I Do you have an example of a truly random phenomenon?

[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

 

[sophiecentaur]

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.

Fair enough. Until we can find some 'pattern' in observed QM results we can't know they are not random. Until then (could be a cosmological timescale involved) the belief in Quantum randomness is just a belief. But, just as with Infinity, we have to go along with the Mathematicians and accept their axioms. Thankfully, they haven't really let us down yet - but that's for another thread.

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

This has been my main point, all along. Any classical model (theoretical) needs initial conditions to be input. However you dress up such a model, there will be that unknown (aka Random) factor which will affect the outcome.
Mostly, we design our systems to suppress the random effect and we try to reduce noise to a level where, for example, an amplifier's output can be relied on as a true version of the input.

Even a Pseudo Random Noise Generator uses circuits that suppress the Q random element.

But, however much we try to cover up the presence of Q randomness, any machine we make and claim to be random, can only get its randomness from Q processes.

 

[tinfoilunderwear]

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?

No but watch this. Nothing up my sleeve, watch me pull a universe out of my hat.

 

[tinfoilunderwear]

Fair enough. Until we can find some 'pattern' in observed QM results we can't know they are not random. Until then (could be a cosmological timescale involved) the belief in Quantum randomness is just a belief. But, just as with Infinity, we have to go along with the Mathematicians and accept their axioms. Thankfully, they haven't really let us down yet - but that's for another thread.

This has been my main point, all along. Any classical model (theoretical) needs initial conditions to be input. However you dress up such a model, there will be that unknown (aka Random) factor which will affect the outcome.
Mostly, we design our systems to suppress the random effect and we try to reduce noise to a level where, for example, an amplifier's output can be relied on as a true version of the input.

Even a Pseudo Random Noise Generator uses circuits that suppress the Q random element.

But, however much we try to cover up the presence of Q randomness, any machine we make and claim to be random, can only get its randomness from Q processes.

You mean like the truth ?

[Mentor Note -- fixed quoted text]

 

[MysticWizard]

I recommend you read this wiki page: https://en.wikipedia.org/wiki/Superdeterminism

I think the definition of a truly random process is hard to prove because even observing certain events changes the outcome: https://en.wikipedia.org/wiki/Observer_effect_(physics)

If you are looking for the best random phenomenon known to man my bet would be on this: https://www.nature.com/articles/s41598-019-56706-2

If you just look for an easy way to get a random number generator, I think this should cover a lot of usecases: https://www.random.org/

 

[sophiecentaur]

If you just look for an easy way to get a random number generator, I think this should cover a lot of usecases: https://www.random.org/

I seem to remember a book in the library at work that was just a list of 'random numbers'. It was the only good source we had as the Eliott 803 computer was too busy doing hard sums at a clock rate of a few kHz.
I wonder if the authors ever challenged anyone under copyright laws?

 

[MysticWizard]

I seem to remember a book in the library at work that was just a list of 'random numbers'. It was the only good source we had as the Eliott 803 computer was too busy doing hard sums at a clock rate of a few kHz.
I wonder if the authors ever challenged anyone under copyright laws?

That makes me wonder if you ask 100 people to name a number between 0 and 100, how random would that be :P

 

[green slime]

Points are fictions, because it would take infinite information to identify any point.
Same with every irrational etc etc

Just for discussion: Origo?

Further the infinite information is impractical; just as the infinite length of every coastline relies on ever closer measurement. Sooner or later, a good approximation is good enough. :)

 

[sysprog]

The random numbers available from random.org are based on atmospheric noise.

 

[gentzen]

I think the definition of a truly random process is hard to prove because even observing ...

Indeed, the definition of a truly random process is hard. However, I don't get the "because even observing ..."

I tried my luck at a definition previously in this thread. I later realized one of its flaws (after reading reactions and other thoughts in this thread), but I didn't try to fix it and elaborate further, since the OP had left already:

The theories of probability and randomness had their origin in gambling and games more general. A "truly random phenomena" in that context would be one producing outcomes that are completely unpredictable. And not just unpredictable for you and me, but for anybody, including the most omniscient opponent. But we need more, we actually need to "know" that our opponent cannot predict it, and if he could predict it nevertheless, then he has somehow cheated.

But the most omniscient opponent is a red herring. What is important are our actual opponents.

The unpredictable for anybody is a mistake. It must be unpredictable for both my opponents and proponents, but if some entity like nature is neither my proponent nor my opponent (or at least does not act in such a way), then it is unproblematic if it is predictable for her. An interesting question arises whether I myself am necessary my proponent, or whether I can act sufficiently neutral such that using a pseudorandom generator would not yet by itself violate the randomness of the process.

(Using a pseudorandom generator gives my a reasonably small ID for reproducing the specific experiment. Such an ID by itself would not violate classical statistics, but could be problematic for quantum randomness, which is fundamentally unclonable.)

 

[MysticWizard]

Indeed, the definition of a truly random process is hard. However, I don't get the "because even observing ..."

