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I'm not sure why you say that sound has three dimensions -- for the most part we can treat sound as one-dimensional; just pressure at a point in space as a func

I'm not sure why you say that sound has three dimensions -- for the most part we can treat sound as one-dimensional; just pressure at a point in space as a function of time. For a complete analysis of sound we need more than that, but that just inherits from the fact that space is three-dimensional so for a complete analysis we need the three-dimensional spatial distribution of pressure. On a similar note, color is not fundamentally three-dimensional; that's a function of our eyes having three band-pass filters. Light itself is infinite dimensional; any function mapping frequency to intensity corresponds to a "color" of sorts. We can only perceive colors in terms of how they activate the three different sensor types (four including intensity).

sudosysgen 6y ago
Not really, no. The human perception of colour is fundamentally three-dimensional. In order to describe a perceived colour, no matter the system you choose, you need three dimensions. For example, you could use frequency and amplitude of a light wave, but that would only be sufficient for pure tones, leading to the need of a third dimension - saturation - for "impurity". Or you could use a B-L B-R pair for tone and a third component for Luma - three-dimensional. Or you can give the amplitude of Red, Green and Blue; three dimensions. You could add a fourth dimension, RGB+Luma, but the fourth dimension is useless in describing a given perceived colour, as the activation of the intensity receptor is a function of the activation of the three colour receptors, it is only there for high-gain situations. Sound is not one-dimensional, as simply considering the pressure of a point is insufficient as a description of sound perception of humans. Indeed, we perceive variations in pressure, not pressure itself (consider the balancing of the pressure of the inner ear). In order to understand sound, you fundamentally need two dimensions, either pressure and time, or frequency and amplitude. This is only for an instantaneous perception of sound, in order to record "a sound", you need three dimensions. Although you could indeed plot a time-series of pressures, this does not describe what actually is happening - for a time-series of pressures to be interpreted as a recorded sound you necessarily need a sample rate, otherwise the physical interpretations are infinite. This is why a spectrogram is three-dimensional - frequency, amplitude, and time. Hence, the sounds we operate on and process are three-dimensional, as any representation of a sound is tridimensional, either a time series of pressure, time and sample rate, or a continuous spectrum of time, frequency and amplitude.
- fsh 6y ago
  This is not how any of this works. Sound simply is a variation of pressure over time, hence a one-dimensional signal (in classical physics, time is not considered a dimension). Sampling is simply a way of approximating this continuous signal on a digital computer. A music instrument doesn't have a sample rate and neither have your ears.
  - sudosysgen 6y ago
    Your ears do have a sample rate. They are bandwidth limited, which is the same thing as having a sample rate. While in classical physics, time is not considered a dimension, if you what you want to do is encode a signal, or construct a mathematical model, time is very much a dimension.
    - fsh 6y ago
      Sorry, but this is completely wrong. Analog systems, such as human ears, can be band-limited but do not have a sample rate. In fact, any digital recording system requires analog lowpass-filtering to avoid aliasing. Otherwise, the original (analog) signal cannot be accurately reproduced from the samples. Of course you are free to use a different definition of "dimension" than the rest of the world. But this won't help making discussions any easier.
      - sudosysgen 6y ago
        A digital signal with a sample rate of 1000hz is an exact representation of an analog signal with a bandwidth of 500hz. The low-pass filter is just part of how you would build a DAC. If you want to use the physics definition of dimensions in a discussion about colourspaces that has nothing to do with physics jargon, that's ok. If you want to represent amplitude over time, you need two dimensions. There is no graphical representation of sound that can be done in less than two dimensions for this reason. If you want to graphically represent the human perception of sound, you need three dimensions, that correspond to frequency, amplitude and time.

sudosysgen 6y ago

Not really, no. The human perception of colour is fundamentally three-dimensional. In order to describe a perceived colour, no matter the system you choose, you need three dimensions. For example, you could use frequency and amplitude of a light wave, but that would only be sufficient for pure tones, leading to the need of a third dimension - saturation - for "impurity". Or you could use a B-L B-R pair for tone and a third component for Luma - three-dimensional. Or you can give the amplitude of Red, Green and Blue; three dimensions. You could add a fourth dimension, RGB+Luma, but the fourth dimension is useless in describing a given perceived colour, as the activation of the intensity receptor is a function of the activation of the three colour receptors, it is only there for high-gain situations. Sound is not one-dimensional, as simply considering the pressure of a point is insufficient as a description of sound perception of humans. Indeed, we perceive variations in pressure, not pressure itself (consider the balancing of the pressure of the inner ear). In order to understand sound, you fundamentally need two dimensions, either pressure and time, or frequency and amplitude. This is only for an instantaneous perception of sound, in order to record "a sound", you need three dimensions. Although you could indeed plot a time-series of pressures, this does not describe what actually is happening - for a time-series of pressures to be interpreted as a recorded sound you necessarily need a sample rate, otherwise the physical interpretations are infinite. This is why a spectrogram is three-dimensional - frequency, amplitude, and time. Hence, the sounds we operate on and process are three-dimensional, as any representation of a sound is tridimensional, either a time series of pressure, time and sample rate, or a continuous spectrum of time, frequency and amplitude.

fsh 6y ago
This is not how any of this works. Sound simply is a variation of pressure over time, hence a one-dimensional signal (in classical physics, time is not considered a dimension). Sampling is simply a way of approximating this continuous signal on a digital computer. A music instrument doesn't have a sample rate and neither have your ears.
- sudosysgen 6y ago
  Your ears do have a sample rate. They are bandwidth limited, which is the same thing as having a sample rate. While in classical physics, time is not considered a dimension, if you what you want to do is encode a signal, or construct a mathematical model, time is very much a dimension.
  - fsh 6y ago
    Sorry, but this is completely wrong. Analog systems, such as human ears, can be band-limited but do not have a sample rate. In fact, any digital recording system requires analog lowpass-filtering to avoid aliasing. Otherwise, the original (analog) signal cannot be accurately reproduced from the samples. Of course you are free to use a different definition of "dimension" than the rest of the world. But this won't help making discussions any easier.
    - sudosysgen 6y ago
      A digital signal with a sample rate of 1000hz is an exact representation of an analog signal with a bandwidth of 500hz. The low-pass filter is just part of how you would build a DAC. If you want to use the physics definition of dimensions in a discussion about colourspaces that has nothing to do with physics jargon, that's ok. If you want to represent amplitude over time, you need two dimensions. There is no graphical representation of sound that can be done in less than two dimensions for this reason. If you want to graphically represent the human perception of sound, you need three dimensions, that correspond to frequency, amplitude and time.