In a controlled environment, reduce all quanitifiable measurements of a snowflake into a string of digits. Repeat. If it’s true that no two snowflakes are alike, must it not follow that the resulting numbers are random?

Zebra Randomiserhttp://www.halfbake.../Zebra_20Randomiser [phoenix, Aug 06 2002, last modified Oct 17 2004]

(?) Physics ideas on randomnesshttp://216.239.39.1...laws&hl=en&ie=UTF-8 Takes randomness as start-point rather than end-point [Guy Fox, Aug 07 2002, last modified Oct 21 2004]

Random Number Generatorhttp://www.halfbake...om/random-idea.html I just invented it. Click on the link to get a choice of random items. You can choose either the 'for' number, the 'against' number or their combined or aggregate total. It even generates a random date from between mid-1999 and today. Can also be used to generate simple 'yes/no' answers by comparing the number of croissants to the number of fishbones. [DrBob, Oct 17 2004]

Having all numbers be "different" doesn't mean that they're good random numbers. Here are some different numbers that are very poor random numbers: 1, 2, 3, 4, ...

And having very good random numbers doesn't mean they're different. Here are some very good random numbers: 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, ...

Didn't SGI have something called Lavarand? Nothing more than a cheap video camera pointed at a lava lamp to generate the seed. They claimed it was true random number generator. I think they patented it even.

gen1000: I don't think a lava lamp would be truly random, merely chaotic; if you ran the thing long enough and logged the results, it's behaviour would converge on the Mandelbrot set. So would snowflakes. In the end, all these systems are deterministic.

Radioactive decay gives better "randomisation" but is still stochastic. <Sits back and waits smugly for someone to drag up Schrodinger's damn cat yet again>

If you're interested, a UK gaming site had its RNG tested by TST in the US and the report is posted. Goes into all the gory details of the tests...
http://www.getminted.com/spg/general/rngletter.pdf
Enjoy =)

po - no, it doesn't. But humans do create concepts to help us understand things, concepts that in reality are not there. "Total randomness" is utterly impossible.

there are concepts like randomness, concepts like law and concepts like chaos theory. we were talking about randomness. I think where a leaf or a seed drops is at random although the overall effect of the resulting forest may look like a planned pattern.

I can accept that total randomness is an unattainable goal - how would you know it when you saw it anyway? I guess that goes to the root of the problem: unknown (and, indeed, unknowable) factors may be determining an unseen pattern in your results.

Having said that, how random do we need numbers to be? Nobody seems to be using number theory to challenge lottery results.

By the way, I thought the snowflake thing was about geometrical and structural differences between flakes; is it just that none have the same number of water molecules, as namaste intimates?

//"Random" is a human concept that does not actually appear in nature.//

//"Total randomness" is utterly impossible.//

I disagree and - the way I read it - so do at least a few physics boffins. [see link]

As far as I understand the concept, randomness is not only a part of nature, but is in fact the fundamental "stuff" of it, from which both the energies and the laws that govern them may, in fact, be generated. It's not so far removed, it seems to me, from the Greek cosmogony which saw the world as developing through a sort of differentiation process from a primal, "oceanic" chaos.

Generating randomness deterministically may be a contradiction-in-terms, but if the ordered features of the universe are just permutations of a greater, underlying randomess, I wouldn't make such bold assertions about what's utterly impossible in this world.

Guy, that is a very well written and respectable observation you make. I maintain my stance, however, that the concept of anything being "random" at all is totally human, and does not and cannot exist in nature.

po, the leaf or seed dropping is chaos, not random. In fact, the landing position of the leaf is determined by hundreds if not thousands if not millions of minute parameters, all of which must have been exactly that certain way in order for the leaf to have landed where it did. That is anything but random.

Randomness does exist, but only as a concept. If two people generate the same "random" sequence, one trying to predict the other's, the first person thinks the sequence is random, the second thinks it is entirely predictable and therefore not random. It's about as unlikely as an unlikely thing, but can happen.

Chaos is a mechanism that can be used to generate random numbers.

