Frequencies and muxing

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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
@Jennifer Solomon

you had chance to look at the two questions yet ?
I did, and I appreciate your willingness... I think I’m all set, though, in the math department with it as of some of the interactions in this thread. There is a metamath component I’m pursuing now, which is part of the underlying question, but this thread is coming to a close; if there’s something very specific you think the math will elucidate, feel free to PM me.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
This is a fundamental property of waves. Bricks are stackable, waves are "nestable". One way to think about it is that, physically, bricks respect addition, while waves respect both addition and subtraction. This allows waves to be mixed. And as with any mixture, with the right kind of work we can separate the parts.


The one wave is a mixture of waves. When we mix salt and water, the mixture is colocated in space in a way that the separated salt and water are not.


Filters, like RC circuits (the simplest type). Filters contain reactive elements (capacitors and/or inductors) that store energy, which gives them the property of being time (and hence frequency) dependent. By tuning the right kinds of filter to the right set of frequencies, the desired bandwidth can literally be extracted from the composite signal.

So, the goal of the mux is to encode the signals (and all their overtones) into chunks of bandwidth that are far enough apart from each other that the demux can easily separate them by filtering. As an analogy, we can mix chalk and clay in water to form a superposition of three components. Since the size of the chalk and clay particles are different enough, we can use two mechanical filters to separate the three components from being in superposition. However, if the size of the two solutes are similar in size, then we lose the ability to filter them distinctly -- this is the equivalent of overlapping bandwidths.
But superposition is intimating more than “information transfer as a function of time.” It’s implying tiered numeric info per point, no? If there are indeed thousands of waves occupying the same space, and they carry unique information, they are discrete and addressable at every single point, and thusly a single voltage is not truly “sufficient” to describe \( f(x) \) in the parent wave. There’s as many f(x)’s in the parent wave as there are x’s! Superposition implies colocation to me of independent data at every point.
 

bogosort

Joined Sep 24, 2011
696
But superposition is intimating more than “information transfer as a function of time.” It’s implying tiered numeric info per point, no? If there are indeed thousands of waves occupying the same space, and they carry unique information, they are discrete and addressable at every single point, and thusly a single voltage is not truly “sufficient” to describe \( f(x) \) in the parent wave. There’s effectively many f(x)’s in the parent wave per x! Superposition implies colocation to me of independent data at every point.
We can model a glass of saltwater in terms of the positions and velocities of every molecule in the mixture (a couple of fs at each point), or we could use mechanical statistics and model the glass of saltwater with a few well-chosen equations. You'll get no argument from me that the first case generates far more information than the second case, but how much does all that extra information matter? We don't need to know the exact positions and velocities of every molecule to determine, for example, the temperature of the mixture. Indeed, this is the very concept of entropy: the larger the number of microstates (like the positions of molecules) that correspond to a single macrostate (like a given temperature), the higher the entropy of the system.

Likewise, if we wanted to capture what the acoustic wave was doing at every point in a room, we would indeed need billions of microphones. But we simply don't care about all of those details -- our ears hear just two points in space, so to get a stereo recording we just need two microphones. The microphones sample the immensely complex wave at these two points, producing two 1D signals that have enough information capacity to capture the details we care about.

It's the same idea if we were to place a tiny pressure sensor in the glass of saltwater and record a one-dimensional signal over time. The sensor responds to molecular impacts, and the force of such impacts is determined by how fast the molecules are moving. Over time our little 1D signal would tell us the average molecular speed, and this is proportional to the mixture's temperature. No need to measure each individual molecule every instant. When all we care about are the macrostates, then the copious amount of extra information in the microstates is redundant and we simply ignore it.

