Why did you quote me? More generally, what's up with your insistence on this thread going in a specific direction? I'm starting to picture you with an orange safety vest with the words "Hall Monitor" written in block lettering on the back.

@bogosort
I thought I had quoted the first and third posts , which say they are from @Jennifer Solomon

BTW: Whats a hall monitor ?

 

Does the mixture exist apart from its solvent? No.

It took me 2 hours to "ping" my intuition for the quandary it was having with the "mixture" metaphor.
This is my take:

A mixture is composed of components, either solid or liquid—either themselves pre-mixed before adding, or unmixed—to create the main mixture.

In the case of dissolved sugar in water, you can extract the sugar, and of course, the water. But if you were to mix the existing mixture called "Sprite" with the existing mixture called "Pepsi," gone are both components as independent elements upon mixing, and there is now a new permanent identity — call it "Spepsi." Spepsi doesn't exist without Sprite and Pepsi, nor can Sprite and Pepsi be extracted from it.

So while you could reverse engineer the Spepsi and derive the "fourier components" of all the ingredients, you're not revealed the ratios of each, so you'd never be able to tell that it was composed of 2 very separate concoctions prior that stood on their own definitionally. The component information is homogenized and the group layer metadata is disappeared.

On the other hand, if carrier signal A is modulated to contain signal A1 and signal A2, I'd say signal A is not technically a mixture of signal A1 and signal A2. If signal A1 can be extracted and 100% maintain its identity as A1, and signal A2 can also be similarly extracted, then signal A isn't really a mixture of A1 and A2—I'd say it is a composite (and potentially more). Signal A is Spepsi, and A1 and A2 are Sprite and Pepsi. Signal A1 and A2 are maintaining their independence definitionally after compositing.

Further, while Spepsi's definition is predicated on Sprite and Pepsi, all 3 mixtures (Sprite, Pepsi, and the final mixture) required a medium prior to mixing—that of a separate container. In the case of signal A, it, too, requires a medium to be defined. Signal A therefore has physical existence as a function of temporal displacement of a medium. The mathematics can show us how Signal A was constructed before constructing it, but it cannot show us how, after mixing, signals A1 and A2 were used to make it. However, if we do know signal A1 and A2 were used, we can squelch everything other than A1 and A2's bandwidth and reveal their existence.

You agree with the above?

If so, signal A has a physical existence irrespective of the medium, then signal A1 and A2 must also.
The question is, precisely "where" — as in, if signal A is sent down a wire, signal A1 and A2 are also—the individual wave shapes of A1 and A2 are retained, which makes signal A look like a meta-data wave that describes its components. How, as in "disturbances in a medium," is the non-philosophical, hard physics question.

Again, whether in mechanical form or EM form, a wave is "carrying" or "representing" or <insert whatever the hell it is> multiple waveling groups metadata that must be accounted for, because at every second there are tiers upon tiers of discrete voltages beyond the one parent wave. Signal A has a waveform shape, and signal A1 and A2 have a unique waveform shape. But each shape is defined as a unique oscillation signature of a medium. Where is the physical existence of A1 and A2 waveforms the math speaks to?

Acoustic waves and electromagnetic waves are very different types of things. More importantly, the amount of information that can be transmitted in any physical wave, including EM waves, is much closer to zero than to infinite. [...] What do you mean exactly by where? A wave doesn't have a well-defined "where" about it. The closest we can get is to say that at point (x, y, z) the medium has this amount of energy. Waves are non-local phenomena; where doesn't work. Likewise, the information isn't "anywhere" -- or, if you prefer, it's everywhere the wave is.

But are they different in terms of information conveyance? The same wave traveling down a wire which is turned into a "flattened" pressurized version of itself from a speaker diaphragm is containing the same meta-information. And "transmitted" is different than stored—I was alluding to real-time representation. And yes, I meant everywhere the wave is. Mathematically, is not the wave cognized in terms of the phenomenon that is ℝ? If so, the wave technically contains infinite information mathematically — some of it human-usable signal I'd call "knowledge", the rest is noise?