It is true that nothing is truely random, but it is easier for us to comprehend things if we say they are random. Only God can keep track of all of the variables and only he knows what every snowflake looks like.

"Here's the thing: I don't like the idea of randomness because it has no root cause. On the other hand, randomness seems to be necessary, for exactly that reason. In order for a system to increase in complexity, it needs a certain amount of non-uniformity."

Agreed. However, the amount of non-uniformity in a system with *unbelievable* complexity could be *very* small. In Wolfram's research into automata, he has discovered remarkably simple one dimensional automata (you can describe the whole thing with a handful of symbols) which create what appears to be a completely unlimited quantity of data with no apparent pattern (it's static as far as statistical analysis has shown).

On the other hand, just because simple mathematical systems can create incredibly complex, chaotic and unmeasurable systems does *not* imply that randomness does not exist *too*. ;-)

For all this banter about whether true randomness exists or instead that countless hidden variables precisely control every behavior, I think we have missed an important point entirely: It doesn't matter! The utility of a random number generator lies in the fact that its output is not predictable. As long as we do not and can not see any pattern in the data, what difference does it make if a hidden pattern actually exists?

"...its behaviour would converge on the mandelbrot set. So would snowflakes. in the end all these systems are deterministic."

True, but Mandelbrot, lacking its quantifiable constant, allows for just that...randomness undeterministic. Snowflakes, running water, lava lamps, clouds...none of these can mathematically quantify into any deterministic pattern. Essentially, there is no common variable (meaning no constant).

"The only thing for certain is that there is no certainty."

trying to find something that is "perfectly random" is like trying to find a ruler that is perfectly straight. No matter how straight it is if you look close enought it is not perfectly straight. However, naturally occuring randomness, like rolling of dice is close enough to being perfect for any real application. If it wasn't we could make millions in Vegas.

I think this is a fundamental question which gets at the heart of existence, causality, determinism, and our sense of will. I wonder if randomness could reflect an interaction between determinism and indeterminism. I have theorized that the decimal expansion of an irrational number (such as pi, or the square root of a prime number) is random, in one sense, yet calculatable in other sense. As we continue the expansion, it will become numerically more and more difficult to calculate the next number. Eventually perhaps it would require a nearly infinite amount of energy or time--or all the energy of the universe-- to calculate the next digit. I would then argue that the next digits would be "even more" random, in that they would be inaccessible to calculation, yet could in theory be calculated. There is order, meaning, and significance in such a digit sequence, yet I would argue that it is random. Conversely, perhaps all random events in nature have meaning and significance; this, then, hints at a kind of spirituality in understanding nature.

Sorry for coming late to the debate. Sounds like the only disagreement going on is caused by a difference in definition of the word "random". I think a good definition to stick with is "difficult to calculate". This would make the ultimate random number anything that is impossible to calculate. Of course, even this definition is imprecise (depends on who is doing the calculating), but I would argue it's as good as any definition.

Using this definition, numbers such as digits within pi are not terribly random. Data input from noise from a radio card would be much more random. Of course, to go all the way to fully random you'd probably need to go to quantum techniques.

Taking a quick step away from philosophy and back to engineering: I'm surprised nobody has mentioned the most popular method of obtaining random numbers: Noise across a resistor.

If 'pi' is irrational, and therefore never repeating, is it not possible to find somewhere within the nonrepeating decimal digits of 'pi', larger and larger subsets of the never repeating decimal digits of 'pi'?

And in this case, would an autocorrelation show more than one peak, showing that indeed, the digits of 'pi' are not entirely uncorrelated?

just my 1/2penny. but I'm with the 'no-such thing as random' crowd on this one, and as such, a snowflake isn't going to work as the root of a TRUE random number.

If you changed the title from "True Random Number Generator" or "Very Hard To Predict Number Generator" you'd have everyone in agreement - I know it's picking hairs, but there are already perfectly good "Very Hard To Predict Number Generator"s about at the moment - see link.

Having all numbers be "different" doesn't mean that they're good random numbers. Here are some different numbers that are very poor random numbers: 1, 2, 3, 4, ...

