shanecurran
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| Is it random? |
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A colleague of mine and I were arguing about the possibility of producing random numbers. So I decided to pose the question to the forum while I do my own research. A math and computer programing opinion would be appreciated.
Is it possible to produce a random number using a computer, or is it impossible to produce a truly random number? In other words at some point the sequence of "random" numbers will repeat and therefore is not random but "pseudo-random".
Please reply with background: for example I would reply with "Math/Economics".
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Fri Apr 08, 2011 7:04 pm |
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coaster
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The documentation, references, and whatnot for the various computer languages I've used for several decades seem to be pretty much unanimous that the answer is no. In fact, the term "pseudo-random" is used. Seeing as how all random number generators are the result of an algorithm, and an algorithm is a structured and organized and human-designed method of producing a desired result given the proper input, then an algorithm cannot, by definition, produce a truly random result.
I suspect true randomness cannot be achieved by a digital machine. I suppose it would be possible to design an analog computer to produce random numbers, but an analog computer wouldn't be very good at doing math. 
Come to think of it, a slide rule is an analog computer. I still have mine (and it still works, requires no batteries, and will probably outlast me and my electronic computers by hundreds of years.....not to mention the results produced by slide rules were good enough to get men to the moon....something we're at present no longer able to do.)
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Sat Apr 09, 2011 6:05 am |
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coaster
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This is an interesting question and had me doing some more thinking. Randomness depends on uncertainty, and there is no uncertainty in a two-state system: i.e. digital computers. There has to be some uncertain intermediate state. An organism is an analog system: an infinity of states. Therefore unpredictable and perfectly random, in the true sense of random.
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Sat Apr 09, 2011 8:47 pm |
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shanecurran
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quote:
Originally posted by coaster
This is an interesting question and had me doing some more thinking. Randomness depends on uncertainty, and there is no uncertainty in a two-state system: i.e. digital computers. There has to be some uncertain intermediate state. An organism is an analog system: an infinity of states. Therefore unpredictable and perfectly random, in the true sense of random.
I don't think you have to have an infinite number of states in order for a result to be random. Think about flipping a coin. There are only two states, heads or tails, and if you flip the coin, the result is "random" Maybe I have a misunderstanding though.
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Mon Apr 11, 2011 1:36 pm |
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shanecurran
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The question began when a friend of mine and I were discussing how a poker machine determines the cards that are drawn. I never really questioned randomness in economics, because when doing certain calculations such as a monte carlo simulation, the random number generators were "random enough" to get an accurate result.
I imagine that a poker machine assigns a number 1 through 52 for each card in the deck. Then a random or "pseudo-random" number generator would choose the cards that are drawn. If the way that cards are chosen is deterministic and repeating, then each outcome is known and someone could theoretically find a pattern and predict the outcome of a poker machine and therefore "break the c*sino".
My friend argued that the c*sino could adjust how cards are determined and therefore adjust payouts. I argued that the c*sino does not adjust the cards that are chosen, that the way they are chosen is random or pseudo-random but "fair" in the sense that the way cards are chosen do not produce better cards for the dealer than it does for the player. The way the c*sino adjusts how much they pay for different hands for example the payout for a pair might be changed from 1 to 1, to 2 to 1. I believe it is illegal for casinos to adjust the way the cards are chosen so that the machine is not "fair" as discussed above.
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Mon Apr 11, 2011 1:56 pm |
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shanecurran
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| Interesting sub-question |
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What if a computer has a pseudo-random number generator but the original state or starting point is randomly chosen? Does this make the number generator truly "random" even thought the algorithm is deterministic and would repeat at some point?
Suppose for example (continuing from the c*sino example) a poker machine has different bets in $1 increments from $1 to $100, and the bettor chooses the amount to bet. If they bet an odd number then the algorithm will start or choose from state 1 but if they bet an even number then the algorithm will choose state 2.
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Mon Apr 11, 2011 2:03 pm |
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coaster
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quote:
Originally posted by shanecurran
Think about flipping a coin. There are only two states, heads or tails, and if you flip the coin, the result is "random".
True. The "next" flip does seem to be random. But there being only two states, the summation of an infinite series is entirely predictable: 50% heads and 50% tails. If the series is predictable, then the next flip is also predictable: there's a 50% chance it's heads and 50% it's tails. If you know the probability of the next state, then the next state isn't random, either. And if done with a computer, there needs to be an algorithm to trigger the next state. There's no way to make the computer come up with the next state on its own.
What you want to do with the cards has already been done, and believe me, they know about it, and don't allow it.
I think what you said about "random enough" is the key. You don't need perfect randomness to get the result. Pseudo-random is good enough. The random number generators are used for encryption schemes and so long as the encryption can't be broken, the randomness is good enough to get the result desired.
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Mon Apr 11, 2011 4:34 pm |
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shanecurran
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I am not suggesting that I or anyone else for that matter could or should try to break the c*sino. I realize it is illegal etc. My point is theoretical and the c*sino example is a way for me to explain my point.
