The Genetic Sequence as OracleJuly 15, 2011
Ernst Haeckel’s Pedigree of Man, 1906. From The Mathematics of Life.
Ernst Haeckel’s Pedigree of Man, 1906. From The Mathematics of Life.
Philip J. Davis
The Mathematics of Life. By Ian Stewart, Basic Books, New York, 2011, 340 pages, $27.50.
When I first joined Brown University's Division of Applied Mathematics a half century ago---in the age of the IBM 650, the "workhorse of modern industry"---the thrust of the division in terms of courses and research areas was toward continuum mechanics. Our distinguished faculty included experts in elasticity, plasticity, rheology, fluid mechanics. Tempora mutantur, nos et mutamur in illis. Times and things change (even our knowledge of Latin compared with Newton's), and we all have to adapt. Today, those traditional subjects have moved a bit toward the back burner as useful theories and tools. The older rational mechanics has been left to NASA and other agencies seeking to visit the moon or massage a spacecraft into an orbit around Mercury.
Meanwhile, our division has moved steadily toward what Ian Stewart calls the "mathematics of life." Courses and research on blood flow, genetics, biostatistics and bioinformatics, molecular and computational biology, acoustic lung imaging are available and perhaps now characterize the division.
Stewart, a prolific and remarkably well informed popularizer of mathematics, opens his book with the statement "Biology used to be about plants, animals and insects, but five great revolutions have changed the way scientists think about life [and] a sixth is on its way." The five revolutions were brought about by the microscope, systematic taxonomy, the theory of evolution, the gene, and the structure of DNA. The sixth, which is "already under way," is the infusion of mathematics into the life sciences by those who come from both the mathematical and the biological sciences. It goes without saying that the computer is hardly a silent partner in all this.
A personal experience, assuming that what goes on in hospitals can be considered part of the practice of the life sciences, may be relevant to the mathematization of the life sciences, and a fortiori of humans. I was recently hospitalized for two days for a minor complaint. I was subjected to all kinds of tests involving a variety of presumably chipified machines that yielded numerical outputs. I was seated and wired up, and hospital technicians noted down number after number. Having also seen yards and yards of EKG waveforms pulled off, I wondered whether a fast Fourier transform would be applied and interpreted. In any case, I felt that, as far as the hospital was concerned, I had been characterized as a 1 x n matrix. A nurse even asked me, "On a scale of zero to ten, how do you feel, Phil?" With tongue in cheek, I answered, "four point five." The nurse marked it down. Numbers carry the cachet of objectivity, and an m x n matrix would allow for a succinct and objective recording of diachronic changes in my condition.
The Mathematics of Life contains 19 chapters, each of which can be read individually. Taxonomy is present, as is Darwinian evolution. Genetics, that brainchild of the Austrian monk Gregor Mendel, is expounded all the way to DNA. As an outgrowth of D'arcy Wentworth Thompson's Growth and Form, a unique book in its day, the relevance of geometric shape and size (morphology) is explained. The patterns on a boxfish and spots like those that the Biblical leopard cannot change are displayed. Polyhedra masquerade here as viruses, and group theory is invoked. Differential equations are brought in to model the spread of disease, as well as the transmission of impulses along nerve fibers.* The folding of proteins into their characteristic three-dimensional shapes is described. Self-replication à la von Neumann is mentioned, as is the phenomenon of swarming, i.e., social aggregation.
In the penultimate chapter Stewart considers life, natural or artificial, not as a tragicomedy, but as a process that involves such things as the workings of an automaton or of a Conway game. The book winds up with the possibility of extraterrestrial life, which should please the SETI community of searchers for such life and intelligence (and provide ammunition for those who have to appear before congressional committees to justify their use of taxpayers' money).
I was amused by Ernst Haeckel's illustration of the pedigree of humans as a Tree of Life. It was Haeckel (1834–1919), a German biologist, evolutionist, prolific researcher, and author, who coined the phrase "ontogeny recapitulates phylogeny." He also produced Art Forms in Nature (1904), a book with eye-popping illustrations of radiolaria and other such animalcules. At the age of twelve or so, I read an abridged version of his book The Riddle of the Universe, which for some reason was lying around my house, and its implied philosophy, as I could then grasp it, nearly turned me into a sun worshipper.
Before opening Stewart's book, I was familiar with only a small proportion of the wealth of material presented. Happily, the treatment is sufficiently friendly that, after studying the text closely and digesting it, I would not, if questioned, appear totally ignorant.
When one considers the various mathematical disciplines that have now been turned to use in the life sciences---combinatorics, simple calculus, topology, network theory, difference and differential equations, knots and their invariants, game theory, probability and statistics---it would seem that there is hardly a branch of mathematics that is not involved. Well, as far as I know, inaccessible cardinal number theory has not yet been so applied. Who knows but that an application will be found next year.
Years ago, for a penny you could obtain a little card giving your "weight and fate" from the scales often found on commercial streets. Today, the desire of eugenics advocates to produce flaw-free humans, along with the desire of individuals to consult oracles, can be satisfied via the A's, C's, G's, and T's making up an individual's complete genetic sequence. The sequence, processed and interpreted mathematically, now gives the individual's fate. The cost of a sequence has come down considerably since Craig Venter paid a reputed $10 million for his.
In the 1967 movie The Graduate, the young hero, Benjamin, is given advice as to what professional or commercial career he should follow to make his reputation and his fortune. The word "plastics" was whispered in his ear. If an update of this movie were made, I would suggest that the guru should not whisper but rather shout into Benjamin's ear the word "genetics." Accompanied by a strong hint that a few selected mathematics courses would provide additional arrows for his professional quiver.
*I cannot restrain myself from mentioning that the first computer instance of the Hodgkin–Huxley equations of the propagation of impulses on nerve fibers was programmed for the SEAC by my colleagues Henry Antosiewicz and Philip Rabinowitz at the National Bureau of Standards and Kenneth S. Cole of the NIH. Their work was reported in 1955 in the Journal of the Society for Industrial and Applied Mathematics.
Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at firstname.lastname@example.org.