6 ms·

It's kinda interesting that color, sound, and space all have three dimensions. What are some other fundamental three-dimensional things?

jmole 6y ago
Color doesn't have 3 dimensions, humans have 3 types of color receptors (and 1 type of broadband receptor). Spacetime has 4 dimensions. Sound can have as many "dimensions" as you care to analyze, but physically you have pressure & velocity embedded in a spacetime continuum. I think the fundamental three-dimensional thing is that we're all mostly limited to reasoning about three-dimensional objects in a three-dimensional world.
- dylan604 6y ago
  For video, a vectorscope is a way used to view the color of the video signal.[0] While it looks like a circular view, it is actually representing a sphere. QED color has 3 dimenisions [0]https://en.wikipedia.org/wiki/Vectorscope https://en.wikipedia.org/wiki/Vectorscope
  - andrewla 6y ago
    A video signal contains the assumption that color can be represented by three parameters. But those three parameters are not capable of expressing the complete gamut of visible colors. It's just close enough that there's really no point in pursuing it further.
    - sudosysgen 6y ago
      There is no biological basis for a fourth dimension of colour perception in humans. It is true that in practice we are unable to replicate the colours we can perceive. But it is possible to create a colourspace that completely contains the gamut of perceivable colours using only three dimensions.
  - slavik81 6y ago
    Our video technology is designed to capture and reproduce what humans can see. If all humans were red-green colourblind, we would only have designed our videos to capture green-blue images, and our TVs would only output green-blue images. To us, they would look like perfect reproductions of the world. In that world, you would be arguing there are only two colours. Yet, the image on those green-blue TVs would obviously not be an accurate reproduction if viewed by a person with normal RGB colour vision from our world. Similarly, compared to Geordi La Forge, we are all colourblind. He can distinguish thousands of different wavelengths of light independently, and to him our current RGB videos look nothing like the reality they attempt to depict, due to all the colours they throw away.
- sudosysgen 6y ago
  Colour does have three dimensions, though. You cannot describe human colour perception without three dimensions - frequency and magnitude is sufficient for pure waves, but saturation is needed to match colour perception of the impurity of a given tone. So colour as perceived by humans is indeed three-dimensional.
  - andrewla 6y ago
    Human color perception is three-ish-dimensional I think would be more accurate. There are no three colors that can be mixed to produce the whole gamut of colors that humans can perceive. That is, there are shades that are visibly distinct that can not be produced by the closest pigments we have to primary cyan/magenta/yellow, and similar cannot be produced by mixing of monochromatic light. Our perception is a window into the infinite dimensional space of frequency/intensity that can be very well-described by three parameters, but that is not adequate to completely describe colors even as perceived by humans.
    - sudosysgen 6y ago
      While you cannot produce all colours humans can perceive using a mix of monochromatic light (indeed, some perceivable colours are entirely impossible to be perceived without afterimages), the colourspace of human colour perception is entirely three-dimensional. This is, fundamentally, because we have three types of receptors. Pigment maps into our perception of colour are possible in theory, but it is impossible to make an ideal pigment in practice nor an ideal substrate, which is why you see the issues you do when trying to produce them in practice.
    - 6gvONxR4sf7o 6y ago
      Not only that, some people have four receptors.
  - jcranmer 6y ago
    Modern color perception theory is actually way more than 3-dimensional. That's because human perception of color isn't driven by the absolute amount of light hitting our various color receptor cells, but by the relative amounts we see in the various parts of the image, and white balance and fatigue enters the perception as well.
- BurningFrog 6y ago
