## Sound in higher dimensions

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### Sound in higher dimensions

According to the dimensional features page, a signal in 5D is distorted such that the signal received is the first derivative of the original signal. I've wondered what that would sound like, but Google and YouTube searches have been terribly fruitless and disappointing. All I get is "put on your headphones, close your eyes, and meditate" >:( What does the first derivative of a sound signal sound like? Like, if you took a song or a voice sample and played it in 5D, what does that first derivative sound like?

http://hi.gher.space/wiki/Dimensional_Features_Summary
ParticleXLR8R
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### Re: Sound in higher dimensions

I seem to recall long ago using an analog synthesizer that had a derivative function. You got a very trebly version of the sound. But that was all a long time ago so I wouldn't swear on it.

It also did integrals, which were bassy.
PatrickPowers
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### Re: Sound in higher dimensions

Hello! I'm a newcomer on this forum, and I'm not that familiar with the ideas of additional dimensions; which is why I've created an account here, I want to fill this void in my brain.
And I have a question: when you are talking about the effects of a 4th of 5th dimension on sound, what dimensions are you talking about? Because the effect of this dimension would be radically different on sound according to what it is; for example, I've heard descriptions of the 4th dimension as a new directional one, some saying that the 4th dimension is time...
Foxbat_25
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### Re: Sound in higher dimensions

There is no particular order to the dimensions. We don't count "time" into this mix.

If you construct three dimensions out of 2d and time, you end up with a pile of slides, where you flick through the slides and get an illusion of time. This is how animation pictures are made. But in that case, you is not just a 'blob', but a lengthy snake-like form, where any section is you at that slice of time.

In practice, we say 'length-width-height', since height is less important than the other two, which are extensive. You can walk miles of length and width, but not of height. The "proper" order for imagining higher dimensions, is 'height, forward, across'. Height supposes we are standing in a gravitaional field, on the ground. Forward suggests a linear time scale, and that motion is to the front. (Plants have lesser need for this, and have no clear front/back thing). The rest are simply variations in turning. You can get an illusion of this, by placing clocks on the floor, and supposing that it's the plan of the room, and the height is 'forward'. The wall-flowers who dot the edge of the dance hall face inwards, (ie clockwise up), but no law of physics tells them the 12's must point the same way. So there is no left/right direction. The clockwise thing still matters.

Sound then, passing through four dimensions, is like three dimensions, an ever-expanding sphere. Our ears are but a point or two in this space, we can hear stereo from the differences in sound.
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the dream we dream together is reality.

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wendy
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### Re: Sound in higher dimensions

Okay, thanks for the in-depth answer, I was sort of lost with all of the new information that's present on the forum at first
Foxbat_25
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### Re: Sound in higher dimensions

ParticleXLR8R wrote:According to the dimensional features page, a signal in 5D is distorted such that the signal received is the first derivative of the original signal. I've wondered what that would sound like, but Google and YouTube searches have been terribly fruitless and disappointing. All I get is "put on your headphones, close your eyes, and meditate" >:( What does the first derivative of a sound signal sound like? Like, if you took a song or a voice sample and played it in 5D, what does that first derivative sound like?

http://hi.gher.space/wiki/Dimensional_Features_Summary

The idea behind this distortion comes from (sound) wave propagation theory, in which you study the solutions of the differential equations that govern wave propagation starting from a point source. For simplicity, a simple sinusoidal source is assumed, and the idea is to study how this signal will be perceived at some point X displaced from the source after the signal has propagated via sound waves over the medium.

I forgot the exact article that presented this study, but basically what they found was that in a space with an even number of dimensions, the solution to the wave propagation differential equation is such that not only the signal propagates forwards, but there are also "back echoes" that propagate back to the source, and from there, they invert and travel outwards again, and this echo would spawn its own echoes, and so on. This can be observed by dropping a pebble in a pond, which has a 2D surface. It's immediately obvious that in addition to the initial circular wave peak that travels outwards from the point where the peddle hits the water, there are smaller peaks that follow it, and each of these have yet smaller peaks that travel backwards and interferes with whatever it coming from the source. So the single pulse (the pebble striking the surface of the water) translates into multiple complex peaks.

A 3D wave apparently does not have such a behaviour; a single pulse propagating in 3D would only propagate forwards without any back-echoes. Thus, the signal can be transmitted undistorted to the receiver some distance away. Remarkably, 3D appears to be the only dimension in which the signal is transmitted undistorted; in 4D, you'd have a similar back-echoing phenomenon with the signal, so that a single pulse at the source might get perceived as a series of pulses, starting with the initial large one following by a trail of smaller ones in a diminishing, but complex pattern.

In 5D, the back-echoes don't happen, but the signal does get distorted in another way, IIRC the listener hears the derivative of the original signal rather than the signal itself. And IIRC, in 7D, 9D, etc., the signal gets progressively more derived (i.e., the 2nd, 3rd, ... derivatives of the original signal).