It's also important to note that the information in the acoustic wave is not discrete and addressable at each point. Remember, it's how the acoustic waveform changes over time that imparts the information. Put another way, frequency is defined over time, it doesn't exist at a point or an instant.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
We can model a glass of saltwater in terms of the positions and velocities of every molecule in the mixture (a couple of fs at each point), or we could use mechanical statistics and model the glass of saltwater with a few well-chosen equations. You'll get no argument from me that the first case generates far more information than the second case, but how much does all that extra information matter? We don't need to know the exact positions and velocities of every molecule to determine, for example, the temperature of the mixture. Indeed, this is the very concept of entropy: the larger the number of microstates (like the positions of molecules) that correspond to a single macrostate (like a given temperature), the higher the entropy of the system.

Likewise, if we wanted to capture what the acoustic wave was doing at every point in a room, we would indeed need billions of microphones. But we simply don't care about all of those details -- our ears hear just two points in space, so to get a stereo recording we just need two microphones. The microphones sample the immensely complex wave at these two points, producing two 1D signals that have enough information capacity to capture the details we care about.

It's the same idea if we were to place a tiny pressure sensor in the glass of saltwater and record a one-dimensional signal over time. The sensor responds to molecular impacts, and the force of such impacts is determined by how fast the molecules are moving. Over time our little 1D signal would tell us the average molecular speed, and this is proportional to the mixture's temperature. No need to measure each individual molecule every instant. When all we care about are the macrostates, then the copious amount of extra information in the microstates is redundant and we simply ignore it.

It's also important to note that the information in the acoustic wave is not discrete and addressable at each point. Remember, it's how the acoustic waveform changes over time that imparts the information. Put another way, frequency is defined over time, it doesn't exist at a point or an instant.
I’m just not sold on the somewhat walk-to-school-or-carry-your-lunch-esque physics of superposition. At the end of the day, it seems aggregate and monolithic to me, OR discrete and componental.

The reason I say this because an audio speaker’s diaphragm is effectively an air-pressurized morse-coding translation device. When said speaker is driven with a wave, it’s moving in and out to reflect just the one wave’s “flattened layers.” The wave coming out of that speaker is ”newly generated” and can’t possibly include both the aggregate AND the layers, because it doesn’t “know” of these ingredients. And yet the math still applies to the aggregate to parse “components” of the post-speaker wave that do not exist!

If the superposition of every single wave supposedly comprising the aggregate wave is “layered,” then theoretically all of the information should be completely conserved in each complex waveling, if all information is conserved? If not, then aggregate-only it is, and yet that doesn’t make sense, because we can access multitudinous co-located modulations even after it has come through a speaker.
 

bogosort

Joined Sep 24, 2011
696
At the end of the day, it seems aggregate and monolithic to me, OR discrete and componental.
How would you describe suger dissolved in water? Aggregate and monolithic? (But then why can we separate the sugar from the water?) Or Discrete and componental? (But then why is the mixture homogeneous and stable?) Is it not fair to say that a mixture is both aggregate/monolithic and discrete/componental at the same time? Or better yet, that a mixture is neither of those things. So it goes with waves.

The reason I say this because an audio speaker’s diaphragm is effectively an air-pressurized morse-coding translation device. When said speaker is driven with a wave, it’s moving in and out to reflect just the one wave’s “flattened layers.” The wave coming out of that speaker is ”newly generated” and can’t possibly include both the aggregate AND the layers, because it doesn’t “know” of these ingredients. And yet the math still applies to the aggregate to parse “components” of the post-speaker wave that do not exist!
The speaker's movement is as simple as the microphone's capsule: in and out. The air close to the speaker moves in kind, reproducing the portion of the pressure wave that was sampled by the microphone capsule. As you correctly surmise, the speaker cannot possibly reproduce anything other than the "flat" one-dimensional pressure changes that the microphone captured. But the history of these pressure changes contains all the information we need to hear the original acoustic wave.

If the superposition of every single wave supposedly comprising the aggregate wave is “layered,” then theoretically all of the information should be completely conserved in each complex waveling, if all information is conserved? If not, then aggregate-only it is, and yet that doesn’t make sense, because we can access multitudinous co-located modulations even after it has come through a speaker.
I'm not sure why superposition is hanging you up conceptually. Does a can of Coke mystify you? Inside the can is a superposition of water, sugar, and carbon dioxide. The information of each is conserved -- we can separate them -- yet their mixture is clearly an aggregation. If we take a dropper and sample a tiny bit of the Coke, we will have all the information we need to recreate it.

