variety of graphs ensue, including com- for the dynamics of the nutrient re- Press, Cambridge, Massachusetts, USA, plete graphs given by the Moran source, R, is coupled to the Eigen- 1980. process of any individual being re- Schuster Equation: [3] R. A. Fisher, The Genetical Theory of Nat- placed by any other with equal proba- n ural Selection. Oxford University Press, Ox- bility, to cyclic graphs, and to a wide x, = ~ xJ/R)qs,- 4,x, ford, UK, 1930. variety of other graphs of great aesthetic j=O [4] J. B. S. Haldane, A mathematical theory of and mathematical beauty. However, natural and artificial selection, Part I. Trans. perhaps because of the newness of this \i=0 Cambridge Philosophical Soc. 23 (1924), approach to evolutionary theory, the where /R and eR are inputs and out- 19-41. biological implications are not as de- puts, respectively, of the nutrient R [5] S. Wright, Evolution in Mendelian popula- tailed as with the chapters that build from and to the external environment. tions. Genetics 16 (1931), 97-159. on dynamical systems and game theo- The function g describes the total re- [6] J. Hofbauer and K. Sigmund, Evolutionary ries. Perhaps this chapter will stimulate lease of nutrient R from dead individ- Games and Population Dynamics. Cam- research into the application of this po- uals of xi based on mi, the mortality bridge University Press, Cambridge, UK, tentially powerful technique to partic- rate of &; ci, the concentration of nu- 1998. ular ecological and evolutionary situa- trient in the dead individuals or dead [7] J. A. Schweitzer, et al, Genetically based tions. shed parts of &; k~, the release rate of trait in a dominant tree affects ecosystem One frontier in evolutionary theory, the nutrient during decomposition; and processes. Ecol. Lett. 7 (2004), 127-134. which has barely begun to be explored, the ellipsis denotes other factors, such is its interface with ecosystems ecology. as climate, that also affect decay rate. Department of Biology Ecosystems ecologists study the biolog- This coupled system is a framework for University of Minnesota Duluth ical and physical processes that control examining how mutations qj, affect the Duluth, MN 55812 the flux of nutrients in forests, lakes, cycling of R and conversely how the USA prairies, oceans, and other ecosystems. cycling of R affects the trajectory of x e-mail: [email protected] The growth of populations is often lim- in sequence space by means of the fit- ited by the availabilities of nutrients. ness function fj(R). The entire system However, individuals also affect their is constrained by the mass balance im- availabilities through such traits as up- posed by IR and eR. One can therefore take rates and the release of nutrients also investigate how increased nutrient during the decay of leaf litter and car- The Trouble with inputs, such as the increased phos- casses when they are returned to the phorus loading of a lake that causes al- soil. It would seem logical to suppose Physics: The Rise gal blooms, affects the evolutionary dy- that the ways in which individuals af- namics of x. Depending on the forms fect resource availability, through their of String Theory, of fj(R) and g( . . . ) there could be uptake and through the decay of dead some interesting bifurcations in this sys- material, could be powerful selective tem. the Fall of a forces. But evolutionary biologists have Nowak's book is a readable, hand- ignored ecosystem processes because somely illustrated, and thought-provok- Science, and What the resources themselves do not evolve ing guide to modern evolutionary the- (and are therefore assumed to remain ory. Some beautiful mathematics is used Comes Next fixed), whereas ecosystem ecologists to illuminate difficult evolutionary ideas, by Lee Smolin have ignored individual variation in or- and evolutionary biology is used to mo- ganismal traits that could affect nutrient tivate the synthesis of dynamical sys- BOSTON, MASSACHUSETTS, HOUGHTON MIFFLIN, cycling, preferring to concentrate on the 2006, 456 pp, HARDCOVER US $26.00.1SBN-10: tems theory, game theory, and graph larger differences between species. But 0618551050,1SBN-13:978-O-8218-3933-1. theory. The book is suitable for gradu- the approach outlined by Nowak could 2007, PAPERBACK, US $15.95.1SBN-13EAN: ate classes in evolution, ecology, or bio- 9780618918683,1SBN-10:O65891868X be used to unify evolutionary and mathematics. In my view, it would be ecosystems theory. For example, the best used in a seminar class where stu- REVIEWED BY JOHN HARNAD chemistry of leaf litter, which often de- dents are encouraged to develop one termines decay rates and the rate of re- or more of these techniques further to lease of nutrients, is partly under ge- ,~uperstring Theory has been the shed some light on their thesis prob- netic control [7]. Different sequences, ~subject of intense study by a sub- lems. &, may therefore have different decay "f~stantial segment of the theoretical rates and influence soil nutrient avail- physics community for over two decades. ability differently. Assume also that the REFERENCES The theory's goal is extremely ambitious, fitness, fi, depends on nutrient avail- [1] G. H. Hardy, Mendelian proportions in a to say the least: nothing less than a uni- ability, perhaps by means of a mixed population. Science 28 (1908), fied quantum framework for all the fun- Michaelis-Menten or other suitable 49-50. damental interactions of matter, a "the- function. We can now propose a dy- [2] E. Mayr and W. B. Provine, editors, The ory of everything" [1, 2]. Its mathematical namical system in which an equation Evolutionary Synthesis. Harvard University intricacies, however, are barely under-