As far as 4D is concerned, this unexpected phenomenon presents very interesting implications. What it seems to imply is that if 4D light had wave-like properties like in 3D, vision would nevertheless behave in a very different way from what we're used to in 3D. Instead of perceiving a single flash of light from the source, for example, a 4D being's eyes would instead see a series of pulses. A radio receiver would have to do a lot more work in order to recover the original signal (if it's even possible!). It would be a very different world indeed.

There's also the very interesting implication that if sound, or whatever the equivalent might be called, were transmitted through a surface rather than through the air, it would have the characteristics of a 3D wave: pristine transmission of the signal. Which in turns seems to imply that for transmission of information where the integrity of the source signal is important, transmission across a surface would be preferable to transmission across a volumetric medium. Which might imply that in 4D it is better, instead of using vocal communications, to use something like seismic communications, say emitting vibrations that spread across the surface of the ground and picked up by the other party's feet. Which is extremely interesting because even in our 3D world, animals like elephants are known for seismic communications (though I'm not sure how exactly that fits into the whole 2D-signal-is-distorted deal).
quickfur
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### Re: Sound in higher dimensions

There really isn't such a thing as electromagnetic waves. This misunderstanding has a long history. For a hundred years it was believed that light and such were vibrations of a medium called the ether. Eventually Albert Einstein did away with this concept, but it is so embedded in the language we will never get rid of it. They do indeed have "wave-like properties," but the mechanism is very different.

It is also possible to have solitonic waves in water. It has to do with pushing the water. For example, tidal bores and tsunamis are solitonic. It's different from throwing a pebble into water, where the force is applied transverse to the surface.

Electromagnetic "waves" are solitonic by nature, no matter the number of dimensions. No one understands where the wave-like properties come from. Richard Feynman's model is the one that physicists use today. Things like electrons are IMO not understood at all. We have math that describes exactly what they will do, but that's it.

That's interesting about elephants. I don't know the answer there. I would suppose the solution depends on the stiffness of the medium. I would further guess that the amount of back propagating waves depends on the stiffness of the medium. In the old days it was assumed that the ether was infinitely stiff, thus explaining the absence of back propagation.

Taking all this a bit further, I also think that the fundamental forces are not transmitted by particles. I have discussed this with real physicists and they tended to agree. The forces do all sorts of things that particles couldn't do. If you are persistent, physicists will tell you that all they know about are "excitations of a field," which for the sake of convenience are called particles. But since no one knows how a field works that isn't much help.

The majority view is to have NO model and just do the math. No one understands how it works, so a model will just mislead and confuse you. The models one reads about in popular science went obsolete seventy or so years ago. They persist largely because there is a demand to relate this weird stuff to that which is familiar. I believe that this is a nigh-impossible task. Quantum things simply have nothing in common with what is familiar to us. If you are interested I'd recommend Richard Feynman's book QED. He was a genius with coming up with simple models for this weird stuff. It works pretty well. But even he gave up on certain things. He said something to the effect that if you don't find it completely weird then you don't know what is going on.

It is tantalizing. Electrons are tiny and all identical, so they MUST be simple. But no one has been able to figure it out. I'm certain that higher dimensions are involved. Quantum spin is mathematically similar to a 4-dimensional rotation. That's a start. The string theorists speak of 11 dimensions. But AFAIK nobody knows what most of those dimensions are or how they relate to one another. There's a multitude of Nobel prizes waiting out there.

On a 4D planet I would expect wind-generated ocean waves to be solitonic. Surfers would not experience "sets" of waves. But my grip on such things is weak. I'm not certain of that.
PatrickPowers
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### Re: Sound in higher dimensions

Thanks Patrick. It is good to hear such open dialogue of where theoretical science is actually at.
A lot of it does still appear to be near to magic; even if we can measure it.

I'll ask your forebearance as I digress to my more literal investigation of our Universe.
I capatilised Universe as it only has one form but any interpretation, including my own, is lower case of course.
If I'm specific I'll use lower case as in "In my universe...".

I would leave the topic alone but it was just interesting to explore this idea against my own portrayal.
In my universe, where light is not special, then there is a volumetric aspect to light.
In my 3D universe light takes on a natural volumetric form of a moving wave; which is a spiral.
A spiral allows for the maximum form when moving through a series of planes that are acting upon the light.

Then 4D becomes interesting because light is actually travelling throug a series of 3-planes (volumes to us).
The maximum spiral form when moving through a series of 3-planes has a longer length per period.
To spread out to maximum uniform shape the spiral must find its longest possible per period length whilst staying fairly relative to itself. It has to follow a spherical spiral against the progress of its movement.