Waves include an element of time, but are otherwise similar. We don't need the entire waveform to recreate it, just a few hundred thousand samples of it.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
How would you describe suger dissolved in water? Aggregate and monolithic? (But then why can we separate the sugar from the water?) Or Discrete and componental? (But then why is the mixture homogeneous and stable?) Is it not fair to say that a mixture is both aggregate/monolithic and discrete/componental at the same time? Or better yet, that a mixture is neither of those things. So it goes with waves.
I think I’d describe it as a molecular reorientation, but still conceptually altogether different from what is seemingly implied by superposition. Whereas a mixture is shorthand for an ensemble of neighboring energy states—where no two objects occupy the same space in the mixture—superposition implies discrete “info and energy elements” occupying the exact same x,y,z coordinates in physical space. A radio wave carrying an FM sports broadcast at 102.7MHz is 2 physical waves co-mingling with each other, or is it one modulated wave? Which is it? It can’t be both.

The speaker's movement is as simple as the microphone's capsule: in and out. The air close to the speaker moves in kind, reproducing the portion of the pressure wave that was sampled by the microphone capsule. As you correctly surmise, the speaker cannot possibly reproduce anything other than the "flat" one-dimensional pressure changes that the microphone captured. But the history of these pressure changes contains all the information we need to hear the original acoustic wave.
Right, but also able to access what should be non-existent “components“ subsequently somewhat! If flattened, there are no superpositioned waves. And how is this wave any different than the one traveling down a coax, presumably also 100% “flattened,“ but containing 900 discrete intra-wave modulations each with a different phone conversation?? “Yes officer, this wave right over here.”

I'm not sure why superposition is hanging you up conceptually. Does a can of Coke mystify you? Inside the can is a superposition of water, sugar, and carbon dioxide. The information of each is conserved -- we can separate them -- yet their mixture is clearly an aggregation. If we take a dropper and sample a tiny bit of the Coke, we will have all the information we need to recreate it.
For the same reason above, I can’t see the can of coke’s contents as a superposition. If the molecules were superpositional, you’d have no liquid solution that yields the single thing called “coke”—which is defined as a molecular co-mingling of a certain ratio of components, each of which do not occupy the same space.

Waves include an element of time, but are otherwise similar. We don't need the entire waveform to recreate it, just a few hundred thousand samples of it.
I’m having a semantic issue with it, because these words carry greatly different implication with respect to the ill-defined ”information” and conservation thereof. I’m just not buying millions of waves stuck together like a nested Medussa-like head traveling through a wire, and then the mux says “Aha! I see you 8K! Let’s just work with you and... oh wait, there’s all your buddies in this 4K bandwidth we’ll invite along too, because, well, they somehow seem grouped JUST to your fundamental so we shouldn’t leave them out.” I’m convinced there’s hidden mapping/metadata somewhere, especially as it relates to ”whatever” these waves emanate from in “physical space,” again undefined.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
For the record, to address any question concerning any “apparent” misgivings about the math of wave mechanics inadvertently conferred from my general direction, it is not at all the math itself; it is about getting at precisely what that math is correlating to in physical space. I am not seeing an intuitive description of how the infinite data are amalgamated yet discrete, componental yet monolithic.
 

Deleted member 115935

Joined Dec 31, 1969
0
I did, and I appreciate your willingness... I think I’m all set, though, in the math department with it as of some of the interactions in this thread. There is a metamath component I’m pursuing now, which is part of the underlying question, but this thread is coming to a close; if there’s something very specific you think the math will elucidate, feel free to PM me.
Thank you @Jennifer Solomon

You asked at the beginning for this question to be maths based,
which is why I have been trying to keep things

As we talked about way back,
you asked about frequency multiplexing, and the maths
and I have taught that lesson a few times, and am willing to to so via the PM,
but you wanted the forum,
If you want to go on as a PM , then the offer is still there.

