playwiths and fun: Arts/Sci: Seeing what you see

An ‘Artificial Spectrum Top’, devised by Mr. C. E. Benham, and sold by Messrs Newton and Co., furnishes an interesting phenomenon to students of physiological optics. The top consists of a disc, one half of which is black, while the other half has twelve concentric circles drawn upon it. Each arc subtends an angle of forty-five degrees. In the first quadrant there are three such concentric arcs, in the next three more, and so on; the only difference being that the arcs are parts of circles of which the radii increase in arithmetic progression. Each quadrant thus contains a group of arcs differing in length from those of the other quadrants. The curious point is that when this disc is revolved, the impression of different colours is produced upon the retina.

—Nature, 51 (1309), November 29, 1894, 113–114.

When toymaker Charles Benham invented his Benham discs, more than 130 years ago, he put these sorts of pattern on the upper surface of a toy top, which may give you a hint about how to spin it.

These small and simple devices will make you wonder just what colour really is. When you spin one, your eyes will often perceive colour. People say spinning the disc in the opposite direction can reverse some of the colours, and there are other interesting effects to find as well. I suspect that they have good imaginations, but why not test the effect out?

Two of Benham’s discs.

Use a pair of compasses and heavy paper to make discs like these, about 10 cm across. You can mount the disc on cardboard, fit a small bolt through the exact centre, and spin the disc in a drill (youngsters: get adult advice on using a variable drill).

The first report of the discs was a brief and anonymous note in the British science journal Nature in 1894. It described the disc as a black semi-circle, with a white half divided in four, and with black arcs on it. As the disc turns, it said, people see different colours from the different black arcs. Soon after Benham said that if you shine a bright sodium flame on the disc, you will see a very clear blue, and a very clear red, but other people said they could not see this at all.

The “official” explanation now says we have three kinds of light receptor in our eyes, in the same way there are three kinds of phosphor in a colour TV. Speaking crudely, these light receptors, the cone cells, are all sensitive to just one of red, green and blue.

According to the theory, you need all three kinds of cone in the retina of your eye to see colours normally. Somehow, the cones that pick up one of the colours (red, for example) must react differently to flashing lights of a particular frequency.

So with different size black bits on the disc, we get different frequency effects, and our eyes are stimulated to “see” different colours. That’s what the theory says, but nothing seems to explain the alleged effects of sodium light.

Some reports said different rotation speeds were needed for different people to see the same effects. Explore this claim, and see what you can discover. There are other patterns for Benham discs, some of them are better, some worse. Do some web research, then see if you can invent a better design.

Some illusions

Here are a few examples of the old standards that are all over the internet. The first two are from 19^th century German sources: a duck or a rabbit on the left and on the right, an old woman or a young one?

Duck or rabbit; and maid or crone?

Next: below, you will find an impossible cube and an impossible triangle: can you find their creators’ names?

Note:

Most of the time, two or three words will find your answer. I used two searches: <cube illusion> and <triangle illusion>. (Note that when a search string is surrounded by angle brackets, you leave the brackets out.)

Where next?

To go further, you really should look into the works of M. C. Escher. Older readers can try Douglas Hofstadter’s Gödel Escher Bach: an Eternal Golden Braid which will teach you a lot about computers and systems. Now I warned you there would be some art in here: go and look up pointillism, and look at the work of Georges Seurat and Paul Signac.

Try pointillism yourself, although stippling, done with an Artline 0.3 mm fine-point is easier. My weevil (below) was done with a 0.3 mm Rotring pen with black ink, and there is not one line there.