I've been dealing a little with these in my attempts to produce the perfect Klein Strip variations.
I do have a good formulation for a Klein Strip now but I'm not sure if it is a perfect one.
It does produce 360° of Klein Strip variations which all have the same change in deflection to each other while all remaining unique (well 0-90° at least are unique) which is pretty cool.
That may seem a lot but 360° in 4D is a natural step up from only left and right in our 3D world.
I will have to study it a bit more to determine that.

However, the principle requires rotating the sphere not in one or two directions but in an overal spiral around itself; more of a tumble.
A tumble does travel through more space per period than does a spiral and is a more natural form of a maximised spiral moving through 3-planes in 4D space.

I guess the consequence of this is that instead of having just left and right light spirals while they travel - as we have in my universe - we would actually have 360° of varieties of light which are subtly different to each other rather than just left and right handed light.

Again this is just the universe that I believe in but it is still interesting to explore the idea of how light travels through 3-planes in 4D instead of 2-planes in our visually 3D Universe.
gonegahgah
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### Re: Sound in higher dimensions

I don't know if this is relevant to the discussion, but it has spawned an idea I am now curious about and would welcome any thoughts.

If a 2D object emitted a sound in a 3D world, my assumption is the 3D being wouldn't be able to "hear" it unless the 3D being's ears/receptors were intersecting that specific plane. My assumption coming from the idea that if a 2D object emits a wave then it can't vibrate within the 3rd dimension. If this is true, does the same hold up in higher dimensions? Would a 4D-being only be able to hear a very tiny slice of the 3D sound so long as it was intercepting that specific 3D realmspace?

Secondly, would it be possible for the 3D wave to interact with the 4D being and get "bounced" into the 4th dimension? Or because the intersection is infinitely small it would be impossible for it to have any angle to reflect against in order to give it a 4th-dimensional velocity?

I hope this makes sense.
Lusion
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### Re: Sound in higher dimensions

The whole idea of 3D space interacting with 4D space (or for that matter, any lower-dimensional space interacting with a higher-dimensional one) is a purely fictitious device to convey the idea of dimensional analogy. A universe that exists in 3D space by definition does not and cannot interact with 4D space, because if it could, it wouldn't be a 3D universe anymore!

Last edited by quickfur on Sun Sep 06, 2020 2:15 pm, edited 1 time in total.
quickfur
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### Re: Sound in higher dimensions

That makes sense. If there is an intersection then the question of can it "bounce" into it is all determined based on how you model the dimensions and their constraints. Thanks quickfur!
Lusion
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### Re: Sound in higher dimensions

Forming the derivative of a pressure wave would not lead to a noticeable change. The derivative of a sine wave is another sine wave shifted by 90° with the same frequency. The derivation thus doesn't change the frequency spectrum we hear. It also does not cause changes in the attack or shifts in time / echos, because it only changes the phase of the waves, not the envelope. In some circumstances, there might be subtle differences in the texture of a sound due to those phase shifts. A lot of the music we hear is actually recorded by cardioid microphones, which unlike our ear, respond to the derivative of the pressure wave.
What is deep in our world is superficial in higher dimensions.
Teragon
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### Re: Sound in higher dimensions

This is not merely about taking derivatives. That's totally over-simplifying the picture.

It's about how an n-spherical wave propagates outwards from its source in the center. Others have explained this much better than I can, so I defer to them: see, for example: this reddit discussion, particularly the answers by Midtek, which goes into some detail about how Huygen's principle implies that in even dimensions, an outwards-propagating wave continues to influence the entire region inside the expanding sphere, producing "echoes" of the original signal. Because of this, it is difficult for a recipient at some non-zero distance to recover the original, pristine signal, because the waveform perceived by the receiver is a superimposition of multiple, decaying copies of the original signal.

In odd dimensions higher than 3, the receiver gets not the original signal, but a derivative of it. Only in 3D will the receiver perceive the original signal unchanged.

Here's a technical paper that describes this phenomenon: article.
quickfur
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### Re: Sound in higher dimensions

Teragon wrote:Forming the derivative of a pressure wave would not lead to a noticeable change. The derivative of a sine wave is another sine wave shifted by 90° with the same frequency. The derivation thus doesn't change the frequency spectrum we hear. It also does not cause changes in the attack or shifts in time / echos, because it only changes the phase of the waves, not the envelope. In some circumstances, there might be subtle differences in the texture of a sound due to those phase shifts. A lot of the music we hear is actually recorded by cardioid microphones, which unlike our ear, respond to the derivative of the pressure wave.

I once used a music synthesizer with a derivative function. The result is a lot more trebly than the original. The amplitude of the derivative of a low frequency wave is less than that of a high frequency wave of equal amplitude.
Last edited by PatrickPowers on Fri Jul 01, 2022 1:43 pm, edited 1 time in total.
PatrickPowers
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### Re: Sound in higher dimensions

In most(all?) sound recording devices, what is recorded is the derivative of the signal. It's called the "RIAA curve." Playback is of the integral.
PatrickPowers
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