  One important fact is that we hear sound frequencies MUCH better than we see light frequencies. With sound, what we hear is pretty much all the frequency information within our range. With light, the huge frequency complexity gets reduced down to our three base colors. This is why a certain "color" can be produced with an uncountable number of frequency combinations.
  - layer8 6y ago
    Part of the reason may be that the visible light spectrum only covers one "octave".
    - OscarCunningham 6y ago
      Also, if we had more types of cones then each type would have to be more spread out over the retina, so we would lose resolution. In some sense the eyes and ears are at opposite ends of a spectrum. The eyes give you lots of information about the direction light is coming from, but barely any information about its spectrum (only three types of cone), whereas the ears give you lots of information about sound's frequency spectrum, but barely any information about its direction (only two ears). Come to think of it, this could be phrased as a tradeoff between resolution in position and resolution in frequency. It's the uncertainty principle!
      - BurningFrog 6y ago
        That actually clarifies things for me. Thanks!
- andi999 6y ago
  Quite a number of humans are tetrachromat:https://en.wikipedia.org/wiki/Tetrachromacy https://en.wikipedia.org/wiki/Tetrachromacy
andrewla 6y ago
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.
6gvONxR4sf7o 6y ago
Color is infinite dimensional. Imagine you shine four lasers each with wavelengths of 100, 200, 300, and 400 nanometers. We might see them smushed together into a combination that's 3 dimensional (unless you're a tetrachromat, a rare person who has extra rods or cones or something), but physically it's just the four frequencies (and phases). You can't combine the first 100, 200, 300nm laser beams to get a 400nm beam, so it's not three dimensional. With N lasers, it's N frequencies, and you can't reproduce them as combinations of fewer frequencies. N goes arbitrarily high. Follow that logic and the dimension of color space is the dimension of the space of frequency distributions, which is infinite dimensional. Likewise with sound, unless you want to describe it as just the amplitude at a single spatial point versus time, in with case sound and color are just 1D (plus time), which isn't a useful model since you now have to account for all spatial points.
- sudosysgen 6y ago
  Colour can't be described as 1D, as you can have multiple amplitudes of different frequencies at once. You could have an infinite amount of points of differing amplitudes, but this conception breaks down because of the reality of limited bandwidth, and so the best representation is a frequency-space. If you want, here is something you can do. Get a square, inside of that square plot the x axis for frequency, and the y axis for time. For every frequency x, at every time y, choose a luminosity level going from 0 from null amplitude to 1 corresponding to the entire amount of energy in the observable universe. That square will be able to represent perfectly colour over time, what you claim is "infinite dimensional", in a three-dimensional space.
  - 6gvONxR4sf7o 6y ago
    Here's a counter argument against what you just said for N dimensions, in almost exactly your words. Get a square, inside of that square, plot the x axis for dimension, and the y axis for time (the x axis is discrete, taking values of 1, 2, 3, ... up to N). For every dimension x, at every time y, choose a luminosity level going from 0 from null amplitude to 1 corresponding to the entire amount of energy in the observable universe. That square will be able to represent perfectly ND position over time, which I claim is N dimensional (plus time), in a three dimensional space. Much more simply, you can represent an Nd point in 2d, with the first dimension indexing dimension, and the second dimension indexing value. The 2D representation isn't the space. It's a single point in the space, which can vary along some number of degrees of freedom (N in this case). If that first dimension of the two (the index dimension) was continuous, and the second still represents value, then we're representing the set of 1D functions, which is infinite dimensional. That's how we represent a frequency distribution.
captaincrowbar 6y ago
"Colour has three dimensions" is a fact about human anatomy, not physics.

