[varsigma (OP)]

I still think there is some conflict between the meaning of a message, and the way the message is encoded.

ChatGPT tells me the information is the meaning; the information content is how much meaning, in that case.
Then I asked about encryption, where the idea is to maximize the entropy of "the information" so its as uncertain as possible.

To have meaning, a message has to be encoded somehow, just as languages like English encode this thing called meaning. So if information is meaning and information content is how much meaning, what are the letters and the words, and the sentences etc, in a natural language? What are the ones and zeros in a binary string with an unknown context (I found it in a computer memory)?

ChatGPT tells me that the meaning is context-dependent. So there is no context-free information. Uh huh.
So what meaning can I assign to a randomly located binary string, other that "it's a string of 1s and 0s". Is that devoid of meaning?

Anihoo, I can see that ChatGPT appears to line up with most of what (I think) I learned in that course. One thing I recall is the surprise factor--a message you don't expect has more information content than a message you do expect.
But unexpected messages are generally less probable, in an ordinary world (most of the information your brain processes is familiar--you expect to see a world that looks like it did the day before, more or less). Hence--entropy.

[alancalverd]

ChatGPT seems like a longwinded philosopher rather than someone who actually understands information theory. Try Wikipedia - the entry seems to have been written by folk who know what they are taking about.

Strictly, of course, a code is a string that identifies a longer string stored in the receiver, whereas a cipher simply substitutes one symbol at a time so that the decrypt contains the same number of bits or whatever as the encrypted string. Thus "BMBO" is a simple cipher for "ALAN", but "ALAN" is a code for "an old geezer in Cambridge with nothing better to do with his time".

The unexpected message will only contain information if the receiver has some preconception of what the sender means. Thus ALAN or even .-  .-..  .-  -. will probably denote at least "a British bloke" to many earthlings but conveys nothing at all to a Martian tree frog.

[varsigma (OP)]

ChatGPT seems like a longwinded philosopher rather than someone who actually understands information theory. Try Wikipedia - the entry seems to have been written by folk who know what they are taking about.

Thanks. Are you really an old guy living in Cambridge, and is that the US or the UK? I had online dealings with a person who was studying string theory at King's College. Bit of a maths rottweiler.
Had an interesting chat once about superfluids and viscosity.
Yes I'm cautious about ChatGPT, and I've managed already to get it to contradict itself about entropy. Such is AI, it comes with a warning label. Actually I've written a few programs that I should have put a warning label on.

As to philosophy, it seems some people think it's about discussing how uncertain you are, how little you can frame in ordinary language. I've read philosophical tracts that were pretty much impenetrable; they appeared to presume that "philosophical meaning" can be packed into a single word so it contains more meaning somehow, than what you find in a dictionary.

Supervenience, for example. The capacity to, something something.
Whereas, in physics the philosophy is start simple, then treat complexity as a sum of simple things, not as a single concept which is, impenetrable, not known, yada  yada. Then the philosophers only have ideas, everything is conceived, so if you can't conceive of it, it fails the test. What test? Who said there's a test?

[varsigma (OP)]

And on the topic of simplification.

Perhaps it's why I find the Information Theory approach a convenient way to look at complex systems.

Binary logic is simple, you can derive nice, hard facts like, it isn't a universal logic, computationally, because it isn't reversible--the laws of physics are though. You get to see that it's because of an insufficiently large phase space (volume) and how to increase the volume by adding more inputs and outputs, solving the universality "problem".

Which of course, engineers don't bother doing because of the cost, in keeping all that information around,

[alancalverd]

Last time I looked, I was definitely an old bloke, and AFAIK this Cambridge is cold, wet, and near the East Coast, just like the other one.

You see, my friend, it all depends on what you think you mean by Cambridge. Is there a universal meme that can be deconstructed as a set of paradigms sufficiently delocalised in spacetime  that your Cambridge and mine are the same but not identical, or identical but not, in whatever sense you think you are talking about, the same? In what sense does the Pythagorean essence of Cambridge heuristically or existentially conflict with the Aristotelian ur-Cambridge such that they cannot coexist?

I could say that in a few minutes I can walk across a bridge over the river Cam, but a philosopher would ask "how do you know that it is really you, and whilst the river was named by the Saxons, since the water that was there at the time is no longer there, is it still the Cam?