I guess that one was meant more as: Be aware that your measurement method can influence the outcome

As for the definition, Wikipedia says:

This means that the particular outcome sequence will contain some patterns, that are detectable in hindsight, however not predictable with foresight.

I would then state that it is impossible to prove something is truly random because you would need a dataset with infinite time to predict any pattern however infrequent it may be.

 

[sophiecentaur]

That makes me wonder if you ask 100 people to name a number between 0 and 100, how random would that be :P

They’d all be trying to second guess the exercise. No one would choose zero or a hundred and also they’d avoid all the round numbers and well known multiples like the five times table. I’d bet that there would be many more ‘known’ prime numbers like 19.
This experiment must have been done. Somebody ( some random person) find a link for me please.

 

[votingmachine]

They’d all be trying to second guess the exercise. No one would choose zero or a hundred and also they’d avoid all the round numbers and well known multiples like the five times table. I’d bet that there would be many more ‘known’ prime numbers like 19.
This experiment must have been done. Somebody ( some random person) find a link for me please.

I would say pi.

 

[BWV]

Or this

https://en.wikipedia.org/wiki/Guess_2/3_of_the_average

zero is pareto optimal, but empirically people will pick a value roughly 1/5 of the highest number

 

[Dale]

That makes me wonder if you ask 100 people to name a number between 0 and 100, how random would that be :P

I always answer $\pi$, which is not random at all.

 

[256bits]

Is information finite classically?

Since there is a past and future light cone, the information from the past increase as -t; and we cannot predict the future . It would seem to be finite at the present.

 

[Dale]

Since there is a past and future light cone, the information from the past increase as -t; and we cannot predict the future . It would seem to be finite at the present.

Have you a reference that makes that argument?

 

[256bits]

Have you a reference that makes that argument?

I was rather wondering what you would reply to the fact that new information is entering a system as time progresses, and if it is a valid argument. Not sure what a reference to what a light cone is would accomplish.

 

[Dale]

I was rather wondering what you would reply to the fact that new information is entering a system as time progresses, and if it is a valid argument. Not sure what a reference to what a light cone is would accomplish.

Not a reference to a light cone. A reference to the argument that the fact that there are light cones implies that information is finite classically.

 

[256bits]

Not a reference to a light cone. A reference to the argument that the fact that there are light cones implies that information is finite classically.

sorry no reference.
i thought that it was self evident that the information that we can process is limited by our past light cone, with new information continuously arriving, information that we become aware of only as we move into the future.
Certainly we can predict from previous information gatherings, the mechanical workings of objects and state future sunrise, and say a solar eclipse, and verify the prediction when the event does occur. We had a limited set of knowledge about sunrise and now we have a bit more.

 

[Dale]

sorry no reference.
i thought that it was self evident …

No. It is not, and being a personal speculation it is not appropriate for PF.

 

[256bits]

No. It is not, and being a personal speculation it is not appropriate for PF.

That's a stinker.
I do value your reply.

 

[Filip Larsen]

Is information finite classically?

Since there is a past and future light cone, the information from the past increase as -t; and we cannot predict the future . It would seem to be finite at the present.

I understood Dales (rhetorical?) question to be about whether or not a (discrete) classical systems allows infinite precise state information or not, or in more practical terms, whether there are finite or infinitely many possible states in an arbitrary small ball around a given reference state?

 

[256bits]

I understood Dales (rhetorical?) question to be about whether or not a (discrete) classical systems allows infinite precise state information or not, or in more practical terms, whether there are finite or infinitely many possible states in an arbitrary small ball around a given reference state?

Thanks.
That's kindof where I was coming from.
But it looks to be a non-starter anyways.

 

[sophiecentaur]

zero is pareto optimal, but empirically people will pick a value roughly 1/5 of the highest number

OMG - like my choice of 19. Makes you want to believe statistics dunnit.

 

[Baluncore]

This experiment must have been done. Somebody ( some random person) find a link for me please.

https://telescoper.wordpress.com/20...to-pick-a-number-at-random-between-1-and-100/

 

[rudy235]

The last 5 digits of the time in microseconds a "random" person takes to answer a "random" yes or no question as evidenced by an atomic clock connecter to a buzzer.

 

[sophiecentaur]

The last 5 digits of the time in microseconds a "random" person takes to answer a "random" yes or no question as evidenced by an atomic clock connecter to a buzzer.

That could be an expensive way of doing it, even on minimum wage.

 

[Baluncore]

a "random" person

Welcome to PF.
How do you find and select a "random" person ?
Can you please let me have a copy of your standard application form.

 

[gmax137]

I do remember a program doing something, needing a random number. The program wrote to screen "please press spacebar to continue" and then timed how long until the spacebar was pressed; the measured time was used as the seed in the rand number generator.

 

[sysprog]

I thought of pointing 2 satellite TV dishes at the CMB and XORing or XNORing the received signals together, then running the result through the SETI filters, and using that subsequent result as if it were a 'truly random with fully Gaussian distribution' bit (binary digit) sequence $-$ so far, no competent math or science guy or gal to whom I've described the notion has to me decried the idea as in any way not ok.