How does a photon carry energy in itself?

[arfa brane]

I think it's another common misconception that writing down some symbols then means you have conceptual information.

The symbols have an information content: you encode something.

What the symbols mean is another thing entirely.

Say I write down some binary words and claim they represent my name. I know both James R and Write4U know this is how ASCII symbols are stored in a digital computer.

But what the binary strings represent, what they mean, is entirely arbitrary, right?

In order to get the binary strings to represent characters in English, they have to be interpreted by a program that outputs characters, on a screen or on paper when they're printed.

Likewise if I want the strings to be numbers, I can have them output as numbers. I'm sure about this, it isn't speculation.

If I want the numbers to represent physical things like kilograms or coulombs. I'm sure I can do that too.

At no time are these strings any more than concatenations of 1s and 0s
Their meaning is an arbitrary choice.

When you recognize your own name when it's encoded as binary strings, this actually has nothing to do with their information content.

So what does three Joules of energy have to do with some binary strings, that you decided are a symbolic representation of three Joules? Nothing, because the information content of strings of symbols has no inherent meaning.

Geddit?

p.s. that arbitrary choice pertains to how I encode the information; whatever that is.
Then I can claim the encoding represents anything I choose it to represent.

Is the message getting through yet?
It is not true that information is a concept. It "just" isn't.

 

[Write4U]

Is the message getting through yet?
It is not true that information is a concept. It "just" isn't.

No, it just isn't "either/or".

Everything, abstract or concrete, is information. Some is physical , some not.

Mathematics is not physical, yet mathematical functions guide pattern formation in physical things.

 

[arfa brane]

There we have it. The misconception that some information isn't physical.

That just doesn't make sense.
Numbers that aren't written down or stored in some kind of physical memory contain no information

Think of a number, then you have a physical representation of it stored in some neurological form.
Don't think of a number, does the number exist? What do you know about this number you didn't think of?

Maybe you know how to do this not-thinking of a particular number. So what? What does that say about abstraction? What does it say about mathematics?

My guess is, nothing concrete.

p.s. in formal language theory, the empty string contains exactly no information . . .

 

[arfa brane]

Introduction to formal languages via Category Theory.

A set of characters is in the category Set, of sets. In formal language theory this set is called an alphabet.

Strings of concatenated characters from the alphabet are 'set products'. That is, a formal language is a set with a function (concatenation) defined on it.

The set of all strings 'over' an alphabet, is also in the category Set.

So we have a morphism from a set to another set, A formal language is the 'target set', the alphabet is the domain of a function (concatenation, or the monoidal tensor product) which maps the alphabet to a set of strings, ordered by their length.

This is the simple end of (the set of) symmmetric monoidal categories. A formal language is a monoid or, roughly, a group without inverses (concatenation has no inverse function).

 

[arfa brane]

Why use an alphabet like {0, 1} to encode information as strings? Why not use an alphabet of one character?

If you have a singleton set for an alphabet, it limits the information content of strings; all you have to differentiate one string from another string is the string length.

Encoding and information content depend on differences between the symbols used. That's like a first principle.

It just is. Encoding meaning in a string is impossible, without at least two languages in a kind of relation to each other, meaningful strings "just don't exist".
You need to shift the context for meaning to, ah, emerge.

 

[Write4U]

Ok, define the physical properties of "Logic"

What is physical about 2 + 2 = 4 ?

math·e·mat·ics
noun

1. the abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics ).
   "a taste for mathematics"
   • the mathematical aspects of something.

German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."

 

[arfa brane]

Ok, define the physical properties of "Logic"

What does that mean? What physical properties could "true" or "false" have? What physical properties do they need?

What about probability? If something is true with a probability of 0.5, what physical units does it need to have so it's "physically true or false"? Is this true or false thing a measurement or isn't it?

What if the true or false thing has no meaning; none at all? Can it still be true or false?

 

[Write4U]

What does that mean? What physical properties could "true" or "false" have? What physical properties do they need?

What about probability? If something is true with a probability of 0.5, what physical units does it need to have so it's "physically true or false"? Is this true or false thing a measurement or isn't it?

Is time physical?

What if the true or false thing has no meaning; none at all? Can it still be true or false?