[geordief]

Last time I looked, I was definitely an old bloke, and AFAIK this Cambridge is cold, wet, and near the East Coast, just like the other one.

You see, my friend, it all depends on what you think you mean by Cambridge. Is there a universal meme that can be deconstructed as a set of paradigms sufficiently delocalised in spacetime  that your Cambridge and mine are the same but not identical, or identical but not, in whatever sense you think you are talking about, the same? In what sense does the Pythagorean essence of Cambridge heuristically or existentially conflict with the Aristotelian ur-Cambridge such that they cannot coexist?

I could say that in a few minutes I can walk across a bridge over the river Cam, but a philosopher would ask "how do you know that it is really you, and whilst the river was named by the Saxons, since the water that was there at the time is no longer there, is it still the Cam?

Does the idea of a convention  have import when discussing  what "information" is?

Is the idea of a convention the mirror image of solipscism?

In philosophy do we,as conscious beings  travel.through time in the same way as a physical object has its worldline in.the "real" world?

Ps ,what on earth is ur-Cambridge when it is at home?

[varsigma (OP)]

Does the idea of a convention  have import when discussing  what "information" is?

Information is what we say it is. But you have to choose a physical basis for it in order that it is "representative".

Why I say the above is because, in the classical domain there are any number of choices for a representation.
Quantum mechanics has fewer choices, perhaps because at that scale nature restricts our choice and so it restricts what we can call it. Maybe.

Conventions, like using bra-ket notation have no real effect on what quantum information "is", since mathematics can't really tell you that. It does tell you about unitarity and the conservation of information though. Whatever it "really" is.

I'll see if I can explain the above with the usual suspect, an interference pattern from a beam of particles.
The pattern is independent of whether you do it one particle at a time, or lots of particles. Either way you see the same pattern and so you see the same information, it's up to you to decide what the context is.

But the reason the pattern is the same, however you sample the distribution in terms of number of particles at a time, is because of unitary logic and conservation laws. So each sample must be representative, even if the sample has one particle in it.

So the question "when does a pattern appear" which is recognizably an interference pattern, is a classical question about a classical pattern, each dot is a classical measurement. We decide when it looks like an interference pattern, or when there is enough information content.

The rule of thumb is that information reduces uncertainty; in this case the information is equivalent to answering the question, how many particles will form a classical pattern? But the number and the pattern aren't the same information, right?

So, context. Seeing a classical interference pattern of dots, each made by a single particle, is in the same philosophical domain as seeing a binary string with a pattern in it. What does the pattern mean?

[alancalverd]

Ps ,what on earth is ur-Cambridge when it is at home?

It is Cambridge, at its original home!

[alancalverd]

We decide when it looks like an interference pattern, or when there is enough information content.

I've just been learning about "hyperuniformity", particularly in the case of the distribution of prime numbers. Humans are very good at discerning patterns but unlike pigeons (who are brilliant at it) we tend to see patterns where by mathematical proof (prime numbers) or statistical sampling (pseudoartefacts on medical images), none exist.

Thus many people think there is a disjuncture between classical and quantum physics because you can't explain the gross interference pattern in terms of particles and you can't explain the distribution of individual events in terms of waves. It's all a matter of vanity: fact is that some folk like to imagine that reality is governed by their preconceived models, but this isn't economics, politics, religion or philosophy - it's science!

[varsigma (OP)]

Thus many people think there is a disjuncture between classical and quantum physics because you can't explain the gross interference pattern in terms of particles and you can't explain the distribution of individual events in terms of waves.

Waves and particles are things we inject into the experiment, we attempt to use that context so we can understand the effects we see.

 They are observations we make from a distance, about how the pattern is encoded in space and time, by some function. It must be a function because it maps particles to locations, and this appears to be procedural; there is an algorithm in there somewhere.

Another thing about experiments with very small things is, no detail is insignificant. After a particle leaves a mark, it leaves altogether--you can know very little about its state, including where it is. This is connected to our notions of writing information and erasing it. That is, for a particle to write a mark on a detector screen it has to vanish after this event. It's a quantum requirement, say.

