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.

[QED]

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?

It shows that the set of unique decision problems is larger than the set of explicit algorithms that could potentially resolve them. If there are more decision problems than deciding programs then it follows that some decision problems cannot be resolved algorithmically. What problems can be solved by computers is equivalent to what decision problems can be solved. If, as it appears to, mathematics bears more than a coincidental relation to physical reality, then it would appear to be showing us a limit to omniscience.

Now I raised this because I could see the inevitable bottleneck imposed by arguing that we know of some physical processes producing randomness. This is a top down approach for which we can seemingly always introduce some underlying layer which permits determinism. But even here there comes a point where the fine-graining of physics introduces a "crash barrier" (Plankian limits) and so presents a distinct possibility of an ultimate solution one way or the other (e.g. acausality does or does not exist).

Consider chaos which is often mistakenly equated to randomness. It is more a statement about sensitivity to inaccuracy. Chaotic systems are theoretically deterministic in nature but in order to be precisely audited they may require infinite precision in measurement. This brings us back to Planckian metrics. As time and distance breaks down at this particular scale then while mathematics may continue to go on adding decimal places to real numbers, nature "rounds" her values in some way. The way in which this occurs takes us into the realm of Quantum Mechanics where no conclusion has yet been formed as to the correct interpretation of what we see.

That last sentence takes in a wide range of experimental and philosophical work conducted over almost a century now. The most pertinent experimental work would probably be that involved in practical tests for Bell's inequalities. I have still to find the simple description I mentioned earlier, but in the meantime my online searching turned up this Analogy to Bell's Theorem with the appropriate background here.

I think an honest answer to the question regarding randomness has to be that it is unknown at present if it exists or not. However, if it doesn't exist then we must abandon the notion of local realism.

---------------

Seeing as how I'm putting a bit of effort into answering your questions, I wonder if you could do a bit of thinking for me: If the universe is fully deterministic such that from initial conditions the entire cosmic performance is pre-scripted down to every last atomic detail from beginning to end, then what is the significance of time? It would only seem to serve to separate inevitable events and the "clock rate" would be wholly arbitrary. For an "external" observer the entire performance might be played out during a tea-break.

Perhaps the "experiment" has been made more interesting by injecting indeterminacy in the shape of living things acting as agencies with free will -- in which case hidden variables might not exist and local realism is preserved.

[Bugmaster]

A. The throw of a die is never random, it is predictable if the angle of throw, resistance , bounce and gravity are known.

I doubt this is true, because of the Brownian motion of air molecules.

B. A random event cannot exclude results less than 1 or greater than 6.

Why not ? This is very consistent with an electron shell within an atom: the probability of finding an electron a certain distance from the nucleus is very high, but drops off rapidly when you leave the range of the shell.

You say that the result you get would approach randomness... What are you measuring this against exactly?

I am measuring the entropy of the sequence, its autocorellation, and its chi-squared, as I mentioned in my previous posts. This is an objective measure of randomness, if you use the definition of "randomness" that's commonly accepted in statistics, mathematics, and information theory. You can always use some other definition of randomness, but then you need to tell me what it is.

We have never seen a random event...

Sure we have. Radioactive decay, cosmic rays, white noise from an electronic circuit... all these are random events.

nor can we create an algorithm that can produce a random event.

By definition, this is true. Algorithms are not random.

Electrons are wave distributions, this is why you can't say electron A is in position x,y,z....

If you say that, you have just automatically affirmed the Uncertainty principle. You can have one without the other; you can check the math yourself. And the Uncertainty principle leads directly to the randomness of quantum decay.

But you can give evidence for the existence of the sun can't you? You can't give evidence to support randomness

I just did, in the previous 2 or 3 posts. You can disagree with my (actually, Bohr's and Oppenheimer's and Heisenberg's) interpretation of the evidence, but please don't say I didn't give any. That's just being disingenuous.

So, in your universe, all order has a degree of predictability?

