Thanks for not making me feel quite so silly. My friend is a maths professor, and I believe his assertion. I just don't understand how you can have that type of information in a single dimension (time).Perhaps you can get him to clarify.
In the case you can argue that audio is 2 dimensional because it needs 2 elements to exist, magnitude (pressure) and time, after all audio is the information conveyed by the difference in pressure over time, even if its commonly represented as 1d vector because of its simplicity in this representation it exist a hidden dimension that is time because each position in the vector represents concrete time. It's possible to represent each point of audio as list of [pressure, time], this representation can led to variable sample rate audio, something exotic but plausible.
Also I can tell that normally a 1D vector is actually a 2D object because we normally omit the magnitude (weight, dimension) of the element in the vector to define its dimension. Basically we have a 1D vector of 1D element making it a 2D object. Or we can represent a vector by a list of [magnitude, position] demonstrating that a vector is a 1D representation of a list of 2D objects.
The devil of this discussion is hidden in the language and concepts.
@infinciThank you for your really interesting and valuable explanation. It seems to be right story. Unfortunately, 1. not fully right; 2. it only affects the surface, not the deep waves. As a result, what appears to be true, in the end became false. Half-truths are dangerous things, they deceive people.
I try to give you a logical explanation...
Explanation little later, I am busy now.
Interesting thread! I'm not a mathematician, just an IT guy with barely enough math knowledge to be dangerous, but hear me out.Have you considered how waveforms not generated by a function are created? It isn't like they are created by some algorithm used to approximate sound.
It always seemed to me that a waveform is something that can only be approximated. Unless it's generated by a function, that is (like a sine wave.) In music, the waveforms can only be approximated since the underlying sounds are very complex and chaotic.
The actual complexity of a waveform makes it a very fractal-like structure. As such, it might make more sense to assign a fractal dimensionality to waveforms, which probably lies somewhere between 1 and 2?Fractal-like? That's quite a leap.
I think --bitrate 12 --set-ctl-int 4008=1104 sounds slightly better than --bitrate 12.1. But the differences are subtle.
Excellent. Thank You.
Will try it later.
P.S. I couldn't find the way to try SWB at 12 kbps as I suspect it can perform better than WB (for speech).
Use 4008 instead of 4004.