How “random” is “randomness”?

[andyandy]

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

Rolfe.

Wouldn't our time stream be one dimensional - ie backwards or forwards along a line?

Not that this affects the consideration at all....

 

[rcronk]

rolfe - thanks for the thoughts - do you have a link or reference for C.S. Lewis' thoughts you referred to?

P.S. I saw elvis at 7-11 last week. ;-)

 

[Folly]

first we take the premise of a bubble universe [BU] which is formed as a result of utterly random quantum contortions in the primoridal vacuum - which means that everything within the observable universe is ultimately the result of random processes that occured in the first split second of the universe's existence. So what is true of our observable universe must be true of all other regions the size of the observable universe in our BU. This means that all possible arrangements of protons in an area the size of our observable universe will occur in other regions of the BU. The way in which protons can be arranged within the observable universe is finite, and so because the BU is infinite it follows that every possible arrangement must occur somewhere - indeed every possible arrangement must occur an infinite number of times in an infinite number of places

it starts by asserting that the number of protons which could fit in the observable universe is about 10^118

and that in each one of these 10^118 locations can either have a proton or no proton, and as such if there are n possible locations for protons, and so there are 2n different universes possible. In our universe where n=10^118 then there are 2^(10^118) possible ways to arrange the protons which is approx equal to 10^(10^118)

I totally agree that follows from the assumptions, and it's an interesting idea.

I don't know about the assumptions, though. My physics stops at classical mechanics augmented by what I've picked up here, but what about non-exclusionary particles? (fermions? or was it bosons... bah - so much for me having learned anything...) Is space-time position actually quantised? If not, if I have an empty space, neighbouring protons could be anywhere in a small real interval of positions and the whole thing is sunk.

 

[Blu]

This thread seems to have leaned on the side of probability rather than what I was expecting to read, i.e. randomness.

What is meant by randomness? Well... there are numerous ways in which people generate "random" numbers, for example, but why can they be called random?

If you take random to mean that you cannot determine the outcome of an event based on previous knowledge, then randomness does exist and is truly random.

Although I can throw dice 1000 times, there may be statistical probabilities that determine the chance of certain numbers coming out so many times each, but that's begger all to do with randomness. Let's keep a clear distinction between the two. Just because I throw a certain combination of numbers on my dice in one throw does not give me any indication of what any subsequent throw is going to be, therefore it's random.

Shemp,

1. Is there really randomness in the macro, non-quantum world, or is it just an illusion and a lack of information and computing power?

You would have to have a computer that knows every variable in the Universe as everything could, potentially at a quantum level, effect everything else. The only thing powerful enough to know all that is the Universe itself. In which case the randomness is an integral part of the very computer universe that is trying to detect it.

2. Similarly, is there really randomness in the quantum world?

Quantum is "theory". Of course randomness can be incorporated into quantum theory, although it does depend on what quantum model you wish to use.

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

Randomness exists in both, no difference, no need for drawing lines (unless you want to draw some pretty pictures of course. )

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Free will is a whole philosophical topic on it's own, however, assuming randomness exists, then there is room for free will to exist.

In answer to Ivor the Engineer...

How does the Many Worlds interpretation of QM affect the randomness?

Each distinct event splits the world (universe) into all possible outcomes. The randomness comes in whichever of those worlds you see your existence in.

 

[Schneibster]

How do we know this (other than by reference to basic principles)?

I assume by "this," you mean my assertion that quantum phenomena are truly random. If I am wrong, please disabuse me of the notion.

We know because we have proven fairly conclusively that characteristics that are uncertain are not merely unmeasurable, but do not have a value. Since such characteristics are omnipresent, that is, some characteristics are rendered uncertain at every quantum interaction, we can be sure that their values after that interaction will be a probability function in every such case; if they actually had values, this probability distribution would be altered by them. The fact that we can measure that it is not is the proof of the randomness of quantum phenomena.

Now, I don't know if that's a basic principle or not. But it's empirically determined data, so I'm not sure it matters.

And is there a discussion somewhere as to the extent that single quantum events influence outcomes in everyday life, as in speculative essays or articles from someone who is knowledgeable in the field? (Much as I appreciate your essays, they must take considerable effort on your part and I don't wish to put you out - I'm willing to do my own legwork if you can point me in a particular direction).

Linda

I don't have anything like that to hand. Let me know if you can't find anything, but I suspect a quick google will get you where you're going. Thanks for your consideration; keep in mind, though, that I do it because I like to.