Yes, the number '4' in this sequence is predictable, but an infinite string of random numbers MUST at some point have the sequence 1,2,3,4,5... So the sequence above is, actually, random, but also highly unlikely.

The annos here touch on several different interpretations of random:

The great thing about it all is the human interpretation. Let's say the perfect random number generator was built. Dignitaries from all nations turn up for the grand opening. And (by an amazingly slim chance and awkward coincidence) the first 10 numbers out of the machine are:

3, 3, 3, 3, 3, 3, 3, 3, 3, 3

What would people say about the machine? How long would you accept more '3' outputs before you said "this is not random!". The correct answer is that you simply have to trust the machine. Even after 20 threes you can't say it isn't random (just highy, highy, highly, highly unlikely).

{Whatever 'unlikely' means, since 3,3,3,3 is just as probable as 4,1,9,5).

I'm way over my head with all this math talk, but I'm with the "human interpretation of randomness is real" crowd. Whether or not everything is determined at the most minute level, if it's impossible to calculate then it's good as random to us. I have a gut feeling that the anthropic principle somehow prevents us as conscious beings from ever cracking determinism. It would be like time-travel or something, paradoxical.

There is nothing that is truly, completely random. The level of randomness in something, I think, is basically how difficult it is to find some pattern or correlation in it. Snowflake measuring might be more random than pseudorandom number generators, but not enough for any practical application.

//There is nothing that is truly,
completely random.//

Actually, everything is truly, completely
random at the quantum level. Take a
photon and fire it at a piece of glass at
a shallow angle. The probability that
it's reflected is (depending on the angle)
say 50%. However, there is absolutely
no way to predict whether any given
photon is going to reflect or transmit.
It doesn't depend on the exact spot
where the photon hits the glass; it
doesn't depend on any properties which
differ from one photon to the next. It
doesn't depend on *anything*.

For practical purposes, random number generation is very much a solved problem. Pseudo random generators are very fast and pass tough tests for statistical randomness. Some are slower but practical for cryptography.

For those who want real random numbers, there are a number of devices for sale in the region of a couple of hundred dollars that spit out random numbers at high speed. If a large number of people needed them they would probably get a lot cheaper.

I was going to say the same thing as the good doc [MB], but he beat me to it.

I find the quantum world a really creepy place - seemingly inhabited by particles that 'know' when they are being watched. It may be that our minds do have a strong link with the physical world. Better end it there before I'm flamed too badly.

//particles that 'know' when they are
being watched//

It's not so much that. It's more a case
that spacetime has a finite computing
capacity per unit volume.

Hence, there is a limit to how far
spacetime can keep track of paths and
particles. So, it only tends to do the
precise maths for big or energetic
things, and it lets small, unobserved
things go by. Only when someone
observes (interacts with) a particle does
spacetime say "Uh-oh, we'd better
decide on a precise value for this or it'll
cause trouble downstream", and it tries
to come up with a value. Unfortunately,
by this time it's too late to go back and
do all the math which would give a
causally-consistent answer, so it plucks
an answer out of thin air.

Of course, for practical use, we need to narrowly restrict our definition of 'numbers' to that laughably tiny subset of real numbers that our computers can handle or even more practically to those numbers with, say, less than 7 digits. So, our current 'random number generators' should more correctly be termed 'restricted field number generators' or 'partially-randomised, capped, positive integer generators'.

Assuming a 'random number generator' could pump out truly random numbers from the entire set of real numbers, the chances of the first number out being able to be read by any of us in our lifetimes would be infinitisimally small - effectively zero.

Further, if we relied on any current processor technology to generate 'random numbers' then there must be a finite limit on the number set available - ergo the nomenclature 'random' is insufficiently descriptive of the output.

I sufficiently detract from your second explanation, [MB]. It's been my experience that the universe doesn't say "uh, oh", nor has it any idea what trouble is. However, I also doubt particles know when they are being watched. Instead, it's all attributable to quantum decoherence and no wave functions actually ever collapse. Life is but a dream.