What? Well, I've been using Evernote to write down thoughts, but they're just to myself, and sometimes I want someone else to read them. You, specifically. I want you to read them.

There's a Youtube video of a podcast called "The Rest is Science" with Vsauce (the curiosity box guy) and Hannah Fry (the British everything to do with maths woman), called " Why Is It A Colour Wheel And Not A Line?" Here, I can probably make a link to it, right?

And it's interesting, but I think they sort of get to the "magenta isn't really a color" conclusion,and think I can describe the phenomenon in a way that is less glib and more enlightening. So I offer this thought: color is like music. Specifically, like hearing different notes. You want to read more, right?

Hm. This is where there's supposed to be a "click to read more...", and it's not working. I can't imagine Blogger has changed anything in the years since my last post...

Anyhoo...

Think about hearing an instrument play a note. What note it is is a musical way to describe its frequency: if the sound we hear is at 440Hz, it's an "A", higher notes are higher frequencies, lower notes are lower frequencies. So far, this is exactly like frequencies of light: we perceive red, a higher frequency is yellow, higher is green, etc. This is the "colo(u)r should be on a line" view.

But the sound of a trumpet playing an A, and a harmonica playing an A, and a piano playing an A, and a guitar playing an A, are all the same frequency but unquestionably different and we perceive those differences clearly -- if I asked you which was which just from the sound, you could do so with confidence. Why? Because your ear gets more information than just what the dominant frequency of a sound is. Your eardrum reacts on a complicated way to the air pressure changes hitting it, capturing lots of information for your neurons to process.

Separately, we can synthetically extract information out of an audio signal with a Fourier Transform, which lets us break a signal into component frequencies that represent the sound if it were decomposed into sine waves. This isn't exactly what your ear is doing, but we can observe with Fourier Transform that these different instruments have their own characteristics of which overtones (frequencies larger than the primary one that identifies the note) appear in the Fourier Transform, with what intensity profile. This "explains" how we can perceive the timbre of an instrument - we don't just hear one frequency, we hear the overtones too. The sound is more than just one sine wave at one frequency, we hear more of the complexity of the actual sound, and we recognize different instruments even though they play the same note. This sentence may seem a little obvious, so just remember that I put it in bold for some reason and keep reading.

A key part of music is playing different notes at the same time: careful constructions of several notes at the same times are chords, and they're what harmony is all about. The three notes of a major chord seem to blend together and produce a sound that seems other than the sum of its parts, even though that's really what it is. Our ear captures some of the complexity of the multi-note sound, and our brain registers it as its own thing, not "just" a mix of three notes, but as some special mix of those three notes. I think almost nobody thinks this is weird, or that our brain is tricking us into hearing something that isn't there. We can describe some interesting frequency relationships between the chords that sound nice and the collections of notes that sound like they have nothing to do with each other, so we shouldn't be surprised that our ear can pick up on that.

Getting back to color, I think the misstep is thinking "color" means "a frequency of light", when our eyes are taking in different information than that. We've got three types of color receptor "cones" in our eyes, which are collecting intensity measures centered on three different frequencies, red, green, and blue. So not unlike the color system for computer graphics, your eye is collecting, not a single frequency, not an average frequency, but three different values, like "this is very blue and a little green and a little less red" or more accurately, "the cones that trigger hard on a blue frequency are triggering hard, the cones that trigger hard on green are triggering a little, and the cones that trigger hard on red are triggering a little less than that."

If the information coming in is the same as we'd get from a single frequency of light, then we perceive that single frequency of light, just like if I play a sine wave, I hear that the note produced by that one frequency. But if the information is coming in is an interesting combination of the cone responses -- lots of red-triggering and blue-triggering, but not green-triggering, for example (but see below), then this is like a musical chord: the light is more than just one sine wave at one frequency, and we see more of the complexity of the actual light. It's not that magenta isn't real, it's that what we see as "color" isn't limited to what's on the linear spectrum of single frequencies, just like we aren't limited to just hearing single frequencies.

And I want to point out that there's no reason to assume that magenta is the only color that isn't on the spectrum - it's just the easiest to describe.

First, let me outline what happens when we see a single frequency of light. There's an orange-yellow, for example, with a frequency f that produces the same response from the red-cones and green-cones. It also produces a response in the blue-cones, but it's much lower. Suppose the intensity of light is such that the red-cones and green-cones is X. Then the blue-cone response Z is perfectly determined from the intensity and the blue-cone response curve to frequency f. In other words, every time we see a pure light of frequency f, with this given intensity, the information the eye sends to the brain will be red-cones X, green-cones X, blue-cones Z.

So every signal of red-cones X, green-cones X, blue-cones (anything but Z) describes a color that is not on the spectrum of single frequencies. This doesn't mean it's made up, or that our brain generates an illusory color: it means that we perceive something more complex than a single frequency, and our brains process that as a color that isn't equivalent to a single frequency, because it's smarter than that.

Color isn't "a frequency of light", but each single frequency of light has a color. It's just that combinations of multiple frequencies have their own color too, and we can tell the difference, just as we can tell the difference between a guitar and a piano, even if the primary frequency they're playing is the same.

I will just conclude by noting that we have analysis (splitting things into parts) going on, like recognizing that white light is made up of a bunch of different frequencies, and that each note is primarily a single frequency, along with synthesis - our ear or eye capturing more than one frequency and our brain putting the multifrequency information it gets into a perception different from the single frequency case.

Click here to return to Gnomicon home page