Yes, by definition. If a sequence of digits has some order to it, then it should be possible to predict it, in principle. Now, we frail humans may not be able to predict it for a billion years, but that's our problem. The exact timings of radioactive decay, on the other hand, cannot be predicted by anyone, ever. Sad but true.

If you disagree, please give me a definition of order and randomness, as you use these words, because I am starting to believe that we're talking about different things.

So would the ordered universe then require a predictor?

This seems like a leap of faith to me. Just because some pattern can be predicted, doesn't mean that it requires a predictor.

[The Persnickety Platypus]

It shows that the set of unique decision problems is larger than the set of explicit algorithms that could potentially resolve them. If there are more decision problems than deciding programs then it follows that some decision problems cannot be resolved algorithmically. What problems can be solved by computers is equivalent to what decision problems can be solved. If, as it appears to, mathematics bears more than a coincidental relation to physical reality, then it would appear to be showing us a limit to omniscience.

This, of course, is assuming that the Haulting Problem actually requires a decision.

From what I can see, it only leaves ONE possible outcome. There is no decision in that. There is no existing algorithm for the haulting problem because it is not actually a problem in need of solving.

X=X.

Why is this not a viable solution?

Seeing as how I'm putting a bit of effort into answering your questions, I wonder if you could do a bit of thinking for me: If the universe is fully deterministic such that from initial conditions the entire cosmic performance is pre-scripted down to every last atomic detail from beginning to end, then what is the significance of time? It would only seem to serve to separate inevitable events and the "clock rate" would be wholly arbitrary. For an "external" observer the entire performance might be played out during a tea-break.

Does time need to have a signifigance?

You seem to be comparing natural history to something like a play. If you know how the story ends, why bother watching it? Why bother taking time between scenes if the plot will remain unchanged regardless?

The universe is not here for anyone's entertainment. The universe is here because it is here. Unless you believe in a god, there is no external agency out there watching history as it unfolds. The only operatives in the universe which can reflect on history are it's sentinent organisms (with the specific members of this description being debatable). But these organisms, of course, are only allotted a mininscule fraction of history to experience.

Why shouldn't there be intervals between natural events? Does eliminating time all together serve some better purpose? Like you said, it will all end the same regardless.

If you are going to question the purpose of having intervals between events, you might as well question the signifigance of these events occurring in the first place.

For what reason should nature be in a hurry to conclude itself? Eager to get to the next Big Bang?

Time, in my view, is arbitrary anyway. It exists exclusively in the minds of sentinent organisms, who use it to measure the duration and intervals between successive events.

Regardless, I for one am quite thankful that nature/my brain has allotted time inbetween all successive events. It gives me a chance to relish the glory unfolding in front of me.



This shift in discussion reminds me of the race of Trafaldamorians in Kurt Vonnegut's "SlaughterHouse-Five/The Children's Crusade". This alien race had no concept of time. They knew exactly what the history of the universe entailed from beginning to end, and the successive stages of their life were spent shifting from one memory to the next, in no particular order.

Perhaps this bears some signifigance to your question?

Perhaps the "experiment" has been made more interesting by injecting indeterminacy in the shape of living things acting as agencies with free will -- in which case hidden variables might not exist and local realism is preserved.

Why should that be any more interesting? Even in a determinist universe we have absolutely no way of knowing what the future has in store for us.

For me, there is something beautiful in the notion that nature, no matter now vast and confusing it may seem to our tiny human perceptions, is underlyed by a consistent, perfect set of laws. To know that all phenomena is interconnected gives me a greater sense of loyalty to my fellow earthen denizens. To know that my actions have possible universal implications gives me a greater sense of self worth.

This is not to say that I could not find beauty in the notion of a random universe. However, determinism (aside from providing a more compelling explanation of the world) much better accompanies my life's philosophy.

[The Persnickety Platypus]

Bugmaster,

We have never seen a random event...

Sure we have. Radioactive decay, cosmic rays, white noise from an electronic circuit... all these are random events.

You have asserted that these events are random.

You have yet to show them to be so.

