Do you have an example of a truly random phenomenon?

[sysprog]

@Jon Richfield You appear to me be attempting to assert limitation against the power of language to define the definable. Whatever the exact value of it is, the square root of two is definitely exactly that number which multplied by itself equals two (as @PeroK indicated), and to know what two is, you have have only to look at your hands, and count as high as almost any mammal can (almost any mammal can distinguish between one and more than one) until you get past one, and then stop. What will you do when the irrational number $\pi$ is perfectly precisely defined as that number which is equal to the ratio of the circumference of a circle to its diameter?

 

[Filip Larsen]

How do we know a physical system with a continuous state (e.g. the distance between two particles in the system) is in a state of exactly 2, and not one of the infinitely many other values that lies within an arbitrary small ball around 2?

 

[Jon Richfield]

@Jon Richfield You appear to me be attempting to assert limitation against the power of language to define the definable. Whatever the exact value of it is, the square root of two is definitely exactly that number which multplied by itself equals two (as @PeroK indicated), and to know what two is, you have have only to look at your hands, and count as high as almost any mammal can (almost any mammal can distinguish between one and more than one) until you get past one, and then stop. What will you do when the irrational number $\pi$ is perfectly precisely defined as that number which is equal to the ratio of the circumference of a circle to its diameter?

The examples you cite are OK in everyday utility, much as you can go to the grocer to buy "a kilo of butter" or "a litre of milk", but, like the map I mentioned, they are fictions. Would you show me an exact hand? And then undertake to show me that hand again? (Or two hands for that matter?) I hardly think so.

And how about showing me an exact circle? Fat chance! There is no such thing: no matter the precision of the equipment you draw it with, or indicate its position in space, it is a formal fiction, with, at one's most charitable, a fuzzy circumference with a poorly defined diameter, that is at all times greater than pi times an idealised diameter.

But two? Which two did you have in mind as defining the coordinate of a point on a notional line, which is what I specifically referred to? I was not speaking of an ordinal 2, which in its artificially conceived integer role of counting only represents a few or perhaps a few million (fat chance!) bits of information, but the value of a coordinate on a line. Not a segment of the line, please note, much less a fuzzy segment, but a point. Without that you simply have not defined the number, just a region with fuzzy boundaries limited by the information at your disposal. If you can discriminate the identity of two even to a precision of say, one googol bits, I would be impressed, though incredulous, but it would do nothing to dispel the vagueness of your identification of a particular point.

In the example(s) you gave, "the power of language to define the definable" is extremely limited, partly by the circularity of its definition; the notional ability of language in this case is not mathematical, but fictional, the pretense at defining the indefinable.

Try again your definition and demonstration of the existence of the number two as distinct from other numbers, not on toy examples of limited sets, such as hands or eggs of hens or of salmon, but points on the continuum.

Not in this universe, words or no words.

 

[sysprog]

Sorry, but your personal opinion on the matter is unconvincing. Do you have an actual peer reviewed reference to support that assertion?

Show me a peer-reviewed reference to establish that
6798214808651328230664709384*460955058223172535940812848=
3133671502935506745060193180452403351940034608653365632

There's no need for a peer-reviewed reference to establish correctness or incorrectness of that equation.

 

[Jon Richfield]

There's no need for a peer-reviewed reference to establish correctness or incorrectness of that equation.

Same for the amount of info required to distinguish a point.

Elementary.

 

[sysprog]

Same for the amount of info required to distinguish a point.

Elementary.

Disagree. You can fuss about the definition of a point. The answer to a multiplication of two finite integers is inarguable.

 

[Lord Jestocost]

I have been thinking about this response and have decided that is a good one.

My formulation is based on the following sentence in Sir Arthur Stanley Eddington’s book „THE NATURE OF THE PHYSICAL WORLD“ (which I highly recommend): „This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone.“

 

[Jon Richfield]

Disagree. You can fuss about the definition of a point. The answer to a multiplication of two finite integers is inarguable.

You can no more (or less fuss about the definition of a point than about anything else; if your definition is not precise enough to distinguish it from every other point you don't have a point, just hand-waving.
Sort of like a high-school geometry problem that you try to solve by saying that the sketch looks sort of equilateral or right angled or something. A point has zero length. it has zero freedom in its coordinates. Anything else and it is not a point. Zero is zero. It is not less than zero. It is no more than zero, not by a kilometre, a light year, a Planck distance.
Zero.
Of course, you might insist that I am being too demanding, but then you are conceding the point that there is no point. Especially where there is fuss. Otherwise known as hand-waving.

 

[Delta2]

@Jon Richfield You are a new age sophist!