In terms of entropy, the time of appearance of a dot reduces classical uncertainty about the position, but at later times the uncertainty is maximal, relative to the frame of the experiment (and its physical basis for the information you decide is there somewhere).

[alancalverd]

Oh dear! I think you are still not distinguishing between observations and models.

I'll allow "inject" as a colloquialism in this context: I think you mean "assign to the model of" an experiment. When we actually inject energy or stuff, the object is to see what happens next - understanding may come later. 

Procedures and algorithms are predetermined processes through which we force data or real stuff. There is nothing predetermined about the fate of a photon in the double-slit experiment, and there can't be: the outcome of any given event is essentially random.

On a grumpy day, I'd even reject "quantum requirement"! Quantum mechanics is how we describe and predict what happens. The fact that we can correctly predict an outcome, is a measure of the validity of the model, not a god-given and preordained demand as to how nature should work.

"Classical uncertainty" is the sum of random and systematic experimental errors that estimates the size of the ballpark that contains the truth. Not to be confused with Heisenberg's indeterminacy, which is an inherent property of the entity, nothing to do with error, and denies the existence of a single truth.

It has been argued that the progress of modern science actually rests on a religious belief that the universe was created and run by a consistent directive, and science is merely a search for the creator's plan. I deplore such arrogance. As I see it, by inventing and polishing mathematical models of what we know, we get better at anticipating the outcome of experiments that we haven't yet done.

[varsigma (OP)]

Oh dear! I think you are still not distinguishing between observations and models.

I'll allow "inject" as a colloquialism in this context: I think you mean "assign to the model of" an experiment. When we actually inject energy or stuff, the object is to see what happens next - understanding may come later.

Procedures and algorithms are predetermined processes through which we force data or real stuff. There is nothing predetermined about the fate of a photon in the double-slit experiment, and there can't be: the outcome of any given event is essentially random.

Yes perhaps I should have said that we decide when we are observing wavelike effects and when we aren't.

I'm more trying to go with the basics in any interference experiment; what is known and what isn't.
This should apply beyond the start or end of the experiment itself. Information is meaning, so what do random or regular patterns of dots mean? One thing it means is you see a symmetrical pattern--an interference pattern with a central maximum and less intense fringes each side--so you don't need the whole thing, half of it will do. You can't do that with a low intensity input beam because it isn't, you know, a large enough sample.

I'm not sure about the algorithmic aspects, but I can't explain then what connection a double-slit experiment might have to quantum computation. I'm pretty sure there is a connection.

[alancalverd]

what do random or regular patterns of dots mean?

The dots arrive at random times, and the position of the next dot cannot be predicted from past events, but every time we repeat the experiment for long enough we get the same overall distribution.

[geordief]

Is there any other way we can reproduce  that effect?

And what is "long enough"?

Two dots? Three?

Is the " overall distribution" always there but we only see it above a certain number?

[alancalverd]

Yes and no! There are plenty of examples of diffraction and interference of macroscopic waves. What is remarkable is that whilst individual particles produce random events (clearly quantum phenomena), the spatial distribution of those events is as predicted by a wave model.

Pattern recognition is an odd business.Humans tend to see "hyperuniformity" - imposing patterns on data where none exist, because  we have a preference for geometry. This has some advantages, say in navigating through a remebnered but now modified landscape, because we can ignore a few anomalies, but it can lead to errors in making very confident predictions that turn out to be completely wrong. Simple example: I say 1,3,5... and you say 7,9.... Wrong! I was enumerating primes, so the amswer is 7,11... and whilst it can be proved that there is no pattern to the occurrence of prime numbers, they do tend to occur in sort-of-periodic clumps!