THE MATHEMATICALINTELLIGENCER standable even to a majority of physi- tiques, Smolin adds some that are more Nobel prizes to eight theoretical physi- cists, and it has yet to prove itself a specific to the String Theory commu- cists, and six more to experimentalists valid physical theory. Nevertheless, in nity. This is an exceptional one, both who discovered or confirmed many of The Trouble with Physics, Lee Smolin in the incomparable ambitiousness of its observable consequences. The theory tries to give an overview, including the its scientific agenda and, according to seems at least to have no intrinsic de- background, history, motivation, and the author, its particular susceptibility to fects other than those shared by any rel- content, as well as a detailed critique, the "group thought" phenomenon. ativistic quantum field theoretic model. at a level accessible to a general read- Apart from this, many would agree that These include, of course, one un- ership. String Theory suffers from a central de- usual feature that physicists have To help understand why a physicist fect that sets it apart from nearly all learned to live with for decades; might want to address an audience that other scientific pursuits: it is unable as namely, the fact that perturbation the- cannot be expected to comprehend yet to provide anything that may be ory, based on successive approxima- such a subject's hermetic details, it subjected to the test of experimental tions, leads at first to infinite quantities should be mentioned that only about a verification, beyond what is already ad- that must be eliminated through a third of the book is concerned with equately provided by more conven- scheme of infinite renormalization be- String Theory per se. The remainder tional frameworks, such as the "Stan- fore arriving at anything that may be consists of an earnest plea for two dard Model." From the viewpoint of the compared with experiment. However, things. The first is greater attention to Scientific Method this is anathema, this is generally not seen as an essen- alternative approaches to the funda- putting the subject into a difficult posi- tial defect but rather a necessary feature mental questions of theoretical physics, tion to defend. Is it really physics, or of the perturbative approach, and the in particular the line of research con- just mathematical conjecture that is too final results do agree with experiment cerning quantum gravity that comprises incomplete to stand up as a physical to a high accuracy -- at least in the the author's own main interests; the sec- theory? All depends on promises of weak and electromagnetic case. The ond is a critique of the assumptions and things to come. fact that perturbation theory is not re- social pressures of the research com- The Standard Model has been very ally applicable to the Strong interactions munity in which he works, with sug- successful in accounting for observable is partially mitigated by the fact that cal- gestions for improvements. Nearly as phenomena involving the electromag- culations valid to all orders, using the much of this book is devoted to the so- netic and Weak nuclear forces as parts <'renormalization group" approach, ciology of science -- more specifically, of a unified theory of electroweak in- demonstrate the existence of "Asymp- the String Theory community -- as to teractions. It also includes a consistent totic Freedom"; that is, the Strong in- science itself. framework, Quantum Chromodynam- teractions become arbitrarily weak at In view of the exceptionally high ics (QCD), for the Strong nuclear sufficiently short distances. level of mathematical preparation that forces, which hold the atomic nucleus No known quantum field theoretical a genuine understanding of the subject together, although these are not yet framework exists, however, that in- would require, only a selective, non- fully understood at a sufficiently de- cludes gravitation and is consistent with technical description of the ingredients tailed level to be able to account for General Relativity. The incompatibility can be presented in such a work. To the huge quantity of strong interaction lies in the fact that when trying to treat make this at all meaningful is a very dif- data accu-mulated over decades in gravitation as a quantum field, infinities ficult task. Smolin succeeds in giving the high-energy physics laboratories. More- persist in the perturbation theoretic cal- interested general reader an idea of the over, the short-range nature of the culations that cannot