 

[Jon Richfield]

 

[Dale]

Sorry, but your personal opinion on the matter is unconvincing. Do you have an actual peer reviewed reference to support that assertion?

Show me a peer-reviewed reference to establish that
6798214808651328230664709384*460955058223172535940812848=
3133671502935506745060193180452403351940034608653365632

@Jon Richfield this is an inappropriate response to a request for a reference. In this forum we require that everyone put aside their personal opinions and post only content that is consistent with the professional scientific literature. One way we ensure that is the case is by asking for and providing references when claims are made.

You have made some claims that I suspect are personal speculation, but I don’t know all of the scientific literature. So asking for references gives you an opportunity either to retract your claim or to educate me. This is not something we take lightly here.

To be clear, your claim that I question is

But information is finite.

Which is specifically in reference to

in terms of objective reality, to the extent that information existing in the universe does not exist, as opposed to the information that is available to you.

So the claim is not based on human information, but on information existing in the universe. I know of nothing classically which places a fundamental limit on information.

 

[PeroK]

Otherwise known as hand-waving.

On this thread I would say your hands are waving more frantically that anyone else's!

 

[Jon Richfield]

>this is an inappropriate response to a request for a reference.

It was entirely appropriate for the offensive context and tone of your demand, which I simply echoed. This subject matter is no more the stuff of peer review than 2K=mv^2; it is standard material available in various forms and contexts either in textbooks or online in the likes of Wikipedia articles on cosmology, astrophysics, information and thermodynamics. To suggest that I was no more than cramming my own conceptions and thumbsucks down other participants' throats (as expessed in "your personal opinion on the matter is unconvincing. Do you have an actual peer reviewed reference to support that assertion?") was downright insulting, and my response was at least as justifiable.

I don't know what you mean by classical in this context, given that thermodynamics dates back only some two centuries, and in any case, what is largely regarded as non-classical started more or less with relativity, QM, and arguably information theory, but none of them affected the relevant basic theories apart from the dismissal of caloric. One could have made a very similar case for the realities of the limits to information in terms of F=ma, if only they had been thinking in those terms in Newton's day. The main thing missing at that time was that there was no concept of observation boundaries or other limits to our meaningful access to verifiable observation. IOW, the implication was that the universe was effectively infinite, so that there would have been no logical limit to the info it could accommodate. Nowadays we are far cosier in our little 10-odd gigaparsec nook, so we have to do with what there is room for and material for.

If you are denying such received wisdom, stop and check out the idea of what constitutes information. Never mind the hard graft of digging for texts, ask yourself why we speak of BInary digiTs. You cannot store, transmit or process information in any form but matter, energy and their physical relationships. Don't blame me, lay it on the likes of Boltzmann, von Neumann, Shannon, Penrose... Hmmm even Einstein, Podolsky, Rosen and Bohr. Check out the current interest in the ratio between the information content of the surface area of a black hole and its surface area.

And you want me to go back and check out their peer reviews for you?

Work it out for yourself: ask yourself how many fermions and bosons there are in the observable universe: aleph-nul? Aleph-n? Ask yourself how many bits of info you can store and retrieve from each particle or quantum.

Then ask yourself how much info there is room for in our universe.

 

[Jon Richfield]

On this thread I would say your hands are waving more frantically that anyone else's!

Welll... suppose you give an example? What did I say that contradicts, or does not follow, from commonsense everyday transactions on the one hand, or formal mathematics or logic on the other?

I didn't invent, say, post-Galileo physics or maths, or astronomy, and I invoke nothing novel, nor predict nothing that is not generally refuted either. Are you going to pull a Dale on me and ask for peer reviews on Boltzmann for example? or of von Neumann's application of entropy to information?

Don't spare my feelings: point out my handwaving. Show how you can have information independent of matter/energy. And show how you can have an infinite-digit expansion of pi without an infinite amount of matter/energy, or an infinite brain to accommodate it, not to mention gravitational collapse. And work out how long it would take you to perform any operation (such as comparison) on a digit say one Gparsec down the line from where you are assimilating nearer digits.

 

[votingmachine]

We don't know for certain that anything is truly random -- it may be that everything is causally determined precisely -- many things appear to be very reliably random from our perspective . . .

How about this hypothetical. Say that you can count the air molecules in a volume of air. And you know the average. Say 1000. Wouldn't the over-under be a random event? (this supposes you can snapshot and add in all the fractional pieces at the edges).

These macro-level random things may all just be Shrodinger boxes. Deep down, depending on some butterfly-effect required precision that exceeds a QM randomness. I might be substituting air molecules for the balls-in-a-bag, mentioned in a previous comment.

