Math in the Media

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Math in the Media 10-2000
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Tony PhillipsTony Phillips' Take on Math in the Media
A monthly survey of math news

October 2000

* Online Math Quiz October 17. "Sharpen your pencils,set your alarm clocks and clean your mouses!" is the start ofa report in the September 15 2000 Science on an online math quiz organizedby the Centre de Recerca Matemática in Barcelona. It startsat midnight Universal Time on October 17. Questions "will challenge evenexperts but are suitable for computer grading." Top five teamswin Sun workstations. Check it out at Maths Quiz 2000. (Should that have been "mice"?)

* Computation with 2-dimensional DNA. The latest news inDNA computation is the use of double-width (and triple-width)DNA molecules.

Triple-crossover DNA molecule TAO35.

Triple-crossover DNA molecule TAE22.
Images from Biomolecular Computation Using Self Assembly of DNA, used with permission.

Assembly of TAO35 molecules.
These molecules can be considered as 2-dimensional tiles, and canself-organize into 2-dimensional patterns, as shown on the left.Since tiling patterns form a very general class of mathematical problems, the extension of DNA structures to 2 dimensions bodes well for theapplications of DNA computing.

Recent progress is reported in "Logical computation using algorithmic self-assembly ofDNA triple-crossover molecules" by a team of two NYU chemists (Chengde Mao, Nadrian C. Seeman) and two DukeComputer Scientists ( Thomas LaBean, John Reif), in the 28 September 2000Nature. They report "a successful one-dimensional algorithmicself-assembly of DNA triple-crossover molecules that performs four steps of acumulative Exclusive-OR operation on a string of 1's and 0's." Background information is available in an "HTML lecture"Biomolecular Computation Using Self Assembly of DNA by LaBean, E. Winfree, and Reif to go along with an article by the same authors.

* More math into biology! That's the aim of a newNational Science Foundation initiative, "Quantitative Environmental andIntegrative Biology," recently announced, and reported in an article byRex Dalton in the 28 September 2000 Nature. Starting budget$ 3 million and scheduled to increase. One goal is toprovide tools for analyzing the large data sets produced byresearch in ecology. Another goalis to improve statistical techniques for studying species spreadover large geographical areas. Targeted sciences: population genetics, ecological system restoration, and animal physiology and behavior."Principal investigators are being encouraged to train undergraduates and graduates in the newtechniques, with a view to them becoming involved in the research. NSF officials see this as away to create a much-needed generation of scientists skilled in both biology and mathematics."

* Math genes? The point is that there are many of them, andthat everyone has enough: "the capacity to do mathematics, at least throughhigh-school algebra and geometry." This is brought out in a charming andon-target piece "Finding your Inner Mathematician" by Keith Devlin in the 29 September 2000 Chronicle ofHigher Education. Devlin reminds us that math only requires "ninebasic mental abilities, which our ancestors developed thousands of yearsago ..." which he enumerates and describes. For example, # 4 is"A sense of cause and effect," and # 7 is "The ability tounderstand abstraction," which he describes "the key." There is a lovelyriff on "math as soap opera," but here are two nuggets from thisexcellent article. "Mathematicians don't have a different kind of brain.They have learned to use a standard-issue brain in a slightly differentway." "The real value of learning basic math skills ... is to make theabstract objects of mathematics become so familiar -and seem so real-that you can reason about them using the same mental capacities you useto reason about everyday things." (See Multiple Mathematical Intelligences in the What'sNew Archive for another take on the same phenomena.)

* Slime-mould topology. "... this simple organism has the ability to find the minimum-length solution between two points in a labyrinth."

Initially the plasmodium forms a net coveringthe entire maze. Images from Nature 407:470 (2000)@2000 Macmillan Magazines Ltd., used with permission.Four hours after the (yellow) food blocks havebeen introduced in the maze, pruning of non-essential branches iswell under way.Eight hours after introduction of food blocks, the organismhas formed into a single thick, minimum-length strand from one food source tothe other.
So state the members of a Japanese-Hungarian team tedby Toshiyuki Nakagaki of RIKEN, authors of "Intelligence: Maze-solving by an amoeboid organism" in the 28 September 2000 Nature. The experimentstarted with seeding the slime-mould Physarum polycephalum on theentire surface of a maze. Then two blocks of nutrient were placed at opposite corners of the maze. Within 8 hours the organism had contractedall unnecessary pseudopods to trace out the shortest path between theblocks. They conclude by saying: "To maximize its foraging efficiency, and therefore its chances of survival, the plasmodium changes itsshape in the maze to form one thick tube covering the shortest distance between the food sources. Thisremarkable process of cellular computation implies that cellular materials can show a primitiveintelligence."

* Retinal Calculus. It has been known that the retina containsdirection-selective ganglion cells (DSGCs) each of which has a "preferred direction," and fires to report adark-light or light-dark separator moving by it in that direction.Motion in non-preferred directions gives much lower output. The cells are performing a kind of directional derivative.An explanation of the synaptic mechanisms involved is given by Rowland Taylor of Australian National University and co-authors ("Dendritic Computation of Direction Selectivity by Retinal Ganglion Cells, " in the September 29 2000 Science.)The authors show by a series of experiments with rabbit retinal cellsthat "the key mechanism underlying direction selectivity in DSGCs is spatially asymmetric inhibition, which counteracts excitation for motion in the null direction but not in the preferred direction." This paper was reviewed in a news piece (same issue) "A New Look at HowNeurons Compute" by Marcia Barinaga, who reports some dissent from theturtle people. The idea that image processingtakes place to some extent in the retina, rather than in the brain,dates back to the oft (but not here) cited 1959 article "What the Frog'sEye Tells the Frog's Mind" byLettvin, Maturana, McCullogh and Pitts,Proceedings of the IRE, Vol. 47, No. 11, pp. 1940-51.

-Tony Phillips
SUNY at Stony Brook

* Math in the Media Archive