The question was if it is physical?

OK, let's see about Logical Truth.

Truth is the property of being in accord with fact or reality.[1] In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.[2]

https://en.wikipedia.org/wiki/Truth

IOW, not necessarily physical. It can be purely conceptual.

i.e. Information is not necessarily physical.

 

[arfa brane]

Is time physical?

According to Einstein it's a "convenient fiction". Brains invent time in order to input information.

In signal processing, time makes sense as a physical parameter and so does distance.

Are they really physical? Are any physical units really physical? Is communication physical or a brain illusion?

The quote from Wikipedia is about physical truth. Logical truth isn't necessarily about real things. It can be about nonsense too as Lewis Carroll showed.

Is it true that the slithy toves did gyre and gimble in the wabe?

Maybe those mome wraths didn't "really" outgrabe after all.

But the true/false logic of any predicates made about any of the above still exists.

I'm sure of this, I've studied predicate logic. If instead of meaningful words you use symbols, you can make valid predicates and propositions with them too.

Physical reality or meaningfulness, aren't a requirement or a restriction

 

[arfa brane]

The logic of your closing proposition is false.

Conceptual information is physical information.
Or perhaps you can show that thought isn't physical.

 

[arfa brane]

So where is all this?

And, do photons carry information?

Does that fibre optic cable you're connected to carry photons? (Hint: yes!)

Are numbers physical? No but a representation of a number needs to be.

Is logic only about real world statements?
No, as already explained.

Is time real? Well, it's physically real, so we have to deal with the fact it has physical units.

Without time which is mapped to real numbers (note carefully this is what we choose to do!), nothing would happen, I suppose. I'm going out on a limb here and supposing I'm not alone in having that concept.

 

[arfa brane]

The category Set isn't like any other category; it's 'foundational', Wikipedia says this:

Set is the prototype of a concrete category; other categories are concrete if they are "built on" Set in some well-defined way. Set is not abelian, additive nor preadditive. The finitely presentable objects in Set are the finite sets. Since every set is a direct limit of its finite subsets, the category Set is a locally finitely presentable category.

--https://en.wikipedia.org/wiki/Category_of_sets

Uh huh. Good to know.

 

[arfa brane]

Conjecture:

The meaning of information depends on a certain mathematical structure. There is also a need for structure-preserving functions {such that the information's structure is preserved). Preserving information is the domain of communications.

Communication might, or might not preserve messages. A message is in the domain of signal processing.
I could start with a set of messages and a set of senders/receivers, the latter would need to be connected logically by a message transmission protocol.
Which is, of course, to say that sender/receiver pairs have a physical relation.

An obvious example of a related sender/receiver pair is sources of visible light, and retinal cells. There are any number of similar anthropic examples.

Information content is not information meaning. The second property depends on an algorithm, we call it interpretation. Lewis Carroll showed that you can logically interpret nonsensical information; it's possible to give it meaning because of a structure called a grammar.

 

[arfa brane]

Category theory proposes that it can simplify "everything". Ok, well, everything that can be described mathematically.

Here is a quote from a good introductory online book:

In this book, we explore a wide variety of situations—in the world of science, engineering, and commerce—where we see something we might call compositionality.
These are cases in which systems or relationships can be combined to form new systems or relationships.
In each case we find category-theoretic constructs—developed for their use in pure math—which beautifully describe the compositionality of the situation.

--https://ocw.mit.edu/courses/mathema...-videos-and-readings/18-s097iap19textbook.pdf

"Composite systems", such as the computer with its screen emitting visible light, are described by this conceptual framework, or context.
Really category theory is a vast simplification of the languages, mathematical and engineering terminology; the mathematical structures in category theory
are supposed to span all the applied and pure abstract mathematics, by classifiying everything. Everything includes Einstein's equations, and all the mathematical forms of the Standard Model.

So my claim, stated earlier that a photon carries energy because it carries information, so far is supported by optical communications along glass fibres.
Category theory says I can describe this in terms of a composite system.

 

[arfa brane]

A correction of sorts.
A symmetric monoidal category isn't commutative, since clearly ab ≠ ba.

