The Friday Fillip: Hues Kidding
Pantone. Pan – tone. All the colours. This is quite a boast and it puts me in mind of the claim by a friend a long, long time ago that his collection of the then new tape cassettes formed, in his words, “the total library of recorded sound.”
How many colours are there?
This is one of those questions that have no answers and far too many answers. On one of its web pages, Pantone, a commercial system for matching colours in printing ink and in paint, claims a measly 2096. “Measly” because logic suggests that there is an infinity of possible colours. Or is there? My head starts to ache at this point, as I hear its forebrain say to me such things as: “A colour is produced by a wavelength of light. Anything that has a length must move from measurement one to measurement two in a discrete fashion. This suggests that we’re not dealing with an immeasurable smear of colour change but rather a finite . . . ” And I give up because it’s bound to turn out to be a case of things too small even to think about, stuff at the sub sub sub atomic level of quanta where analog runs into digital and they both plotz.
Let’s retreat to unity, before all this regression makes you mean. There is a single colour, one colour: the colour of the year. Pantone declares it . . . well, annually, a few weeks before the inauguration. Next year, 2015, the colour is Marsala (Pantone 18-1438):
According to the director of Pantone’s Color Institute:
Marsala enriches our mind, body and soul, exuding confidence and stability. Marsala is a subtly seductive shade, one that draws us in to its embracing warmth.
(This sounds like the colour the legal profession should adopt posthaste. No?)
Or, if one is too lonely a number, I’ve another way to get you calmed and yet contemplating a great variety of colours — that is, if you’re game. And I know you are because you’ve got skin in the game. Angélica Dass has a glorious “work in progress” on her Tumblr Humanæ. Her aim is to document all the skin colours in her native Brazil, and indeed elsewhere I think, giving each human hue its proper Pantone number. Here’s a mere strip of the many beautiful people who have volunteered to be exemplars in her taxonomy, each placed against a background that is the colour of their skin:
Click on image to enlarge.
(What a pleasure it is to scroll through the gathering of faces, to see oneself reflected again and again and again.)
Now, Pantone is a commercial enterprise. You have to pay to get the best out of their colour matching service. But the web has thrown up other systems, free systems for identifying and reproducing colour. There’s one that you don’t have to be specially tech-adept to use. It’s fun to play with and a whole lot neater than klarting about in paints (though rather less viscerally satisfying). Putting aside the problem of how making colours by mixing light isn’t the same thing as making colours by mixing inks, you might find it useful, among other things, for carrying an ideal colour via your cellphone all the way from your wall to the paint store. The system uses base 16. Everybody on board with that?
You don’t need to do the math. You just need to know that the count starts at 0 and once it gets to nine it then goes on to A, B, C, D and E. This is hexadecimal counting, or simply “hex.” Each colour is represented as an amalgam of a particular shade of red, green, and blue; and each shade of each “primary” colours is identified by a pair of hex numbers — 55 or 5F or DD, for example. Marsala — remember the colour of next year? — is most closely reproduced as AD655F, for instance. This system yields something like more than sixteen million possible colours, or so I’m told, though your computer might only be able to display a mere eight million plus. Which is enough to be going on with, I’ve found.
Okay, so how do you operate this “Freetone” system? The simplest way for most of us is to use one of the smart web pages set up to render colour from our inputs. I recommend the W3 Color Picker. It lets you fashion a colour by putting in the hex number or by working your way down the spectrum after having plumped for a starting hue on the colour map. Just to be helpful, I’ve landed you on Marsala with the link above.
I’ve taken up enough of your time, even for a fillip. And if money is time, so is colour. Now that you know about the RGB hex system, you can appreciate the strange clock that tells you the colour. Double digit hour, double digit minute, double digit second = colour. Sadly, only the base ten portion of the hex range is useful in this exercise — and the clock will never strike AD:65:5F for more than one reason. So, thankfully perhaps, your screen will never glow Marsala using this web app.
For some of us, Marsala is a wonderful dusty town on the southern coast of Sicily, which produces a lovely range of extraordinary wines – most of which don’t get into Canada, outside Alberta. Amazing colour tones, deep dried fruit flavours. Where would zabaglione be without its perfume and magic. And we can argue indefinitely about whether the word is Sicilian for boiled milk or Dalmatian for beer. Savour its flavour anyway.
The answer is roughly 1.92×10^28. That’s how many colours there are. Just divide the width of the visible spectrum (300nm) by the Planck length (1.6×10^-35). For reference, that is fewer colours than there are kilograms in our Sun, but more colours than there are stars in the universe.
John, that would be how many wavelengths in the visible spectrum. However the number of colours differs.
A colour can be a combination of two or more wavelengths (something from the blue side of the visual spectrum and something from the red side resulting in a purple appearance for example).
So, with a start of 1.92×10^28 discrete wavelengths we would then need to multiply by the number of potential combinations between those wavelengths (1.92×10^28 x 1.92×10^28). However, that’s if we’re only dealing with 2 photon systems. When we start getting to 3 photon combinations, 4 photons onwards to 1.92×10^28 number of systems, we Still a limited number, in that there’s only 1.92×10^28 numbers to play around with, but far more combinations than there are stars (or to put it another way, you could have unique combinations being presented to a person as fast as they could perceive it for their entire life, and you could probably do the same thing with every other person, without having any duplicate combinations between people.
Only that still doesn’t cover the full possibilities. The ratio between the photons matters as well (10 photons of red light to one of blue produces a different impact than 10 photons of blue light to one of red). So we need to consider all the potential ratios between different combinations of different wavelengths. These should approach infinity, in that any combination of number and wavelength could be used, and while the wavelengths are finite, numbers are not. (although practically the number of photons of any wavelength that can be generated in a finite universe is of course finite).
And on top of this, the ‘visible’ light spectrum can be influenced by areas of the near visible (infrared light looks ‘warmer’ (think fireplace), UV light looks ‘brighter’ (think sunny day, or newly died tea shirts) which further impacts the number of colours available.
What brings this number down to something more manageable is that these individual photons need to be registered by our brains in order to produce the perception of colour. So, while there might be an infinite combination of photons of light, our eyes+brains are probably limited to a set number of colours. At a certain point, your eye or brain is unable to distinguish variations between the photons or their ratio.
(For example, discrete wavelengths of lights with similar energy levels will excite the same photo-receptor, which would create the same electrical signal to the brain).
Similarly our ability to detect ratios is dependent on how many photoreceptor are present, how fast they can signal individually, how fast the retina can send separate signals to the brain, and how fast our brain can process signals.
Consequently, the number of colours that can be perceived comes down to a number probably around the 16 million or so mentioned by Simon.
However, the fun part is that each of us probably perceives most of those 16 million colours slightly differently than everyone else, and not everyone has the same range of colours (beyond colour blindness and blindness, there is also numerous variations in sensitivity to certain wavelengths and numbers of photoreceptors).
I agree with you James. To everybody else: I retract my earlier estimate and apologize for it completely.
See? See? I told you heads would hurt if this continued. I’m only glad it ended just short of tears.
Thanks James and John, and all my admiration for being able to think in this wonderful way. I wish that Emil H. J. Rintleman, who taught me highschool math, had been even only 1 x 10^1 better as a teacher.
So, just to be clear, it’s still more stars than there are in the universe? Because, I quite liked that bit. : )