I think it was two years ago just after New Year I received an email, the result of a "we're back at work, but wish we weren't" discussion.

we are having one of those discussions at work, debating if white & black are colours.
... In the spectrum, is white the result of a compound of all colours?
Is black the result of total absence of colour? Do actual colours (e.g. ink or paint) have the same properties as light, do then the colours white & black exist?

My first thought was "Wow, what a question!", and then I found the answer was even more rich than I had imagined.

First, the answers for white and black are a little different, so I'll note this when important. Also I found 'answers' at three levels: cultural/linguistic, physical and perceptual ... and the last has three aspects itself!! As with any question, however, the answering is as much a questioning of the question and the deep question it drives us back to is "what is colour?"

Culture and use

Wittgenstein basically says (which I don't completely believe, but let's stick with it) that we should not worry about looking for an objective meaning of a word - the word is defined by and in use - it is how it is used by people.

A woman walks into a clothes shop and says "I'm looking for an evening dress". The salesperson asks: "what colour were you thinking of?" Would white or black be valid answers?

I think so. But of course if you were an amateur photographer and someone asked you "do you take colour", then you would say "no" if you only took black and white ... So much for Wittgenstein.

Physics

One way to define colour would be via wavelength of light. A pure light of a given wavelength (like the strong sodium yellow) is a colour. This would include all the colours of the spectrum, rainbow or standard colour wheels. By this definition white and black would not be colours since white light is always a mix of wavelengths and black is none. However, this would then not include 'unsaturated' colours like pink. Pink is pure red mixed with white - there is no 'pink' wavelength. This 'spectrum' definition of colour is called 'hue' and is perhaps the closest we can come to a clear idea of colour at a physical level.

Physically at least one can see that black is special, being the absence of light. It is a 'coming together' point in that all 'colours' move to black as their intensity reduces. So black is at least (physically) unambiguously defined.

White is more difficult. It is always a mix, and in fact different mixes will all appear white. I'm not even sure whether a uniform mix of wavelengths will give you white - especially as there are two completely different meanings of uniform - do we mean equal numbers of photons, or equal energy in each frequency? I think it is close to the equal energy, but I'm not sure (more on this below).

Surface perception - the eye

Here we get closer. The reason we see colour at all is because we have eyes. Furthermore the reason that all colour systems have essentially three dimensions is because we have three kinds of colour sensor (called cones) in our eyes. Because of this it is possible to have a light source consisting of some pure red light and some pure green light and have it appear yellow, even though there is none of the wavelength for yellow in the light we see. This is rather like in music if we heard a C and G played as a chord, but heard the E between them (see www.hcibook.com/alan/papers/is-white-a-colour-2005/ for more about this).

We see a mix of red and green light as yellow simply because the combination 'excites' our three types of colour sensor in exactly the same way as the pure yellow light would. Two things look the same 'colour' (and here I will include black and white) if they excite the three sensors in the same way. Again black is easy - no sensor is excited at all! Hence wavelengths of 'light' outside the visual range (e.g. ultraviolet or infrared) appear black even though there are actually photons hitting the eye. White - well there is a particular mix of red, green and blue that 'looks' white, but equally well there are lots of mixes of wavelengths that look white.

Ecology - the sun

As I said, I'm not sure of the exact mix in terms of wavelengths that give white, whether it is a uniform mix or not. But actually we can understand white in terms of the sun. Basically, white is the 'average' of all the wavelengths that reach us from the sun. I say 'average', as if we look (as of course we shouldn't) at the sun it looks yellow, but this is because the blue light is scattered by the atmosphere reducing the direct blue light hitting us, but making the sky blue. The 'average' is white. This is sensible, our eyes record only the deviation from the average - the average itself is nothing - white.

I say this with confidence, but I've not done the accurate measurements myself. But I don't need to ... mother nature has helped out (she of the white lab coat). Snow and clouds scatter all light that hits them uniformly - blue from the sky and direct light from the sun, re-mixing them for us ... and they are ... white.

