Four Dimensional Reverb

Source: Four Dimensional Reverb, AIHVHIA, 11:06, uploaded 2025-03-04, Watch Later position 557.

AIHVHIA begins with an impossible request: build a four-dimensional room and let a guitar play inside it. The room cannot exist in the physical space we inhabit, yet its sound can be simulated. That gap between an impossible object and a possible sound becomes the starting point for a reverb made from four-dimensional geometry.

From impossible objects to physical synthesis

The idea extends beyond this one effect. AIHVHIA imagines audio plugins that generate sounds from impossible objects, such as an M. C. Escher-style object or a guitar with a black hole in the middle. A black hole would distort space and time, so its guitar would carry a different physical history from an ordinary instrument. The video places these ideas beside physical synthesis, which simulates the sound of a string, metal bar, or another object from a model of its physics.

The four-dimensional reverb offers a first example of that wider instrument family. AIHVHIA describes impossible-object synthesis as an underexplored area. A listener can hear the result of a room that cannot be built, even though the room itself remains a mathematical construction.

The wave equation grows too large

The first route follows the wave equation. AIHVHIA starts in one dimension, treating a string as a one-dimensional object. A signal enters at one end and the simulation measures the output at the other. Adding another dimension produces a two-dimensional surface, then a three-dimensional space, and finally the four-dimensional version.

The mathematics keeps the same basic shape as the dimensions increase. Each new dimension adds another term to the equation, and the resulting expression remains manageable in principle. The computation grows much faster. A string represented by 100 points needs 10,000 points for a comparable two-dimensional surface and one million points for a three-dimensional room. By the time the simulation reaches four dimensions, it has already become too large for the approach used in the video.

This is the first useful failure. Higher-dimensional wave simulation is conceptually direct, yet the number of points makes the straightforward method impractical. The video shows the equations on screen, while the captions describe their role and leave the notation unstated. The important result is the change of method that follows.

Ray tracing as a model of sound

AIHVHIA switches to ray tracing, a method familiar from computer graphics and games. A ray travels in a straight line from a source, bounces around the scene, and may reach a virtual camera. A sound ray can follow the same path through a room. The simulation records when it arrives and how many walls it has struck.

Those two measurements shape the sound. The travel time becomes a delay before the guitar signal reaches the speakers. The number of wall bounces affects its level and tone. A ray that travels farther and hits perhaps 50 walls arrives later and quieter than a ray that takes a shorter route. Each wall removes more high frequencies than low ones, so the later signal also sounds more muffled.

The four-dimensional version requires the same operations in a space with one more coordinate. AIHVHIA treats a ray carrying the guitar signal as a line and represents the room through the boundaries that contain it. The remaining work lies in calculating the angle at which a ray bounces off a wall and the length of its path. AIHVHIA presents the Pythagorean theorem in two, three, and four dimensions as an example of this extension. The formula gains another coordinate while its purpose stays familiar.

Repeating the process thousands of times produces thousands of delayed copies of the guitar. The first paths arrive with more energy. Later paths arrive after more travel and more absorption, so they become quieter and less bright. The overlapping copies form the reverb. AIHVHIA stores the result as a room impulse response, a format that ordinary audio programs can load and apply to other sounds.

The large room behind the name

The first full demonstration is deliberately disappointing. The four-dimensional reverb sounds like a large room. That result follows from the construction. An extra dimension gives the sound more space in which to travel, and the extra distance spreads the reflections over a longer time. The sound does not acquire a separate higher-dimensional character simply because the simulation has another coordinate.

The video then compares the effect with familiar reverb types. A sound sent through a string returns with the pitch of the string, which gives spring reverb its ringing quality. A plate reverb has more vibration modes and therefore sounds less like a single ringing tone. Three-dimensional rooms have six walls and more ways for reflections to bounce around. A tesseract, the four-dimensional equivalent of a cube, has eight boundaries, so its reverb becomes more diffuse.

That diffusion has an ordinary explanation. A complex three-dimensional room can create a similar density of reflections without adding a fourth spatial dimension. AIHVHIA therefore finds little extra sonic value in the 4D room itself. The interesting part sits in the instrument that could come from the same method: a sound source whose impossible geometry changes the response in a way a physical object cannot.

Three dimensions as a threshold

The video keeps the sonic result modest and lets the geometry carry the final movement. Higher dimensionality does not transform the reverb into a new acoustic category, yet moving from three to four dimensions creates useful thought experiments. AIHVHIA mentions Edwin Abbott Abbott’s Flatland, in which flat creatures encounter three-dimensional beings. A four-dimensional creature would relate to us through the same kind of asymmetry.

From that perspective, such a creature could see through a wall or into a person’s stomach. It could open a safe from outside, teleport, change shape, or vanish from our view. The video also recalls an unnamed video game that allows travel through a fourth dimension. AIHVHIA has not played it, so the example remains a report about a game rather than a demonstrated reference.

Mathematics, physics, and the extra dimension

The closing question asks whether a fourth spatial dimension exists. AIHVHIA describes a tension between mathematics and physics. Mathematics can extend a construction by adding another coordinate. Physics gains confidence when a mathematical prediction follows from axioms that experiments have already supported and then proves true in the physical world.

The speaker leaves the question open because current physics does not require an extra spatial dimension for this reverb. That may change with a physical theory that needs one. String theory appears as the example: depending on the version, it requires 10 or 11 dimensions. AIHVHIA also says that string theory has not received the same acceptance in physics as quantum theory or relativity, then marks the statement as uncertain and outside their depth.

The reverb therefore ends where it began. A physically impossible room can produce a real sound, and the sound can be useful as a demonstration of geometry, computation, and listening. Its value lies in the instrument and in the question it opens. The extra dimension has to earn its place through a physical reason, since adding it to a simulation alone changes the size of the room more clearly than it changes the sound.

Limits

This note follows the video’s explanation and demonstrations. The source gives no code, numerical implementation details, wall materials, ray count, sampling resolution for the final simulation, or comparison measurements between the 3D and 4D reverbs. Its statements about the audible result remain the creator’s listening assessment. The captions also contain recognition errors, including “mcer” for M. C. Escher and “40” for 4D, which I have corrected from context.

The final remarks on string theory are explicitly tentative in the source. They qualify a speculative physical framework and do not establish that a fourth spatial dimension exists. The description contains album and merchandise links, while the narration names Flatland and an unnamed video game without supplying further reading links.

Further reading / references

• Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions. The video uses its two-dimensional inhabitants to imagine how a four-dimensional creature might interact with us.