

Current date and time.

Just bang away at the full keyboard for 50-100 characters?

You need a seed, and a previous hash. The seed is usually sourced from another random generator, that uses environmental noise and some (salted) hashing as well.

In practice, a precise clock and a few difficult to guess events like keyboard and mouse inputs are enough to get a descent seed.

Do you mean, after picking a million numbers, then every number in the range should have been picked exactly once?

Definitely not this. That wouldn't be random at all. For example, after picking 999,999 numbers you would be able to predict the next number with certainty. What it means is that every time you select a number, every number in the range has an equal probability of being selected.

Which means that there must be more state in the generator than is output as a random number; otherwise each time number X was produced then number Y would follow it. (Perhaps obvious, but I like stating the obvious.)

No, each number has a 1 in a 1,000,000 chance each time the generator is used.

That's not a uniform distribution. Probability doesn't remember previous state, so the chance of picking the number 241 out of 1 million numbers remains exactly the same after picking 241 once. In particular, the chance of getting no duplicate numbers if you pick a million times, is very close to zero.

Technically, it's not actually uniform, or "random" - it only has to be indistinguishable from random, e.g. if you had access to a true random source and a pseudo-random one, it should be computationally infeasible to distinguish them.

Given a finite amount of sample.values, you can always find a polynomial to match the values.

You can only proclaim that something is "truly random" on epistemological grounds, assuming that true randomness is somehow exposed by the universe. This holds under quantum physics, but not under classical mechanics. Unless there is some quantum effect, RNGs based on fluid dynamics, like lava lamps, may be completely deterministic, we just don't know how to set their initial conditions precisely enough.to reproduce a phase trajectory.

Your polynomial has no predictive value in almost all cases.

Yes. Finding out the nature of a PRNG and its initial state would allow one to predict next values, at least theoretically, that is, if it can be computed faster than the values are generated by the process we're looking at.

But the presence or absence of such a function for a naturally occurring process is, again, an epistemological question. That is, whether we can reverse-engineer the universe deeply enough. Unless we find its source code, we're stuck with retrofitting some formulas, and a "random process" is such for which we can't retrofit any better description than a statistical one.

You're right that we can never find conclusive empirical evidence for something being truly random, but we can say with confidence that a PRNG is not random because we can look at the algorithm.

It still is a 1 in a million chance if you have no a priori knowledge about the way the random numbers are distributed.

>If it's a person picking the number that definitely isn't a 1 in a million chance for most numbers.

Only if the person isn't aware of the issues involved.

How bout this guy

https://images.app.goo.gl/aqh2AP5tj7JBkVKZ9

I think true randomness was implied in GP’s comment. A person picking a number “randomly” from a million is not random in the mathematical sense.

There's no evidence of true randomness though. There's only evidence of us having missing information to do the prediction of what any RNG would offer us next.

It would be interesting what kind of clustering (if any) there would be if 1 million people were asked to pick a number between 1 and a million.

This is the right answer. I estimate no more than 1 human in a million can choose such a number at random.

Therefore if a human picks a number between 1 and 1 million, there's only a 1 in a million chance that the number was picked randomly.

Nope, picking a random integer between zero and one million and one would be though.

I am seeing this same/similar comment on this thread which has been posted by three quite new accounts. Is this quite normal on HN now or is it some bots farming engagement? Btw, I'm a new member here, knew about HN since a long time but never bothered to make an account up until now

Looks like one old-ish account with a number of submissions and comments, and two very-similarly-named copycats that are getting voted down to oblivion. Not very common here, but it happens.

One of them seems to have deleted the comment just as I commented about this. Also downvoting is an option? It doesn't seem to be visible here.

Downvoting is only available to users above a certain karma threshold, I believe around 500 or so.

>Is this quite normal on HN now or is it some bots farming engagement?

As you can see, my account is not new. I thought the comment will be funny. Not every comment should be terribly ingenious, long thought and crafted to show people how smart the commenter is. As a commenter you have the right to be spontaneous.

> As you can see, my account is not new. I thought the comment will be funny.

Yeah I did find it funny, no doubt. Was just asking of general culture here

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