In any case, are you claiming that each distinct bandwidth has 900 signals, or that there are 900 different bandwidths? If the former, then -- unless they are all sinusoids of different frequencies -- they are not distinct. If the latter, that is an enormous signal and unlikely to be physically realizable.

I used 900 to round-off what another user claimed was being embedded in signal he worked with at an employer. Let's go with 100 unique bandwidths to keep it more reasonable.

This is way out of scope, but the magnetic field doesn't exist. It's a simplified model, useful to study certain properties of the electromagnetic field, but there is no physical invariant that corresponds to a magnetic field. The EM field "exists" in the sense that it has a physical invariant -- something "out there" that we model with QED. As best as we can tell, the EM field is not "made of" anything -- rather, space is "made of" the EM field (along with many others).

Ok, EM field. So the EM field is the medium that EM waves oscillate in. The same questions apply though, no?

Conservation of information is a hypothesis, with no good ways to test it (unless you happen to have tiny blackholes in your lab to experiment with). I don't know what you mean by "undefined information", but information doesn't have anything to do with EM fields or waves. Information capacity is just the number of ways a thing can change, its degrees of freedom.

We do not have a scientifically satiating definition of information, so "capacity" here is a modifier for something we don't fully know the scope of. So I'm not so sure information doesn't have anything to do with those things.

 

And then I later realized the core topic was more the relationship between the physics and the math describing it. As such, I edited the first thread to accurately denote the aim, which we are staying within. Also, this is not about the human reason component, so don’t know why you think that’s an issue.

Is this 1984? Lol.

@Jennifer Solomon
thank you for highlighting that you did change the original question,

certainly to me, the new question is not one that I would have replied to
not least as it is so similar to the one you had blocked,

 

@Jennifer Solomon
thank you for highlighting that you did change the original question,

certainly to me, the new question is not one that I would have replied to
not least as it is so similar to the one you had blocked,

The one that was blocked was not blocked due to the original contents. It was blocked because it got derailed from them, and I wanted a fresh thread that spoke more to the heart of the matter.

 

Your original question in this post, before it was edited many days later,
highlighted your intention to keep this mathematical,

We never got to the end of the maths, and you never answered the first two check questions we asked,
and then said then you were ok with the maths,
and posted a big cut / paste on a saxaphone.

and then you come up with the idea of "Spepsi"
which is a mixture of two chemical solutions that both contain some elements and chemicals that are the same, and say how can we separate them ?

That has nothing to do with the original question about frequency muliplexing, Spepsi is chemicals, frequencies' are not chemicals,

 

Your original question in this post, before it was edited many days later,
highlighted your intention to keep this mathematical,

We never got to the end of the maths, and you never answered the first two check questions we asked,
and then said then you were ok with the maths,
and posted a big cut / paste on a saxaphone.

and then you come up with the idea of "Spepsi"
which is a mixture of two chemical solutions that both contain some elements and chemicals that are the same, and say how can we separate them ?

That has nothing to do with the original question about frequency muliplexing, Spepsi is chemicals, frequencies' are not chemicals,

Maybe you’re not seeing all the messages in context? Did you see bogosort’s post on comparing waves to a solvent? The “Spepsi” is a reply to that. We’re discussing the nature of waves, nature’s multiplexing, and how the waves are kept discrete mathematically, and how that relates to the physics post-processing. The nature is being discussed via metaphor right now. Somehow it seems like you’re only physically seeing a small percentage of what we’re discussing?

 

Maybe you’re not seeing all the messages in context? Did you see bogosort’s post on comparing waves to a solvent? The “Spepsi” is a reply to that. We’re discussing the nature of waves, nature’s multiplexing, and how the waves are kept discrete mathematically, and how that relates to the physics post-processing. The nature is being discussed via metaphor right now. Somehow it seems like you’re only physically seeing a small percentage of what we’re discussing?

