Does Randomness Exist?

[997GT3]

Even random, or pseudo-random rather, numbers generated by computers are calculated by an equation. Is there a such thing as randomness?

Aren't all things connected?

Wouldn't it be possible for an event on the other side of the world some 20 years ago and everything else (how we were raised; our past; our genes; our immunities; our environment; even the little molecules invisible to the naked eye; etc.) to affect our next actions and the way we see the world?

Does God know what we're going to do next by knowing all the variables to a huge equation and plugging them in? God even knows when we'll pray.

Is Free Will truly Free Will?

Free will is essential to Christianity in that we have to choose to accept Jesus Christ. Is it really "choosing"? Are some people pre-destined to accept Him on Earth and some later?

Please discuss.

[Bugmaster]

Radioactive decay is not proven to be random. Radioactive decay seems to be not random at all. Even apparent "quantum randomness" cannot be said to be proven to be random.

Care to share your proof with us ?

More to the point, you can stage an experiment by yourself. Get a very sensitive Geiger counter, and a radioactive source (you can get a nice one from one of these old smoke detectors). Record the timings of alpha-particles as they are emitted from the radioactive chunk, and try to find a pattern. Calculate the entropy of your timings, and see how close it approaches randomness. I am guessing the answer would be "pretty damn close", and the longer you run the experiment, the closer you'll get.

As I'd mentioned before, another good piece of evidence for quantum randomness is the entirety of modern chemistry. Chemistry advanced quite a bit when people discarded the idea of electrons as orbiting particles, and started thinking of them as probability distributions.

The insistence that an occurrence is random requires the absolute understanding of everything that could theoretically contribute to the occurrence.

No, this is not true, except in the trivial sense that knowing anything at all 100% would require absolute knowledge (I'm not 100% sure that the Sun exists, but I'm pretty damn sure).

And of course, wave-particle duality, as demonstrated by ye olde double slit experiment, is a direct consequence of the Uncertainty Principle (it's basically the Uncertainty Principle written in different terms), and that's an experiment you could stage yourself with a piece of foil, a laser pointer, and a sharp razor blade. Also of course, you can always observe Brownian Motion yourself in a cup of water or something, just as the Ancient Greek philosophers have done.

Note that all of this matters only on the quantum level. On the macro level, objects become so big and heavy that the uncertainty in their position or momentum, while nonzero, is negligible. Still, the topic of this thread is not, "are chairs random", but "does randomness exist", and the answer is "yes".

Note, again, that "random" doesn't just mean "following some pattern we aren't yet able to determine". Random means just that -- random -- following no pattern at all. It may be uncomfortable to think about the electrons in your body as being unknowable, but that doesn't make it any less true. Good thing, too, because most of modern electronics is based on quantum physics, and that's what lets us have all these nice computers and stuff.

[McCulloch]

Note, again, that "random" doesn't just mean "following some pattern we aren't yet able to determine". Random means just that -- random -- following no pattern at all.

I am at a loss as to how one shows that some particular series of events is truly random. If random means following no pattern at all, then the only way to prove randomness would be to match the series of event against every possible pattern and rule them all out. To illustrate, I could write (and others have written) pseudo-random number generators which use the current date|time as a seed value. Without knowing the seed value, this series of numbers is indistinguishable from a truly random series, yet it is an entirely predictable and repeatable pattern.

One could postulate the ultimate God-of-the-gaps, a powerful and extremely busy being who dwells outside of our time-space who sits all day and night deciding every apparently random event. You could not disprove such a being, however much you might invoke the mighty Occam against him.

[Bugmaster]

I am at a loss as to how one shows that some particular series of events is truly random.

Oh, that's easy -- all it takes is some statistics.

To illustrate, I could write (and others have written) pseudo-random number generators which use the current date|time as a seed value. Without knowing the seed value, this series of numbers is indistinguishable from a truly random series...

