The latest entry in the register of futile utility is a letter to the New York Review of Books, signed
Bard Professor and Chairman Emeritus
Department of Molecular Biophysics and Physiology
Rush University Medical Center
objecting to a display of “profound ignorance of the role of mathematics in creating the world we live in” in Jim Holt’s “otherwise admirable review” of MWA. After enumerating some useful applications of mathematics (design of buildings, electronic devices, imaging technology, an amplifier), Eisenberg affirms that
The necessity of mathematics is indeed obvious to everyone in computer science, to anyone who has programmed at all, and of course to all engineers and almost all scientists.
and formulates a wish:
Perhaps it would be helpful if the public, or at least the educated public, realized that our standard of living is directly the result of that tiny part of the world that mathematics describes accurately (with simple equations and unchanging parameters).
Holt replied by politely pointing out that Eisenberg is “absolutely right” about the “technological usefulness of mathematics” — even the Rolling Stones need calculus, Holt agrees — and that Eisenberg simply misread the review. That’s certainly true, but since some of the most negative reviews of MWA have been motivated by a similar misreading, perhaps it would be helpful if we tried to figure out what accounts for such persistent reading in to my book, and now to Holt’s review, of something that is clearly not there.
My reactions to negative comments on this blog have been mild because I know their authors’ words, like Eisenberg’s, are not their own. Stefan Collini’s article in the latest issue of the London Review of Books offers a clue as to how these words entered their authors’ minds. Collini has for years been chronicling the attempts of successive governments to browbeat British academia into mindless utilitarianism, and I shamelessly mined his articles for material for MWA. Collini points out that the expression “value for money”
occurs four times in the one-page foreword to the new Green Paper written by Jo Johnson, the minister for universities and science
The British way has the merit of crude clarity, and one senses the British touch in expressions like “entrepreneurial mindset” (as in “Insufficient entrepreneurial mindset among students,” an obstacle to EU Strategic and Priority Initiatives in a report dated 2009 — the term is American, however) sprinkled throughout MWA, particularly in Chapter 10. This helps explain why Collini is able to write so clearly:
Much of our contemporary discourse about universities still draws on, or unwittingly presumes, [a] pattern of assumptions [that remained stable for 30 years or so after 1945]: the idea that the university is a partly protected space in which the search for deeper and wider understanding takes precedence over all more immediate goals; the belief that, in addition to preparing the young for future employment, the aim of developing analytical and creative human capacities is a worthwhile social purpose; the conviction that the existence of centres of disinterested inquiry and the transmission of a cultural and intellectual inheritance are self-evident public goods; and so on.
If that boldface passage (my emphasis) looks familiar, it’s because the self-evidence in question was invoked on p. 70 of MWA and already quoted on this blog:
if the notion of “general [or public] interest” means anything at all, it should be a matter of general interest that work be a source of pleasure for as many people as possible.
That’s the sort of thing that nowadays gets you in trouble with revolting taxpayers, but MWA, like Collini, invites readers to imagine a time not so long ago when it really was self-evident. Revolting taxpayers are officially the motors of the change of attitude, as Collini reports, but the real culprits are elsewhere:
If ‘prosperity’ is the overriding value in market democracies, then universities must be repurposed as ‘engines of growth’. The value of research has then to be understood in terms of its contribution to economic innovation, and the value of teaching in terms of preparing people for particular forms of employment. There are tensions and inconsistencies within this newer conception, just as there are in the larger framework of neoliberalism: neoliberal thinking promotes ‘free competition’ in international markets, while the rhetoric of national advantage in the ‘global struggle’ often echoes mercantilist assumptions. But, gradually, what we still call universities are coming to be reshaped as centres of applied expertise and vocational training that are subordinate to a society’s ‘economic strategy’.
That’s MWA‘s thesis on “usefulness” in a nutshell, and Collini puts it into words much better than I ever could. This post’s title is taken from Collini’s very next paragraph, and you should probably just skip this post (and MWA) entirely and just read Collini’s columns on British universities, working back from the most recent one. Collini has his fellow literary scholars in mind, no doubt, but it applies just as well to pure mathematics. This is harder to perceive, of course, because the Golden Goose argument makes a superficially persuasive case for the unpredictable utility of blue skies research in theoretical science. So even if Eisenberg’s underlying motivation is to fend off the inevitable accusation (by legislators in Illinois, North Carolina, or elsewhere) that academic institutions are spending revolting taxpayers’ money to support people (useless or otherwise) doing useless work, what he actually writes seems to make sense.
The utility of work in mathematics, however, is not self-evident — or at least it’s less self-evident that “the existence of centres of disinterested inquiry and the transmission of a cultural and intellectual inheritance” used to be. Eisenberg hopes to settle the matter by pointing out that mathematical work is useful because it is responsible for the persistence of something whose utility is self evident, namely our standard of living. Depending on how “our” is understood, however, the self-evidence of this criterion for utility can immediately be disproved. Algebraic geometry turns out to be useful, according to an essay entitled “Mathematics: Accepting the Increasing Energy Demand Challenge” for Shell’s Algebraic Oil project. Consider
a collection of measurements of physical production quantities. This collection of quantities may be considered as causing the production; the associated indeterminates are called the causing indeterminates. The production itself is considered as the effect of the action of the causing variables. The production is – assumed to be – an element of the special ring under consideration. This is admittedly still a modeling assumption, albeit – relatively – weak: the production is assumed to be a polynomial, but its structure – coefficients and support – are not known upfront. Now there will of course be relations among the causing variables, that is polynomials in these variables that when evaluated over [the measurements], vanish. From the point of view of value – size – of the production, all production polynomials that differ by a relation in the causing variables are the ‘identical’ an in particular for Shell sensible point of view. So production polynomials are considered modulo relations among the causing variables. Mathematically speaking this means that the production is considered in another ring, in which the relations among the causing variables are declared to belong to the zero of that new ring.
The essay was the contribution of Dr. Jan van der Eijk, Group Chief Technology Officer of Shell Research, to the book Mathematik—Motor der Wirtschaft which was quoted at some length in chapter 10 of MWA. The above paragraph is on pp. 95-96; there are also extensive discussions of applications of PDE and control theory. All of this is useful because
The world’s growing population and the rapid development of new economies will result in a sharp rise of energy demand. Although sustainable energy sources will play an increasingly important role, fossil fuels will remain the backbone of the global energy supply for the foreseeable future.
Thus mathematics is directly responsible not only for the maintenance of our standard of living, as Eisenberg would have it, but the improvement of the standard of living in “new economies.” Ivar Ekeland, in his Syndrome de la grenouille, has a different notion of utility:
…the problem of global warming is posed solely in economic terms, and human beings have been reduced to their utilitarian dimension. We have made them into machines for optimizing their individual well-being. The miracle of the market is that individual self-interests lead finally to a collective optimum, but in the case of global warming, and other public goods, the miracle did not take place, the invisible hand is not operating, and the mere search for individual economic advantage leads to a collective catastrophe.
Less catastrophically, MWA invokes the eminent cultural critic Tom Waits to ask how to balance the necessity of number theory for e-commerce against the utility of independent bookstores and record shops.
The point is that it’s meaningless to say that mathematics contributes to our standard of living without specifying when and for how long; that applications of mathematics are necessary or useful without specifying for whom? That should be obvious, but if it were obvious, why do people like Eisenberg (and certain hostile reviewers) feel the need to insist on the utility of mathematics in the abstract, as if the notion made sense?