You ask about the maths,
we are nearly there, and now into the part of the lesson where i check that we are all understanding,
It will answer your questions about frequency muxing, before we take the last big step which should tie it all together,
Its not magic, jus want to help you ensure you have the basic solid foundation,
 

Deleted member 115935

Joined Dec 31, 1969
0
I’m just not sold on the somewhat walk-to-school-or-carry-your-lunch-esque physics of superposition. At the end of the day, it seems aggregate and monolithic to me, OR discrete and componental.

The reason I say this because an audio speaker’s diaphragm is effectively an air-pressurized morse-coding translation device. When said speaker is driven with a wave, it’s moving in and out to reflect just the one wave’s “flattened layers.” The wave coming out of that speaker is ”newly generated” and can’t possibly include both the aggregate AND the layers, because it doesn’t “know” of these ingredients. And yet the math still applies to the aggregate to parse “components” of the post-speaker wave that do not exist!

If the superposition of every single wave supposedly comprising the aggregate wave is “layered,” then theoretically all of the information should be completely conserved in each complex waveling, if all information is conserved? If not, then aggregate-only it is, and yet that doesn’t make sense, because we can access multitudinous co-located modulations even after it has come through a speaker.
The maths is the answer,
let us know if you want to go on with the maths @Jennifer Solomon , either PM or in this forum
 

Deleted member 115935

Joined Dec 31, 1969
0
For the record, to address any question concerning any “apparent” misgivings about the math of wave mechanics inadvertently conferred from my general direction, it is not at all the math itself; it is about getting at precisely what that math is correlating to in physical space. I am not seeing an intuitive description of how the infinite data are amalgamated yet discrete, componental yet monolithic.

The maths is the answer,
let us know if you want to go on with the maths @Jennifer Solomon , either PM or in this forum
 

Deleted member 115935

Joined Dec 31, 1969
0
I think I’d describe it as a molecular reorientation, but still conceptually altogether different from what is seemingly implied by superposition. Whereas a mixture is shorthand for an ensemble of neighboring energy states—where no two objects occupy the same space in the mixture—superposition implies discrete “info and energy elements” occupying the exact same (x, y, z) coordinates (tri-ordinates) in physical space. A radio wave carrying an FM sports broadcast at 102.7MHz is 2 physical waves co-mingling with each other, or is it one modulated wave? Which is it? It can’t be both.



Right, but also able to access what should be non-existent “components“ subsequently somewhat! If flattened, there are no superpositioned waves. And how is this wave any different than the one traveling down a coax, presumably also 100% “flattened,“ but containing 900 discrete intra-wave modulations each with a different phone conversation?? “Yes officer, this wave right over here.”



For the same reason above, I can’t see the can of coke’s contents as a superposition. If the molecules were superpositional, you’d have no liquid solution that yields the single thing called “coke”—which is defined as a molecular co-mingling of a certain ratio of components—each of which do not occupy the same space.



I’m having a semantic issue with it, because these words carry greatly different implication with respect to the ill-defined
”information” and conservation thereof. I’m just not buying millions of waves stuck together like a nested Medussa-like head traveling through a wire, and then the mux says “Aha! I see you 8K! Let’s just work with you and... oh wait, there’s all your buddies in this 6K-10K bandwidth we’ll invite along too, because, well, they somehow seem grouped JUST to your fundamental so we shouldn’t leave them out.” I’m convinced there’s hidden mapping/metadata somewhere, especially as it relates to ”whatever” these waves emanate from in “physical space,” again undefined.

The maths is the answer,
let us knwo if you want to go on with the maths @Jennifer Solomon , either PM or in this forum
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
The maths is the answer,
let us knwo if you want to go on with the maths @Jennifer Solomon , either PM or in this forum
I know the math works, but if you read the above another time, you will see the central issue is what precisely the math is describing in physical space. This portion is a physics portion, involving the concurrency of multiple modulated waves superpositioned in space.