 

[PeroK]

Welll... suppose you give an example? What did I say that contradicts, or does not follow, from commonsense everyday transactions on the one hand, or formal mathematics or logic on the other?

I didn't invent, say, post-Galileo physics or maths, or astronomy, and I invoke nothing novel, nor predict nothing that is not generally refuted either. Are you going to pull a Dale on me and ask for peer reviews on Boltzmann for example? or of von Neumann's application of entropy to information?

Don't spare my feelings: point out my handwaving. Show how you can have information independent of matter/energy. And show how you can have an infinite-digit expansion of pi without an infinite amount of matter/energy, or an infinite brain to accommodate it, not to mention gravitational collapse. And work out how long it would take you to perform any operation (such as comparison) on a digit say one Gparsec down the line from where you are assimilating nearer digits.

This post is hand waving and a confusion of physical and mathematical ideas. You've invoked Galileo, Bolzmann and von Neumann which just leads to a certain incoherence of ideas.

Your assertion that $\pi$ requires an infinite amount of information to define is simply false. This is a common error to confuse a number and its infinite decimal expansion. Your ideas in this regard are based on an elementary misunderstanding of pure mathematics.

 

[PeroK]

PS $\sqrt 2$ is defined as the positive solution of the equation $x^2 = 2$. It's decimal expansion is irrelevant mathematically.

 

[Lord Jestocost]

To be clear, your claim that I question is

But information is finite.

Maybe, one finds answers under the keyword "Bekenstein bound": https://en.wikipedia.org/wiki/Bekenstein_bound

 

[votingmachine]

As some folks point out, randomness is slippery because there are independent definitions. I refer you to the book by the late I. Prigogine: "The End of Certainty". Following its logic, you are left without practically no fully non-random events.

As I see it, the difference between random events and non-random events is information. An event/outcome is random to the extent that you lack information on the event. And it is random in terms of objective reality, to the extent that information existing in the universe does not exist, as opposed to the information that is available to you. If enough information exists to determine how your coin toss works, then the outcome might be random to you, but the universe would "know", and "determine" the outcome in advance.

But information is finite. Now, consider symmetry-breaking. Someone mentioned crumpling paper: a large part of its unpredictable nature is because it involves a lot of symmetry breaking, much of it only roughly, but some of it beyond any probable information available. Even the universe could not tell you exactly how it would crumple.

Let's choose a different form of symmetry breaking: the needle test. Imagine a horizontal rigid surface in a vacuum in neutral gravitational and electromagnetic fields. You have a device that tosses the needle so that at least sometimes that needle lands balanced on its tip. The game is to bet on which way it eventually will topple. Laplace does not forbid such a possibility, and offers no prediction.

The needle and surface offer no information to the universe about how that symmetry will break. To the extent that information on any bias exists, it will affect the direction and reduce the randomness accordingly, and affect the precision of the outcome..

If you happen not to like the needle, try the ball test: start with a rigid surface and vacuum as already described. Take a vertical, symmetrical stack of rigid, notionally perfect spheres of excellent coefficient of restitution, and drop them. As long as there is no information on any asymmetrical bias (not just your ignorance, and ignoring any quantum asymmetry, those balls, in obedience to F=ma, will bounce vertically for a long time till they stop and remain balanced. Right?

Wrong.
For that to happen there would have to be infinite information determining the symmetry of the system. It follows from the nature of the geometry of the balls. But we live in an observable universe that lacks capacity for infinite information.

It follows that, QM or no QM, there could not be a completely non-random system in our universe. And your personal capacity for information is a good deal smaller than that of the universe.

1. There is QM, so any statement that disregards it becomes somewhat meaningless.
2. The needle would not topple. Classical physics would hold that it takes a force for it to move one way or the other. If you know the forces, you know the direction of topple. Absent forces, it doesn't move.
3. Yes. the perfect sphere balls in perfect alignment would stack vertically. That isn't wrong. You say perfect spheres and then say "can't be done". Too hard to get that perfection.

I'm puzzled by your assertion that a requirement for infinite information is the same to you as random. We all agree that ordinary randomness exists. Things can be beyond our ability to predict. And in general, we agree that there are determinate things. Things we can predict.

"there could not be a completely non-random system in our universe."

Double negatives are hard to parse. I read this as:

"there could not be a completely determinate system in our universe."

I can arrange a deck of cards, and know the order of the cards. That is a determinate system. I can cut the deck, without the ability to choose a number of cards, and the card is "random".

I don't need infinite information to know the order of the cards in the deck. I need 52 pieces of information. It is a determinate system. There are non-random systems.