I just did, in the previous 2 or 3 posts. You can disagree with my (actually, Bohr's and Oppenheimer's and Heisenberg's) interpretation of the evidence, but please don't say I didn't give any. That's just being disingenuous.

Your so called "evidence" concludes that phenomena such as radioactive decay are random because we have yet to decifer any specific pattern in their behavior.

That does not convince me.

You have yet to address the heart of the question: how an effect can lack a cause.

We know of various conditions that must be satisfied in order for an atom to decay. Can you explicitly show that the nature of these conditions (in addition to the atomic forces at play) do not define a pattern by which subatomic particles in a decaying atom move?

With our limited information on this matter (not to mention our limited abilitys in deciphering patterns), is this not the more logical conclusion?

[Curious]

A. The throw of a die is never random, it is predictable if the angle of throw, resistance , bounce and gravity are known.

I doubt this is true, because of the Brownian motion of air molecules.

Brownian motion depends on the interaction of molecules and requires energy. This cannot be said to be random then as the motion is caused by external forces. The actual direction of singular movements might be presently impossible to predict but the overall direction of movement can be predicted by suspending a particle between different concentrations of energy or density.

B. A random event cannot exclude results less than 1 or greater than 6.

Why not ? This is very consistent with an electron shell within an atom: the probability of finding an electron a certain distance from the nucleus is very high, but drops off rapidly when you leave the range of the shell.

The chance of finding a bee next to a hive is great but drops of rapidly when you leave the area. the chance of finding a ripple next to a splash in a pond is high until you travel outwards and then they become more infrequent. Neither of these are random events, so what makes you think your example shows evidence of randomness?

You say that the result you get would approach randomness... What are you measuring this against exactly?

I am measuring the entropy of the sequence, its autocorellation, and its chi-squared, as I mentioned in my previous posts. This is an objective measure of randomness, if you use the definition of "randomness" that's commonly accepted in statistics, mathematics, and information theory. You can always use some other definition of randomness, but then you need to tell me what it is.

How about without cause.

We have never seen a random event...

Sure we have. Radioactive decay, cosmic rays, white noise from an electronic circuit... all these are random events.

I assume you mean cosmic background radiation when you say cosmic rays, which in turn create electronic white noise (unless you mean due to interference from another source ). Background radiation is thought to be an echo from the big bang so this is not random. The noise is created by interference by the radiation. Radioactive decay is not random at all. Particular elements decay at given rates. The decay is therefore dependent upon the element involved. The properties of the element determine the rate of it's decay.

Electrons are wave distributions, this is why you can't say electron A is in position x,y,z....

If you say that, you have just automatically affirmed the Uncertainty principle. You can have one without the other; you can check the math yourself. And the Uncertainty principle leads directly to the randomness of quantum decay.

The uncertainty principle is not referring to universal uncertainty but to human uncertainty. The principle basically says that when we measure one thing accurately we become less accurate in determining something else (eg. position and momentum). This has nothing whatsoever to do with indeterminacy within the atom but is to do with difficulty in our measurement of the atomic structure. You might not be able to say how a lump of uranium will decay but the uranium itself has no problem in decaying at an absolutely precise rate. The inability to accurately measure phenomena, in my opinion, should lead to uncertainty in your conclusion.

But you can give evidence for the existence of the sun can't you? You can't give evidence to support randomness

I just did, in the previous 2 or 3 posts. You can disagree with my (actually, Bohr's and Oppenheimer's and Heisenberg's) interpretation of the evidence, but please don't say I didn't give any. That's just being disingenuous.

You gave no evidence. What you did give was an assertion that randomness existed and referenced a principle which did not support the claim. I could just as easily say that a dog is a cat because a mouse has whiskers. It isn't evidence just because I say it is.

So, in your universe, all order has a degree of predictability?

Yes, by definition. If a sequence of digits has some order to it, then it should be possible to predict it, in principle. Now, we frail humans may not be able to predict it for a billion years, but that's our problem. The exact timings of radioactive decay, on the other hand, cannot be predicted by anyone, ever. Sad but true.

