A Pigment of the Imagination

The Indefinite Article

With this edition of the column, I will leave you with some puzzles. These puzzles all have a connection with the world of computer science, but they all have applications closer to home. I have correct answers for the first two, but I do not have a good answer for the third. All contributions gratefully accepted! As always, please send your answers via the Web site feedback page.

The Enigma

Firstly, a simple exercise in coding. The basis for most computer storage and transmission of data uses a system known as "ASCII". This acronym, pronounced "ass-key", stands for the American Standard Code for Information Interchange. In its simplest common form, it uses a system of seven "bits" of binary information. These bits may be represented by the polarity of magnetic particles on a disk, or pulses on a transmission line. I can remember a time when data was stored on paper tape, and each bit was represented by a hole (or absence of a hole) in a strip of paper. Each symbol was represented by a row of seven dots across the tape. In this system, there are thus 27 possible characters, which gives 128.

This is a generous amount; it provides sufficient possibilities for both upper- and lower-case alphabetic characters, the digits zero to nine and the space character. This uses 63 characters. The remainder of the codes then provide 32 punctuation characters, and 33 control characters. These control characters are important; they provide special characters required by the data transmission techniques in use when the system was developed - codes for "start of text", "acknowledge", etc. They also provide for display or printing control - carriage return, line feed, etc. There was even a code to ring a bell on the terminal.

An earlier form of communication was telegraph. This system used a 5-bit code, known as "Baudot" code - five holes on paper tape. In this system, there are 25 possible characters, or 32. This system used upper case only, but here's the puzzle - 26 letters plus 10 digits requires 36 characters. How does this happen with a code with only 32 possible elements? Yet, Baudot code also provided a number of control and punctuation characters in addition to these 36, including a bell code and a space. How was it done? (Remember, this was an old code; we are all much smarter now!)

Form a Queue

You know the story. You go to a bank at lunchtime, and there are fifteen people in the queue in front of you, and three tellers serving. The queue seems to get longer rather than shorter. It's times like these that you start to wonder about how queuing theory actually works. (If you're a Mensan, maybe.) Queuing theory is a fundamental element of data communications. The basic variables in queuing theory are the average queue arrival rate, A, and the average queue service time, S. (We'll choose these names for now, anyway.) To keep it simple, we will have a single queue only, with a single teller. Both these figures are measured on a statistical average over a period of time, rather than as an absolute measurement.

It is easy to imagine what happens if the service time, S, is less that the arrival rate, A. Eg, if it takes an average of three minutes to be served, and new people arrive only once every six minutes, then the queue length will be low, and tend towards zero.

Conversely, if S is greater that A, eg, if it takes six minutes to be served, and new people arrive every three minutes, then the queue length will grow, and in theory tend towards infinite. (Sounds like my bank.) So, the puzzle is, what happens to queue length when S = A? (This should give you something to think about the next time you are waiting at the bank.)

All the Colours of the Rainbow

I actually suggested in an earlier column (just over twelve months ago) that I would visit this topic. I have many memories from my childhood of watching both my mother and my sister painting pictures. It always amazed me how creative they both were; I never seemed to have any creative skill whatsoever. It was many years before it ever occurred to me that I was creative at all - it was just that my creative ability lay in different areas of expression.

One thing I remember learning well was the set of primary and secondary colours - red, yellow and blue were all you really needed to make any other colour. By simply mixing any pair of these, you could produce the secondary colour of orange, green and violet. Of course, if you mixed all three, you generally ended up with a dirty dark brown!

Some years later, during my senior years at high school, I worked in stage lighting, and was amazed to learn a different set of primary colours. Red, green and blue lights focussed on the same spot made white. I also learnt a different set of secondary colours; mixing any pair of the primaries produced cyan (a light blue), yellow and magenta. This "RGB" system, as it is known, is also fundamental to colour TV and computer monitors. If you have a really close look at your screen, you will see the little colour dots.

Eventually, I learned that these two colour systems are known as "subtractive" and "additive" respectively. When you mix coloured pigments, you subtract colours from the light that is reflected from them to your eyes. Hence, the mixture of all three pigments tends to approach black. When you combine coloured lights, you add together their different parts of the visible spectrum to produce white light. (A prism shows the reverse effect.)

Each of these two ways of approaching colour come from two different worlds, each with their own philosophy and language - the world of creative artists, and the world of physicists and technicians. Chemists also visit the former world, but do not seem to claim the ownership of it that the other groups do. Computer scientists have now encroached beyond the physicist's realm, however.

The physicist takes the view that the RGB system of additive colour is absolute, and that the RYB system of the artist is in fact a misinterpretation. They state that subtractive colour is merely a complement of additive, and that the real primary colours of the subtractive system are the additive secondary colours of cyan, magenta and yellow. This is known as the "CMY" system, a term commonly seen in colour printing, particularly common now in personal computer printers. As CMY alone does not easily produce a very convincing black, most colour printers are now "CMYK", where "K" is the symbol for a pure black ink.

And so to the unsolved puzzle. Is it true that artists have been using the wrong colours for hundreds of years? Or did they just give their colours the wrong names? I am not totally convinced that the simplistic argument of complements relating the additive and subtractive systems is completely correct. There are some fudgey arguments about different qualities of pigments - colour inks are more transparent than paints - but this does not seem completely convincing, either. Then there seems to be a big hole when you push the complementary argument further. Yellow is fine, maybe magenta and red and cyan and blue are the same colours by different names, but let's go the other way. That should mean that the artist's secondaries match the technician's primaries. Green seems to match, but then try to convince the artist that violet is really blue, and orange is really red!

It appears to me that the two systems are not directly complementary. I would be interested in a convincing argument that proves that they are; I would be equally interested to hear a convincing argument that explains why they are not complementary, and if not, what the relationship between them really is.

For the Answers: Go to the next edition.

Updated: 5 Jun 2000

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