Can the mind generate random numbers?

[Whovian]

Yea, thought it was Euclid, but didn't want to say that in case I got the wrong Ancient Greek mathematician.

 

[Chronos]

I believe it was Cantor.

 

[Whovian]

I believe it was Cantor.

http://en.wikipedia.org/wiki/Euclid's_theorem]See[/PLAIN] here. Unfortunately, it appears Cantor had nothing to do with this. Maybe you're thinking about his work on Transcendentals?

 

[Brainguy]

Define random. Name something in our universe that is truly random. Its hard for me to answer this question because I don't even know what random is. For example: when you roll dice, you can calculate the friction of the table, force Of the throw, which number is facing up when it's thrown, spin, and many other factors that all loop back to how hard the brain decided to throw the dice, which we have established by now is not random. Think about that.

 

[Pythagorean]

Radioactive decay

 

[RMnumbers]

Okay, preliminary definition of (uniformly) random then: Write down a few hundred 1s or 0s. I don't know how to do the statistics exactly, but I do know that:

0 and 1 should each appear about 50% of the time
01, 10, 00, 11 should each appear about 25% of the time
etc...

It's the "about" part that I don't know how to quantify. I assume that you find the 'degree' of randomness in terms of deviation from this expected distribution, rather than a binary 'is or is not random'. But whatever way you phrase it, no we aren't good at generating random numbers. People tend to swap numbers too often in such situations (so strings like 111 or 0000 almost never occur where they should be more common). It's been shown several times that people aren't good at *consciously* generating random numbers. Whether subconscious ticks and things can is a different story. My guess is that they'd at least be much closer than real attempts, because even when trying to generate random numbers people peg out certain patterns as being more 'random' than others, which doesn't work out properly.

 

[viraltux]

Randomness is nothing more than a useful mathematical concept, just like infinitesimals or infinity.

When you start wondering whether those concepts actually exist this is mathematics no more but philosophy, and when you go philosophy on something then everything goes.

Roger Penrose in his book The Emperor's New Mind set up his mind to disprove a computer scientist statement in TV claiming that it is perfectly possible for machines to think like humans do and be indistinguishable. I really enjoyed this book because you could see how convinced was Sin Roger of his success at the beginning of his journey and how, little by little and being the excellent mathematician Sir Penrose is, he realizes that the computer scientist was actually right.

Yet, at the end of the book Sir Roger resorts to Quantum Mechanics to try to escape the mathematical inevitable conclusion, he knew that if he could prove that any quantum random event takes place in the brain then human thoughts can never be fully replicated by standard computers. Unfortunately for his theory neurologist agreed that no quantum effect might ever have any impact in the human cognitive process.

So do random events exist? does it make any sense to compare infinity cardinalities? do infinitesimals exist? Well, grab a drink and have your go...

 

[Borek]

Unfortunately for his theory neurologist agreed that no quantum effect might ever have any impact in the human cognitive process.

Did they? I was under - perhaps false - impression that he was criticized for his statements that consciousness can't be explained by the known physics and for his way of incorporating randomly selected anatomical features to speculate about "quantum engine" present in our brains. But just because he is wrong doesn't mean quantum effects can't have any impact. that's a logical fallacy.

Rested eye can record single photons. I suppose at this level of sensitivity now and then eye will "detect" photons that don't exist - after all that's just a sensor and a noise. Such a signal can trigger some thought process ("wow, light, there must be an exit there!"). That would be an impact of quantum effects on the cognitive process, wouldn't it?

 

[viraltux]

Did they? I was under - perhaps false - impression that he was criticized for his statements that consciousness can't be explained by the known physics and for his way of incorporating randomly selected anatomical features to speculate about "quantum engine" present in our brains. But just because he is wrong doesn't mean quantum effects can't have any impact. that's a logical fallacy.

Implying that I imply that something is wrong because Sir Roger Penrose might be wrong in other subject probably has a name too... and probably it's a very meanie one...

Rested eye can record single photons. I suppose at this level of sensitivity now and then eye will "detect" photons that don't exist - after all that's just a sensor and a noise. Such a signal can trigger some thought process ("wow, light, there must be an exit there!"). That would be an impact of quantum effects on the cognitive process, wouldn't it?