But this is because of our clumsiness at measuring. A particle may have precise momentum and position but we can only accurately measure one or the other. Just because we cannot accurately measure the position of a particle does not mean it has no definite position and the same goes for momentum.

If you disagree, please give me a definition of order and randomness, as you use these words, because I am starting to believe that we're talking about different things.

random- without cause.
order- having cause and/or structure

So would the ordered universe then require a predictor?

This seems like a leap of faith to me. Just because some pattern can be predicted, doesn't mean that it requires a predictor.

I agree, there is no reason that a predictor is required for an action to take place. So why do you think that radioactive decay is random just because you can't predict it?

[Bugmaster]

I think you're misinterpreting "random" to mean "uncaused". That is not necessarily the case, though I'd be the first to admit that I don't know how, or even whether, causality works on the quantum level. Causality is not a concept used in physics, anyhow.

Brownian motion depends on the interaction of molecules and requires energy. This cannot be said to be random then as the motion is caused by external forces.

Motion caused by external forces can still be random. When I'm heating up a tank of gas, I'm not controlling each molecule manually. Their movements are still random. In fact, it's just like you said:

The actual direction of singular movements might be presently impossible to predict but the overall direction of movement can be predicted...

Right, "random" doesn't mean "completely unknown". As I'd mentioned in my original post (I think), we can accurately predict the rate of decay of some radioactive material, but we cannot predict when individual particles will decay. There's no contradiction in this; all this means is that the random decay of particles follows some distribution, which, when averaged out over millions of decay events, is quite predictable.

Why not ? This is very consistent with an electron shell within an atom: the probability of finding an electron a certain distance from the nucleus is very high, but drops off rapidly when you leave the range of the shell.

The chance of finding a bee next to a hive is great but drops of rapidly when you leave the area. the chance of finding a ripple next to a splash in a pond is high until you travel outwards and then they become more infrequent. Neither of these are random events, so what makes you think your example shows evidence of randomness?

I'm not sure what you're driving at. I certainly didn't say that all events that follow some sort of a probability distribution are random. I only said that some random events follow a probability distribution. However, you bring up an interesting point about the bees: I actually don't know if the movements of individual bees are random or not. Does anyone else know ?

How about without cause.

Sure, but this is not the randomness I meant, so I have no argument with you. I was talking about a totally different thing.

[Curious]

I think you're misinterpreting "random" to mean "uncaused". That is not necessarily the case, though I'd be the first to admit that I don't know how, or even whether, causality works on the quantum level. Causality is not a concept used in physics, anyhow.

It would be rather difficult to explain physics without causality. Momentum is a prime example.

Brownian motion depends on the interaction of molecules and requires energy. This cannot be said to be random then as the motion is caused by external forces.

Motion caused by external forces can still be random. When I'm heating up a tank of gas, I'm not controlling each molecule manually. Their movements are still random. In fact, it's just like you said:

The actual direction of singular movements might be presently impossible to predict but the overall direction of movement can be predicted...

Right, "random" doesn't mean "completely unknown". As I'd mentioned in my original post (I think), we can accurately predict the rate of decay of some radioactive material, but we cannot predict when individual particles will decay. There's no contradiction in this; all this means is that the random decay of particles follows some distribution, which, when averaged out over millions of decay events, is quite predictable.

For something to be non-random does not require YOU to have any idea of the mechanics involved. Ergo, a lack of understanding of the mechanics does not imply randomness. The fact that these "random" motions can be affected by environmental factors shows that they are not random at all but are caused by external (or even internal) forces.( Just to make it clear, I am aware that radioactive decay is not affected by normal environmental variation such as temperature or pressure).

Why not ? This is very consistent with an electron shell within an atom: the probability of finding an electron a certain distance from the nucleus is very high, but drops off rapidly when you leave the range of the shell.

