Is it possible to create a perfect random number generator?

I define it as having no pattern on any level.

Not being able to predict it isn't something I consider random otherwise stupidity would generate randomness.

In other words, without understanding things we are frequently not able to predict them. This doesn't mean there is no pattern just that we can't identify it.

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Heliotrope wrote:

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.

sure build it, and Kent State U. will turn it into a 'prediction'! Rolling Eyes

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Gotcha. Thanks Craven.
If I'm reading you right, randomness is more of a concept than an actuality, akin to infinity.

Predicatability is different from randomness because the seemingly unpredictable can become tractable after analysis and future progress.

No pattern on any scale.
That is a big concept. I'm having a rethink about some of my own ideas now.

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BoGoWo wrote:

sure build it, and Kent State U. will turn it into a 'prediction'!

I don't have to build it.
There are thousands of them all over the planet in assorted optical, laser and quantum mechanics research labs.

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Heliotrope wrote:

If I'm reading you right, randomness is more of a concept than an actuality, akin to infinity.

Yep, but that's just my definition, otehr definitions in use include "not being predictable (to the individual)" or "equal probability".

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We know energy is quantised, which implies mass is too, and theoritical physics are developing models to explore is time really quantised at the planck level (10 ^ -43 of a second) and is space (at 10^-99).

These processes may give us a better understanding of randomness.

Craven what about if there are some fundamental processes that we understand but turn out to be unpredictable. Hawking radiation at the edge of a black holes event horizon seems a likely candidate. My concern is your definition implies we need ultimate knowledge before a ruling can be made on whether randomness exists or not. I have several concerns with this:

1) We not likely to achieve this, so poo!
2) A system of enough complexity generates unknownable conditions (proven in maths and logic)

If the world's leading theoretcial physiscts say reality at a sub-atomic level is non deterministic - then surely observing it either generates a random pattern or echos of the underlying reality that isn't of our universe but of another one or more (adjacent p-branes in M-Theory)?

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G_Day, what is your definition of randomness? Is it when the cause events are incalculable by any conceivable means, or inexpressible... or even just NOT calculated or expressed?

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g__day wrote:

Craven what about if there are some fundamental processes that we understand but turn out to be unpredictable.

I don't define randomness as unpredictability. Many do, and I call it a euphemism for randomness.

Not being able to predict something is not what I consider pure randomness.

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Define exhibiting randomness to mean any statstically series of tests - f, p, chi square etc would say the numbers or results exhibit behaviour with no bias of an underlying pattern no matter how you slice the data.

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*thoughts flitting through the blancmange I call a brain*

Take an irrational number, for example Pi, the digits are unpredictable as in we have no idea what numbers are coming next but on a very deep level they must conform to a pattern. After all they are being generated by an equation which is describing the number albeit on a different scale.
So Pi is unpredictable but not random.

On a deeper level, no number can be considered random, no matter how it's arrived at. Because all numbers are part of a set and are thus amenable to description either by direct writing or by generation through a process, which is not random by definition and practice.
That some of the numbers may never end is not even a factor in randomness.

Hmmmmm, information theory. I need to know more about it.

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Saying a number can not be random is like saying a colour can't be random!

Its a sequence of numbers that I refer too. The randomness refers to the sequence.

You don't know if the digits of Pi are un-predictable or not, given they can be determined at any point in the sequence.

I could equally ask are the sum of the digits of the next prime random?

/aside

It might be interesting looking at what patterns emerge for primes as they get very large (from memory their frequency of occurence is similar to n / log(n), so counting primes using a^2 + b^4 gives a very fine funnel to estimate primes. Another interesting observation is if you pick two integers at random, the probability that they have no common prime divisor is 6/pi^2 or apprximately 0.6079271

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g__day wrote:

Saying a number can not be random is like saying a colour can't be random!

So? I'll say it:

"Colours can't be random, just like numbers can't."

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Fine I'll pick a single number from an infinite set - lets say I choose 9 - and I'll pick a colour lets say navy blue.

Now show me that either my number or my colour wasn't random or show that 9 was more or less random than navy blue please!

You can't confidentally test for a statistical randomness in a single event!

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That's an absurd test, but still easy. Through the use of limitations you influence the outcome, thereby rendering it both deterministic and not random.

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Well it has to be deterministic - as I actually did pick a number and colour! Smile

I had no limitations on me - so that is not a proof it wasn't random event in even such a trivial example!

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You do, in fact have limitations. For just one example there are some numbers you won't live long enough to be ablt to comprehend/say/write.

Pointless because like we both note, it is a deterministic selection. Not a random one.

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I can circumvent the limitations for 'infinite' numbers trivially though by simply using a known inifinite series plus or minus a constant, e.g 50 * pi but no period after the 3.141 which is 50 * pi * limit 10^n as n approaches infinity.

I don't at all see determinisitic equates to non random, but I do infer non-deterministic implies random.

If someone asks do i want coke or pepsi and I truly don't care - then I make a random choice.

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Quote:

If someone asks do i want coke or pepsi and I truly don't care - then I make a random choice.

Well there's your random number generator then. :wink:

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g__day wrote:

Fine I'll pick a single number from an infinite set - lets say I choose 9 - and I'll pick a colour lets say navy blue.

Now show me that either my number or my colour wasn't random or show that 9 was more or less random than navy blue please!

You can't confidentally test for a statistical randomness in a single event!

Your mind is too complicated for us to guess which factors took place. However, there are factors which influenced the decision. If it had been a robot, for example, which made the descision, it would be easier to trace the exact relevant factors. But that is only because a robot's "brain" is much simpler, and we may have access to the exact programming, whereas your brain has an evolving program, which we cannot possibly trace.

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g__day wrote:

I can circumvent the limitations for 'infinite' numbers trivially though by simply using a known inifinite series plus or minus a constant, e.g 50 * pi but no period after the 3.141 which is 50 * pi * limit 10^n as n approaches infinity.

That's a clever way of putting off that limitation but it doesn't circumvent it. Ultimately there will be some numbers too large for you to express at all because of the limitations of your body (e.g. lifespan).

Quote:

I don't at all see determinisitic equates to non random, but I do infer non-deterministic implies random.

I know, and we're using different definitons.

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If someone asks do i want coke or pepsi and I truly don't care - then I make a random choice.

The reason why I'd not call this random is because this decision is deterministic in that the available options were determined by the market.

The reason why it's not, for example, "coke, Pepsi and new coke" is because of the market killing off new coke.

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Is it possible to create a perfect random number generator?

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