The free monoid of all strings over an alphabet is a strict monoidal category.
Also, in the context of strings in a language, the alphabet is a set of strings of length 1; the domain and codomain now contain only strings by applying this mathematical trick (notational change).

 

[arfa brane]

A correction of sorts.
A symmetric monoidal category isn't commutative, since clearly ab ≠ ba.

Dammit, I didn't actually intend to say that; I must have been thinking about Mr Hammond.

A symmetric monoidal category is as commutative as possible, according to nLab.
What I should have posted is that a free monoid is not commutative.

Moreover, the set of all strings over an alphabet (which is non-empty) has infinite cardinality. This is otherwise known as the Kleene closure.

Ok, well, now can I consider a stream of photons as a set product; is there an alphabet? And so on.

Some stuff from Wikipedia about formal languages:

In computer science and computer programming, the set of strings built from a given set of characters is a free monoid.
Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for process calculi and concurrent computing.

In theoretical computer science, the study of monoids is fundamental for automata theory (Krohn–Rhodes theory), and formal language theory (star height problem).

--https://en.wikipedia.org/wiki/Monoid

 

[arfa brane]

I thought I'd revisit something I posted earlier, for no particular reason.

Think of a number, then you have a physical representation of it stored in some neurological form.
Don't think of a number, does the number exist? What do you know about this number you didn't think of?

A mathematician might offer the POV that numbers can be put into sets; you don't have to think about them or write them down.
In fact, we can represent entire sets, even infinite sets, of numbers with a symbol. Symbolic representations of sets of numbers (e.g. $$\mathbb {R, C, Z, N} $$) enable abstractions to exist in human brains . . .

So my questions: Don't think of a number, does the number exist? What do you know about this number you didn't think of?

. . . might come down to whether thinking of a set of numbers is the same as thinking of a particular number. In either case you know something about numbers--you have "brain information".

If that's true, thinking of a set of strings (e.g. 0-1 strings), gives you certain information.
But hell, any observation must result in the same outcome.

 

[arfa brane]

Modulating beams of light is what you do in high-speed communications.

So google finds me an online course at MIT. --https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/resources/lec1/
Now, I already know there are several ways to introduce, via modulation, a signal into beams of light.
In optical communication (high-speed by default) one way is to switch the source on and off. But you have coherent laser light, at a fixed frequency nowadays.

Switching from one state to another modifies the amplitude, so you can transmit information that way. There are quite a few others.
One noticeable thing is that you don't need a complicated circuit; each optical fibre is an individual waveguide with practically no inductance/impedance.
But where (or how) is energy being transported? Certainly the modulations of the beam(s) as the course lectures outline, transport information and information has entropy.

There's a conclusion in there somewhere . . .

 

[James R]

There we have it. The misconception that some information isn't physical.

The word "physical" has been tossed around a lot in the last few posts, and not just by you.

What does "physical" mean?

Give an example of something that is not physical, and explain to me why information is fundamentally in a different category from that thing.

Think of a number, then you have a physical representation of it stored in some neurological form.

The map is not the same as the territory. A physical representation of a number is a not a number.

Coming back to our earlier discussion: is energy the "physical representation" of something, or is it just a number? Tell me why. (But make sure you answer my previous question first - what does "physical" mean?)

 

[arfa brane]

The word "physical" has been tossed around a lot in the last few posts, and not just by you.

What does "physical" mean?

I prefer to accept that anything in physics that has physical units, is physical.
It's simple enough, and it seems to work in communication theory.

Give an example of something that is not physical, and explain to me why information is fundamentally in a different category from that thing.

Any set of numbers is not physical, numbers themselves ("physically unitless") are not physical. Slithy toves might or might not be physical; I've never seen or heard one.
I have no meaningful knowledge of slithy toves.

A number is something I can use, I can write a formula and use the number or any number, depending on the formula.
Using slithy toves, not so much. But they are just as useful as numbers are, in predicate calculus.

Why is information in a different category than a slithy tove? Information has physical units attached, all I can attach to slithy toves, is logic.

The map is not the same as the territory. A physical representation of a number is a not a number.

How is that not a useless statement?
I'll concede it's bloody obvious. The other obvious thing is, there is a map from sets to a physical representation. It's needed for some abstract reason . . .

How am I doing with the on-demand logic, James?