Considering this, I'm not sure I properly answered your question. So assuming that was wrong, and "this" means my assertion that individual quantum events can influence macroscopic reality, I'll point to the fact that a scintillation counter is, at simplest, a screen that emits a photon every time an electron hits it. The photons can be seen by the human eye, individually. Quantum events therefore individually are capable of generating macroscopically observable phenomena.

But this is a trivial example, and one might dismiss Schroedinger's Cat as a fanciful one.

Do the search I have suggested and come back if you don't get anything; I'll assume you're looking for a credible instance in which classical motion is affected by individual quantum events, and I'll go hunt one up for you.

 

[Rolfe]

rolfe - thanks for the thoughts - do you have a link or reference for C.S. Lewis' thoughts you referred to?

P.S. I saw elvis at 7-11 last week. ;-)

Unfortunately I've recently moved house and I've no idea which of the distressingly large number of boxes the "L" books are in. (That and the one about the Lockerbie bombing I referenced in the CT forum, can't even remember the name of the author of that one....)

I'll see if a quick glance in a few boxes reveals anything.

Rolfe.

 

[Rolfe]

Wouldn't our time stream be one dimensional - ie backwards or forwards along a line?

Not that this affects the consideration at all....

I stand corrected, you're right.

Rolfe.

 

[Rolfe]

But in this case, you are effectively trying to find an explanation for something for which there is no evidence, or God is magic, and anything goes - including a number of paradoxes.

Rcronk is starting from that premise. I see no objection to continuing the discussion assuming the premise, for the sake of the discussion.

Rolfe.

 

[fls]

I assume by "this," you mean my assertion that quantum phenomena are truly random. If I am wrong, please disabuse me of the notion.

Sorry, I meant a single quantum event influencing the outcome of a die roll; perhaps some relevant (i.e. relevant to classical motion, not dice specifically) empirically determined data.

Do the search I have suggested and come back if you don't get anything; I'll assume you're looking for a credible instance in which classical motion is affected by individual quantum events, and I'll go hunt one up for you.

Yes, that is what I'm looking for. I'm having trouble finding something that specific (that's not related to consciousness).

Thank you.

Linda

 

[Soapy Sam]

I think the multiple universes of this thread nicely illustrate the differences in meaning of words like "random" when used in (any of several) scientific contexts as opposed to general daily usage. Miscommunication can arise from this phenomenon and I feel it needs a name if it does not have one already. I propose "definistrition" , since at least one definition must be thrown out of the window for the duration of the discussion;- or we end up arguing about "inorganic" potatoes again.

Unpredictability seems to me largely an issue of time. Before I flip a coin, even given exact data on air resistance, humidity, windspeed, thumb stickiness, coin weight, local gravity etc, all I can predict is that it will be heads, tails, passing seagull or some other edge / lost variant. This is true even without introducing the quantum acausality Schneibster describes. We just couldn't do the maths fast enough, even if the results were inherently predictable, the start values had clearly defined values, or if there were no macroscopic results of quantum events.

After the spinning coin stops moving, predictability is either 0 again, or 1, depending how we define "predictability".
But about 1/100,000th of a second before the coin stops moving, predictability is around 0.999..., which as we are all very tired of hearing, equals 1.
And there is a gradually lesser spectrum of predictability ranging backward in time, all the way to the original, pre toss value of zero.
At which point do we call a halt? Off track betting is usually not permitted after the race starts. Bookies do not believe in randomness.

As for free will, I have never believed in it. Whether this is because I chose not to do so, or because I never believed in it, I cannot say.

 

[Schneibster]

How does the Many Worlds interpretation of QM affect the randomness?

Which World do we wind up in? The answer looks pretty random to me.

ETA: And Bell Test loopholes?

Technically, there aren't any loopholes in Bell's Theorem; either locality is true, or local realism is true. There are various loopholes in the actual tests done. I would not state definitively at this time that all these loopholes are closed in a single experiment; it appears to be the considered opinion of most physicists that closing various loopholes in different experiments is sufficient to decide the matter, and actually that it was really decided by Aspect, and I have to say that I agree. There are bigger and better fish to fry.

 

[SirPhilip]

What about black holes, damnit.

 

[Schneibster]

Sorry, I meant a single quantum event influencing the outcome of a die roll; perhaps some relevant (i.e. relevant to classical motion, not dice specifically) empirically determined data.

Yes, that is what I'm looking for. I'm having trouble finding something that specific (that's not related to consciousness).

Thank you.

Linda

OK, here you go:

http://findarticles.com/p/articles/mi_m1200/is_n14_v138/ai_8986262

This discusses how, in classically chaotic situations like rolling dice, the uncertainty of the underlying quantum description of the system increases to permit the chaotic behavior.