[varsigma (OP)]

One of the first observations if not the very first one of the implications of the quantum mechanics to the computational complexity was made by a most famous physicist, Nobel Prize winner Richard P. Feynman, who proposed in his seminal article [8] that a quantum physical system of R particles cannot be simulated by an ordinary computer without an exponential slowdown in the speed of the simulation. On the other hand, the simulation of a system of R particles in classical physics is possible with only a polynomial slowdown.
The main reason for this is that the mathematical description size of a particle system is linear in R in classical physics but exponential in R according to quantum physics. As Feynman himself expressed:

. . . But the full description of quantum mechanics for a large system with R particles is given by a function ψ(x1, x2, . . . , xR, t) which we call the amplitude to find the particles x1, . . ., xR, and therefore, because it has too many variables, it cannot be simulated with a normal computer with a number of elements proportional to R or proportional to N . [8]

Number N in the previous citation refers to the accuracy of the simulation: the number of points in the space, as Feynman formulates. In the same article, Feynman considered the problem of negative probabilities, and returned to the same issue a couple of years later [9]. Feynman's approach may be earliest formulations to understand the role of interference in the probabilities induced by quantum mechanics.

--https://www.utupub.fi/bitstream/handle/10024/162051/Hirvensalo_InterferenceV3.pdf?sequence=1

Following Feynman's idea and using quantum mechanical systems for bearing the information and carrying out the computation, it is possible to design algorithms that benefit from the interference: the undesired computational paths may cancel each other, whereas the desired ones may amplify.
This phenomenon is generally believed to be the very source of the power of quantum computing.

--ibid.

I myself would classify the appearance of an interference pattern, in single particle or low particle number experiments as a computation. A computation of what, apart from what can be seen, is in the details I guess.
Simulations of quantum interference are around; how do these differ from the real deal?

[varsigma (OP)]

In physics, on the theoretical side, you eventually encounter symmetry groups.

You also encounter the fact that there aren't any fixed ways to describe physical stuff like light.
The photon, the Standard Model asserts, is an exchange particle that carries the electromagnetic force.

That is actually quite a loose definition or description. A photon is a gauge boson; the electromagnetic field is a connection in a fiber bundle over spacetime. A photon is representative of the field in that it has the same dimensions as the field. An electromagnetic force is the analog of a Newtonian mechanical force; there's a symmetry in the equations of motion for an LRC circuit and a simple pendulum.

This only tells you that Newtonian momentum has an electromagnetic equivalent, which is inductance multiplied by the current. There is a correspondence between Newtonian oscillations and Maxwellian ones. Ok, but what does it mean?

I don't know if I can say, or if anyone can. It suggests that mass is a way to store energy though. If inductance represents a way to. Mass curves spacetime around it, magnetic potential does that for electrons.

Right, so the electromagnetic field is the gauge field or U(1) symmetry, of the fermion field or SU(2) symmetry in the first family of the Standard Model. Another detail here is you can't break the gauge symmetry of a theory, or then it's unphysical.

I've studied group theory and I'm still wondering why there are so many, but only a handful in the best model we have of fundamental physics.
Perhaps the answer is the universe needs these ones to make itself classical, with complexity. Entropy being one of the complexities, meaning is another complex thing. Is that only relevant to sentient life, and so on.

[varsigma (OP)]

Is there any other way we can reproduce  that effect?

And what is "long enough"?

Two dots? Three?

I think I can give a tentative answer to your question, which is, it depends.
In experiments that demonstrate interference, it's nice to see a pattern that we can say is definitely there.
But in quantum computers, the wavefunctions of two particles can be in superposition, such that it's a form of constructive or destructive interference.
We arrange for this to happen that way, and so it must have a nonzero probability of occuring in that case.

[varsigma (OP)]

Talking about physics, or trying to, means talking about things like mass, or charge, or intrinsic angular momentum.

Newtonian mass is defined in terms of a resistance to being displaced from rest, or from regular motion.
I'd say that since Newton the heuristic has changed some. Nowadays there seems to be a difference in meaning between a heuristic and an ansatz, which can mean in German, an educated guess. Which is what heuristic means.

But scientists like to borrow words and give them a closely defined meaning, so ordinary usage is excluded. A mass ansatz is more a way to employ a technique, mathematically, to solve a certain kind of problem.

For instance, a photon with a large energy can decay spontaneously into an electron and a positron. The gauge transformation conserves charge and mass; the electron and its antiparticle are a (complex) conjugate pair whose product is the required mass ansatz--the right tool.

[alancalverd]

Not complex. They are both real particles with charge and mass.

And beware of "required": it is a technical term in mathematics that constrains our models, but nothing is "required" in physics - it either happens or it doesn't, and if it doesn't, we have to change our model.