I updated the first message to reflect a broader ”bandwidth” for the topic to incorporate these elements.
 

bogosort

Joined Sep 24, 2011
696
I think I’d describe it as a molecular reorientation, but still conceptually altogether different from what is seemingly implied by superposition. Whereas a mixture is shorthand for an ensemble of neighboring energy states—where no two objects occupy the same space in the mixture—superposition implies discrete “info and energy elements” occupying the exact same (x, y, z) coordinates (tri-ordinates) in physical space.
Let's keep in mind the scale of our analysis. At the molecular level, I agree that the mixture is indeed just a group of distinct objects and not something I'd call a superposition. It's only when we zoom out that we notice an actual mixture.

But the same is true for a waveform. Zoom in on any given (x, y, z) coordinate and you'll see distinct molecules, mostly nitrogen and oxygen, with no hint of wave-like behavior. At this scale, there's no superposition, no frequency, no phase -- just energetic molecules. Only when we zoom out do the waveform properties emerge. This is crucial, I think, to your conceptual hangup -- any single point in space is not even a "flat" wave, nevermind a layered wave with nested information. There is no such thing as a wave at a point.

The wave is the changes in the aggregate states of all the molecules in the air. Each molecule reacts locally, with lots of random, chaotic movement having nothing to do with the waveform. But the energy that started the wave imparts a time-varying force that, over time, can be seen to be influencing the net motion of groups of molecules. A microphone samples some small chunk of the air, a few trillion molecules, and records this net motion -- which are periodic changes -- and so captures the details of the wave (not the molecules).

In other words, just like our eyes capture the aggregation that is the the mixture in the glass of Coke, and not the discrete molecules, the microphone (and our ears) capture the aggregation that is the wave, even though that wave "doesn't exist" at any single point. I'm emphasizing the glass of Coke because I think it is the proxy by which your cognitive dissonance over emergent superposition can be resolved.

A radio wave carrying an FM sports broadcast at 102.7MHz is 2 physical waves co-mingling with each other, or is it one modulated wave? Which is it? It can’t be both.
It's both. Mathematically, modulation literally means multiplication. To make radio waves we multiply the carrier wave with the modulating wave. This creates a new waveform, the product of two other waveforms. So your question is equivalent to asking, Is 3*2 = 6 a single number or two numbers? It's both; 6 is a single number that is a product of two numbers.
 

Deleted member 115935

Joined Dec 31, 1969
0
I know the math works, but if you read the above another time, you will see the central issue is what precisely the math is describing in physical space. This portion is a physics portion, involving the concurrency of multiple modulated waves superpositioned in space.

I updated the thread’s first message to reflect a broader ”bandwidth” for the topic to incorporate these elements.
@Jennifer Solomon

you said " what precisely the math is describing in physical space "

I think as we have covered, which I thought is why in the original question, you quoted you wanted to go into the maths.

It seems your saying now that you have learnt the maths,
well done, what have you been studying ?

As for "frequency multiplexing" and your question about "physical space"

As we discussed back at the beginning,
all science works on theories and models,
And the maths models the science,


But if as you say, we have gone past the maths,
it sounds like this forum is closed, and can only now go off topic,

I suggest that you request this topic closed and start a new post on a new topic.

@Jennifer Solomon, I wish you the best, and if you decide you want to learn a bit more on frequency muxing and the maths, drop us a PM.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
Let's keep in mind the scale of our analysis. At the molecular level, I agree that the mixture is indeed just a group of distinct objects and not something I'd call a superposition. It's only when we zoom out that we notice an actual mixture.

But the same is true for a waveform. Zoom in on any given (x, y, z) coordinate and you'll see distinct molecules, mostly nitrogen and oxygen, with no hint of wave-like behavior. At this scale, there's no superposition, no frequency, no phase -- just energetic molecules. Only when we zoom out do the waveform properties emerge. This is crucial, I think, to your conceptual hangup -- any single point in space is not even a "flat" wave, nevermind a layered wave with nested information. There is no such thing as a wave at a point.

