Random Numbers: Is there anything really random?
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We can clearly see that the only sources of true random numbers lie in nature. Nowhere else. But then again, is nature truly random? or is God just joking with us? Let's say God thinks and put numbers into nature. We then really need to analyze God's brain and thinking patterns, because that's where the real generation algorithm will lie. Various factors like emotions, mood, stress etc. will have to quantitatively dealt with, and one will need to see how each of those factors relate to the numbers God churns out into nature. In a similar light, we ourselves are the true source of random numbers. When we think of random numbers, they really are random. Truly random. And the functioning of the human brain (how it related to the numbers we think of), is beyond the analysis abilites of science today. If that sounded crazy, let me assure you that I didn't intend it to. Just sharing some honest thoughts, which you might assume has come from a mentally ill person.
ASP - AJAX is SEXY. PERIOD.
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We can clearly see that the only sources of true random numbers lie in nature. Nowhere else. But then again, is nature truly random? or is God just joking with us? Let's say God thinks and put numbers into nature. We then really need to analyze God's brain and thinking patterns, because that's where the real generation algorithm will lie. Various factors like emotions, mood, stress etc. will have to quantitatively dealt with, and one will need to see how each of those factors relate to the numbers God churns out into nature. In a similar light, we ourselves are the true source of random numbers. When we think of random numbers, they really are random. Truly random. And the functioning of the human brain (how it related to the numbers we think of), is beyond the analysis abilites of science today. If that sounded crazy, let me assure you that I didn't intend it to. Just sharing some honest thoughts, which you might assume has come from a mentally ill person.
ASP - AJAX is SEXY. PERIOD.
There are some pretty random posts on these forums - I guess that if we hashed them then that would have to be random - or maybe it would make more sense!
Peter "Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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We can clearly see that the only sources of true random numbers lie in nature. Nowhere else. But then again, is nature truly random? or is God just joking with us? Let's say God thinks and put numbers into nature. We then really need to analyze God's brain and thinking patterns, because that's where the real generation algorithm will lie. Various factors like emotions, mood, stress etc. will have to quantitatively dealt with, and one will need to see how each of those factors relate to the numbers God churns out into nature. In a similar light, we ourselves are the true source of random numbers. When we think of random numbers, they really are random. Truly random. And the functioning of the human brain (how it related to the numbers we think of), is beyond the analysis abilites of science today. If that sounded crazy, let me assure you that I didn't intend it to. Just sharing some honest thoughts, which you might assume has come from a mentally ill person.
ASP - AJAX is SEXY. PERIOD.
It's an interesting discussion, and to really get into it, you have to define what random means. Every physical system has various numbers attached to it, which are the things you can "measure" about that system. So a flying plane, for example, has numbers like "momentum", "position of the z axis", "acceleration", etc. Furthermore, these values aren't completely independent. If you know the "momentum" and "acceleration" at time 0, you can make a really good guess for the momentum at future times (with guesses for sooner times better than future times). The implication would be that for a physical system, there is a "purely mathematical" part, that describes the abstract system. There is also a random part added in though. This implies that the physical system is somewhat random. So if the velocity of a falling block is 0 at time =0 and it's acceleration is -g, then you can make a solid guess as to the velocity at t=1.0 seconds -- it won't be random at all. However, if you factor out the mathematical part, you'll get a purely random part. So if, for instance, you expected the velocity at t=1 to equal -g meters/second, you could sample the actual velocity at t=1 and would get a Gaussian out. In the real world, this particular example has a very strong physical/mathematical component and a very small random component. On the other hand, with various quantum mechanical systems, it has been proven that the "physical/mathematical" component is 0, and the answer you will get out is completely random. So I disagree with you that people are a good source of randomness. You can ask someone to give you 100,000 random numbers between 0 and 100 and you'll find that the output is very non-random. In my interpretation, this reflects some "laws of the mind" that are totally non-random (the fact that I really "feel" 17 is random, and "1" is not would be one example). That said, if you were able to figure out the physical laws, you can factor those out and get something purely random out. So a physical law of the brain would say that I feel "17" is so random, I will pick it 10% of the time, as opposed to 1%, but whether in a particular run I pick it more or less than exactly 10% will be completely random. So if you want to find purely random numbers, pick a physical system. Either pick one that has no relationships between it's variables -- these are found mostly in quantum mechanical systems -- and are really completely random, or pick one where you know the physical system perfectly and factor out
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It's an interesting discussion, and to really get into it, you have to define what random means. Every physical system has various numbers attached to it, which are the things you can "measure" about that system. So a flying plane, for example, has numbers like "momentum", "position of the z axis", "acceleration", etc. Furthermore, these values aren't completely independent. If you know the "momentum" and "acceleration" at time 0, you can make a really good guess for the momentum at future times (with guesses for sooner times better than future times). The implication would be that for a physical system, there is a "purely mathematical" part, that describes the abstract system. There is also a random part added in though. This implies that the physical system is somewhat random. So if the velocity of a falling block is 0 at time =0 and it's acceleration is -g, then you can make a solid guess as to the velocity at t=1.0 seconds -- it won't be random at all. However, if you factor out the mathematical part, you'll get a purely random part. So if, for instance, you expected the velocity at t=1 to equal -g meters/second, you could sample the actual velocity at t=1 and would get a Gaussian out. In the real world, this particular example has a very strong physical/mathematical component and a very small random component. On the other hand, with various quantum mechanical systems, it has been proven that the "physical/mathematical" component is 0, and the answer you will get out is completely random. So I disagree with you that people are a good source of randomness. You can ask someone to give you 100,000 random numbers between 0 and 100 and you'll find that the output is very non-random. In my interpretation, this reflects some "laws of the mind" that are totally non-random (the fact that I really "feel" 17 is random, and "1" is not would be one example). That said, if you were able to figure out the physical laws, you can factor those out and get something purely random out. So a physical law of the brain would say that I feel "17" is so random, I will pick it 10% of the time, as opposed to 1%, but whether in a particular run I pick it more or less than exactly 10% will be completely random. So if you want to find purely random numbers, pick a physical system. Either pick one that has no relationships between it's variables -- these are found mostly in quantum mechanical systems -- and are really completely random, or pick one where you know the physical system perfectly and factor out
My reply was rather tongue in cheek - as much of a comment on the original post as anything. Clearly there are potentially major problems with using this sort of thing to generate random numbers - predictable diurnal variations to do with time-zones and culture shifts come to mind. That said, if we use a good hash function - the hashes of the posts are probably pretty random.
