Schrödinger's Kitten

Irreverent Science for Everyone

Tuesday 17 November 2009

Beyond Rainbow Country

  • quantum
  • pedantry
  • colour

Red and yellow and pink and green, orange and purple and blue...

As well as being a highly dull song, it's also incomplete and what it does include is wrong. If you can show me the location of pink in the rainbow, you can have a cookie.

However, if they're drivelling about colour in general, there's a deeper issue afoot. There are colours beyond "all the colours of the rainbow" and we rather like them.

What do we really mean by colour, anyway, man?

Philosophers, hippies, and other people with too much time and not enough quadratic equations to keep them on the straight and narrow often like to debate the nature of colour. Does it have existence outside of experience? Is my concept of 'red' the same as your concept of 'red'? What do we mean by 'red' anyway, man? And other such speculations.

This is of course an entirely solved problem for anyone who's studied light or indeed seen a filter. Colour is uniquely defined by knowing the wavelength (or frequency, depending on personal taste) of the light you're talking about1. Since both these are numbers, they shouldn't really be subject to debate (unless you're really stoned) or any other sophistry and illusion2 for that matter.

Over the rainbow

However. This elegant definition kind of falls down with certain colours that we can see, but nevertheless aren't in the spectrum. The ringleader of these for me is magenta. It's a perfectly good colour — I would love to have my hair that colour — but it's persistently uncategorisable and doesn't have an independent existence.

The colour wheel, which most people who went to their art classes are familiar with, wraps around on itself so violet (shortest wavelength, around 400nm) meets red (longest wavelength, around 700nm) by way of magenta (wavelength ... ? ).

Colour wheel

Where troubles melt like lemon drops

How do we handle this? Well, we could just say magenta is a 400nm wavelength and an 700nm wavelength hanging out together. That's true as far as it goes, but it does place some limitations on what magenta can do. A single photon of light can't have a wavelength of partly 400nm and partly 700nm (it could be a superposition of 400nm and 700nm but it would have to just be one or the other once it hit your retina, so you'd never know it had been superposited). That's what makes magenta different from the other colours — it can't be reduced to a single photon. It's a macroscopic phenomenomenomenon. Which puts it, I guess, firmly in the camp of all other human senses. But we can still describe magenta without waving our hands around and saying 'like' a lot: we just need to talk about the relative intensity of red light to violet.

It would be a sad, and unnecessarily psychedelic, world without colours like magenta. Extra-spectral colours, those that can't be found in the rainbow, include everything that's not at maximum saturation - that's pastels, browns, and general muted shades - as well as black and white. Bizarrely enough 'pure' red is also extra-spectral: a beam of light at 700nm looks less red than the same beam adulterated with a few shorter wavelengths.

Rainbow, Or Your Genius's Bloody Illuminati-esque Vagary

On the other hand, not everything that's in the oligarchy of the spectrum deserves to be there. All English-speaking schoolchildren are taught that there are seven colours in the rainbow: red, orange, yellow, green, blue, indigo, violet. In the 400 years since Isaac Newton came up with these classifications (for the English language — in Russian, for example, there is a much more reasonable division) noone, it seems, has questioned this.

But there's one that doesn't fit. Red, yellow and blue are the subtractive primaries: orange, green and violet their secondary colours (if we stretch violet a bit to cover purple; of course if we're using particularly vivid shades of red and blue then we're looking at magenta again). Indigo is nowhere near this class of colours. Indigo is a specific shade; it's an artist's colour, an interior designer's colour, a colour for people who drink from Pantone mugs. What, then, is indigo doing there in the canonical rainbow?

Short answer: making Isaac happy. Isaac Newton, big alchemist that he was, was out to find harmony and interrelationship in the world, to the everlasting glory of his Creator3. How sweet. In this case, when naming the colours he found in the spectrum, he was keen to make links to that other mystic discipline, music. Since there were 7 notes in the Western musical scale, Sir Isaac decided there must be 7 colours in the spectrum to match. The 6 obvious ones, and then an extra one, which he picked indigo for.

So the reason that every child has 'Richard Of York Gave Battle In Vain' embedded in their consciousness, as well as the sleeper agent Roy G. Biv lurking in their visual cortices, is a 17th century genius' idea of what's pretty. Now Newton did some really good stuff and all, but some of it was... kind of wrong. Mainly about the philosopher's stone, but I'd nominate indigo for that list too.

End Coloured Segregation Now

So what's so wonderful about the rainbow? Let's put extra-spectral colours on the map and end this artificial segregation. Sure, they're different from spectral colours - but they're no worse! In fact, as colours that we mix in our own head from the firing of our retinal cells, they should mean more to us than the staid old spectral colours that are generically available at outlets throughout the universe.

Show your support: start wearing magenta... or its sister, purple.

1. Assuming you're in the same reference frame, natch.

2. "When we run over our libraries [...] what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames; for it can contain nothing but sophistry and illusion." — David Hume, my main man when it comes to bigging up science and facts over frivolity. Not much fun at parties though.

3. To the extent that he was concerned about creating a universe that could run on its own without a creator. He carefully left room in his construction of a galaxy held together by gravity for god; in this case, god was responsible for holding the stars apart and keeping them from crashing in together (pile on!). A somewhat menial job, in my opinion, but at least it keeps Him off the streets.

Content: Scary Boots — Design: Canis Lupus