be eliminated flavor of the subject, and a vantage Strong interactions remains to be satis- through renormalization. This problem point from which to make some sense factorily explained as a direct conse- has never been overcome in any quan- of the critiques that follow. quence of the model. This is all as- tum field theory setting. The desire to It is hard to disagree with the gen- cribed to the complicated collective include gravitation within a quantum eral socio-academic critiques, but many effects that are necessarily present in framework unifying all the fundamen- are far from unique to this particular such a relativistic many-body setting, in tal interactions of physics has been the field; in fact, they are rather common- which any number of particles may be main justification for the huge effort to place within the broader academic com- created or destroyed within extremely develop String Theory over the past munity: the pressures upon young short time and space intervals. twenty-five years. This alternative to researchers to fit into an already estab- The discovery of this framework and quantum field theory conceives of all lished "niche," the lack of incentive or proof of its consistency were hailed as particles, including the graviton, as reward for independent thought, the a great breakthrough in our under- quantum excitations of strings. This is tendency towards "tribalism" and "group standing of the laws governing the in- very different from the usual quantum thought," the tendency by more senior teractions of elementary particles. It fol- field theory framework, but the latter is scientists, who can provide or deny op- lowed four decades of struggle, was expected to be recoverable in a suitable portunities to younger researchers, to consolidated within the short period "low energy" regime (which includes all judge the merits of candidates by how 1970-1974, and confirmed to be in energies accessible to high energy lab- well they agree with their own outlook agreement with experiment in the years oratories to date). and interests, etc. that followed. It led within the subse- Smolin's own research priorities are To these general sociological cri- quent two decades to the award of three spelled out in the first chapter, entitled

2008 Springer Science+Business Media, Inc., Volume 30, Number 3, 2008 67 "The Five Great Problems in Theoreti- interactions. Phenomenological expla- detection, without any dynamical mech- cal Physics". In his view, these are: (1) nations, based on "flux tubes," and anism implying such a process, or its To combine General Relativity and "quark confinement" (neither of which stability, and no physical explanation of Quantum Theory in a single, complete have actually been demonstrated to fol- why one or another of these "back- theory of nature; (2) To resolve what low directly from the model) have been grounds" (in ten or eleven dimensions) he regards as problems in the founda- put forward. But the fact remains that is preferred. The vast multiplicity of pos- tions of Quantum Mechanics. These in- the Weak and Electromagnetic interac- sible background geometries available clude finding a better epistemological tions can be dealt with directly; that is, in the "string landscape" seem to make explanation of quantum theory, or an the scattering amplitudes, decay rates, it impossible to arrive at definite pre- alternative theory that is not based on and correlations can be computed and dictions since they introduce a huge the necessity of involving the observer compared, successfully, with experi- number of additional parameters (the as part of the measurement process; (3) ment, whereas the same cannot as yet "moduli") whose values the theory is in- To come up with a unified theory that be done for the Strong interactions us- capable of determining; (2) The lack of combines all the known forces of na- ing just QCD as a starting point. any experimental evidence for the dis- ture (a bit redundant, when compared No one expects to improve on the tinct consequences of string theory. In with Great Problem 1); (4) To explain accuracy of the results of perturbative particular, the essential ingredient of all the apparently arbitrary constants ap- calculations, but it would be nice to "supersymmetry" (from which derives pearing in the "Standard Model"; (5) To have them on a logically complete the name "Superstrings") is required to account for the existence (or nonexis- mathematical footing. Some (though not assure finiteness. At the very least, this tence) of "Dark Matter" and "Dark En- all) theoreticians see it as desirable that means a matched pairing of all the ergy." (This is a conjectured explana- the foundations of quantum field the- fermionic particles in the universe, hav- tion of the apparent inconsistency ory be revamped so as to make the ex- ing 1/2 integer spins (such as electrons, between the amount of observed mat- istence of interacting quantum fields ac- neutrinos, quarks) with bosonic part- ter in galaxies and the rates at which cord with our current level of ners, sharing similar properties, but hav- stars and