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Tony Phillips' Take on Math in the Media A monthly survey of math news |

**September 2000**

- Updating Ramanujan
- Making RNA think
- 5 + 2 = yellow
- Contentious disciples
- A Figure-8 knot in a protein
- Math in Los Angeles

** Making RNA think**. In the first and classic example of DNA computing (The Hamiltonian Path Problem) the problem involved constructing a certain path, and so was naturally suitable for attack using strings of DNA to represent segments of the path. A new approach using RNA seems much more flexible, since the strings are abstract encodings of of configurations, and the chemical operations correspond to the logical *either-or* statements constituting the problem. Charles Seife reports in the 18 February 2000 *Science* on work by the evolutionary biologist Laura Landweber and her associates at Princeton. They unleashed their RNA on the "3x3 knight's problem:" finding all the ways of placing knights on a 3 by 3 chessboard so that no knight can attack another. The holy grail of this line of research is the nucleic-acid solution of a problem that cannot be done by a human in a reasonable amount of time.

**5 + 2 = yellow**. Synaesthesia is a condition in which stimuli from one sense (typically, sounds) elicit impressions related to a different sense (typically, colors). A rare form is digit-color synaesthesia, where the decimal digits 1, 2, etc. evoke colors in the mind of the synaesthete. A team at the University of Waterloo, led by Mike Dixon, set up an ingenious experiment to show that in their subject the synaesthesia was between the concept of the number (and not, for example, the shape of the digit) and the corresponding color. This subject associated seven and yellow; in the experiment she showed significantly longer reaction times in naming color patches which were not yellow when they were shown next to an equation (e.g. 5 + 2) which implied seven. This work was reported in the July 27 2000 issue of *Nature*.

** Contentious disciples.** What happens when 10 people all want to be as close as possible to a central point, but want to stay as far away from each other as possible? A team at Harvard (B. Grzybowski, H. Stone and G. Whitesides) set up an experiment using 1mm-diameter magnetizable washers floating in a dish above a rotating bar magnet. The net magnetic force attracts them to the center, but each one picks up a rotation which drags the nearby fluid into a tiny whirlpool, and these whirlpools repel each other. An article in the June 29 2000 *Nature* shows the resulting configurations. Some (for *n* = 2, 3, 4, 5 washers) are what one might expect: the vertices of a regular *n*-gon. But then it gets more complicated. For *n* = 10, 12 and 19 (as high as they could go with this set-up) there are two possible optimal configurations:

The two stable configurations ("polymorphs") of 10 mutually repelling points all attracted to the center. "... the patterns spontaneously interconvert between the polymorphs."

** A Figure-8 knot in a protein**. W. R. Taylor of the National Institute for Medical Research in London has discovered a Figure-8 knot deeply embedded in the string of amino acids that make up the plant protein acetohydroxy acid isomeroreductase, as reported in the 24 August 2000 *Nature.* "Deeply" means here that even though an open string cannot be topologically knotted, the knot is so far from the ends of the string that for practical purposes it is a topological invariant. Taylor started from the three-dimensional structure of the protein, and interpreted it as a curve in space. He then applied a smoothing algorithm just like the ones topologists use to produce nice round pictures of knots, except that he kept the free ends fixed. Taylor proposes a mechanism for how this knot could be formed during the folding of the protein.

** Math in Los Angeles**. David Ferrell had a very nice piece in the August 12 2000 *Los Angeles Times* on the giant MathFest 2000, which ended that day. He interviewed Tony Chan, head of UCLA's new Math Institute, Peter Sarnak on the Riemann Hypothesis ("Right now ... we go around trying to fix things with a screwdriver. But once we prove this we'll have a machine gun. It'll just blow away problems.") and Ed Witten. He asked Witten if he found it "distressing that so few appreciate -much less understand- the radical concepts that govern his life, that may change our whole understanding of reality?

[Witten] thought a minute. `It bothers me more,' he said, `that *I* don't understand the math.'"

* -Tony Phillips SUNY at Stony Brook*