 

[sysprog]

I don't need infinite information to know the order of the cards in the deck. I need 52 pieces of information. It is a determinate system. There are non-random systems.

Don't 51 positional addresses suffice to establish the 52nd? (we use that fact in 'bubble' sorts) . . .

 

[votingmachine]

Don't 51 positional addresses suffice to establish the 52nd? (we use that fact in 'bubble' sorts) . . .

True.

Although then the 52nd piece of information might be that it is a deck of cards with 4 suits, ace-to-king, and no jokers. But I think you re right ... 51.

 

[Dale]

And you want me to go back and check out their peer reviews for you?

Yes, that is precisely what a request for references entails. I don’t think any of them made the claim that you are making. It is your claim and the onus is on you to justify it.

 

[Dale]

Maybe, one finds answers under the keyword "Bekenstein bound": https://en.wikipedia.org/wiki/Bekenstein_bound

Yes, I did think of that before asking for references, but classically there is nothing that requires the universe to be finite (nor is the universe necessarily finite in GR). So the Bekenstein bound need not be finite either. So I don’t know of any classical requirement that leads to the assertion that information is finite.

 

[Baluncore]

But I also guess that Johnson noise is a very clear example of "directly amplified" thermodynamic noise, i.e. quantum noise. I think it is an interesting question if it is possible to make an unpredictable system where the source of uncertainty is not quantum noise, not directly at least.

Back to square 1.
If all things described by QT ceased to operate, our universe and time would cease, along with all the things we call random. Let's accept the fact that QT was always in the background somewhere.

Johnson noise is thermodynamic noise derived from the sum of a great many individual vectors of quantum origin. If I low-pass filter that noise spectrum, I can eliminate all the individual quantum events from the record, leaving only the thermodynamic noise spectrum.

Now, I take two quite independent spectral sources of quantum generated thermodynamic noise, I divide one by the other, so any remaining quantum dimension must be cancelled. I have then eliminated quantum from the deal, what remains is a scalar non-dimensional signal that moves randomly either side of zero in a particular statistical way.

I take two of those quite independent Q free signals and band-pass limit them into two wide but separate parts of the spectrum. They cannot correlate, because their spectra share no common frequency, (the product of their Fourier transforms will always be zero).

I eliminate the amplification gain factor from the process by comparing the band-limited signal voltages with zero, then digitally divide the frequency of the serial bit streams by two with flip-flops, which eliminates any zero offset errors that might bias the result.

I use the positive edges of the slower stream, that occur at random times, as the clock that samples the state of the faster random stream, which yields a sequential stream of random bits.

OK, so the random stream is derived from this QT described universe, but all Q has been eliminated at least twice from the statistics of the signals.

 

[Filip Larsen]

the random stream is derived from this QT described universe, but all Q has been eliminated at least twice from the statistics of the signals.

It is an interesting model you describe, but it sounds like there are a lot of details in the statistics that has to work out, at least to understand what the process is. I am also not sure what you mean by "eliminating quantum"? I understand it like you use the two junctions to get a normalized (flat) noise spectrum, but that the noise or decorrelation between the two junctions is still directly driven by the thermal (quantum) noise?

Unless I completely misunderstand your description I think my comments still applies about how such a system seem pretty well married to quantum models for its randomness, at least in some practical sense. For example compare this system to, say, a lava lamp, which can have its dynamics modeled using purely classical deterministic laws with its unpredictability originating from the (classical) phenomenon of turbulence. I know that deep down, this randomness of a lava lamp is also tied to quantum phenomenons (like the measurement uncertainty for the initial state of an otherwise classical system), but after establishing an initial state its dynamics seems way more determinstic.

 

[Baluncore]

I believe the important thing is to avoid small numbers of quantum events. To do that look at the running average of a trillion events, where the statistical profile of the population swamps the individuals many times over.

 

[George Keeling]

Isn't Norton's dome an example of a classical system that is indeterminate (i.e. truly random)? It's a bit like

You have a device that tosses the needle so that at least sometimes that needle lands balanced on its tip.

In it a perfect ball balances on something that looks like a perfect pointy helmet (imperfectly drawn below). It either stays there for ever (like what somebody said about the needle) or it suddenly starts to roll down at a random time in a random direction. It something to do with being able to propel the ball up the helmet at such a well chosen velocity that it exactly stops at the top. And the equations are reversible.

people dispute this!

 

[Baluncore]

The problem with a single event is that it may not happen, the random generator may suffer from a halting problem. It is also predictable.
The advantage of band-limited noise, with zero crossings, is that there will always be a stream of random bits, even though they will arrive at an irregular rate.

