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Almost every case of what appears random to us is due to not knowing enough about the situation. For example, when you flip a coin, you don't know exactly how you flipped it (how much force you applied, how fast it will rotate, how it left your hand, air currents, etc.) If you did know all this, it wouldn't be random: you could predict whether it would land heads or tails. Because you don't know any of this, it seems random. The same goes for computers, only moreso. They use complex algorithms to generate "random" numbers, but if you know exactly how these algorithms work, you can predict the numbers.The only place I know of that truly has randomness is the quantum world. If you have a particle that has a 50/50 chance of being in state A or B, no amount of information will tell you which state it's in before measuring it. As for choosing a banana, who knows? No one knows how consciousness really works, so no one can say whether there's randomness involved or not.

Before the discovery that quantum mechanics laid at the heart of everything the universe was supposed to be purely deterministic I believe."An intelligence which at a given instant knew all the forces acting in nature and the position of every object in the universe – if endowed with a brain sufficiently vast to make all necessary calculations – could describe with a single formula the motions of the largest astronomical bodies and those of the smallest atoms. To such an intelligence, nothing would be uncertain; the future, like the past, would be an open book."— Pierre-Simon LaplaceSaying that the majority of everyday large-scale 'choices' are still classed as predictable.But scale doesn't always smooth out the microscopic randomness as much as we would have initially thought - look at the Earth's weather system. It was supposed for a most of science's history that weather could be predicted faultlessly once enough measurements could be taken and the calculations made fast enough, but that was before the discovery of Chaotic-systems, that appear to amplify the tiniest effects with almost infinite unpredictability. So, although not truly random, these systems become computationally impossible to do with zero error.BTW this doesn't mean that Climatic trends are unpredictable because, again, at the most macro scales (of size & time), the Chaotic nature of the systems is self-cancelling. [p.s. Digital Computers are indeed incapable of presenting truly random number sequences because they rely of logic (the Boolean kind), so they use pseudo-random number generators.]{sorry to repeat that JP was typing at same time!}

Modern microprocessors do have a very much improved random number generator, which uses the noise of a built in reverse biased diode on the CPU die to give a much more random number in the random number register. It is updated on each clock cycle, and thus is pretty much going to be very close to a random number, the noise being used as an added input to the pseudo random shift register that is used to provide the number. It is only the same on the first cycle after the external reset input is deasserted, and will be random therafter ( and you cannot read it at this period, as there is going to be a few hundred cycles before the first instruction is loaded into the decoder from the relatively slow BIOS ROM, it is only readable by using a test mode that is not able to be used when the unit is installed in a socket, as the test pins are only available on the unpackaged die). Thus the numbers are truly random, though there may be biases in the range due to other reason, but the next number cannot be determined, just that the numbers do not have a perfect Gaussian distribution, but have a slightly higher probability of having certain numbers in a range showing up over time.

So, randomness may have a life outside the quantum world !

Quote from: neilep on 11/08/2011 11:46:57So, randomness may have a life outside the quantum world !Well, not really. A lot of the noise that Sean talked about is caused by quantum effects []Unfortunately, the diodes are not immune from external nonrandom influences (like interference from your cellophone for example), so there may still be a bias in the numbers generated.

Aren't these chaotic systems just chaotic because we can't compute them yet ?No.

Quote from: Bored chemist on 11/08/2011 19:14:58Aren't these chaotic systems just chaotic because we can't compute them yet ?No.why ?

Quote from: neilep on 11/08/2011 19:26:52Quote from: Bored chemist on 11/08/2011 19:14:58Aren't these chaotic systems just chaotic because we can't compute them yet ?No.why ?Chaos theory reminds me a bit of the Mega-computer in Hitchhiker's Guide to the Galaxy that says "I am not the computer who can answer the question 'what is life, the universe and everything', but I can design the one that will!"Because of the way that Chaotic maths operates, our computers can predict the complexity of the problem of calculating the weather systems of the Earth at the local scale, but can never actually come close to calculating the answer. Terms start getting banded about such as 'it would take a thousand times the current age of the universe to calculate tomorrow's weather to a >95% accuracy and that is after having placed sensors every three metres in every direction throughout the whole atmosphere!'.Chaos maths is unlike any 'everyday' maths.In a way choosing the name Chaos for it has led many non-mathematicians astray because it implies that, as we think of everyday chaotic things, it just describes very complex (but underlyingly standard) systems.... Which it doesn't.

There are even very simple chaotic systems, such as the billiard problem: ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN It's fully determined by Newton's laws (in the classical case), so there's no randomness. The chaos comes in because the path the ball takes will never repeat itself in certain cases.