I'm seeing

The title, frequencies and multiplexing,
the orriginal start, that this was not to get off topic, and was to concentrate on the maths,
so as not to be blocked as per your last post.
and your comment in the forum

" I’m not looking for the human reason component. I simply said that’s what the question is ultimately about, and not a “trolling” question. I only want the specific mathematics, if available, that describes the modulated data retention in a wave aggregation. This is an engineering question "

and you agreed to post #4, and the basic theories

"
Can we agree that by using the word frequency , we are talking about a time variable signal ?
after all, frequency is "cycles per second"

So any instantaneous point in time can not tell you anything about a frequency .

So if we agree the above,
lets define a signal as varying in amplitude over time.,

theory one.
Any signal, can be made up by adding a number of single frequencies, which are phase / amplitude modulated.
This can be shown with sine waves or walsh codes et all ( there are many ways )

theory two
Any signal we wish to send over a cable is band limited,

theory three, Take a sine wave for simplicity, but it works for square waves et all,
Any frequency at frequency A, does not interfere with a separate and different frequency at frequency b.

"


can not see correlation between a chemical and waves or multiplexing
sounds to me as if things are going well off topic here.


I don't know why you don't seem to want to stick to your original question in this post, or why you wanted to change your post so long after the post started , or why you are by the fact you are replying enfusiasticly to evidently off topic posts, you are encouraging things to go off topic.

If you want to get back on track, no problem, we all wander, the original question and your posts were aiming at learning and understanding the maths,

 

I'd like to clarify please @Jennifer Solomon

I see you have been at this same question a few times on the forum
not least https://forum.allaboutcircuits.com/threads/theory-of-everything.168244/
and you have repeatably edited the first post , some times months after the start of the post,

Why do you feel that you need to do that ?

 

I'm seeing

The title, frequencies and multiplexing,
the orriginal start, that this was not to get off topic, and was to concentrate on the maths,
so as not to be blocked as per your last post.
and your comment in the forum

" I’m not looking for the human reason component. I simply said that’s what the question is ultimately about, and not a “trolling” question. I only want the specific mathematics, if available, that describes the modulated data retention in a wave aggregation. This is an engineering question "

and you agreed to post #4, and the basic theories

"
Can we agree that by using the word frequency , we are talking about a time variable signal ?
after all, frequency is "cycles per second"

So any instantaneous point in time can not tell you anything about a frequency .

So if we agree the above,
lets define a signal as varying in amplitude over time.,

theory one.
Any signal, can be made up by adding a number of single frequencies, which are phase / amplitude modulated.
This can be shown with sine waves or walsh codes et all ( there are many ways )

theory two
Any signal we wish to send over a cable is band limited,

theory three, Take a sine wave for simplicity, but it works for square waves et all,
Any frequency at frequency A, does not interfere with a separate and different frequency at frequency b.

"


can not see correlation between a chemical and waves or multiplexing
sounds to me as if things are going well off topic here.


I don't know why you don't seem to want to stick to your original question in this post, or why you wanted to change your post so long after the post started , or why you are by the fact you are replying enfusiasticly to evidently off topic posts, you are encouraging things to go off topic.

If you want to get back on track, no problem, we all wander, the original question and your posts were aiming at learning and understanding the maths,

Threads, like frequencies, can be modulated, as this one has. ;--)

I appreciate your concern, but we have an active moderator in here (MrChips) that has contributed to the thread. The former thread of Theory of Everything thread started with a similar question, but not quite the same, and it evolved into something much different. Therefore, it was renamed and properly filed after internal discussion.

This thread is perfectly on topic with a more honed pursuit of understand how the math interfaces with the physics of multiplexing.

So you really don’t have to burden yourself any longer with this specific issue ;—)... everything is fine, but thanks for your concern and willingness to teach! We really don’t need to discuss the topic of relevancy any further. Let’s leave that to the moderators.

 

Just for the record,
when you say " internal discussion."

who was that with ? one or more moderators ?

 

Just for the record,
when you say " internal discussion."

who was that with ? one or more moderators ?

Yep.