So, imagine an alien coming from another planet, with a sun of a different 'average' colour (say a bit more red). The aliens of course call things 'white' if they are the same average colour as their own sun. They look at a post box (UK) and say - "what a pure white box". You show them a white sheet of paper and they say "a little green, I prefer white paper myself".

So white is relative to where in the universe we find ourselves. It would therefore be xeno-species-ist to call white anything other than colour.
Black, however, is different. When faced with no light whatsoever (in either of our visible ranges) we could happily agree with our alien that it is black.

Deep perception - the brain

Well, that is almost the whole story.

However, there is a last twist - isn't there always? You may have seen before the way that if you put a patch of a colour on a background it will look different depending on the background's colour. If the background is strong red, then the colour will look more blue/green; if the background is blue, the colour will look more yellow.

The reason for this is that our eyes and brain between them are trying to adjust their sensors so that things look pretty much the same colour no matter whether it is near sunset with a largely red tinge, or the sun is behind a cloud so that the light is more blue from the sky.

You notice this if you take a photograph inside under an incandescent bulb. The colours appear 'natural', but in the photo everything has a yellow tinge. In fact the photograph is accurate, the things really did have the yellow tinge because of the yellow light, but our eyes have adjusted so that things 'look' right.

The same things happen with dark and light. The difference in the quantity of light hitting our eye in bright sunlight compared with a cloudy day, or inside, is many thousandfold. But things do not look that much darker inside unless you go quickly between the two. Our eyes again adjust.

Now imagine a TV screen when it is off. Depending on the screen it may be a dull grey, or perhaps slightly grey-green, colour. Now turn on the TV and imagine a person wearing a jet black jacket. Now the 'black' parts of the picture are just those places where the TV is showing no additional light ... that is the 'black' is the same colour as the TV screen when it is off ... a green/grey.

The effect is even more dramatic with a projector screen. It is white... Now take a slide with, say, a black cross extending across a white slide. Turn on the projector... You see the black cross. But the 'black' is simply the parts of the screen that are not illuminated by the projector. That is the same 'white' as the screen.

On a sunny day you drive down a road and are about to go under a wide bridge. It seems black underneath. But once you are under the shade of the bridge the colours appear - including the white snowdrops by the roadside. Even black is somewhat relative!

So, now you still don't know what colour is or black or white... but perhaps, if this is new to you, then you may know better that you don't know.

Strange that the more one knows, the more things are like this.

Paint on the page

The question also asked:

Does the same apply to light as to actual colours, e.g. paint?

The colours you see on a surface are the wavelengths it reflects. The rest of the colours are absorbed (slightly warming the surface) - so a red surface is one that absorbs light in the green/blue end of the spectrum (see diagrams on the web for a bit about why paint works the way it does (subtractive versus additive colour).

White paint (or a white coloured surface) is simply one that reflects all or most of the light hitting it and does so uniformly (does not favour any particular wavelengths). It may actually look red, green or black depending on what coloured light is hitting it, or no light at all. It is because the colour white reflects everything that white (or light coloured) fabrics are cooler in summer.

Black paint just absorbs everything (or nearly everything, you may get shining glare on a wet 'black' road). There is an interesting paradox in that things that absorb colours when they are shone on them tend to emit the absorbed colours when heated themselves.

This is why a black road gets hot - it absorbs all wavelengths. Conversely, radiators are black so that when hot they emit a lot of their energy. 'Modern' radiators are often metal painted white, but this is because they are primarily not radiators (radiating heat), but convectors (heating air in contact with them which then rises). In fact I think the old Victorian black radiators are mainly convectors as well, the Victorians just liked black.

And the aliens ...

Finally, back to the aliens ... show them a sheet of white paper on their own planet ... it reflects all colours evenly and so has (to your eyes) a red tinge, but they see "pure white". Of course if you look at the same sheet under our light you say "it is white" and they say "a bit greenish". So earthling white paint would count as white paint on our distant planet and also here.

The same would be true for black paint that would absorb all light on both planets and be perceived as equally black on each.
And, of course, the perceptual effects for black and white would also be true on the distant planet, so the grey paint on a white background might look black both on earth and Alpha Centauri.

Alan Dix 2/3/2005