galaxies are moving, which mathematical understanding. (This is, ing integer spins. Nothing remotely like supposes the existence of matter and roughly, the other part of the Millen- this exists in the currently observed energy that is "invisible," adding up to nium Problem referred to previously.) spectrum of elementary particles. The as much as 96% of the total energy in These goals are no less compelling usual reply to this is: "Yes, but it is a the universe.) than the ones listed by Smolin, and spontaneously broken symmetry", which These may all be worthy goals, but probably several more could be added. just suggests sweeping an essential fea- not everyone would agree on their pri- Perhaps the reason for his particular ture under the rug because it is incon- macy or achievability. In fact, there are choices was to keep within a range that venient to face up to its observable many other outstanding problems that could possibly be addressed by String implications; (3)The absence of a "com- are at least as worthy of attention, but Theory (although he concedes that (2) plete" version of string theory. In par- do not appear on this list. For example, is not one of these). Or perhaps, the ticular, there is no "Superstring Field the so-called "Mass Gap Problem," others are not listed because they con- Theory" that would allow for processes which was one of the "Millennium Prize sist of improving or completing our un- involving the creation and annihilation Problems" [31 announced as a challenge derstanding of an already existing the- of strings. in the year 2000 by the Clay Institute in ory, and therefore do not figure as Beyond these broad critiques, there its list of outstanding, mainly mathe- "revolutionary" (cf. T. S. Kuhn [4]). are a number of doubts raised regard- matical problems (one of which -- the Although Smolin repeatedly empha- ing more technical points, such as the Poincar6 conjecture -- has since been sizes his preference for independent interpretation of the various types of solved), that would gain for the suc- approaches, and abhorrence of "group "duality" that enter into the theory, cessful solver, besides fame and glory, thought," it seems that some assump- which help to reduce what might be a modest prize of $1,000,000. For a tions of the community he is criticizing five distinct versions to one, and the physicist, the most concrete part of this have also been adopted by him. In par- sign of the cosmological constant, problem consists of explaining, as a ticular, little mention is made in The which has direct implications for the be- consequence of QCD -- or some vari- Trouble with Physics of approaches haviour of matter in the large. Whether ant -- why it is that the Strong nuclear other than String Theory, except for his right or wrong, these are best left to the interactions are short range. Although own specialty of Loop Gravity, which specialists to debate, since they do not the short-range nature of the Weak in- is given nearly equal prominence and in themselves imply fundamental trou- teractions follows directly from the Stan- space, although it only represents the ble with the theory, simply differences dard Model through the mechanism of interests of a rather small sector of the of view regarding its implications. (See, "spontaneous symmetry breaking," an research community. e.g., [5] for a discussion and rebuttal of essential ingredient, the existence of the The main scientific critiques of String some of these points.) massive, spinless "Higgs Boson" re- Theory elaborated in the book are: (1) Smolin also regrets that an entire mains to be confirmed experimentally. The necessity for introducing unob- generation of theoretical elementary QCD, however, does not allow for a servable "higher dimensions" that are particle physicists has been raised to similar breaking of the underlying understood as spontaneously "curled work with such a highly esoteric math- gauge symmetry governing the strong up" to such small sizes that they escape ematical model, founded on far-fetched

~8 THE MATHEMATICALINTELLIGENCER speculation, without seeing the neces- to dismiss as unworthy of mention un- concerned the precise understanding of sity for pinning down their conjectures der the title The Trouble with Physics scaling properties in critical phenomena by precise mathematical demonstration, the many wonderful discoveries, both in two dimensions, and related phe- and without adequate consideration of experimental and theoretical, that have nomena such as percolation, and criti- possible alternatives. Finally, there are been made over the past three decades cal wetting. In the high-energy domain the further sociological-psychological in other areas of physics. it should also be mentioned that the critiques: the arrogance with which The most interesting of these, which prediction of "asymptotic freedom", 5 many string-theorists have vaunted the have merited not a few Nobel Prizes in which was an essential step in making relative importance of their work, and recent years, have tended to concern sense of a quantum field theory of the the pressure