## Can the mind generate random numbers?

 Quote by Whovian The've actually been proven to be infinite. The proof's relatively basic.
Euclid proved this more than 2000 years ago.
 Yea, thought it was Euclid, but didn't want to say that in case I got the wrong Ancient Greek mathematician.
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 Quote by Chronos I believe it was Cantor.
See here. Unfortunately, it appears Cantor had nothing to do with this. Maybe you're thinking about his work on Transcendentals?
 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.
 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.
 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...

 Quote by viraltux 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?

 Quote by Borek 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...

 Quote by Borek 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.

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 Quote by Chronos 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
 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.

 Quote by Ivan Seeking 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.

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 Quote by ThomasT 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?

 Quote by Ivan Seeking 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?

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 Quote by ThomasT 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.

 Quote by Ivan Seeking 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.

 Quote by Ivan Seeking 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?