Nathan Addy wrote:
you have to define what random means
I agree.
Nathan Addy wrote:
for a physical system, there is a "purely mathematical" part, that describes the abstract system. There is also a random part added in though
I don't know what you mean by this - are you simply implying the Heisenberg uncertainty principle, or the uncertainty in your measurement or both?
Nathan Addy wrote:
So if, for instance, you expected the velocity at t=1 to equal -g meters/second, you could sample the actual velocity at t=1 and would get a Gaussian out
Why, and why Gaussian?
Nathan Addy wrote:
So if you want to find purely random numbers, pick a physical system
I agree, sytems based on thermal noise or shot noise I believe are good examples of this - and seem to be the best types of generators of randomness that we have. Interesting question - are they truly random or is it just that our theories at this stage are not good enough?
Nathan Addy wrote:
But there are truly random entities in math. If you're familiar with the halting problem, the probability that a random program (basically a program that consists of a random 1 or 0 everytime the computer needs some input) is completely random
It's been a long time since I studied Turing machines - but you example sounds circular - do you really need random data to generate random output?
Nathan Addy wrote:
You can actually buy a physical random number generator, but unless you are worried about cryptographic stuff, it won't do any better for you than a software RNG, and if it breaks, you might not be able to tell, which isn't a problem with software RNGS
I agree - I have done a reasonable amount of Monte-Carlo simulation and the pseudo-random generators these days are pretty good, just don't use the basic rand() function. If
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We can clearly see that the only sources of true random numbers lie in nature. Nowhere else. But then again, is nature truly random? or is God just joking with us? Let's say God thinks and put numbers into nature. We then really need to analyze God's brain and thinking patterns, because that's where the real generation algorithm will lie. Various factors like emotions, mood, stress etc. will have to quantitatively dealt with, and one will need to see how each of those factors relate to the numbers God churns out into nature. In a similar light, we ourselves are the true source of random numbers. When we think of random numbers, they really are random. Truly random. And the functioning of the human brain (how it related to the numbers we think of), is beyond the analysis abilites of science today. If that sounded crazy, let me assure you that I didn't intend it to. Just sharing some honest thoughts, which you might assume has come from a mentally ill person.
ASP - AJAX is SEXY. PERIOD.
http://www.hmtown.com/random.htm[^] Feel free to comment here or to PICguy@hmtown.com.
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http://www.hmtown.com/random.htm[^] Feel free to comment here or to PICguy@hmtown.com.
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The background is terrible - I gave up reading after a few lines.
Peter "Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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Thanks for the comment. Try kicking up the text size. (^+ in Mozilla.) I will have to try reading my stuff in IE on a display set well below the 1600x1200 I use on my machine. I use ^+ with many sites. High res, small display 65yo eyeballs....
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We can clearly see that the only sources of true random numbers lie in nature. Nowhere else. But then again, is nature truly random? or is God just joking with us? Let's say God thinks and put numbers into nature. We then really need to analyze God's brain and thinking patterns, because that's where the real generation algorithm will lie. Various factors like emotions, mood, stress etc. will have to quantitatively dealt with, and one will need to see how each of those factors relate to the numbers God churns out into nature. In a similar light, we ourselves are the true source of random numbers. When we think of random numbers, they really are random. Truly random. And the functioning of the human brain (how it related to the numbers we think of), is beyond the analysis abilites of science today. If that sounded crazy, let me assure you that I didn't intend it to. Just sharing some honest thoughts, which you might assume has come from a mentally ill person.
ASP - AJAX is SEXY. PERIOD.
Yes any food bill with have a random total independant of item or cost of each item. Bristromatics is its offical name.
Grady Booch: I told Google to their face...what you need is some serious adult supervision. (2007 Turing lecture) http://www.frankkerrigan.com/[^]