Is it possible to create a perfect random number generator?

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Another thread brought up this question. Lets divide it into two parts,

1) Can one produce utterly random integers falling within a finite range - like from -50 to +888

2) Can one produce totally random numbers, in an infinite range to infinite precisions (e.g. pi or e or ary irrational or otherwise infinite numbers should be randomly produced).

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1) may be possible, 2) seems alot harder (as there are infinitiely more infinite numbers than finite ones so you could almost never expect to see finite numbers occuring hence it would take you infinite time to observe even a single number popping out of a model 2) generator!)

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Remember any mathematical function generates psuedo random numbers, whilst hardware - like a resistor or diode feedback counter produces an amplified noise function with a possible non-random underlying distribution curve.

http://www.robertnz.net/true_rng.html

Is a good description of each type - especially the hardware variants, as the mathematical models of (I stress everyday) maths seem limited to psuedo numbers.

It also states that you can test a group of numbers and determine if they are perfectly random (which surprises me greatly - I would have expected you can say no more than you can have a confidence interval about them - like its 1 in 3 chance or its 1 in 10 ^ 2,000 likely that these numbers are or are not random etc...)

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My thoughts are that this will quickly lead into views of statistics and distribution and underlying philosophy - around what is perfect randomness or is a noise function really random.

For instance I could count photons hitting a detector so I am really detecting radiation emitted by the Sun - without knowing if it applies to a precise non random mathematical formulea I could model given enough resources (hypothetically).

I could counter this very powerfully with Heinsenberg's uncertainity principle and say any technology capable of measuring quantum virtual particle/anti particle annihilations (Cassimir effect) is perfectly random noise. But we don't know enough about this to ensure its correct.

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This is outside my key area of study so I am very interested in people thoughts and insights!

/humility += 10 Smile

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Already a thread that addresses this. the general consensus was "There is no such thing as truly random." Just the more ignorant we are of variables, the more random it seems. I'll be back in a moment to link the thread.

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http://www.able2know.com/forums/viewtopic.php?t=19716

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Ewww, ahh, thanks... but thats a philosophy thread, and I wanted to do something useful Smile

* 100

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Yes, I realize it is not entirely the same, but it's still interesting reading. Honestly, some of your thoughts or what gave me the idea to start the thread. I was wondering how to program randomness, when I decided there was no such thing. I am interested, as usual, in hearing any debate you generate. Smile

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I have responded with my thoughts in your thread. If they want the scientific or mathematical views they can ask wherever they'd like and we can try and help them!

I'll try and stick to your topic as best we can!

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1) no

2) no

Why? Because there's no such thing (within our observable world) as truely random.

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But Heinsberg's uncertainity prinicple shows the entire Universe is non deterministic at a sub atomic level. Find an unbiased way to measure it and there's your totally random functions - see my other post in SCoates thread about measuring the Cassimir effect in a total vaccum at 0.1mm spacings!

Quantum foam may be totally random and possibly measurable without inflicting bias!

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On what basis is it considered random? And what proves that the universe in non deterministic at any level?

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The Uncertainity Principle shows it is non-deterministic - as do black holes.

There is a rather famous proof by Hawking's (included in his The Universe in a Nutshell book (pages 107 - 109) - that goes Not even God can can know both the position and velocity of an electron its proof is online from memory - I found it a month ago on google

I will look it up and post the relevant links as soon as I can.

Done here http://www.able2know.com/forums/viewtopic.php?p=624482#624482

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And you don't believe there is any possibility that is incorrect? My understanding is very limited on the subject, by I find it difficult to believe impossibilities can be proven.

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There are wider theories such as M-Theory and Field Theory that take account of the multidimensional nature of the universe(s).
Many 'random' phenomena such as quantum foam can be traced to the short range interaction of the dimension membranes and the energy transfer between them.

Personally I can only think of one thing that I accept as random and that is the action of police officers when confronted with a blatently speeding motorist who will not lie to them.