The wave is the changes in the aggregate states of all the molecules in the air. Each molecule reacts locally, with lots of random, chaotic movement having nothing to do with the waveform. But the energy that started the wave imparts a time-varying force that, over time, can be seen to be influencing the net motion of groups of molecules. A microphone samples some small chunk of the air, a few trillion molecules, and records this net motion -- which are periodic changes -- and so captures the details of the wave (not the molecules).

In other words, just like our eyes capture the aggregation that is the the mixture in the glass of Coke, and not the discrete molecules, the microphone (and our ears) capture the aggregation that is the wave, even though that wave "doesn't exist" at any single point. I'm emphasizing the glass of Coke because I think it is the proxy by which your cognitive dissonance over emergent superposition can be resolved.

It's both. Mathematically, modulation literally means multiplication. To make radio waves we multiply the carrier wave with the modulating wave. This creates a new waveform, the product of two other waveforms. So your question is equivalent to asking, Is 3*2 = 6 a single number or two numbers? It's both; 6 is a single number that is a product of two numbers.

Since a wave is a disturbance in a medium, when we’re talking about waves lexically, it’s often conflating a noun and a verb into a “function-object.“ Does the waveexist in nature apart from the medium as “something?” No.

A wave is the temporal condition of a medium. We don’t define a car by whether or not it’s at rest or moving. The medium is more important than the temporal condition of it.

This statement, “The wave is the changes in the aggregate states of all the molecules in the air” is true for mechanical waves, when things like air or water is part of the “equation.” But the same “wave“ that disturbed the air molecules is the same wave that can disturb its own self-generating magnetic field in a vacuum, and carry all of the encoded, disparate modulations with mathematically infinite information, though seemingly finite extent in physicality.

Multiplying the carrier wave with the modulating wave yields a new wave mathematically, sure. But in that same numbers-as-waves analogy, if 12 were seen as a wave, then wave-3 multiplied by wave-4 can yield wave-12, but so can wave-6 and wave-2 multiplied yield wave-12. Wave 12 sent down the wire can carry either 3 and 4 OR 6 and 2. But 6 and 4 carry 3 and 2 themselves, yet they themselves possess entirely different identities, or we’d never be able to reference them independent of their more elementary factors. Wave-12 seems to be defined as a medium disturbance and also conserve WHICH specific waves made it up in THAT specific case, therefore simultaneously carrying them along with 12, which physically speaks to 3 independent, but conserved field disturbances in the same space, and that makes zero sense.

As in the case of a modulated EM wave containing 900 unique concurrent modulations within different bandwidths, this again logically speaks to the discrete physicality of those 900 waves. In order to exist independently, they must be making concurrent disturbances in the magnetic field to qualify as existing as “something” because the waves don’t exist without the medium.

The information is stored where exactly in transit? “In the wave” as an answer focuses the light on the “sauce“ that is the wave and marginalizes the meat and potatoes that is the role of the medium.

Also, the question, “what is a magnetic field made of” is undefined. If it is a physical fundament, and we can’t reduce it further, but it’s required for information conservation, then it is something having undiscernible further properties involving a clearer definition of the physicality of information, yes?
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
@Jennifer Solomon

you said " what precisely the math is describing in physical space "

I think as we have covered, which I thought is why in the original question, you quoted you wanted to go into the maths.

It seems your saying now that you have learnt the maths,
well done, what have you been studying ?

As for "frequency multiplexing" and your question about "physical space"

As we discussed back at the beginning,
all science works on theories and models,
And the maths models the science,


But if as you say, we have gone past the maths,
it sounds like this forum is closed, and can only now go off topic,

I suggest that you request this topic closed and start a new post on a new topic.

@Jennifer Solomon, I wish you the best, and if you decide you want to learn a bit more on frequency muxing and the maths, drop us a PM.
Check out the first message in the thread in red text. ;)
 

Deleted member 115935

Joined Dec 31, 1969
0
This is false for linear systems. Only nonlinear systems will produce intermodulation distortion. The linear sum of multiple of sine waves (or any other waveform) is indeed perfect.


