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science press or voices in the air, that a newform of warfare is on the horizon. In this newblitzkrieg, taking out the enemy’s informa-tion systems has the potential to do vastlymore damage than the physical destructioncaused by Second World War bombers.What would these weapons look like? Oneexample Druffel cites is that of a ‘rogue’ pro-gram that floods the networks with bogusmessages, impeding the free flow of informa-tion. The more advanced the economy, thegreater the potential for devastation. Takeout Albania’s information systems and itprobably wouldn’t notice for three weeks.But do the same for the United States, 20years down the road when it is totally depen-dent on the Internet, and the consequenceswould be awesome.

On a more upbeat note comes thedelightful essay “There and Not There” byWilliam Mitchell, the architect and culturalcritic from the Massachusetts Institute ofTechnology, and Oliver Strimple, director ofthe Computer Museum in Boston. They askwhy would anyone ever go out when every-thing they might want to see is on-line? Inthis articulate and optimistic essay, theauthors persuasively argue that telepresenceis no substitute for ‘being there’. Television ora Web-browser simply cannot capture thefull experience of going to a live pop concert,theatre performance, art gallery or soccermatch. That indefinable, emotional some-thing one gets at the real event they call ‘aura’.We all knew it in our hearts, but they havegiven us a word for it. Martin Campbell-Kelly is in the Department ofComputer Science, University of Warwick,Coventry CV4 7AL, UK.

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and people on the fringe of computing. The20 essays in this fin de siècle collection havebeen seamlessly edited, and only three orfour of the papers are evident pot-boilers.

The book is divided into three parts, deal-ing respectively with technology, computingand human identity, and business and eco-nomic issues. Of the six chapters in the tech-nology stream, one of the highlights is anessay by Mark Weiser and John Seely Brown,both senior researchers at the famous XeroxPARC in Palo Alto, California. In the 1970sPARC researchers came up with the graphi-cal user interface that 15 years later, asMicrosoft Windows, made Bill Gates’s for-tune. Now workers at PARC have moved onto what they call “calm technology” — whencomputers become invisible and disappearinto the woodwork. They foresee “clocks thatfind out the correct time after a power fail-ure, kids’ toys that are ever-refreshed withnew software and vocabularies, paint thatcleans off dust and notifies you of intruders,and walls that selectively dampen sounds.”Got all that, Bill?

The first of the six essays on computersand human identity is by the eminent socialresearcher Sherry Turkle, who reflects onwhat it means for kids to grow up in a cultureof video games and simulation. “Fifty yearsago,” she reminds us, “a child’s world was fullof things that could be understood in simple,mechanical ways. A bicycle could be under-stood in terms of its pedals and gears and awind-up car in terms of its clockworksprings.” But lever the back off a Gameboy,and the child is confronted by an impen-etrable chip. Thus children are led to psycho-logical rather than mechanical explanationsof their playthings; in effect, they perceivemachines as having a kind of inner life —“more alive than a car, but less alive than a bacterium”.

Another essayist on computers andhuman identity is Terry Winograd, onceenfant terrible of artificial intelligence, butnow with his feet planted firmly on the floor.His essay touches on the vexed issue of theboundaries of computer science. Today thereare terrific tensions and frustrations in com-puting research because a researcher oninterface design probably has more in com-mon with social psychologists on the otherside of the campus than with the computertheoreticians in the same building. Winogradsupposes that there may eventually be a splitbetween interface designers and computerscientists, rather like the complementaryroles of architect and civil engineer.

The final set of essays deals with economicand business issues. I think everyone willtake away from this book a particular visionthat captures their imagination above theothers. For me it was an essay on “Informa-tion Warfare” by Larry Druffel, former direc-tor of the Software Engineering Institute. Wehave all picked up the idea, from the popular

IncompletetheoremsWhat is Mathematics, Really?by Reuben HershOxford University Press/Cape: 1997. Pp. 343.$35, £18.99

Ivar Ekeland

The title poses quite a question, and addingthe word ‘really’ does not make it any easier.Empty words will not do: hard definitions arerequired. So what does ‘really’ really meanhere?