As for the theories being incorrect, well really incorrect is the wrong word.
Newton wasn't incorrect just because everything he did was superseeded by Einstein. His theories were improved upon. Relativity didn't make him wrong it just made things clearer and accounted for more observations.
Just as the M-Theory theorists are probably not wrong (we will know when there is a lot more data) they just have an incomplete picture.

This of course is the whole basis of the argument above about randomness and the ignorance of the variables involved. One can say however, that the universe is not deterministic on the scales that we can experience it. So even if it is deterministic on the scale of hyper-intelligent-pan-dimensional-beings it doesn't make any difference to us.

You are basically getting back the old 'true nature of reality' discussion id you go down this route.

Even saying that though, if you're prepared to tolerate limits on your randomness like the number generator that only produces numbers in a certain range then that particular brand of randomness is achievable on our scales.
There are tunnel diode oscillators (only describable using quantum mechanics) used in military radar for generating random settings for frequency agility characteristics.
These are about as random as it gets.

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g__day,

Non deterministics as far as we can determine. Then again, other studies claim that nothing can be observed without being changed. What you reference is a claim that their behavior can't be predicted, and "random" tends to be a euphemism for that.

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I like Helio's point, but there are plenty of cases of "essentially random" seeing as their are plenty of cases of ignorance among us. And "plenty" is very conservative in the latter usage.

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Craven de Kere wrote:

g__day,

Non deterministics as far as we can determine. Then again, other studies claim that nothing can be observed without being changed.

That's not strictly true now. There have been experiments done where the quantum state of an atom has been observed and measurememnts take without disturbing it in any way that can be found. The technique involves the use of mirror superpositions and to be honest it was on the edges of what I understand but basically you can get information about the atom/object etc... in a statistical form so that you can say with, for example 80% certainty that the atom is in a particular state (if you'll pardon the piss-poor pun).
The experiment I'm thinking of consisted of some hypothetical bombs that would be triggered off by any interaction with them. There was a way to tell which ones were the real bombs and which were fake with a certain probability. One you'd trigger, two you would probably not and one you definitely wouldn't. The upshot of which was that you were getting information about a quantum system in a superposition of states without interacting with it.
I'm desperately trying to remember the file reference so I can post it. Have a search through PRL or the New Scientist archive anyway.

Craven de Kere wrote:

What you reference is a claim that their behavior can't be predicted, and "random" tends to be a euphemism for that.

Aye It does indeed. Which is a shame and bugs me almost as much as when idiots say "Well it's only a theory."
But what is the difference to us if something is random on our scales and not on others ?
Even if it is deterministic to others, on our scales that we can probe and interact with the thing may be completely random. The nature of our consciousness may in fact prevent us from ever understanding it any other way.

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Heliotrope wrote:

Craven de Kere wrote:
g__day,

Non deterministics as far as we can determine. Then again, other studies claim that nothing can be observed without being changed.

That's not strictly true now.

Incorrect, it is "strictly true".

There are indeed studies that claim that nothing can be observed without being changed.

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Ahhhh. Sorry.
I see what you mean.
Very Happy

Nice one

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in a world in which chaos is the only given, and people are constantly claiming that the examination of the way things are, somehow produces 'laws', rather than mere descriptions of 'expected results', 'randomness' is a figment of the imagination, squared!

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It's an impossible thesis to disprove, but I don't necessarily subscribe to it.

I don't know enough to be certain (and I'm nearly certain that nobody else does) but I do not think true randomness exists. And humans finding something to be non-deterministic is something I do not think proves pure randomness either.

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Ahhh, Craven, now I understand where you're coming from.

How do you define randomness ? Yourself, personally that is.

The reason I ask is that it is possible to build a device that makes photons with a random polarisation, left and right for argument's sake, at say one per second.
It isn't possible to predict what the photon is going to be on an individual basis but you allready know that it can only be one or the other and that at the mythical 'End Of The Day' there will be 50% left and 50% right polarisations.

So such a device is deterministic on some scales but not on others.

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Is it possible to create a perfect random number generator?

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