Well, you could integrate every quantum effect detector known to mankind into someone's brain and the way the brain process information will still be completely unaffected by quantum events.

But even if it was so, which neurologist claim it is not, it would be the same that saying a quantum effect can flip a bit in a computer and that we need to take into account those "random" flips to understand how a computer works, and, in this scenario, since both brain and computer might be altered by "random" events they both might again be considered equivalent.

After reading Sir Roger Penrose's book I am quite convinced that his passion trying to differentiate humans from machines is rooted in the same feelings scientist had when Darwin postulated "we are monkeys". We want to be special, but the more we know the less that seems to be so... And this is a hard thing to accept.

And by the way, to see how hard is to let go this "human mind is special" feeling it is quite interesting to check the statements people made through history about the capabilities of computers to play chess game against humans... They went from "Impossible to beat a any human" to "My cellphone can beat a World's Chess Champion". The reading is interesting because you can see the titanic resistance some offered to believe such thing was possible and only accepting it when they themselves were beaten by a machine.

I think Sir Roger's arguments, though really interesting, are nurtured by this dismay and denial feelings about human nature.

 

[atyy]

Keys used in computer security are prime numbers [which is believed to be an infinite set]. It would be interesting to see if prime numbers can be proven random.

Terence Tao: Structure and Randomness in the Prime Numbers
slides available

 

[Farahday]

The set of all possible integers is infinite. For a number to be truly random, it must include all of them - else the range of the set is predictable. The VAST majority of numbers have more digits than a human could possibly conceive in a million lifetimes. If you add decimals...well the probability is infinitesimal.

 

[ThomasT]

A bit off the wall, but anyone who plays with random number generators quickly learns that it is impossible to make one that is truly random, using software alone. Has anyone ever considered whether people can actually generate random numbers? How does the mind produce a number "randomly"? Do we have any idea?

It is pretty easy to imagine analyzing person-generated random numbers and looking for a pattern.

I'm pretty sure that I can generate lists of, say, 10 numbers, that you can't predict. Or even one number. Given that, am I producing truly random numbers?

Wrt software random number generators, if you know the algorithm, then you can predict the numbers. Not random. But if you don't, then you can't. Random.

So, what's the difference between a random number and a truly random number.

 

[Ivan Seeking]

I'm pretty sure that I can generate lists of, say, 10 numbers, that you can't predict. Or even one number. Given that, am I producing truly random numbers?

Not necessarily; a sequence of numbers can be non-random but not predictable. The question is, does a pattern emerge given a large set of selected numbers?

 

[ThomasT]

Not necessarily ...

Yes, necessarily. I can generate lists of numbers, independent of any discernable algorithm, that you can't predict.

Are they random? Are they truly random? What's the difference?

What does the word random refer to?

 

[Ivan Seeking]

Yes, necessarily. I can generate lists of numbers, independent of any discernable algorithm, that you can't predict.

Are they random? Are they truly random? What's the difference?

What does the word random refer to?

How do you know your list of numbers is random?

If there is a pattern, after enough numbers we could in principle predict your next choice. But it may require an extraordinarily large set of numbers before a pattern emerges.

 

[ThomasT]

How do you know your list of numbers is random?

As I asked ... define what you mean by random. Then we should be able to ascertain if my list of numbers is random, or not.

If there is a pattern, after enough numbers we could in principle predict your next choice. But it may require an extraordinarily large set of numbers before a pattern emerges.

Suppose no discernible pattern emerges. Then, in principle, you would never be able to predict my next choice. So, are the numbers I'm spewing random? Are they truly random?

 

[Ivan Seeking]

As I asked ... define what you mean by random. Then we should be able to ascertain if my list of numbers is random, or not.

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

Suppose no discernible pattern emerges. Then, in principle, you would never be able to predict my next choice. So, are the numbers I'm spewing random? Are they truly random?

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]

As far as I know, we have no way to know... or at least we don't know.

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]

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.

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]

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.

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]

No. Random has a specific meaning.

What is it?

Whether or not truly random events exist is a deep question.

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

...I think the correct answer is, we don't know.

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

 

[chiro]

Not necessarily; a sequence of numbers can be non-random but not predictable. The question is, does a pattern emerge given a large set of selected numbers?

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]

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.

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.