 

[blobru]

I agree with those who say dice tosses (and coin flips) are unpredictable, but does that make them perfectly random? (To return to Shemp's original question: "How random is 'random'?")

If it were possible say to exactly repeat all the influences on a given dice toss -- the position of the thrower's hand, how he holds the dice, the impetus he gives to the dice, various environmental factors -- and then repeat that same dice toss over and over -- I don't think you'd get perfect randomness, but rather a skewed version of the two dice probability curve.

It seems too that dice should be much more unpredictable in such a scenario than coins, given their different geometry. Coins have two faces and one edge. Dice have six faces, twelve edges, and eight corners. How the object will react after a 'face' collision with whatever surface you're using should be much easier to predict than an 'edge' collision (teetering between two faces), and a 'corner' collision (between three faces) should be hardest of all.

A coin moreover, if you catch it in your palm so it doesn't bounce and then repeat the motions, unless it lands almost upright on its edge, should be very predictable. At the other extreme, the outcome for a coin tipped upright and spun on a table should be almost impossible to predict, even after several ideal repetitions. And here, unlike the coin flip example where the probability slides from 0 to 1 the closer the coin comes to rest, the probability seems to stay at 0 until the spinning coin wobbles, and then shift instantly to 1.

Interesting to note that philosophers who believe in determinism prefer billiards to dice in their examples. Billiard balls of course have no edges, and always collide face to face (much easier to predict). Not sure though how 'predictable' pool breaks are: my experience playing was that hitting a rack in almost the same spot with almost the same force could produce wildly different outcomes!

 

[shemp]

I agree with those who say dice tosses (and coin flips) are unpredictable, but does that make them perfectly random? (To return to Shemp's original question: "How random is 'random'?")

If it were possible say to exactly repeat all the influences on a given dice toss -- the position of the thrower's hand, how he holds the dice, the impetus he gives to the dice, various environmental factors -- and then repeat that same dice toss over and over -- I don't think you'd get perfect randomness, but rather a skewed version of the two dice probability curve.

It seems too that dice should be much more unpredictable in such a scenario than coins, given their different geometry. Coins have two faces and one edge. Dice have six faces, twelve edges, and eight corners. How the object will react after a 'face' collision with whatever surface you're using should be much easier to predict than an 'edge' collision (teetering between two faces), and a 'corner' collision (between three faces) should be hardest of all.

A coin moreover, if you catch it in your palm so it doesn't bounce and then repeat the motions, unless it lands almost upright on its edge, should be very predictable. At the other extreme, the outcome for a coin tipped upright and spun on a table should be almost impossible to predict, even after several ideal repetitions. And here, unlike the coin flip example where the probability slides from 0 to 1 the closer the coin comes to rest, the probability seems to stay at 0 until the spinning coin wobbles, and then shift instantly to 1.

Interesting to note that philosophers who believe in determinism prefer billiards to dice in their examples. Billiard balls of course have no edges, and always collide face to face (much easier to predict). Not sure though how 'predictable' pool breaks are: my experience playing was that hitting a rack in almost the same spot with almost the same force could produce wildly different outcomes!

As a thought exercise, let's say that we build a machine that throws dice onto a table; the dice are perfectly cubic and uniformly balanced; they are always in the exact same position before the throw; that the machine always throws them in the same direction with the same force; that the table is perfectly flat and hard; that this takes place in a vacuum; in short, at scales larger than the molecular level, EVERY condition is exactly the same EVERY time. Therefore, if there is any variance in the results, it should be due to quantum fluctuation. How much variance can we expect in the results compared to the normal probabilities we see in a typical craps game?

 

[andyandy]

As a thought exercise, let's say that we build a machine that throws dice onto a table; the dice are perfectly cubic and uniformly balanced; they are always in the exact same position before the throw; that the machine always throws them in the same direction with the same force; that the table is perfectly flat and hard; that this takes place in a vacuum; in short, at scales larger than the molecular level, EVERY condition is exactly the same EVERY time. Therefore, if there is any variance in the results, it should be due to quantum fluctuation. How much variance can we expect in the results compared to the normal probabilities we see in a typical craps game?

they should in that case always land on exactly the same number. With a coin toss you should also be able to achieve 100% predictability through controlling the height, force, number of rotations - it's easy enough with a couple of minutes practice to skew it 60-40 without the use of any machine....
could a 3 [moving] ball collision be predicted if we knew everything about the system - or is there an inherent randomness? I'd tend towards it being wholly determinable, but i'm not sure

 

[cyborg]

1. Is there really randomness in the macro, non-quantum world, or is it just an illusion and a lack of information and computing power?

From the computing perspective the Kolmogorov Complexity is probably most relevant.