No, this is not true. If you were to take the output from the generator, and compute its entropy, it would be lower than that of a truly random sequence. I am betting that the output from the generator would also have a low Kolmogorov Complexity and a high autocorrelation. This is why pseudorandom number generators are not used by casinos anymore (AFAIK); instead, they use some sort of a white noise generator, or maybe something similar to random.org .

You can always say, "well, statistical randomness is not what I mean, I was talking about some sort of other randomness", but then you need to define what you mean. I like statistics because it's quantitative.

One could postulate the ultimate God-of-the-gaps, a powerful and extremely busy being who dwells outside of our time-space who sits all day and night deciding every apparently random event. You could not disprove such a being, however much you might invoke the mighty Occam against him.

Agreed. You could invoke such a God to "disprove" anything, really, not just randomness.

[QED]

But I can easily decide the outcome of this situation. Niether machine will hault.

So how is randomness demonstrated?

Perhaps it would be more helpful (and relatable) if you explained a random process found in nature, such as the previously mentioned radioactive decay.

Well I guess it's not particularly easy to relate to the halting problem but it exists nonetheless. The point is in the conclusion; that the halting problem is undecidable meaning that no algorithm can be created to decide the question "will a given program halt". It's a very effective "reductio" proof which applies Georg Cantor's Diagonalisation. There are many online explanations of the halting problem, if I was to set it out for you here I couldn't do any better than to copy this explanation verbatim.

Of course it would be nice to produce a specific example of natural randomness for you, but no doubt it would be argued that all things can be audited for causes irrespective of practical issues of complexity. Quantum events, however, remain questionable in this respect. In order to accommodate determinism current Quantum Theory must be modified to include hidden variables. Significant obstacles to hidden variables are presented in theorems presented by John Bell and Simon Kochen & Ernst Specker.

But then any hidden-variable theory has also to be non-local, i.e. it implies instantaneous causal relations between physically separated entities. Both Louis de Broglie and David Bohm have presented non-local hidden variable theories for which me must abandon all notions of "Local Realism". I've got nothing particular against this, but it seems nothing decisive yet exists in theoretical physics to answer your question. That's why I prefer to look at the issues raised by undecidability in mathematics. I believe this gives us a head-start on the findings that will emerge from Physics.

[The Persnickety Platypus]

Bugmaster,

More to the point, you can stage an experiment by yourself. Get a very sensitive Geiger counter, and a radioactive source (you can get a nice one from one of these old smoke detectors). Record the timings of alpha-particles as they are emitted from the radioactive chunk, and try to find a pattern. Calculate the entropy of your timings, and see how close it approaches randomness. I am guessing the answer would be "pretty damn close", and the longer you run the experiment, the closer you'll get.

I get it. So if I look at a set of numbers, and can find no pattern, then the process that yielded these numbers is irrevocably random, right?

Obviously there is no chance that the pattern relating to this phenomena is in fact too complex for me to comprehend. Right?


Simply pointing to a seemingly orderless process does not prove much. I want to know what causes this randomness. Under what conditions can it exist? How can an effect lack a cause?

The interactions of the strong/weak nuclear forces and the electrostatic forces is what drives radioactive decay. In order for the decay to be random, musn't these forces cease to play a factor in the process all together? Afterall, if a "random" process cannot have determinents.

As I'd mentioned before, another good piece of evidence for quantum randomness is the entirety of modern chemistry. Chemistry advanced quite a bit when people discarded the idea of electrons as orbiting particles, and started thinking of them as probability distributions.

And since we know everything about chemistry, it is entirely impossible that our observations of "random" electron orbitals disregard any essential hidden factors. Right?


No, the probability distributions you mentioned prove right away that there is something governing even the most basic atomic processes. We know from observation (or at least, we think we know) that electrons tend to congregate more often in certain areas around the nucleus. Correct me if I am wrong, but in a truely random process absent of any determining factors, wouldn't the electron have an equal chance of appearing in any given location?

Something must be shifting the probability scale, causing the electrons to conform to their familiar orbits. Perhaps there is even a (*gasp*) consistent underlying pattern to their orbits?