 

You avoided the question as to who it was who encouraged you to change the first post months after it started .

which would be of interest please

If you are reluctant to say @Jennifer Solomon
my be the moderators could pop in here and say it was them,

you have mentioned on the forums before that you have discussions with @MrChips and @bogosort outside of the forums

 

You avoided the question as to who it was who encouraged you to change the first post months after it started .

which would be of interest please

Speaking of things that derail threads, you do realize you are now ironically guilty of the very thing you are relentlessly complaining about as happening in this thread? Last courtesy answer for you, before we return to the actual discussion, because a Hall Monitor, for your information, is someone who is policing the movement of things, and in this case, you have anointed yourself the thread police for some odd reason, and you are not even an AAC moderator.

So one last courtesy reply before we continue with the actual topic, as this may indeed be helpful to anyone else wondering:

The Theory of Everything thread started out as being named, “Information in an analog wave”. It was a lively discussion about retrieving specific information from a wave. The question stemmed from my desire to alter one single note in a polyphonic, monotimbral piano piece. It then morphed into a broader topic of information- and wave-processing in general.

Because the question was a child topic of a larger one I was working on (a model for reason and a Theory of Everything), and I saw active interest in the that sub-discussion from a particular member (bogosort/Javier), it effortlessly cascaded into the topic, and continued to be contributed to by many, including moderators.

Because of this “multiple topic morphing,“ as things do in life, I changed the first post to reflect the current active discussion as a courtesy so that people would not feel it was off-topic, because there were complaints that the discussion had veered off from the thread title. I’ve done the exact same thing here.

I hope this answers your question, and now back to your regularly scheduled on-topic replies...

 

In the case of dissolved sugar in water, you can extract the sugar, and of course, the water. But if you were to mix the existing mixture called "Sprite" with the existing mixture called "Pepsi," gone are both components as independent elements after mixing, and there is now a new permanent identity — call it "Spepsi." Spepsi doesn't exist without Sprite and Pepsi, nor can Sprite and Pepsi be extracted from it.

So while you could reverse-engineer the Spepsi and derive the "fourier components" of all the ingredients, you're not revealed the ratios of each pre-mixture, so you'd never be able to tell that it was composed of 2 very separate concoctions prior that stood on their own definitionally. The component information is homogenized and the group layer metadata is disappeared.

Agreed.

On the other hand, if carrier signal A is modulated to contain signal A1 and signal A2, I'd say signal A is not technically a mixture of signal A1 and signal A2. If signal A1 can be extracted and 100% maintain its identity as A1, and signal A2 can also be similarly extracted, then signal A isn't really a mixture of A1 and A2—I'd say it is a composite (and potentially more). Signal A is Spepsi, and A1 and A2 are Sprite and Pepsi. Signal A1 and A2 are maintaining their independence definitionally after compositing: this is the difference between the metaphors.

Not quite. A composite signal is separable when its components each have distinct bandwidths. So Pepsi as a signal is separable, as is Sprite. But Spepsi is the case of mixing component bandwidths. Therefore, Spepsi is like signal A1 (or A2).

In other words, the demux can reliably separate/distill Pepsi and it can reliably separate/distill Sprite, but it cannot reliable separate/distill Spepsi. Therefore, signal A is not Spepsi.

Further, while Spepsi's definition is predicated on Sprite and Pepsi, all 3 mixtures (Sprite, Pepsi, and the final mixture) required a medium prior to mixing—that of a separate container. In the case of signal A, it, too, requires a medium to be defined. Signal A therefore has physical existence as a function of temporal displacement of a medium. The mathematics can show us how Signal A was constructed before constructing it, but it cannot show us how, after mixing, signals A1 and A2 were used to make it. However, if we do know signal A1 and A2 were used, we can squelch everything other than A1 and A2's bandwidth and reveal their existence.

Sort of. Even without the prior knowledge of A1 and A2, an analysis of signal A will reveal the existence of A1 and A2 -- they would stand out like sore thumbs on a spectrum analyzer, basically screaming "there is information here!" in two distinct places.