For any finite sequence we can define a machine and a language to construct it. A language is any finite set of symbols. A machine can output language symbols. We can define the machine in terms of those language symbols to form a program for outputting the symbols. Now we can measure the complexity of a sequence as the smallest set of symbols from our language that describes both the machine and its output.

Now our machine can also define infinite sequences if it is able perform recursion in the language. We can now define a random sequence as any infinite sequence which cannot be constructed by any finite machine. That is to say the Kolmogorov Complexity is infinite.

Computing equivalence can tell us what machines are equivalent. Every algorithm we have thus been able to think of can be described by a well known class of machines - the Turing Machine equivalence.

Are there infinite sequences for which there is a finite machine that is not equivalent to a Turing Machine that can describe them?

If so does every infinite sequence have a finite machine that can construct it?
If not then everything is deterministic - we could always build a machine that could describe even the behaviour of QM precisely.

If not we might then consider if we can have more powerful computation with random behaviour in the machine. Here we need to have some notion about the meaning of the output sequence in order to have any notion about computational power. We can now construct a class of sequences that have equivalent meaning. We can reduce our random set by excluding those sequences which have an equivalent sequence that can be described by a machine without random behaviour. We have not computed any more meaning therefore the power of the computation is the same.

So what we want to know is if there are infinite sequences for which no meaning can be constructed for finitely. These would be truly random in the fullest sense of the word; in that there is absolutely no purpose behind it at all. If we could prove otherwise then there would be no randomness at all.

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Humans can be described in terms of the machine/language defined above - as humans are finite we can construct some machine with some associated meaning that can completely describe a human's life. Now in order for free-will to be term with a meaning beyond that the already defined for our machines it would have to be a mechanism that provides more computing power than we already have. If it didn't then either free-will is randomness or free-will is deterministic - the later is clearly not acceptable for the 'free' concept and the former for the 'will' concept.

As such free-will would have to describe some meaningful sequence that does not have some equivalent sequence describable by a machine using randomness and determinism to formulate its output.

 

[Soapy Sam]

Shemp, if we are going to control all possible variables so far as nature will permit, it would surely be simpler to paint a six on every side of the die, or to build a machine that simply laid it down with the six uppermost, even if quantum fluctuation somehow tried to turn it into a four.

The point is that usually, most of those variables are not controlled. That's where the genuine unpredictability comes from. I agree this is not the same thing as randomness by some definition, but for practical purposes it may as well be.
The quantum issue is rather different, but I suspect there's a limit to it's importance too, in that no matter how acausal or odd a quantum event, the macroscopic universe only seems to permit certain outcomes.
No matter how the quantum event is amplified, the answer may be constrained to be 0 or 1, but never "Penguin", so there's a discarding of acausal randomness at some point- which may indeed be at a molecular scale size wise and somewhere else timewise.

I really think this is a debate about definitions.

 

[Schneibster]

they should in that case always land on exactly the same number. With a coin toss you should also be able to achieve 100% predictability through controlling the height, force, number of rotations - it's easy enough with a couple of minutes practice to skew it 60-40 without the use of any machine....

I suspect that you'd find you could skew the odds, probably quite far, but not reproduce the same number (or heads, for example) on every throw.

could a 3 [moving] ball collision be predicted if we knew everything about the system - or is there an inherent randomness? I'd tend towards it being wholly determinable, but i'm not sure

You're forgetting: the three-body problem has no tractable solution.

 

[Schneibster]

You do realize, cyborg, that the Kolmogorov complexity of a string is not computable, right? A function that could compute Kolmogorov complexity would be the Turing equivalent of the halting function- one that can compute whether another function yields a terminating or non-terminating result. This is a relatively well-known result based on the same characteristic of computation that Godel's theorem rests upon.

Your statement therefore boils down to whether it is possible to define a finite machine that can produce an infinite string that is not describable in shorter terms (for example, an infinite string of the character "3" endlessly repeated obviously has a low Kolmogorov complexity).

This is Turing equivalent to the halting program. Which means...

<gives everyone a moment to think about it>

We can never know by computation whether randomness exists or not.

This sentence is false.

ETA: Just so everyone's clear, the fact that Turing was able to prove that we cannot construct a general algorithm that can tell whether another algorithm will halt or not means that we cannot use finite computation (that is, computation in which each step takes a finite amount of time) to determine that a program will produce infinite output; in other words, to find out in a finite period if a computer program can generate infinite Kolmogorov complexity, we would have to use the Turing halting program, which we already have proven cannot exist. It is therefore obvious that the shortest way to find out is to run the program and examine its output to see if it's infinite; which, equally obviously, being a finite computation, takes an infinite amount of time.