If I lived in a two-dimensional world, spread out flat as if everything was happening on a piece of paper, what might life sound like?
And if I was living in a four, five, or six-dimensional world (not counting time), what would I hear?
I believe that because of how the physics of sound and hearing works as a relatively one-dimensional form of resonance, experiences similar to sound could theoretically be found in universes with every non-zero number of dimensions. And excitingly, this could meant that we can make every sound and form of music in our universe that could be physically possible in any and all other universes with any number of physical dimensions.
I started thinking about this concept after watching the following video, which outlines how to replicate the way sounds might reverberate in a physical space that has more dimensions than are possible in our universe:
I was absolutely fascinated. The video itself touches on some amazing math and theories that are delightfully beyond my world of expertise, which got my brain going in really exciting ways. Immediately I hopped into my journal, playing with a stream of my first thoughts:
“Are there any musical instruments that fully utilize the dimensionality of our physical universe?
My mind goes to how strings could be used in a 2-D universe (though they couldn’t be plucked; they would probably be played more like a drum because there would be no way to reach “around” them).
Could a familiar drumhead be "plucked" in a 4-dimensional universe? Would the equivalent in that universe be a 3-dimensional "drumhead" that's a surface with height, width, and depth, which must be impacted from one side through the 4th dimension, but could then itself be "plucked" in a 5-D world?
Each of those examples is N minus 1 dimensions relative to the world it's in to be played as a drum, then N minus 2 to be played as a string. For example, a 2-D drumhead in a 3-D world, and a 1-D drumhead in a 2-D world.
Is there another way of playing an instrument when it’s N minus 3 dimensions relative to the universe it’s in? Would this mean there are new ways of playing a string for each additional dimension added, then the other ways of making sounds “ascend” the order of dimensions for instruments (for example plucking a 1-D string in our universe, “plucking” a 2-D drum in a 4-D world, then “plucking” a solid cube in a 5-D world)?
Is there any way to simulate what a 5-D resonating volume might sound like when plucked in a 7-D universe? Probably boring if it's just resonating back and forth, because that might sound disappointingly familiar to our ears, especially relative to all the crazy computation it would take for us to simulate. But still fun to wonder. And is there any sound-making apparatus that fully utilities any amount of dimensionality?
I imagine leaving one or more dimension "unutilized" is what gives any instrument the freedom to physically resonate anyway.”
While these first messy thoughts were forming, I found my way to something of an answer to my starting question by following a chain of connected questions: Are there indeed any musical instruments that fully utilize the dimensionality of our physical universe?
Yes and no: Musical instruments can occupy all the dimensions of the universe they are in, but they have to utilize at least one dimension as the one they resonate back and forth through. And that vibration makes a resonance that is effectively one-dimensional.
My harp strings need to vibrate through the air by resonating back and forth in order to make a pressure wave in the air that I perceive as sound. They can do so in two dimensions relatively freely, since they are relatively one-dimensional (e.g. they have significant height, but not a lot of width and depth). Since our universe is 3-D, strings have those two remaining dimensions open to resonate easily.
A drum or a reed also needs to be able to move back and forth in one dimension order to make a sound, even though it’s relatively stable in the other dimensions. It takes a spatial dimension to resonate.
A three-dimensional object in a three-dimensional universe can indeed still resonate, for example ringing rocks, but it takes more force to make these sounds, and the materials have to internally have the freedom to still resonate by vibrating back and forth through space.
Our perception of sound is one-dimensional in the sense that we’re experiencing a resonating pressure wave that moves our eardrums back and forth through a single dimension. The patterns and frequencies of these waves compose what we experience as sound, speech, and music.
Those patterns can carry information, artistry, chaos, memorized associations, experiences of time, and connect us with the world around us as well as the worlds within each other.
And the worlds inside each of us have many more dimensions than three. We are complex and nuanced beings, and we can experience some of each other’s inner worlds through the music and words we create.
We can condense our incredibly complex internal experiences into sound and music, and this can be true of imaginary or theoretical universes with higher numbers of dimensions too.
Even with how hard it can be, it’s fun to try to conceptualize some of what these higher-dimensional universes might be like. A favorite thought experiment comes to mind, where you can play with imagining a barstool in any number of dimensions. Assuming this stool has a number of narrow legs and a “seat”, it needs a minimum of the same number of legs in order to stand up as there are dimensions in its world:
In a two-dimensional “flat” universe, a barstool would need 2 legs to stand up — think of a stool drawn on a piece of paper. In a three-dimensional universe, a barstool needs a minimum of 3 points of contact with the ground — for each additional dimension, it needs a way to stabilize itself across that dimension.
In a four-dimensional universe, a 3-legged stool would fall over “flat” unless it had a 4th leg that stabilized it in the additional dimension. The same concept extends to 5, 6, 300, or any number of spatial dimensions. You need that same number of barstool legs for stability.
And like I said, all of the examples of instruments I can think of in our physical universe need at least one “dimension” to be the one that they vibrate back and forth through in order to make sound. So in our 3-dimensional universe, we have 2-dimensional drumheads that are free to resonate more easily because they are relatively “flat” across the third dimension.
In a 4-dimensional universe, even a solid 3-D cube of a non-resonant material could make a sound by vibrating back and forth through the fourth dimension. Just like a drumhead, it would be “flat” in that 4th direction, so that could be the direction it resonates in.
As we ascend in dimensions, new instruments become possible, as well as new ways of playing the instruments from the previous numbers of dimensions. For example, a 2-D drumhead could be free to resonate in 2 directions in a 4-D world, and a 1-D string could vibrate in three different directions freely.
Each of these dimensions could also be utilized to access and manipulate physical musical instruments in new ways. If you think of the example of a hollow triangle in a 2-D world, it’s a closed shape. You’re either inside of it or outside of it, and you’d have to hit it from one of those sides to make a sound. But in a 3-D universe, this same triangle can be played by reaching into it with a metal “beater” from the third dimension, ringing it to call Pa’ in for dinner.
A closed, hollow cube could itself be reached inside of from the 4th dimension, since this new dimension would be perpendicular to all the previous dimensions. So there could be a delightful array of new instruments that could be played in countless new ways as you add dimensions.
Each of these instruments could vibrate through space, and these vibrations could be carried as a pressure wave. While there might indeed be entirely new phenomena akin to resonance that take place in these universes too, the equivalent of what we think of as “sound” would still be possible to create and perceive in any number of dimensions because it is effectively just vibrations back and forth in a single dimension.
That means all possible forms of music and sound from all possible universes with any number of spatial dimensions would compose vibrations and patterns across one dimension. And this means that we can make and listen to all of the possible sounds of all possible worlds in our 3-dimensional universe. I adore that thought.
For you sci-fi writers out there, this means if there were ever to be communication between universes with different numbers of physical dimensions from each other, music could literally be a universal language. We could talk with 326-Dimensional beings through sound, and they could talk back. They would have more complex ways of making and perceiving those vibrations, but the patterns of vibration they could perceive and produce would all be physically possible to make and hear in our universe too.
Whoa. Anybody hearing things?
—
Alex