No, this is not true, except in the trivial sense that knowing anything at all 100% would require absolute knowledge (I'm not 100% sure that the Sun exists, but I'm pretty damn sure).

I don't think I am alone when I say that the pattern of decay for a radioactive nucleus is a tad more controvertible than the existence of the sun.

The assertion that humans know any more than a negligible fraction of all that there is to know is a giant assumption on your part.

[The Persnickety Platypus]

Well I guess it's not particularly easy to relate to the halting problem but it exists nonetheless. The point is in the conclusion; that the halting problem is undecidable meaning that no algorithm can be created to decide the question "will a given program halt".

How about.......... X=X?

I could also write it as "if X, then X"

I am confused as to why you would ever need an algorithm. So far, I have yet to see a problem that needs solving.

If both machines are governed exclusively by the given circumstance (the haulting of the other), then niether machine will ever hault. So what is the issue?

X=X
Machine A does not hault= Machine B does not hault.
If A+B=X, then B+A=X


Am I missing something?

Significant obstacles to hidden variables are presented in theorems presented by John Bell and Simon Kochen & Ernst Specker.

Such as?

[QED]

How about.......... X=X?

I could also write it as "if X, then X"

I am confused as to why you would ever need an algorithm. So far, I have yet to see a problem that needs solving.

How about the one in the link I posted for you? Your examples are explicitly defined. Look at the example of BAD_NUMBER -- an binary expansion of an entire program fed as input to a program. Perhaps you're not familiar with the concept of a Universal Turing Machine? I really wouldn't know where to start with a complete explanation; you need to see a good illustration of the concept to understand the proof that Turing originally presented.

In the example I linked you to a reductio absurdum is constructed around the supposition that a program is capable of deciding whether any given program with a given input will halt. With Turing machines it is possible to feed entire programs in as "single input numbers". This is used in Turing's proof to show the impossibility of the supposed program which can determine if any program will halt or not.

Am I missing something?

I'm a pretty lousy teacher when it comes to things that get a little bit more complicated than "natural selection". So pardon me for not producing a beautifully illustrated explanation of the Halting Problem. But it's not as Esoteric as you might think. If I were as skillful a communicator as mathematicians such as Roger Penrose or Ian Stewart, I could probably walk you through it in a couple of pages. But I'm afraid I'm not, nor can I spare the time. If you're genuinely interested in this proof I can only encourage you to get your teeth into the sources I've mentioned.

Significant obstacles to hidden variables are presented in theorems presented by John Bell and Simon Kochen & Ernst Specker.

Such as?

Again we have another reasonably involved story to relate. As I'm short on time I'll draw your attention to The EPR paradox and Bell's Theorem. I did read a fairly concise explanation of how the Aspect experiment violated Bell's inequalities -- I'll try and locate it if I can. IIRC it involved the X-File agents Scully and Mulder receiving mystery packages -- can anyone else recall the Book or the Author?

[Curious]

Radioactive decay is not proven to be random. Radioactive decay seems to be not random at all. Even apparent "quantum randomness" cannot be said to be proven to be random.

Care to share your proof with us ?

My answer is concerning the lack of proof in regard to randomness. We can say anything is random if we don't know the mechanisms or factors involved in the event, but this doesn't make it a random event.

More to the point, you can stage an experiment by yourself. Get a very sensitive Geiger counter, and a radioactive source (you can get a nice one from one of these old smoke detectors). Record the timings of alpha-particles as they are emitted from the radioactive chunk, and try to find a pattern. Calculate the entropy of your timings, and see how close it approaches randomness. I am guessing the answer would be "pretty damn close", and the longer you run the experiment, the closer you'll get.

You can get a piece of paper and jot down the results of a million throws of a die. the results appear random but you have an average throw pretty close to (3.5). When you record the results in pairs though you find that you get more 7s than 2s or 12s. This might be interpreted as random events leading to structure but this is not correct because:
A. The throw of a die is never random, it is predictable if the angle of throw, resistance , bounce and gravity are known.
B. A random event cannot exclude results less than 1 or greater than 6.

