Random Number Questions
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1) Is ANYTHING truly random? Or does randomness mean nothing more (or less) than unpredictability?
2) My friend declares he’s invented a random number generator.
2a) Is a random number generator an oxymoron?
2b) The machine generates a series of 9’s and has been doing nothing but 9’s for days. After how many 9’s can it be concluded that something is wrong with his machine? Remember, to believe that what came before in a random series has any influence on future random outcomes is called The Gambler’s Fallacy. Given a truly random system, is a continual series of one number an impossible outcome? and given that mathematically infinite series are not just possible but inevitable, surely an ongoing series of 9’s is one such possible series, is it not?
As usual, just pondering strange things. Frittering away my last days on Earth when I could be doing something useful.
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This topic was modified 7 years, 4 months ago by
Unseen.
@unseen, I’m stuck on the “frittering away my last days on Earth” comment you made. Is something up? If so, I’m very sorry to hear it.
1) It depends what you mean by “truly random”. I believe the mathematicians have a very specific definition for that; indeed I believe there are several different classifications of randomness. For ordinary people, I suspect a good working definition is “unpredictable and without any accessible underlying structure or trend.”
I would argue that as far as we are able to measure any number of quantum phenomena are “truly random”, albeit within a well-defined distribution.
2) Digital random number generators typically use algorithms that create complexity, i.e. that show sensitive dependence on initial conditions, or what is often termed “chaos”. These require a seed that sets those initial conditions, and they are deterministic for any given seed.
Usually what’s done is the seed is derived from some physical process within the computer. One method often used is to be running a system clock counting in nanoseconds, and then take the lowest digits on the clock captured when the last keyboard key was pressed or the last mouse button was clicked. That is generally a sufficiently random seed for all practical purposes, but obviously is still not “truly” random.
2a) Well, if not an oxymoron it’s at least very difficult to do macroscopically. I believe I read that even the ping-pong-ball thing that American lotteries use to generate lottery numbers can be shown not to be truly random because of the small differences in the mass of each ping pong ball.
2b) This just depends on how sure you want to be about it. In traditional parametric statistics, researchers arbitrarily set a 5% chance as being too small to worry about. So when the chance of getting a series of 9’s of a certain length falls below 5%, we conclude that’s probably not due to random chance. Of course, as you say, if you try enough times you will get a series of 9’s of any length so it’s important to test only once. Two 9’s in a row should do it. 😉
[Edited for @Reg: It’s an interesting thought with regard to free will/determinism. In the other direction, it’s also an interesting thought with respect to evolution and “random” mutations. 😉 Of course as far as we know the QED processes that underlie such things really are truly random, at least until we get into the speculations about time reversible interactions. 8-*} ]
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Anyways, thought I would comment just to see how you were doing and if you were OK. It seems the TA site has disappeared while I was away, and this new one has the site rules that don’t allow old professors like me around, but wanted you to know I cared.
Bob
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This reply was modified 7 years, 4 months ago by
DrBob.
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