If so, signal A has a physical existence irrespective of the medium, then signal A1 and A2 must also.

Yeah, a wave needs a medium, but the medium isn't the wave. The medium constrains the range of the waveform's various parameters, but otherwise the wave is independent of the medium.

The question is, precisely "where" — as in, if signal A is sent down a wire, signal A1 and A2 are also—the individual wave shapes of A1 and A2 are retained, which makes signal A look like a meta-data wave that describes its components. How— as in "disturbances in a medium"— is the non-philosophical question.

"Where" is not a precisely answered question about waves. Look at an ocean wave; can you tell me "where" exactly it is? No.

As for the how, this boils down to the physical properties of waves. You're fine with accepting that bricks combine additively, right? We stack some bricks and don't freak out. Why is it so difficult to accept that waves combine algebraically (addition and subtraction)? Drop a small rock in a pool and concentric rings of waves will be generated. Lovely. Now drop two small rocks and the result will be far more interesting as the waves combine algebraically, reinforcing each other in some places and cancelling each other out in other places.

Note that we can transmit as much information with bricks as we can with waves. The only differences between the two, as information transmitters, are that 1) waves are more easily generated than bricks, and 2) waves have more parameters that we can reliably play with and so are more efficient carriers for our particular abilities of discernment. It's just a convenience thing. If we had enough bricks and a suitable encoding system, we could broadcast the London Philharmonic's 1969 performance of Beethoven's 9th symphony by launching bricks at a receiver. The receiver would transduce brick strikes into a time-varying voltage that drives a pair of speakers, generating all the details of the original performance. We could even do an FFT analysis on the brick stream and see all of the music's frequencies encoded in the bricks.

Again, whether in mechanical form or EM form, a wave is "carrying" or "representing" or <insert whatever the hell it is> multiple waveling groups metadata that must be accounted for, because at every second there are tiers upon tiers of discrete voltages beyond the one parent wave.

The only metadata in the waves is the encoding used. If the receiver has pre-knowledge of the encoding, they can simply decode the output; otherwise, the encoding has to be guessed (but that's not very difficult to do, which is why we need cryptography to double-encode for privacy). That's the only metadata. The waveform itself, in all its complexity, is just a physical response to a driving force. And if there is distinct information encoded in the wave, e.g., an NFL broadcast and a music performance, their separability is achieved before creating the wave. We must shift the two performances apart in frequency or time before we broadcast the wave, otherwise they will not be separable.

Mathematically, is not the wave cognized in terms of the phenomenon that is ℝ? If so, the wave technically contains infinite information mathematically — some of it human-usable signal I'd call "knowledge", the rest is noise?

No, the wave is assuredly a finite form of energy transfer. Finite energy = finite information.

We do not have a scientifically satiating definition of information, so "capacity" here is a modifier for something we don't fully know the scope of. So I'm not so sure information doesn't have anything to do with those things.

Information, as originally defined by information theory and now used by physicists, is degrees of freedom. A coin flip has two degrees of freedom -- heads or tails -- and so flipping a coin can transmit 1 bit of information.

 

and then you come up with the idea of "Spepsi"
which is a mixture of two chemical solutions that both contain some elements and chemicals that are the same, and say how can we separate them ?

That has nothing to do with the original question about frequency muliplexing, Spepsi is chemicals, frequencies' are not chemicals,

If you have a better analogy for understanding superposition, by all means, please contribute. But in my experience there is little insight gained by insisting that physical superposition works because the math says it does.

 

@Jennifer Solomon

First- your question is WRONG (if you're thinking telecommunications- that's the only context this fits to me): We can take hundreds of independent conversations and modulate them on separate analog frequencies, combine those modulated frequencies into one aggregate frequency, which we can then send down a coax wire, where it can be demuxed back into the individual components.

