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).