 

[BWV]

Will an AFC or NFC team win the 2030 Super Bowl?

no possible knowledge today could predict that outcome

 

[sysprog]

Will an AFC or NFC team win the 2030 Super Bowl?

no possible knowledge today could predict that outcome

Any Given Sunday . . .

 

[sophiecentaur]

I take two of those quite independent Q free signals and band-pass limit them into two wide but separate parts of the spectrum. They cannot correlate, because their spectra share no common frequency, (the product of their Fourier transforms will always be zero).

The cross correlation of many maths functions can be zero. That doesn't mean they are random.

You'd have to explain how you are taking the Q out of your original processes. It's true to say that you can apply an appropriate filter that can 'reduce' the randomness - for instance if you put a resonator with very narrow passband (I avoided punning with "Q factor" lol) then you can be pretty certain that the volts across it will be very near what you'd expect from an ideal oscillator but the phase of what you observe will still be random ( a very low frequency phase mod) and due to Q effects in your noise source.

I think your problem is that you are ignoring the fact that deterministic processes can't be random because they follow the axioms of Mathematics. You want random out so you need random in. Adding extra steps doesn't take that away.
"Near enough' Random is much easier to achieve with a big enough computer nowadays. But you need to specify the degree of randomness to decide if it really is good enough. The processes that are used in encryption and e-currencies may be cracked one day.
Bringing chaos into this is no help because, if you actually know the initial conditions in a chaotic model (i.e. you put the numbers into a simulation) you know the result. For the outcome to be random, you need a real situation and that will be subject to QM.
An electronic random generator will be random because somewhere inside it, there is the probability of a Q mechanical process crossing some threshold at random and being interpreted by the 'observer' / Ernie machine as a discrete value.

Your example of a lava lamp being "way more" deterministic is a bit like virginity. You're either a virgin or not and your acknowledged Quantum component, way back along the track, makes it still truly random.

 

[Filip Larsen]

Your example of a lava lamp being "way more" deterministic is a bit like virginity. You're either a virgin or not and your acknowledged Quantum component, way back along the track, makes it still truly random.

I mentioned lava lamps and my point still stands, namely that the dynamics of a lava lamp is classical deterministic, whereas the Josephson junctions is not. If we want to search for a "truly random classical system" (however vain we kind of all agree such a search will be) we surely are better off starting with a classical system that exhibit unpredictable behavior (that may appear random due to lack of knowledge of the initial conditions), than with a system that has a dynamics that "directly" taps into quantum events. The lava lamp (or similar system) can be modeled with a fully deterministic (mathematical) model, whereas a model of the junctions need a stochastic process to capture the same behavior.

Norton's Dome, as mentioned earlier in the discussion, is perhaps a very good example of such an interesting system with fully deterministic dynamics and symmetry breaking (even in finite time which I hadn't considered was possible). The question is then if a system such as Norton's Dome can be regarded as example of a classical system exhibiting true random behavior?

PS: @sophiecentaur your analogy with virginity is a bit amusing considering what your "tagline" says

 

[Baluncore]

The cross correlation of many maths functions can be zero. That doesn't mean they are random.

Obviously it does not work backwards.
If the two signals do correlate, then product detection will synchronously raise the signal in the noise, which will certainly not be random.

Your example of a lava lamp being "way more" deterministic is a bit like virginity.

Not my example; but the loss of virginity, by the light of a lava lamp, could not be random.

 

[andrewkirk]

Randomness cannot be a property of phenomena. It can only be a property of models, which we use to describe and understand phenomena.

To see this, consider a model of our spacetime that consists of a list of everything that ever happens in it. Nobody in our spacetime could compile such a list but, subject to certain not too onerous restrictions, a higher-dimensional organism that observed our spacetime from outside could. Such a model contains no randomness, because for every potential phenomenon, the model tells us whether it happens or not, with absolute certainty.

An interpretation of quantum mechanics is a model that contains QM as a proper submodel. The interpretation is not falsifiable (testable), at least with our current experimental capability. That's why we only call it an interpretation rather than a theory. In Karl Popper's terms it is not science but philosophy - metaphysics to be precise.

Some (probably most) interpretations of quantum mechanics involve randomness. Some do not.

 

[Giulio Prisco]

I tried to think of a truly random phenomena thatis not related to quantum physics, and i can't. Let's take heads or tails as an example, if you had all of the data about the throwing of the coin you could tell on which side it will land.

So does anyone know a random phenomena?

Or could you? It can be argued that "having all the data" doesn't make physical sense.

See:
Time is real, real numbers are not: Nicolas Gisin
and links therein