To answer you actual question since my other response completely missed your point, I don’t know if it’s actually possible to properly describe light and color as a one dimensional signal.
I think we need at least two dimensions to describe it properly. Frequency and amplitude. Amplitude is needed to describe how intense/bright the light is and frequency describes what color the light is. Technically there is also polarization which could be thought of as another necessary dimension.
We could likely simplify it just down to the frequency and consider amplitude and polarization to be constants.
But since color is a really a property of the specific kind eye we talk about, and not universal truth, we get kind of stuck on how we could explain it to aliens which possibly have very different eyes or don’t even have eyes at all.
We have to accept that colour is a pretty subjective thing and not a universal truth.
The idea of frequency (vibration) itself though is very likely a universal concept that would be well understood by any human like intelligence in the universe. So we have something to work with.
We can maybe explain how OUR eyes work pretty well just by using frequency alone (just one dimension).
To explain this to an alien with no eyes, the best analogy would be one based on a sense they might have, such as hearing. We could describe the different colors as different pitches of a sound. Just as our ears perceive a low-frequency sound as a low pitch (like a bass drum) and a high-frequency sound as a high pitch (like a piccolo), the different frequencies of light waves correspond to different colors.
Red light has the lowest frequency of the three. Its frequency is approximately in the range of 400 to 484 THz. This corresponds to a wavelength range of about 620 to 750 nanometers (nm).
Green light falls in the middle of the visible spectrum, between red and blue. Its frequency is approximately in the range of 530 to 600 THz. This corresponds to a wavelength range of about 500 to 565 nm.
Blue light has a higher frequency and shorter wavelength than both red and green. Its frequency is approximately in the range of 620 to 670 THz. This corresponds to a wavelength range of about 450 to 485 nm.
We could put this in a neat one dimensional table:
400 - 484 THz,
530 - 600 THz,
620 - 670 THz,
We could of course encode this data into binary (ones and zeros).
What it really all comes down to is that the universe is full of things vibrating (slight over simplification, photons oscillate not vibrate) at different frequencies and amplitudes. We have organs that turn vibrating air molecules into sound and we have organs that turn vibrating photons into vision.
Living things often develop organs that let them turn these abstract vibrations into useful inputs that their brains can do stuff with. Things like color and sound are really more a property of biology than physics/math. So explaining them in terms of pure physics/math is pretty challenging.
Hope that was a kind of interesting answer at least.
To answer you actual question since my other response completely missed your point, I don’t know if it’s actually possible to properly describe light and color as a one dimensional signal.
I think we need at least two dimensions to describe it properly. Frequency and amplitude. Amplitude is needed to describe how intense/bright the light is and frequency describes what color the light is. Technically there is also polarization which could be thought of as another necessary dimension.
We could likely simplify it just down to the frequency and consider amplitude and polarization to be constants.
But since color is a really a property of the specific kind eye we talk about, and not universal truth, we get kind of stuck on how we could explain it to aliens which possibly have very different eyes or don’t even have eyes at all.
We have to accept that colour is a pretty subjective thing and not a universal truth.
The idea of frequency (vibration) itself though is very likely a universal concept that would be well understood by any human like intelligence in the universe. So we have something to work with.
We can maybe explain how OUR eyes work pretty well just by using frequency alone (just one dimension).
To explain this to an alien with no eyes, the best analogy would be one based on a sense they might have, such as hearing. We could describe the different colors as different pitches of a sound. Just as our ears perceive a low-frequency sound as a low pitch (like a bass drum) and a high-frequency sound as a high pitch (like a piccolo), the different frequencies of light waves correspond to different colors.
Red light has the lowest frequency of the three. Its frequency is approximately in the range of 400 to 484 THz. This corresponds to a wavelength range of about 620 to 750 nanometers (nm).
Green light falls in the middle of the visible spectrum, between red and blue. Its frequency is approximately in the range of 530 to 600 THz. This corresponds to a wavelength range of about 500 to 565 nm.
Blue light has a higher frequency and shorter wavelength than both red and green. Its frequency is approximately in the range of 620 to 670 THz. This corresponds to a wavelength range of about 450 to 485 nm.
We could put this in a neat one dimensional table:
We could of course encode this data into binary (ones and zeros).
What it really all comes down to is that the universe is full of things vibrating (slight over simplification, photons oscillate not vibrate) at different frequencies and amplitudes. We have organs that turn vibrating air molecules into sound and we have organs that turn vibrating photons into vision.
Living things often develop organs that let them turn these abstract vibrations into useful inputs that their brains can do stuff with. Things like color and sound are really more a property of biology than physics/math. So explaining them in terms of pure physics/math is pretty challenging.
Hope that was a kind of interesting answer at least.