It's all in the physics; the math is a model.

The interesting thing in the "orriginal post"
is the message
" Edited starting question: "

and the date of the edit.


Can I also remind you of your forum post #3
when we were still discussing as to the difference between this post any your last one that was blocked.

" Hey, 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. I’ve edited any data in the original post that may obfuscate the intention. "


Ah well,
history is flexible,
thats why I stick to logic and maths
 
Last edited by a moderator:

bogosort

Joined Sep 24, 2011
696
Since a wave is a disturbance in a medium, when we’re talking about waves lexically, it’s often a case of conflating a noun and a verb into a “function-object.“ Does the wave exist in nature apart from the medium as “something?” No.
Does the mixture exist apart from its solvent? No.

This statement, “The wave is the changes in the aggregate states of all the molecules in the air” is true for mechanical waves, when things like air or water is part of the “equation.” But the same “wave“ that disturbed the air molecules is the same wave that can disturb its own self-generating magnetic field in a vacuum, and carry all of the encoded, disparate modulations with mathematically infinite information, though seemingly finite extent in physicality.
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.

Multiplying the carrier wave with the modulating wave yields a new wave mathematically, sure. But in that same numbers-as-waves analogy, if 12 were seen as a wave, then wave-3 multiplied by wave-4 can yield wave-12, but so can wave-6 and wave-2 multiplied yield wave-12. Wave-12 sent down the wire can carry either “3 and 4“ OR “6 and 2.” But 6 and 4 carry 3 and 2 themselves, yet they themselves possess entirely different identities, or we’d never be able to reference them independent of their more elementary factors. Wave-12 seems to be defined as a temporal medium disturbance and also conserve WHICH specific waves made it up in THAT specific case, therefore simultaneously carrying them along with 12, which physically implies 3 independent, but conserved field disturbances in the same space—yet that makes zero sense.
The same ambiguity is true of waves when we multiplex or sample a waveform (see frequency aliasing). For example, at a sample rate of 100 kHz, we literally cannot tell the difference between 40 kHz and 160 kHz, To fix the ambiguity, we impose bandwidth restrictions on the input signal, i.e., the Nyquist criterion. By preventing the input singal from containing any frequencies greater than 50 kHz, we ensure that whatever frequencies we do find are not aliases.

As in the case of a modulated EM wave containing 900 unique concurrent modulations within different bandwidths, this again logically speaks to the discrete physicality of those 900 waves. In order to exist independently, they must be making concurrent disturbances in the magnetic field to qualify as existing as “something” because the waves don’t exist without the medium.
"Magnetic fields" is a red herring, so if your goal is to better understand the information-packing properties of waves, I'd recommend sticking to acoustic waveforms, which have exactly the same information-packing properties and none of the quantum complexity of EM waves.

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.

The information is stored where exactly in transit?
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.

Also, the question, “what is a magnetic field made of” is undefined. If it is a physical fundament, and we can’t reduce it further, but it’s required for information conservation, then it is something having undiscernible further properties involving a clearer definition of the physicality of undefined “information,” yes? The math transcends the physics in the use of infinity describing the finite, and also seems to be transcending the actual physicality itself.
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).

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.
 

bogosort

Joined Sep 24, 2011
696
The interesting thing in the "orriginal post"
is the message
" Edited starting question: "

and the date of the edit.


Can I also remind you of your forum post #3
when we were still discussing as to the difference between this post any your last one that was blocked.

" Hey, 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. I’ve edited any data in the original post that may obfuscate the intention. "


Ah well,
history is flexible,
thats why I stick to logic and maths
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.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
The interesting thing in the "orriginal post"
is the message
" Edited starting question: "

and the date of the edit.


Can I also remind you of your forum post #3
when we were still discussing as to the difference between this post any your last one that was blocked.

" Hey, 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. I’ve edited any data in the original post that may obfuscate the intention. "


Ah well,
history is flexible,
thats why I stick to logic and maths
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.
 
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