It could mean: “What is modern mathe-matics, what makes it important in — or irrel-evant to — our everyday life, what is it like tobe an active mathematician?” There is muchto say here. There has been an exponentialgrowth in the number of scholars, books,journals, papers and theorems produced inthe past century. Whole fields, such as proba-bility theory, functional and numerical analy-sis, and noncommutative geometry, havebeen created. Older fields, such as algebraic

geometry or number theory, have enjoyedtremendous progress, the solution of Fermat’slast theorem being a case in point. The use ofmathematics has become pervasive in engi-neering for filtering noisy signals and control-ling processes, as well as in economics orfinance, as shown by the success of theBlack–Scholes model for pricing derivativesecurities.

It could also mean: “What is the innermeaning of mathematics?” Is there anythingmore to mathematics than its outward successstory? Is it an activity to be pursued for its ownsake, independently of material rewards?Painters or writers are supposed to be aimingfor timeless achievement in art, not for recog-nition among their contemporaries, whichmay not even come during their lifetime. Is itthe same with mathematicians? Are theyartists in their own way? And, if so, what kindof art is theirs?

Strangely enough, this book goes neitherway. It describes nothing of modern mathe-matics, except for a discussion about the foun-dations of mathematics and its connectionwith logic, which is far from the preoccupa-tions of most working mathematicians. Thereis nothing at all to suggest the breadth andscope of mathematics today, or how much ithas changed in the past century. It is alwaysannoying to see the same tired, age-old exam-ples crop up again and again: how to provethat the square root of two is irrational, how touse the tools of differentiation to exploitGalileo’s law of falling bodies, and so on.

The book fails also to answer the questionabout the nature of mathematics. It dismissesit as “futile”, leaving to forthcoming progress

Facets of history: details of a wooden tarsia in thechurch of Santa Maria in Organo, Verona, Italy.From Polyhedra by Peter R. Cromwell(Cambridge University Press, £30, $44.95).

Nature © Macmillan Publishers Ltd 1997

in the neurosciences whatever kind of answeris possible. To quote the author: “How doesmathematics come about, in a daily, down-to-earth sense? That question belongs to psy-chology, to the history of thought, and toother disciplines of empirical science. It can’tbe answered with philosophy.”

So what does the author do? He presentshis own philosophy of mathematics, which isnow a fairly easy thing, considering all thequestions he has decided such a philosophyshould not answer. This philosophy he calls“humanism”. The basic principle is: “A worldof ideas exists, created by human beings, exist-ing in their shared consciousness. These ideashave objective properties, in the same sensethat material objects have objective proper-ties. The construction of proof and coun-terexample is the method of discovering theproperties of these ideas. This branch ofknowledge is called mathematics.”

I find it hard to understand what is meantby “shared consciousness” and to see howideas could have “objective properties” in the“same sense” that material objects do. If I ven-tured such views in public, I would certainlytry to clarify them, referring to such sciencesas linguistics (after all, shared consciousness,whatever it is, must be mediated through lan-guage, and Chomsky has gone a long waytowards a scientific analysis of the phenome-non) or to history (does a historical fact sharethe same objective properties as an experi-mental fact in physics?). Here, of course, suchpreoccupations are dismissed as “futile”, sothe author can take his “philosophy” forgranted and proceed without further ado.

In the first part of the book, the authordevelops the ideas that “mathematics ishuman. It’s part of and fits into human cul-ture” and that “mathematics knowledge isn’tinfallible. Like science, mathematics canadvance by making mistakes, correcting andrecorrecting them.” He contrasts these (veryreasonable) ideas with a Platonist approach,which would take the stand that mathemat-ics already ‘exists’ somewhere (written downin God’s great book), so that theorems arediscovered (unveiled), and not created, byhumans. Mathematicians are then dividedinto humanists and Platonists, and the sec-ond part of the book is devoted to a review ofprominent mathematicians through theages, classified according to the stand theyhave taken on this question. At the end, theirpolitical opinions are reviewed as well, and,not surprisingly, even with the help of someelementary statistics, Platonists are found tobe mostly conservative-righties whereashumanists are mostly democrat-lefties.