As for the idea that probabilities cannot be assigned to something that is truly random I disagree. I need to do some more thinking/research before I get myself in a jam. But just to clarify, are you saying that a sequence of numbers 1 through 9 that is infinite and never repeats is not random?
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Mon Apr 11, 2011 5:20 pm |
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coaster
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A sequence of infinite numbers that does not repeat isn't random. In fact, there are such numbers. They're called irrational numbers. The number pi is an example. Before computers, mathemeticians were always competing with each other to see who could figure pi to the greatest number of digits. Now of course with computers, it can be figured to as many digits as desired.
But here's the key: even though the series is non-repeating to infinity, its sequence is known and/or can be figured as far out as desired. The property of randomness comes with the uncertainty, not with the non-repetition. The greater the uncertainty (which can be expressed as a probability) the greater the degree of randomness. Carried to the limit, it would follow that a probability of zero equals truly random. Though that conclusion is logics, not mathematics. My mathematics is way too rusty to come up with a proof.
I hope when you've finished your research you publish your results here. I'd like to see what you come up with. This is the most interesting question that's come up here, period, IMO.
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Tue Apr 12, 2011 3:09 am |
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shanecurran
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My example of a sequence of numbers that never repeats itself is a bad example, because one could assume that the sequence is deterministic. Here in lies the problem, anyone of those particular numbers could be randomly generated or they could come from an irrational number (which is by nature deterministic) and this is at the crux of the question. The question is what is a truly random number and can it be generated by a computer?
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Tue Apr 12, 2011 3:36 pm |
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shanecurran
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quote:
Originally posted by coaster
The greater the uncertainty (which can be expressed as a probability) the greater the degree of randomness. Carried to the limit, it would follow that a probability of zero equals truly random.
I think you are confusing some terms here: uncertainty, randomness and probability. A probability of zero? The probability of what?
First lets clarify (since you are a logic guy I will try to explain this using logic terms): In order for something to be random it is necessary, but not sufficient that there is a uniform distribution. In other words, each state (or outcome) is equally probable. I don't think you will dispute this but if you do let me know.
I propose that it is necessary (but obviously not sufficient) for there to be at least two states or outcomes (we can call the number of possible outcomes "x"). i.e. x is greater than or equal to 2, where x is an integer from 2 to infinity. You say that a probability of zero is truly random, but this can only be achieved with an infinite number of possible outcomes. I explain below.
EX. 1 Lets assume there are two possible outcomes: heads or tails. I flip the coin, the outcome of that flip is random. Granted the probability that the coin comes up heads or tails is 1/2. According to you this is not random.
Ex. 2 Lets assume there are 6 possible outcomes: We roll a six sided die. The outcome is random: The probability of rolling each one of the six sides is 1/6.
With a uniform distribution, the probability of a particular outcome is equal to 1/number of possible outcomes or prob = 1/x. The probability approaches zero as x approaches infinity. So you are saying that a necessary and sufficient condition for randomness is that there are an infinite number of possible outcomes. This is obviously false.
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Tue Apr 12, 2011 3:39 pm |
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shanecurran
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I will summarize what I propose I know at this point and I would like to confine the argument to numbers at this point so that we don't get off on another tangent:
1. A random number is chosen from a set of possible numbers. Each number in the set is equally probable (therefore we have a uniform distribution).
2. Each random number drawn is independent from the other numbers. For example if I can draw either a 1 or a 2, and draw a 1 this does not make it any more or less likely that I will draw a 2 (or another 1 for that matter).
3. A set of random numbers drawn is not deterministic. It is impossible to predict the next outcome with greater certainty than the probability of that outcome. Continuing with previous example. The probability of drawing a 1 or a 2 is 1/2. It should be impossible to predict what the next number will be with a probability greater than 1/2. I should not for example be able to predict the outcome with greater than 1/2 certainty.
4. A computer by nature cannot produce truly random numbers by itself because its processes are deterministic.
5. It may be possible for a computer to produce random numbers by observing a naturally occurring random phenomenon. This method introduces philosophical/scientific/religious debate: Is phenomena in nature deterministic or random?
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Tue Apr 12, 2011 4:02 pm |
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shanecurran
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quote:
Originally posted by coaster
I hope when you've finished your research you publish your results here. I'd like to see what you come up with. This is the most interesting question that's come up here, period, IMO.
I know you said that you have been busy lately. Have you had a chance to check out the posts? I would like to continue the conversation.
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Tue Apr 19, 2011 2:50 pm |
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coaster
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I'll have to think about your posts and respond another time. We have six to ten inches of snow coming later today. 
Remind me again later in the week. 
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Tue Apr 19, 2011 3:30 pm |
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coaster
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I haven't forgotten; it's been a nuts week. But if I don't get to it this weekend, please remind me again via pm.
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Fri Apr 22, 2011 5:45 am |
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