Durer's geometrical mystery finally uncovered
Take a look at Albrecht Durer's famous 16th-century copperplate ''Melencolia I,'' reproduced herewith. Can you identify the geometrical figure that perplexes the winged Muse?
Its identity has eluded art historians for centuries. However, Philip C. Ritterbush, program director at the Institute for Cultural Progress in Washington, says he has solved what he calls this ''puzzle that has pained scholars.''
It's a rhombohedron. That's a six-sided prism, each face of which is a rhombus. A rhombus is a parallelogram with equal sides, like a square, whose angles do not have to be right angles.
In working this out, Ritterbush says he has discovered aspects of Durer's much-studied work that have escaped art analysts. Among other things, the German master appears to have anticipated the mathematical science of descriptive geometry by which three-dimensional objects are accurately represented on paper.
The picture is rife with symbolism. And, as Ritterbush explains in Nature, the now-recognized rhombohedron with the sleeping dog and sphere below it represents the most remarkable symbolism of all. This includes a subtle pun that no one seems to have noticed before.
In trying to identify the figure, scholars have used cubes, octahedrons, and other polyhedrons. None of these could be truncated to look like Durer's figure. Thus many scholars saw it as an artist's symbol for some mystical idea or value, the philosopher's stone, perhaps. Ritterbush explains that the way to solve the puzzle is to stop trying to find such meanings in the figure and simply ask what geometrical solid it might represent. The answer, he says, would be a figure that can be truncated as shown and yet maintain its symmetry. This figure is the rhombohedron.
Ritterbush notes that Durer invites comparison between the sphere, with its perfect symmetry; the dog, which has none; and the mystery figure. Herein lies the visual pun. Ritterbush explains, ''Not until almost three centuries later would naturalists observe that the mineral calcite, when it takes the form of the acute rhombohedron in crystals familiarly known as dogtooth spar, sometimes occurs in truncated examples without loss of symmetry.''
Thus there is much more intellectual punch in the picture than art historians may imagine. In fact, Ritterbush says, they have missed ''one of the dramatic qualities of the work, that the artist knew the answer to the puzzle that perplexes the heroine of the engraving.''
Rather than treating the figure as a mystical symbol, Ritterbush adds, ''It would be more fitting to credit Albrecht Durer with anticipatory intuitions about the science of descriptive geometry established long after his death. What appears in this remarkable work of art is that by 1514 magic had lost its grip on the educated mind.'' Sharp-eyed physicists
According to Prof. Sir Brian Pippard of Britain's Cambridge University, our ability to distinguish patterns is far more acute than we may realize, and physicists should learn to make the most of it. He is also concerned that, by not paying strict attention to subtleties of perception, physicists can make erroneous measurements.
In tests with students, for example, Sir Brian has found a tendency to get the wrong answer two times out of three where the position of a line between two markers is estimated to the nearest tenth of their separation. Yet, he notes, most people can estimate such a position to better than a tenth. He says this ability should be cultivated, not thrown away.
Sir Brian originally reported his work in a paper in the European Journal of Physics. This has been summarized recently in the Physics Bulletin published by Britain's Institute of Physics.
To show how acute our perception can be, he tackled the old question of how many times the Lord's Prayer could be written legibly on the head of a pin, given a microscope for reading it. He found that, using the wavelength of light in the visible range as a unit, letters as small as 0.75 units wide by 0.81 units high give a clear image. Even letters only 0.55 units wide can still be read, especially with help from the context in which they occur. Radio astronomers' 'bad dream'
US radio astronomers are threatened with loss of an important observatory - the joint facility of Ohio State and Ohio Wesleyan Universities. The threat comes not from cuts in federal funding but from the fact that Ohio Wesleyan has literally sold the land out from under the facility.
This observatory has discovered some of the most distant objects in the universe. Its ''all sky'' survey added 20,000 new objects to the radio astronomers' listings. To non-astronomers, however, it may be best known as the site of a long-running search for radio signals from alien civilizations.
Built for about $2 million of National Science Foundation money in the 1960s, the radiotelescope now runs on small grants, mainly from the National Aeronautics and Space Administration.
Originally, Ohio State supplied equipment, staff, and expertise, while Ohio Wesleyan supplied the land. As it turned out, Ohio State uses the facility far more than does Ohio Wesleyan. Now the latter has sold the land to a country club that wants to expand its golf course.
Ohio State officials are hoping to work out an arrangement with the new landlords to keep the observatory going. Meanwhile, however, an Ohio State press release has likened the situation to ''a bad dream for radio astronomers.'' Holes in the deep-sea floor
British oceanographers have discovered deep burrows made in sea bottom sediments by animals. These suggest that experts will have to think again about the permeability of the deep-sea bed. This could be important, among other things, for studies concerned with burying radioactive wastes at sea.
Until now, deep-sea animal burrows were thought to extend only about 10 to 30 centimeters into the sediments. However, P. P. E. Weaver and P. J. Schultheiss of the Institute for Oceanographic Sciences report in Nature that they have found vertical burrows over two meters in length in the northeast Atlantic. These burrows, only 0.5 centimeters wide, make the sediments much more permeable than suspected. The scientists note that their effect is to change ''the calculated permeability from the equivalent of a clay to that of a coarse sand.''
The safety of radioactive wastes buried in such sediments, as is sometimes proposed, depends partly on the permeability of the sediments. The scientists note that the new findings ''are significant'' for studies of such disposal.