that has been put upon up- the "other" frontier of experimental and strong interactions, obtained its experi- coming researchers to work along cur- theoretical physics: the physics of tem- mental verification within the past two rently accepted lines, at risk of achiev- peratures near to absolute zero and decades. ing nothing of any real significance (and macroscopic quantum phenomena. The There are numerous other examples getting no employment). The criticism latter largely concern quantum effects that could be cited. Perhaps none of the of immodest swagger, however, comes and states of matter that can be ob- above can be compared in ambition or from an author who ends his book by served at or near macroscopic scales, scope with seeking a "Theory of Every- stating, with no hint of irony or self- both at very low temperatures, and at thing", nor to the impact of the revolu- mockery, that he will now return to his temperatures at which it was never pre- tionary developments of the early twen- "real job," which is to "finish the revo- viously imagined such collective quan- tieth century: Relativity Theory and lution that Einstein started." tum effects could occur. These include Quantum Mechanics. They nevertheless Although some of the most brilliant many of the really remarkable achieve- represent very exciting advances in our and talented researchers of our day ments of physics of the past few understanding of the physical world, have devoted themselves to String The- decades. For example, there was the and provide abundant evidence that ory, it is undeniable that advances have creation, in plasma physics laboratories, much more is healthy and robust in the largely been driven by far-reaching, but of a "Bose-Einstein Condensate," an en- physics of the past three decades than incompletely demonstrated conjectures. tirely new state of matter, achievable what might, by narrowly focusing on New ideas have had an esoteric, self- only at the lowest temperatures, pre- the shortfalls of String Theory, lead to contained character, independent of the dicted by Einstein in the 1920s, but not the conclusion that physics of our time traditional checks based on careful observed in a laboratory until the is in trouble. comparison with experiment. There is 1990s. 1 Related to this is the remarkable no doubt that Einstein, who ahvays was use of "laser cooling" and optical or REFERENCES concerned with testing theoretical pre- other methods for reducing the motion [1] Brian R. Greene, The Elegant Universe." Su- dictions against observation, would be of individual molecules to such a slow perstrings, Hidden Dimensions, and the point that they can be individually stud- astonished at such a situation persisting Quest for the Ultimate Theory, Norton, after more than two decades of research ied and controlled, and together with 1999. in the subject. The most important con- this, the creation of purely optical grids, [2] Paul C. W. Davies, Julian Brown (eds.), Su- cern for String Theory, in the end, may and traps. 2 There have also been im- perstrings: A Theory of Everything?, Cam- be that the legacy of the current gen- portant theoretical advances in the un- bridge University Press (1988). eration of theorists risks being purely derstanding of disordered systems, liq- [3] A. Jaffe, E. Witten, 'Tang-Mills and the mathematical in nature if no contact is uid crystals, and polymer dynamics. -~ made within a reasonable time with ex- There have been the observation and Mass Gap," Clay Institute Millenium Prize perimentally verifiable phenomena. theoretical explanation of the "fractional Problem. URL: http://www.claymath.org/ Whatever the validity of the argu- quantum Hall effect", a phenomenon millennium/Yang-Mills Theory. ments in this book as a critique of String that brings to light the beautiful role [4] T. S. Kuhn, The Structure of Scientific Rev- Theory, they do not justify the sweep- played by topology in the electromag- olutions, 3rd. ed., University of Chicago ing conclusion implied in the title. The netic properties of ordinary matter in a Press, 1996. Trouble with String Theory might have suitable quantum regime/~ The discov- [5] J. Polchinski, "All strung out," The Ameri- sold fewer copies, but it would have ery of high-temperature superconduc- can Scientist online, Jan-Feb 2007. been a more accurate characterization tivity has led to fundamental challenges of the content of this book. It is a poor to explain associated recently-discov- Centre de Recherches Math6matiques service to potential young physicists, ered phenomena. Another dramatic de- Montreal, Canada and an injustice to the rest of physics, velopment in theoretical physics has e-mail: [email protected]

1Nobel prize to E. Cornell, W. Ketterle, and C. Wiemann (2001). 2Nobel prize to S. Chu, C. Cohen-Tannoudji, and W.D. Phillips (1997). 3Nobel Prize to Pierre-Gilles de Gennes (1991). 4Nobel Prize to R. B. Laughlin, H. L. St6rmer, and D. C. Tsui (1998). 5Nobel Prize to some of the theoreticians who derived it: D. Gross, D. Politzer, and F. Wilczek (2004).

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