The Chief Cause of Problems is Solutions

The Indefinite Article

And so to some solutions for last edition's puzzles. There were a number of e-mails received in response to the puzzles, but no complete correct answers to any of the three, although I am not sure if there is a complete answer to the third.

Cracking the Code

The 5-bit Baudot code used for early telegraph transmissions has 32 possible discrete characters, yet in addition to its 36 (upper case only) alphabetic and numeric characters, Baudot code also provided control and punctuation characters. Alastair Munro was on the right track by supposing that control characters were used to create extra characters.

To find the answer, you need to think back to the type of machines that the early teleprinters were based on. Why do we still have a "carriage return" key on a computer? Mechanical typewriters had moving print carriages that needed to be physically returned at the end of each line. As anyone who has used a keyboard knows, the "qwerty" keyboard was not laid out to make typing quick; on the contrary, it was laid out this way effectively to slow down typists. The most commonly-occurring letters were spaced out to prevent the typing heads from jamming. The "shift" keys physically shifted the type heads up or down in relation to the print carriage to cause a different part of the type head to strike the ribbon on to the paper. Hence, "upper case" and "lower case".

This was the principal used by the Baudot code. Two "shift" control codes were provided, letter-shift (LTRS) and figure-shift (FIGS). LTRS indicated to the receiver that the set of alphabetic characters be used for all following codes until otherwise indicated; FIGS indicated that numbers and symbols followed. This effectively stretched the code from 32 characters to 64. These control codes and Space, Carriage Return and Line Feed were always treated the same regardless of shift, and the all-zero code was not used, effectively accounting for 12 codes. This still left codes for 26 letters, 10 numerics, 14 punctuation symbols and 2 more control characters.

The End of the Queue

The best way to illustrate what happens in a queue is to write a computer simulation. To do this correctly, it must be made clear that the two variables mentioned - the average queue arrival rate, A, and the average queue service time, S - are both randomly variable numbers, with defined average values. As described last issue, where these numbers are significantly different, results are predictable - a queue averaging near zero length, or a queue becoming infinitely long.

So, what happens to queue length when S = A? Queue length becomes totally indeterminate. It may be any value from zero to infinity. This makes for interesting results in a simulation, watching the queue length growing and shrinking with no pattern to it whatsoever.

Again, Alastair Munro struggled valiantly with a simulation, but didn't seem to quite get this result. If you find yourself in the position of the biblical Thomas at this point, contact me and I will see if I can make a simulation program available on my Web site.

The Eye of the Beholder

This question raised the dichotomy between different ways of approaching colour from two different worlds, those of creative artists, and technicians. (This touches on a broader phenomenon - the jealousies between related fields of knowledge - which is a fine topic for a future column.)

This question also generated some response, but no complete solutions. Ben Carbery discussed the structure of the human eye. The retina of the human eye is composed of two fundamental types of cells - rods, which sense luminance or brightness; and cones, which sense colour. There are three different types of cone, effectively red, green and blue. The relative levels of excitation of the three cone types determine the signal sent down the optic nerve from the retina. As Ben points out, colour blindness results from flaws in one or more of these sets of cones.

Ben states that the only absolute factor is the actual frequency of light we are viewing, but the combination of frequencies is also important, as we rarely see only a single frequency of light. Perceived colours are not necessarily pure spectral colours; neither pink nor brown appear in a prism. Even purple is a mixture of wavelengths, as opposed to violet, which is a pure spectral colour. A colour may appear to be very different when viewed alone, or beside another colour - have a close look at an Impressionist painting. Colours will also change when lit by different light sources.

Have you ever noticed a dim light out of the corner of your eye on a dark night that disappears when you look directly at it? The edges of the retina have a higher concentration of rods, which are more sensitive to light than cones. The light that just activates the edge of the retina vanishes when you look directly at it because the higher concentration of cones in the centre of the retina can't detect it. This also explains why colours can't be seen in very dim lights - the cones become inactive.

Have you ever noticed that men and women usually disagree about their descriptions of some blue-green colours? Male and female eyes actually have a small difference in the structure of the cones in the retina, resulting in an actual difference in the signal transmitted to the brain in this colour range. Political correctness can't argue this one away - we are actually differently wired.

Visual perception is not only biological, as suggested by Alastair, but also neuro-psychological. It is not the retina that has the final say in how we perceive colour, but the visual centres in the brain. The effects of different colours on the mind are many and varied. Colours can impact on mood, appetite, memory and can even cause headaches.

Notwithstanding some of the muddier aspects of visual perception, I am still of the opinion that there should be some explainable connection between the artistic and technical colour systems. To make this clear - the argument is not whether one of these systems is "right" or "wrong"; they both undeniably exist. The question is only about the relationship between the two, and the impact of this on definitions of colour.

To recap - the artist's colour system is referred to as subtractive colour. In this system, the primary colours are red, yellow and blue, (RYB) and the secondary colours are orange, green and violet. If you mix all three primaries, you get a dirty dark brown that ideally approximates black, the absence of colour. The TV technician's colour system is additive colour. Here the primaries are red, green, blue (RGB) and the secondaries cyan, (a light blue) magenta and yellow (CMY). When you mix the primaries, you get white light, the presence of all colours of the spectrum. The human eye uses its additive system (red, green and blue cones) to perceive colour created by either system.

The puzzle is that the technician refers to these two systems as inversions of each other, and claims that the artist's RYB is in fact a misinterpretation of cyan, magenta and yellow. I find this difficult to accept in this simplistic form; in particular, it is hard to correlate orange, green and violet with red, green and blue. Alastair suggests that maybe the choice of primary colours is arbitrary, and that any three colours sufficiently widely separated in the visible spectrum would do. Experience would tend to dispute this; mixing violet and green paint produces brown, not blue.

The only approach to a solution that I have found so far is the one I glossed over in the last issue - the different qualities of pigments. Ink is transparent; paint is opaque. Given this, coloured inks can be interpreted as coloured filters on the light reflected from white paper. In this way, the printer's CMY subtractive system is in fact a very simple inversion of additive RGB. This would then leave the artist's RYB system as completely separate. Maybe RYB is a different subtractive system, more chemical and maybe less precise in nature than CMY, which may add some weight to Alastair's argument after all.

This, of course, leaves the original question even further from an answer!

Updated: 5 Jun 2000

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