You say that the result you get would approach randomness... What are you measuring this against exactly? We have never seen a random event, nor can we create an algorithm that can produce a random event. we can easily produce an algorithm that seems to produce random outputs (but this is not the same is it?).

As I'd mentioned before, another good piece of evidence for quantum randomness is the entirety of modern chemistry. Chemistry advanced quite a bit when people discarded the idea of electrons as orbiting particles, and started thinking of them as probability distributions.

Electrons are wave distributions, this is why you can't say electron A is in position x,y,z. Electron shell strength and absolute charge don't support randomness at all as far as I can see. I might be wrong so feel free to give evidence and the reasoning behind it.

The insistence that an occurrence is random requires the absolute understanding of everything that could theoretically contribute to the occurrence.

No, this is not true, except in the trivial sense that knowing anything at all 100% would require absolute knowledge (I'm not 100% sure that the Sun exists, but I'm pretty damn sure).

But you can give evidence for the existence of the sun can't you? You can't give evidence to support randomness, you give a lack of evidence to support order. You cannot prove randomness because it is fallacious. Certain scientific theories require randomness to be viable, that is why the concept of randomness is even entertained. Why don't we use black bile instead, it has the same level of proof? Why not say that before matter, the random creation caused God?

And of course, wave-particle duality, as demonstrated by ye olde double slit experiment, is a direct consequence of the Uncertainty Principle (it's basically the Uncertainty Principle written in different terms), and that's an experiment you could stage yourself with a piece of foil, a laser pointer, and a sharp razor blade. Also of course, you can always observe Brownian Motion yourself in a cup of water or something, just as the Ancient Greek philosophers have done.

Cool. Explain to me why this shows randomness and I will explain to you why it does not. The investigation into wave particle duality is moderately interesting but it has nothing at all to do with randomness. Brownian motion on the other hand is quite enlightening. Get a hot cup of tea and study the action around it.

Note that all of this matters only on the quantum level. On the macro level, objects become so big and heavy that the uncertainty in their position or momentum, while nonzero, is negligible. Still, the topic of this thread is not, "are chairs random", but "does randomness exist", and the answer is "yes".

Then tell us how it exists. It might exist in your mind, but how does it exist in the real world.

Note, again, that "random" doesn't just mean "following some pattern we aren't yet able to determine". Random means just that -- random -- following no pattern at all. It may be uncomfortable to think about the electrons in your body as being unknowable, but that doesn't make it any less true. Good thing, too, because most of modern electronics is based on quantum physics, and that's what lets us have all these nice computers and stuff.

Really, and I thought that electronics was based on science.
You state:
"It may be uncomfortable to think about the electrons in your body as being unknowable, but that doesn't make it any less true".
You seem to equate non randomness with predictability and randomness with predictability. So, in your universe, all order has a degree of predictability? So would the ordered universe then require a predictor? Action does not, in my opinion, require a prediction before the event. Prediction assumes sentience or intelligence. Or maybe you are saying that humans are so intelligent that they can see order in all structure?

[Curious]

submitted post to wrong subject for some strange reason.

[The Persnickety Platypus]

I'm a pretty lousy teacher when it comes to things that get a little bit more complicated than "natural selection". So pardon me for not producing a beautifully illustrated explanation of the Halting Problem. But it's not as Esoteric as you might think. If I were as skillful a communicator as mathematicians such as Roger Penrose or Ian Stewart, I could probably walk you through it in a couple of pages. But I'm afraid I'm not, nor can I spare the time. If you're genuinely interested in this proof I can only encourage you to get your teeth into the sources I've mentioned.

Okay. But before I (further) sink my teeth into anything, tell me- what relevance does any of this have?

If the Haulting Problem does indeed prove whatever it is supposed to prove, what implications does this have for determinism and causuality?