As a source of information about mathe-matics in general, the book is a failure. Thereremains scattered information, mostly in theform of quotations, about the foundationsdebate in mathematics. And the author doesgive unexpected entertainment at times. It isdifficult to keep a straight face while reading

that Pythagoras, for instance, for whom nobiographical data are available, except thefacts that he lived in the sixth century BC andthat none of his writings survive, was a ‘right-ie’. There is also some humour in seeing thatthe author, presumably wishing to spare thecritics time and trouble, concludes his bookwith a “self-graded report card”. The result:“Could be worse.” Of course.Ivar Ekeland is at the Ceremade et Institut deFinance, Université Paris-Dauphine, 75775 ParisCedex 15, France.

depressed (as well as anxious, phobic, obses-sional, anorectic, bulimic, gambling-addict-ed, violent, paranoid, alcoholic, drug-hookedand sexually promiscuous) than in 1950, thecommon denominator being reduced brainserotonin (present mainly as metaphor ratherthan molecule). Society has changed since1950, becoming more competitive, less cer-tain and less predictable. We know moreabout other people, and compare ourselvesmore, often with high-profile media-inflatedrole models, and find ourselves wanting. Anda war between the sexes (“gender rancour” inJames’s quaint phrase), with less well-definedroles, increases divorce and disrupts child-hood. This potent mixture makes naked apes,recently out of Africa, more depressed (andanxious, and so on). Is this plausible?

The book’s argument depends criticallyon depression being more common now thanhalf a century ago. Two other current contro-versies indicate the methodological prob-lems. Is childhood asthma truly increasing, oris there just increased willingness to reportsymptoms or make diagnoses? Has intelli-gence really increased this century (scores onidentical tests are certainly higher), or is therejust increased impulsivity, test-wiseness,guessing or visual literacy?

For psychiatry the problems are muchgreater. Standardized instruments such as theGeneral Health Questionnaire now routinelyuse higher cut-offs for ‘caseness’, as peoplemore willingly acknowledge problems. His-torical studies of depression have not usedequivalent criteria. James’s brief appendix on“the scientific evidence” depends almostentirely on retrospective self-diagnoses inKlerman’s controversial study of subjects ofdifferent ages. Even if depression hasincreased, proving causation is even moreproblematic; we see what we want to see, par-ticularly when social and political factors areinvolved.

The final chapters give James’s prescrip-tions for raising our low serotonin levels.Twenty million of the UK population wouldbenefit from that contemporary soma Prozac(despite the claimed low libido, erectile failureor anorgasmia in 30–70 per cent of users).Psychotherapy and a more collectivist, com-munitarian “advanced capitalism” wouldalso help.

Neither is diet neglected, with a serotonin-boosting recipe reminiscent of GeorgeBernard Shaw’s crankiness: “One approach isto consume only the juice extracted frompears, sweet beetroot... and carrots, from ajuice extractor for a period of three days everymonth, consuming as many apples as arerequired if hungry in the interim.” Surpising-ly, James — unlike G. B. S. — doesn’t tell us tostimulate the phagocytes.Chris McManus is at the Centre for HealthInformatics and Multiprofessional Education,University College London Medical School,Whittington Hospital, London N19 5NF, UK.

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O brave new worldthat has Prozac in’t!Britain on the Couch: Why We'reUnhappier Compared With 1950Despite Being Richer — A Treatmentfor the Low-Serotonin Societyby Oliver JamesCentury: 1997. Pp. 402. £16.99

Chris McManus

Two subtitles maketh a reviewer’s job easier.And should one miss the quasi-eighteenth-century prolixity of the title page, the openinglines also summarize the argument: “Thepremise of this book is that we are unhappiercompared with 1950... that people who areunhappy tend to have low levels of serotoninand that levels thereof are largely caused byour social psychological environment.”

Then follows a rambling mishmash ofreviews of published research (always withhundreds of studies, thousands of subjectsand unanimity of scientific interpretation),supplemented by case-histories from theauthor’s experience, or his television docu-mentaries, or secondary analysis of dysfunc-tionality in the British royal family. Only thelatter, coupled with refreshing references toBritish rather than US television, justifies“Britain” in the title. As worldwide sales mustbe reduced, and the scientific evidence isinternational, I wondered about parallel edi-tions for other countries — say, Albania on the Couch, detailing dysfunctionality in KingZog’s descendants?

James’s main argument is that we (“Thisbook is about... people like us”) are now more