jmole 6y ago

Color doesn't have 3 dimensions, humans have 3 types of color receptors (and 1 type of broadband receptor). Spacetime has 4 dimensions. Sound can have as many "dimensions" as you care to analyze, but physically you have pressure & velocity embedded in a spacetime continuum. I think the fundamental three-dimensional thing is that we're all mostly limited to reasoning about three-dimensional objects in a three-dimensional world.

dylan604 6y ago
For video, a vectorscope is a way used to view the color of the video signal.[0] While it looks like a circular view, it is actually representing a sphere. QED color has 3 dimenisions [0]https://en.wikipedia.org/wiki/Vectorscope https://en.wikipedia.org/wiki/Vectorscope
- andrewla 6y ago
  A video signal contains the assumption that color can be represented by three parameters. But those three parameters are not capable of expressing the complete gamut of visible colors. It's just close enough that there's really no point in pursuing it further.
  - sudosysgen 6y ago
    There is no biological basis for a fourth dimension of colour perception in humans. It is true that in practice we are unable to replicate the colours we can perceive. But it is possible to create a colourspace that completely contains the gamut of perceivable colours using only three dimensions.
- slavik81 6y ago
  Our video technology is designed to capture and reproduce what humans can see. If all humans were red-green colourblind, we would only have designed our videos to capture green-blue images, and our TVs would only output green-blue images. To us, they would look like perfect reproductions of the world. In that world, you would be arguing there are only two colours. Yet, the image on those green-blue TVs would obviously not be an accurate reproduction if viewed by a person with normal RGB colour vision from our world. Similarly, compared to Geordi La Forge, we are all colourblind. He can distinguish thousands of different wavelengths of light independently, and to him our current RGB videos look nothing like the reality they attempt to depict, due to all the colours they throw away.
sudosysgen 6y ago
Colour does have three dimensions, though. You cannot describe human colour perception without three dimensions - frequency and magnitude is sufficient for pure waves, but saturation is needed to match colour perception of the impurity of a given tone. So colour as perceived by humans is indeed three-dimensional.
- andrewla 6y ago
  Human color perception is three-ish-dimensional I think would be more accurate. There are no three colors that can be mixed to produce the whole gamut of colors that humans can perceive. That is, there are shades that are visibly distinct that can not be produced by the closest pigments we have to primary cyan/magenta/yellow, and similar cannot be produced by mixing of monochromatic light. Our perception is a window into the infinite dimensional space of frequency/intensity that can be very well-described by three parameters, but that is not adequate to completely describe colors even as perceived by humans.
  - sudosysgen 6y ago
    While you cannot produce all colours humans can perceive using a mix of monochromatic light (indeed, some perceivable colours are entirely impossible to be perceived without afterimages), the colourspace of human colour perception is entirely three-dimensional. This is, fundamentally, because we have three types of receptors. Pigment maps into our perception of colour are possible in theory, but it is impossible to make an ideal pigment in practice nor an ideal substrate, which is why you see the issues you do when trying to produce them in practice.
  - 6gvONxR4sf7o 6y ago
    Not only that, some people have four receptors.
- jcranmer 6y ago
  Modern color perception theory is actually way more than 3-dimensional. That's because human perception of color isn't driven by the absolute amount of light hitting our various color receptor cells, but by the relative amounts we see in the various parts of the image, and white balance and fatigue enters the perception as well.
BurningFrog 6y ago
One important fact is that we hear sound frequencies MUCH better than we see light frequencies. With sound, what we hear is pretty much all the frequency information within our range. With light, the huge frequency complexity gets reduced down to our three base colors. This is why a certain "color" can be produced with an uncountable number of frequency combinations.
- layer8 6y ago
  Part of the reason may be that the visible light spectrum only covers one "octave".
  - OscarCunningham 6y ago
    Also, if we had more types of cones then each type would have to be more spread out over the retina, so we would lose resolution. In some sense the eyes and ears are at opposite ends of a spectrum. The eyes give you lots of information about the direction light is coming from, but barely any information about its spectrum (only three types of cone), whereas the ears give you lots of information about sound's frequency spectrum, but barely any information about its direction (only two ears). Come to think of it, this could be phrased as a tradeoff between resolution in position and resolution in frequency. It's the uncertainty principle!
    - BurningFrog 6y ago
      That actually clarifies things for me. Thanks!
andi999 6y ago
Quite a number of humans are tetrachromat:https://en.wikipedia.org/wiki/Tetrachromacy https://en.wikipedia.org/wiki/Tetrachromacy

andrewla 6y ago

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.

6gvONxR4sf7o 6y ago

Color is infinite dimensional. Imagine you shine four lasers each with wavelengths of 100, 200, 300, and 400 nanometers. We might see them smushed together into a combination that's 3 dimensional (unless you're a tetrachromat, a rare person who has extra rods or cones or something), but physically it's just the four frequencies (and phases). You can't combine the first 100, 200, 300nm laser beams to get a 400nm beam, so it's not three dimensional. With N lasers, it's N frequencies, and you can't reproduce them as combinations of fewer frequencies. N goes arbitrarily high. Follow that logic and the dimension of color space is the dimension of the space of frequency distributions, which is infinite dimensional. Likewise with sound, unless you want to describe it as just the amplitude at a single spatial point versus time, in with case sound and color are just 1D (plus time), which isn't a useful model since you now have to account for all spatial points.

sudosysgen 6y ago
Colour can't be described as 1D, as you can have multiple amplitudes of different frequencies at once. You could have an infinite amount of points of differing amplitudes, but this conception breaks down because of the reality of limited bandwidth, and so the best representation is a frequency-space. If you want, here is something you can do. Get a square, inside of that square plot the x axis for frequency, and the y axis for time. For every frequency x, at every time y, choose a luminosity level going from 0 from null amplitude to 1 corresponding to the entire amount of energy in the observable universe. That square will be able to represent perfectly colour over time, what you claim is "infinite dimensional", in a three-dimensional space.
- 6gvONxR4sf7o 6y ago
  Here's a counter argument against what you just said for N dimensions, in almost exactly your words. Get a square, inside of that square, plot the x axis for dimension, and the y axis for time (the x axis is discrete, taking values of 1, 2, 3, ... up to N). For every dimension x, at every time y, choose a luminosity level going from 0 from null amplitude to 1 corresponding to the entire amount of energy in the observable universe. That square will be able to represent perfectly ND position over time, which I claim is N dimensional (plus time), in a three dimensional space. Much more simply, you can represent an Nd point in 2d, with the first dimension indexing dimension, and the second dimension indexing value. The 2D representation isn't the space. It's a single point in the space, which can vary along some number of degrees of freedom (N in this case). If that first dimension of the two (the index dimension) was continuous, and the second still represents value, then we're representing the set of 1D functions, which is infinite dimensional. That's how we represent a frequency distribution.

captaincrowbar 6y ago

"Colour has three dimensions" is a fact about human anatomy, not physics.