That isn't how it works in telecom. Analog signals are digitized using TDM- that is how they are DE/MUXed. The digital signal is then sent down a wire or fiber. Usually DS0's are MUXED to DS1. DS1 is then DE/MUXed to DS3 and so on, using variations of signaling/encoding (like B8ZS, and ESF, etc). This is ultimately put on the carrier backbone in the form of ATM and up to OC-192 fiber/circuits.

If you are thinking of a different context, please state that real-world case.

 

Back when I was a tech I worked on Telecommunications, back then it was all analog, muxed frequencies. Now it is all digital, but I may be able to offer insight to your questions. During WW1 the needed to be multiple conversation on one pair of wires for battlefield communications which is where a lot of early standards started and lasted until the late 90's (my heyday).

What exactly are your questions? My stroke screwed over my mind pretty badly so I have not been following this thread closely as my reading speed is way slowed down as has my memory. This thread has my attention now.

 

@Jennifer Solomon

First- your question is WRONG (if you're thinking telecommunications- that's the only context this fits to me): We can take hundreds of independent conversations and modulate them on separate analog frequencies, combine those modulated frequencies into one aggregate frequency, which we can then send down a coax wire, where it can be demuxed back into the individual components.

That isn't how it works in telecom. Analog signals are digitized using TDM- that is how they are DE/MUXed. The digital signal is then sent down a wire or fiber. Usually DS0's are MUXED to DS1. DS1 is then DE/MUXed to DS3 and so on, using variations of signaling/encoding (like B8ZS, and ESF, etc). This is ultimately put on the carrier backbone in the form of ATM and up to OC-192 fiber/circuits.

If you are thinking of a different context, please state that real-world case.

 

Speaking of things that derail threads, you do realize you are now ironically guilty of the very thing you are relentlessly complaining about as happening in this thread? Last courtesy answer for you, before we return to the actual discussion, because a hall monitor, for your information, is someone who is policing the movement of things, and in this case, you have anointed yourself the thread police for some odd reason, and you are not even an AAC moderator.

So one last courtesy reply before we continue with the actual topic, as this may indeed be helpful to anyone else wondering:

The Theory of Everything thread started out as being named, “Information in an analog wave”. It was a lively discussion about retrieving specific information from a wave. The question stemmed from my desire to alter one single note in a polyphonic, monotimbral piano piece. It then morphed into a broader topic of information- and wave-processing in general.

Because the question was a child topic of a larger one I was working on (a model for reason and a Theory of Everything), and I saw active interest in that specific sub-discussion from a particular member (bogosort/Javier), it effortlessly cascaded into the topic, and continued to be contributed to by many, including moderators.

Because of this “multiple topic morphing,“ as things do in life, I changed the first post to reflect the current active discussion as a courtesy so that people would not feel it was off-topic, because there were complaints that the discussion had veered off from the thread title. I’ve done the exact same thing here in this thread, so people know what they’e getting into.

I hope this answers your question, and now back to your regularly scheduled on-topic replies...

You avoided the question as to who it was who encouraged you to change the first post months after it started .

which would be of interest please

If you are reluctant to say @Jennifer Solomon
my be the moderators could pop in here and say it was them,

you have mentioned on the forums before that you have discussions with @MrChips and @bogosort outside of the forums

 

You avoided the question as to who it was who encouraged you to change the first post months after it started .

which would be of interest please

If you are reluctant to say @Jennifer Solomon
my be the moderators could pop in here and say it was them,

you have mentioned on the forums before that you have discussions with @MrChips and @bogosort outside of the forums

What in the name of Claude Shannon and George Boole occupying the same space!? I did not actively "avoid" the question. You are not reading my replies close enough to see that question has no meaning when my intention was to update it as a topic-broadening courtesy for those watching the thread. But just for the holy record, your honor! No separate human who can fog a mirror specifically encouraged me to change the first post months after it started! I did, because the topic changed and the first post sets the tone of the discourse and I wanted it to encapsulate the change in discourse. Things change! The Berlin Wall is now available in souvenir shops! Do you want to go visit it? Can you now kindly bandpass filter yourself from this sub-topic at your earliest inconvenience? Much appreciated!