The chance of finding a bee next to a hive is great but drops of rapidly when you leave the area. the chance of finding a ripple next to a splash in a pond is high until you travel outwards and then they become more infrequent. Neither of these are random events, so what makes you think your example shows evidence of randomness?

I'm not sure what you're driving at. I certainly didn't say that all events that follow some sort of a probability distribution are random. I only said that some random events follow a probability distribution. However, you bring up an interesting point about the bees: I actually don't know if the movements of individual bees are random or not. Does anyone else know ?

The individual movement of bees is not random but can be seen as such.The movement of 100 bees can be interpreted as random. The movement of 25000 bees is seen to be not random. It is difficult to extrapolate from the movement of a few bees in isolation or from a great many bees over a long period. You really need to understand the bees within a particular context. In other words, it is pointless to try to understand the intricacies of social interaction by focusing on the actions of individuals in isolation.

How about without cause.

Sure, but this is not the randomness I meant, so I have no argument with you. I was talking about a totally different thing.

Well, if you are talking about a "randomness" that is caused, then it is not really random at all. A change in the cause would affect the outcome and show that the effect was deterministic.

[Bugmaster]

It would be rather difficult to explain physics without causality. Momentum is a prime example.

I'm not sure I follow...

For something to be non-random does not require YOU to have any idea of the mechanics involved.

Sorry, my bad -- I slipped into the first-person omniscient perspective in my previous post. It's probably all that arrogant atheism talking. Anyway, when I said, "I cannot predict X", or "you cannot predict X", what I meant was, "no one, not even an omniscient deity, could predict X". Sorry for the confusion.

Anyway, I do not say "random" to mean "uncaused". All I mean is, "unpredictable in principle, except on average". When I heat up that canister of gas, the molecules inside will move faster, on average, due to the heat that I applied. However, neither I nor you nor anyone else, includiong the omni-God, could predict the motions of each individual molecule. Similarly, God could tell you with great accuracy when a lump of radium (does radium come in lumps ?) would decay, but even he could not tell you the exact timings of all the particle emissions. Not even if it was him who created the radium to begin with -- despite the fact that he knows full well what causes radioactive decay (just as we do). That is what I mean by "random".

The individual movement of bees is not random but can be seen as such.

I'm not sure what this means.

Well, if you are talking about a "randomness" that is caused, then it is not really random at all. A change in the cause would affect the outcome and show that the effect was deterministic.

I guess it depends on whether you're looking at the "big picture", statistically speaking, or at the individual particles.

[Goat]

It would be rather difficult to explain physics without causality. Momentum is a prime example.

I'm not sure I follow...

For something to be non-random does not require YOU to have any idea of the mechanics involved.

Sorry, my bad -- I slipped into the first-person omniscient perspective in my previous post. It's probably all that arrogant atheism talking. Anyway, when I said, "I cannot predict X", or "you cannot predict X", what I meant was, "no one, not even an omniscient deity, could predict X". Sorry for the confusion.

Anyway, I do not say "random" to mean "uncaused". All I mean is, "unpredictable in principle, except on average". When I heat up that canister of gas, the molecules inside will move faster, on average, due to the heat that I applied. However, neither I nor you nor anyone else, includiong the omni-God, could predict the motions of each individual molecule. Similarly, God could tell you with great accuracy when a lump of radium (does radium come in lumps ?) would decay, but even he could not tell you the exact timings of all the particle emissions. Not even if it was him who created the radium to begin with -- despite the fact that he knows full well what causes radioactive decay (just as we do). That is what I mean by "random".

The individual movement of bees is not random but can be seen as such.

I'm not sure what this means.

Well, if you are talking about a "randomness" that is caused, then it is not really random at all. A change in the cause would affect the outcome and show that the effect was deterministic.

I guess it depends on whether you're looking at the "big picture", statistically speaking, or at the individual particles.

In other words, you are talking something that is probabalistic, rather than determinalistic.

[Bugmaster]

In other words, you are talking something that is probabalistic, rather than determinalistic.

I think so, but I'm not sure what "determinalistic" means.