'S COMPASS the transformationof propagulesfrom inert of thisfield. In ViralDynamics, they offer "a muchof theirdiscussion can be followedby to trophicforms and back, and the limitsof personalview of one emergingand poten- anyonewith a first-year-undergraduatetrain- life at high temperaturesand extremeacidi- tiallyhighly useful area" of the subjectrather ing in mathematics.Readers with less mathe- ties. Suchtopics remain of interestto modem than an exhaustivetextbook on theoretical maticalbackground might wish that some microbiology,as does, most importantly,the .Both authorscome to the sub- steps in the reasoningwere explainedmore extentto whichany of.these "thought-style" ject fromtheory and mathematics, not from fully.However, Nowak and May have tried issuesare even approachable by experiment. experiment.As a result.the biol- hard(andc by andlarge. success- ogy is pareddown to the mini- Dynamics fully)to give simpleverbal ren- References mumand sometimes reads like a ditionsof the assumptionsand 1. L.Fleck, Genesis and Development of a Scientific Fact Mathematical (Univ.of ChicagoPress, Chicago, 1979). student'slecture notes. This ap- Principlesof conclusionsin eachchapter. proachmay annoysome experi- Immunology and The idealreader of ViralDy- namicswill be someoneprepared BOOKS: THEORETICAL BIOLOGY mentalbiologists, because it can Virology the impressionthat the au- to bridgethe gulf between theory give by MartinA. Nowak and thors long to escape from the RobertM. May and experiment.The book is Viral Immunology overgrownjungle of experiment more suited to one from the from Math intothe clearair of theory.But it , mathematicalside of thegulf, but carriesthe advantagesof precise Oxford, 2000. 249 pp. experimentalistswill gaingreatly $70, ?40. ISBN 0-19- Charles R. M. Bangham and Becca Asquith andit frombeing asked for more preci- andeconomical reasoning, 850418-7. Paper,$34.95, demonstratesthe wealthof con- ?19.50. ISBN 0-19- sion abouttheir assumptions and I t is a widespreadfallacy that what mathe- clusionsthat can follow from a 850417-9. their reasoning.As biological maticscontributes to biologyis quantifi- smallnumber of assumptions. knowledgebecomes ever more cationof an otherwiseinnumerate science. The HIV epidemichas given complexand detailedc so natural But experimentalbiologists have long been the field a strongimpetus and a naturalfocus, languagebecomes more inadequate for certain expertat measuringand quantifying. The real so it is no surpriseto find thatmost of the types of biologicalquestions. Mathematics contributionof mathematicslies in a precise bookis concernedwith the dynamicsof HIV- providesan efflcient,precise, and rigorous al- qualitativeframework of reasoning.The rate- 1. The chief questionsthe authorstackle are temative;as the authorsnote, "mathematics is limitingstep in theadvance of biologyis usu- the most importantin HIV-1biology: Why no more,but no less, thana way of thinking ally experiment,not theory.(One of the very does the CD4+T cell countslowly and inex- clearly."It is unfortunatethat the authors omit- few notableexceptions was the theory of evo- orablydecline in most HIV-1-infectedpeo- ted a chapterexplaining the mathematical lution by naturalselection.) Experiment, ple? Whatpart does the immuneresponse techniquesthey use to those biologistswho however,is in no sensesuperior to theory,nor play in limitingthe progressionof the infec- wish to crossthe gulf but lackthe necessary vice versa:both are necessary ingredients of tion?What is the role, if any,played in dis- mathematicaltraining. a properunderstanding of .An experi- ease progressionby the virus'simmune es- In the book'spreface, Nowak and May mentdone with no theoreticalframework to cape?What determines the rate of emergence emphasizethe extraordinarydisparity be- analyzeor interpretthe results (let alone a hy- of drugresistance in HIV-1?What is thebest tweenthe richnessand sophistication of bio- pothesis)is meaningless;theory in the ab- strategyfor drug treatment of theinfection? logicalknowledge and the fundamentalna- senceof experimentremains mere theory. Although other virus are tureof certainquestions that biology remains Mathematicsnow occupiesa centralpo- mentioned,particularly hepatitis B virus ill-equippedto answer.Mathematics pro- sition in ecology, ,and , ,there remains a dangerthat con- videsan extremelyuseful tool to helpanswer and it has providedvital contributionsto clusionsfrom HIV-1 infection are assumed some of thesequestions, by makingpossible countless other areas of biology such as to be generallytrue for all ,where- thoughtexperiments in which the variables nerveconduction. But untilrecently it made as thereare often good reasonsto suppose can be precisely controlled.We hope that littleimpact on immunology,largely because the opposite. both mathematicaland experimentalbiolo- of ourignorance of muchof the basicbiolo- Theauthors rely on simpleordinary differ- gists will readthis book andbring their two gy. In the last decade,immunologists have entialequations and basic linear algebra, and fields closertogether; both will gain. realizedthat the dynamicsof the responseto an infection within one host might be amenableto mathematicalanalysis. Such BROWSINGS analysisis particularlyapplicable to viralin- The Shape of the Heart. PierreVinken. Elsevier, Amsterdam, 1999. 208 pp. $20, NLG44. fections,because of the relativelysimple ge- ISBN0-444-82987-3. netic structureof viruses and the rapidity With its scallopedtop, convexsides, and pointedbottom, the redValentine heart is instan- with whichthey reproduceand generate ge- taneouslyrecognizable. The actualhuman heart, however, is a "lightbrown, cone-shaped clod." netic variation.In addition,experiments us- In his considerationof how the icon got its shape, ing viral infectionsto test evolutionaryhy- Vinkendiscusses the findingsof classicaland me- potheses can often be completedin days; dievalanatomists and presentsexamples of depic- virusesprovide the kindsof samplenumbers zu0 0 9g tions of hearts rangingfrom 3000-year-old Mexi- and reproductiverates that epidemiologists can ceramics to contemporary advertising. He

andanimal geneticists can only dream about. a r'. ; 7 E | S A traces the crucialindented crown,which first ap- Martin Nowak and Robert have in the arts in May peared visual early 14th-centuryItaly, cc playedan importantpart in the development n 5 Vr Q i to an errorin an anatomicaltext by Aristotle.As 0

this illustrationfrom Vesalius's Fabrica (1543) indi- TL cates, the 16th anatomistshad correct- The authorsare in the Departmentof Immunology, by century z Butthe was "I WrightFleming Institute, Imperial College School of ed the mistake. Valentineshape already Medicine,Norfolk Place, London W2 1PG, UK. E-mail: ubiquitousand so it remains. [email protected] [email protected]

992 9 FEBRUARY2001 VOL 291 SCIENCE www.sciencemag.org