Can the mind generate random numbers?

Ivan Seeking

A truly random set could never be predicted [after the fact using some logical basis] no matter how many numbers the set may contain.

As far as I know, we have no way to know... or at least we don't know. That was the point of the thread.

What you are calling random and truly random, is probably better referred to as pseudo-random, and random.

ThomasT

I agree. So, the term random, like the term spontaneous, or the term god, refers to our ignorance. When we don't know how/why an event occurs, then we call it random, or spontaneous, or say that god did it.

Ivan Seeking

No. Random has a specific meaning. Whether or not truly random events exist is a deep question. I am out of touch on this stuff but I think the correct answer is, we don't know.

If you go back and review the links in this thread, much of this is addressed.

ThomasT

The effective, de facto meaning of the term random is unpredictability. When a particular phenomenon is unpredictable, then that necessarily means that there is no deeper understanding of the phenomenon. If you can't predict it, you can't predict it. Period.

ThomasT

What is it?

I don't think it's deep, but rather just a matter of semantics.

Wrt stuff we label as random, spontaneous, etc., I agree. Thus, these terms refer to our ignorance.

chiro

Very good point.

Humans are often hopeless at seeing the majority of patterns out there, even for things that are highly deterministic like recurrence relations to name one.

As soon as the 'random-like' behaviour crosses a threshold, it becomes too hard to make sense of.

Chronos

There is no unambiguous test for 'randomness'. Lotteries have been attempting to do this forever. While non-random patterns are rather easily detected, it is, by definition, impossible to devise an algorithm that 'proves' any set is truly 'random'. Oddly enough, the difficulty actually increases with set size.

viraltux

What does truly 'random' means for you?

RMnumbers

"Truly random" is almost meaningless: for any finite sequence of numbers there are always multiple options for what the next number might be. You can always adjust your 'formula' to account for whatever other number or sequence of numbers gets thrown out, so given a finite sequence you can never be completely sure that you have the 'right' formula. And for an infinite sequence, well then you already have the whole thing, so there's nothing to predict.

The only meaningful definition of random is *statistically* random, meaning "given the start of a sequence, do we have a greater than even chance of predicting some parts of the sequence we haven't seen yet?" And people have repeatedly been shown to be very bad at that. This arguing of "you can't predict my next number so it's random" is irrelevant: you can *never* predict the next number with 100% accuracy given a prior sequence. Never.
1,2,4,8,16,?

32? If they're powers of 2.

31? if they're the maximum number of pieces you get from connecting n points on a circle into a complete graph.

Any 5 points determine a quartic, so you could setup ax^4+bx^3+cx^2+dx+e and sub in the points (0,1), (1,2), (2,4), (3,8), (4,16) into that equation and solve for the coefficients, then take the value at x=5 as your next number. Or you could create any sequence of x values (say squares), and plug in the next x value in that sequence.

If you're using random to mean anything other than statistics, you're doing it wrong. 100% predictability of a sequence when you don't know what generates it is a useless thing to even bother talking about, because it never exists, even mathematically.

Pythagorean

Wolfram Mathword says:

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying distribution. Almost always, such numbers are also required to be independent, so that there are no correlations between successive numbers. Computer-generated random numbers are sometimes called pseudorandom numbers, while the term "random" is reserved for the output of unpredictable physical processes. When used without qualification, the word "random" usually means "random with a uniform distribution." Other distributions are of course possible. For example, the Box-Muller transformation allows pairs of uniform random numbers to be transformed to corresponding random numbers having a two-dimensional normal distribution.

CHollman82

I don't think randomness is possible, in any regard. Something that seems random is merely because we are unaware of the causal history of the outcome.

Yes I am aware of quantum mechanics... I still don't believe in true randomness, I believe we have more to learn.