Is it possible to create a perfect random number generator?

Perfect anything is improbable, especially if you want no limit on extremely small and extremely large. If you want numbers up to one google, nearly all the numbers would have to be between 90 and 100 digits before the decimal point and numbers less than one such as 0.0000764 or 0.000020044 would not occur even one in a trillion. If you allow only whole numbers you cannot even define "perfectly random" in my opinion. Neil

Actually Craven there are infinite numbers that I can't or wont express because I will never have the time or inclination. To me this doesn't affect randomness other than to say normally we are focused on numbers with less than ten digits centred around zero.

I ponder your equating determinism and randomness. Additionally you imply unless there is an infinity variety of possible outcomes randomness can not possible be present. If I say something is either true or false does your definition say well that is determinisitic and therefore non random because you have prescribed my choices - unless I have infinite choices randomness can not even start to be considered?

I never said that infinite options were required, I think that deterministic limitation precludes randomness.

Please clarify what "deterministic limitation" means.

Coke vs. Pepsi, for example. A set determined by the market which though complex is not random.

That's too cryptic for me to understand your intended meaning fully - "a set determined by the market" -

What is the filter or the cut off level or threshold you apply to say that at or below this level of selection/choice set / determinism one has just eliminated the possibility of truly random outcome?

Imagine it you were blindfolded and choosing identical partially coloured or internally numbered marbles from a bag. After each choice your selection is noted then returrned to the bag and the bag shaken. By your application of determinism what is the minimum number of marbles there has to be in the bag to allow the possibility of random choice to exist? For me its two marbles allows random choice. Do you need, 10, 20, 100, a million etc before you will say a selection can be potentitally random?

I'm not sure that could be any clearer.



When there is any determinism at all, it's not random by my definition.



You keep barking up the wrong tree. It's not about infinity it's about no determinism.



No, just non-determinism. Look, if you think picking marbles is perfect randomness then you already have your machine.

Please clearly define your understanding and usage of the word determinism - I sense you are using some exotic definition of the word that I was not aware existed.

http://dictionary.reference.com/search?q=determinism

The philosophical doctrine that every state of affairs, including every human event, act, and decision is the inevitable consequence of antecedent states of affairs.

Wow - that is a strong definition, even the Webster "The doctrine that the will is not free, but is inevitably and invincibly determined by motives!" is powerful.

* * *

As someone who studies physics this gives me troubles. I probably mis-used the word deterministic to mean certain pre-conditions plus a pre-defined interaction arrives reliably at a foreseen conclusion. Like petrol + oxygen + spark equals boom.

To the theoretical physicist for the last 70 years the Universe has been fundamentally non deterministic at its component pieces. Heinsenberg's uncertainity principle goes far beyond simply the inaccuracy or limited precision in measurement; that is the very least of its implications. The more powerful implication is our reality is fundamentally indeterminate and undeterministic at its most elemental levels. Schrondinger then halved the remainding information we had at this level with the famous wave equation. As an aside there is a famous adage that goes:

Schrodinger rules the waves, but Heinsenberg waives the rules!

Because Heinsenberg showed it was possible to waive a rule for a finite amount of time. Not just show error in the measurement of the rule - but waive the actual rule at a quantum level for a moment in time.

Heinsenberg's principle is one of the most powerful an unalterable cornerstones of modern physics. Relativity, M-Theory, the speed of light, E=mc^2, gravity everything is subject to Heinsenbergs principle (note time is an external, not intrinsic proper of quantum physics).

Heinsenberg himself said

There were also far-reaching implications for the concept of causality and the determinacy of past and future events. These are discussed on the page about the origins of uncertainty. Because the uncertainty relations are more than just mathematical relations, but have profound scientific and philosophical implications, physicists sometimes speak of the "uncertainty principle."

In the sharp formulation of the law of causality-- "if we know the present exactly, we can calculate the future"-it is not the conclusion that is wrong but the premise.
--Heisenberg, in uncertainty principle paper, 1927
http://www.aip.org/history/heisenberg/p08c.htm

Hawking slatter showed that our current present could have come from multiple possible pasts - due to the effects black holes have on everything swallowed - all information within anything swallowed by a black hole is lost - and as it is swallowed its energy is emitted consistently without regard to what is being swallowed - dealing casuality a major blow.

Hawking's showed that a body such as a black hole can't be at absolute zero - else it violates the Uncertainity or indertiminacy principle.

So basically a theoretical physics is going to tell you that we live in a world that at its most fundamental level it is non deterministic.

The questis as we summ this up - we live in a world of far more than trillions of trillions of particles that make everything we can interact with. And stastically an Uncertainity in a group of atoms studied as a whole is minute. But Hawking sshowe the entire Universe is non determine - our study lab is on a boiling quantum foam of indeterminate - crazy particles.

Measured at this level randomness rules - order itslef doesn't much exist!

Yes it is a strong definition. ;-) And I told you a long time ago that we have definitional incompatibility, so all I have left to say is:

not being able to determine != non-deterministic

Then you were correct in definition, but

science tells us in this Universe, everything = non deterministic

(at a sub atomic level when you mandate better than planck precision).

So by your definition and 70+ years of accepted physics everything is random

No g__day, science does not tell us that "everything = non deterministic".

But I've communicated this several times and will make this one my last, in order to avoid repetitive redundancy.

Enlighten me - what phenomia is deterministic beyond Planck levels?

I am unaware of any type of quark, boson, Higgs particle, lepton, photon etc that doesn't comply with the Uncertainity Principle, so if mass, spacetime and energy have to comply what is left beside abstract thought?

What does the uncertainty principle or determinism have to do with randomness? For example, not being able to measure statistics does not mean they do not exist.

By my basic understanding of the uncertainty principle, or determinism, they are BASED on cause and effect, whereas randomness is based on an effect without a cause. Flipping a coin does not produce a random result, but a result to which we are ignorant. Using the methods you suggest initially in this thread we could not create a random-number generator, but an ignorant number generator, where the generator is ignorant of the basis for the numbers it generates.

SCoates

Craven linked randomness with determinism - I was curious to understand how. He was going well up to trying to identify something that is actually determinisitic at the sub-atomic or slightly larger scale due to the Uncertainity Principle. Personally I think its too much of a stumbling block to get around

The Uncertainity Priniciple is not dependent on cause and effect - it actually defines itself as a root attribute of all the components of our reality. Its not a side effect, nor strictly a measurement error caused by imprecise equipment, its an inherent property or attribute of our Universe.

Secondly define "ignorant result" and differentiate it from randomness please!

Well, it has been a matter of semantics all along, as I see it, but a result to which we are ignorant of the factors could not on that basis be considered random, unless you give the word a definition relative to the user... or to whom it applies anyway. In that case what is random to one person may not be random to another, depending on whether or not you are privy to the factors at play.

I suppose my definition of random would be a causeless effect. Otherwise I don't see it as being random. Are we working with the same definition?

Not fully - because I sense us need perfect knowlege of a system to deem it as truly random, wheras I hold both that is not a requirement and that it is in fact unattainable.

I also see you could have a black box that randomly gives you a one or zero and you could test to prove this. But unless I explain the box to you you can't accept it or say acceptance is relative to the beholder. I accept neither of these premises. You could look at the past results of my box in operation and ask its it truly random or not for any period of time. You might not be able to verify it will continue to be random into teh future - but without realativity andy beholder could examine its outputs and comment precisely on its achieved randomness in my world!