Tuesday, March 11, 2014

Math anxiety: Additive and subtractive colours




Math was never my strong suit. I went as far as an elective pre-Grade 12 summer school course in Advanced Algebra, taken solely because two of my active crushes were math brains who thought it would be fun. When I heard the term "imaginary numbers," I was hopeful these would be something you could dress in costumes and write your own scripts for. When this turned out not to be so, my eyes glazed over.

Fast forward to my art studies and my current year's goals. At this stage in my self-study -- after ten years, I sometimes pretend I'm working on my "home-grown MFA" -- I decided I should complement my learn-by-doing approach with some formal knowledge. One area for study has been colour theory, and I started off by replicating the familiar colour wheel.


Almost everyone is at least vaguely familiar with this concept and the primary colours red, yellow and blue that combined in pairs make orange, green and purple. But that's only the half of it. Or the third, really. This is something I learned, with math-induced knots in my stomach, as I bumped into additive and subtractive colours. Huh?

In addition to the colour wheel system of artist's pigments, there's a system describing the interaction of coloured lights, such as stage lighting -- colours that are called "additive." There's also the world of transparent dyes, such as those used in printing and photographic processing -- a group of colours called "subtractive" -- or in my own terminology, Subtractive One. The colours and colour relationships in these alternate universes are, at first glance, so bizarre that I decided I needed some "pneumonic devices" (as someone I once worked with would have said) to help me get a fix on them. Then I had so much fun with this project I decided to share it.

Abacus ready?

The terms "additive" and "subtractive" in themselves make little sense to me, even after they're defined. To remember that additive colours = coloured light, I hold in mind an ad (get it?) for a theatre performance:



Now follow closely: With coloured light, the primary colours are red, green and blue-violet. Once you've accepted this (it took me several weeks), consider that each pair will produce one of the secondary colours: yellow, magenta, or cyan (a zesty turquoise tone). Red and green combine to make yellow. Red and blue-violet combine to make magenta. Green and blue-violet combine to make cyan. I know. Mind-boggling.

So here's my nifty pneumonic cheat sheet, with small fruit icons (sorry about the cyan-coloured lime -- closest I could come -- and as for the relationship between fruit and theatre performances.....?) for the colours, their relationships, and the stunning information that, when combined, these colours produce "white light" ...since all colours are reflected and none absorbed by the surface they're directed to.


On to Subtractive One, as I call it:-- The transparent dyes of print processing consist of the primary colours magenta, cyan and yellow, and the secondary colours red, blue, green. Magenta and cyan combined produce blue. Magenta and yellow combined make red. Cyan and yellow combined make green. Tricky, eh? Take a deep breath and browse through my colourful cheat sheet of "open book" icons and note the punch line: When combined, these colours produce black ...since all colours are absorbed and none are reflected.


Just think: You are now empowered to make a little sense of the small coloured test swatches that you'll find somewhere on virtually any printed packaging or publication.


Full circle now -- back to the original colour wheel and artist's pigments. These colours are also subtractive (aka Subtractive Two), since theoretically all the colours combined, as with Subtractive One, make black -- and for the same reason that all colours are absorbed and none reflected. This is the familiar territory of oft-quoted but rarely accurate maxims such as "Blue and yellow make green." The thing is that artist's pigments are mostly opaque so they don't behave like Subtractive One. And a "green" colour can be produced from various different "blue" and "yellow" colours because different chemicals can produce similar colours. In practice, blue and yellow are as likely to make mud as to make green -- one reason why there are literally hundreds of manufactured artist's pigments from dozens of manufacturers.

Here's a riff on the typical colour wheel, produced with all the tube colours I have on hand.


It's really rather absorbing, to the likes of me anyway. But without all this technicality, let's consider colour another way, as expressed by the artist Wolf Kahn. His paintings seem to have almost all the same subject -- the vertical tree trunks of a dense wood -- but each varies with his astonishing colour choices. He says:

(Because one)..."is more alert to the possibilities of color, all sorts of other possibilities go along with that:-- the possibilities of greater affection for all things, greater tenderness toward the world at large, greater generosity in life generally....If you are an artist in any kind of way, what you are really driving toward is to become a deeper person." -Artist Wolf Kahn

And a further note about something that's made my life more colourful: As it happens, I snagged a math brain after all. Little did I know 43 years ago that the love of my life would find it a pleasant recreation to get out pencil and paper and work on quadratic equations.