Category Archives: Values

The belief that there are natural laws of finance

I continue the discussion of Frédéric Lordon’s Jusqu’à quand, which contains an explanation of the practices that made the 2008 crash inevitable that has yet to be translated into English although it is more specific and complete than Margot Robbie in a bubble bath or celebrity chef Anthony Bourdain making fish stew.  Here is a quotation that grapples directly with the most dangerous of the many illusions promoted by the manufacturers of mathematical models, namely that the objectivity of such models can be separated not only from the empirical observations needed to confirm and perfect them but also from need for a conceptual framework in which the question of the model’s objectivity can be raised.   Lordon argues that quantitative (probabilistic) models of finance are meaningless if there is no reason to believe that finance is governed by natural laws:

Obviously the most devoted partisans of quantitative finance will argue that any imperfection is transitory and remind us how the development of science is progressive but irresistible; even if today’s models still make a few mistakes, there is no problem that won’t eventually give way to hard work and research.  There are nevertheless reasons to think that this optimism will come up against a fundamental and insurmountable obstacle, rooted in the very question of knowing whether it is possible, and if so how far, to grasp financial risk through the calculus of probabilities.    Transcribing risk in the language of probability is such a common practice that it is never called into question.  The modelers, who consider the question trivial, are thus barely aware of the — absolutely non-trivial — theoretical choices they undertake when they make the hypothesis that the prices of financial assets are governed by this or that probabilistic law. … Of all the tools offered by the calculus of probability, the so-called “Gaussian” law is the one most commonly used … because it’s the simplest to manipulate.  But Gaussian laws have the unfortunate property of considering large price variations as events of minuscule probability… even though they are frequently observed in financial reality.  [Thus there is a competition to find the most realistic law…]  But the more frenetic the search for the “right hypothesis” becomes, the more one loses sight of the essential point…:  the belief that one will someday find the “right probability density” amounts to the belief that there are natural laws of finance.  This belief can be given the name of “objective probabilism” because it presupposes that there objectively exists a certain law of probability — “we’ll find it in the end” — that governs the price of assets.

Lordon finds more credible an “alternative approach,” which he associates with the name of André Orléan, according to which

“the” probability density doesn’t fall from the sky of “objective natures” but is rather the endogenous product of the interaction of financial operatives.  … It’s the radical modification of the configuration of interactions between operatives, expressed notably by the brutal variation of the degree of heterogeneity (or homogeneity) of behaviors, that produces the regime shift, and the qualitative transformation of the relevant probability density.

Students of dynamical systems will recognize the similarity to the language of René Thom’s catastrophe theory.  Lordon continues:

If one is absolutely set on maintaining the notion of law to describe the phenomena of finance — and the observation can be extended to all the phenomena of economics — one must bear in mind that the laws in question are not natural and invariant but rather temporary, variable, and contingent.   If one wishes, one can therefore preserve the general probabilistic framework but only after amending it substantially… where quantitative finance believes firmly in an objective probabilism, what one could even call a transcendent probabilism, there is in reality only an immanent probabilism:  the laws of probability do not fall to earth from a heaven of ideas, they emerge from below, shaped by the concrete interactions of agents — another way to rediscover that God doesn’t exist.

The last few words notwithstanding, here we see Lordon on the road to Spinozism.  We will not follow him there, but rather draw the conclusion that, if “There is no alternative,” the formula associated with Margaret Thatcher, it’s because the decision-makers, the Powerful Beings, as they are called in MWA, have contrived to make alternatives impossible.  It’s certainly not because alternatives are mathematically unthinkable.


The alternative is to change the frame

Lordon at Bourse du Travail

Frédéric Lordon at the Bourse du Travail, Paris, April 20 (March 51), 2016

In their haste to titter about the drama to which Guido Menzio was subjected the other day at Philadelphia International Airport — the University of Pennsylvania economist was pulled off his flight and briefly questioned by the FBI, before he was allowed to reboard, because he had been spotted scribbling differential equations in his note pad — the journalists (and the FBI agents as well, apparently) neglected to ask the obvious question:  were his equations blueprints for what Warren Buffett called “financial weapons of mass destruction?”

The answer:  apparently not.  Menzio, who is linked to the author of this blog by seven degrees of separation, Menzio

is a specialist in the equilibrium of job search models, not in financial derivatives.  The journalists nevertheless squandered an opportunity to remind their readers that economics can be no less life-threatening than suicide bombers and that a quantitative comparison of their relative dangers is urgently needed.

I first encountered Frédéric Lordon’s elegantly ironic prose in the pages of Le Monde Diplomatique, probably in 2004, when he was already writing about the destructive effects of finance, long before the crash of 2008 showed him in retrospect to have been a prophet.  As the warning signs of the coming catastrophe accumulated in 2007, Lordon was there to point them out;  when the crash finally did arrive, I immediately turned to the book Lordon had completed, a few weeks before the Lehman Brothers collapse, for an explanation of what had brought the world’s economy to the brink of disaster.  Lordon’s book contained an introduction to what was then the arcane superstructure of MBSs, SPVs, CDOs, and CDSs that the “mad mathematicians of Wall Street” had erected on what would soon be the smoking ruins of what is politely called the “real economy,” and although MWA didn’t cite Lordon explicitly, I regret not including his book in the bibliography, since Chapter 4 could not have been written without it.

My next post will translate an excerpt from Lordon’s 2008 book of particular relevance to mathematics and mathematicians.  The witty and multiply-talented Lordon has since gone on to write many articles in Le Monde Diplomatique as well as many books, including what must be the only comedy in rhyming alexandrine verse (since made into a film) about the subprime crisis:

Le banquier

Monsieur le Président, votre haut patronage
Nous offre l’occasion de multiples hommages.
A votre action d’abord qui fut incomparable
Et victorieusement éloigna l’innommable.
Mais à votre sagesse nous devons tout autant
La grâce que nous vaut le parfait agrément
De vous entretenir et d’avoir votre oreille,
Pour éloigner de vous tous les mauvais conseils.

Le quatrième banquier

Nous savons le courroux qui saisit l’opinion,
Tout ce que s’y fermente, toute l’agitation.
Nous entendons la rue rougeoyant comme forge
Vouloir nous châtier, nous faire rendre gorge.
Le peuple est ignorant, livré aux démagogues,
Outrance et déraison sont ses violentes drogues.
Il n’est que passion brute, impulsion sans contrôle,
Un bloc d’emportement, et de fureur un môle.

Le troisième banquier

Mais nous craignons surtout que des opportunistes,
Sans vergogne excitant la fibre populiste,
Propagent leurs idées, infestent les esprits.
Ils ne nous veulent plus que raides et occis.
Même les modérés sont assez dangereux.
Incontestablement ils semblent moins hargneux,
Et s’ils n’ont nul projet de nous éradiquer,
Ils ne veulent pas moins nous faire réguler…

In recent years he had switched his attention (and his academic affiliation) to philosophy and was calling himself a Spinozist — the only one of his books translated into English is entitled Willing Slaves of Capital:  Spinoza and Marx on Desire.   But when le peuple began their nightly occupations of the Place de la République in Paris, calling themselves Nuit Debout,

Nuit Debout - 1.jpg

Nuit Debout by day, March 49, 2016

Lordon was acknowledged as an intellectual reference — a maître de penser, according to Le Monde.  The image at the top of this post is a screen capture of his (seated) intervention at a mass meeting around the corner from the Place de la République devoted to the “next step.”  The passage that starts at about 7’05” is particularly recommended.  I translate the climax (from 7’50” to 8’20”):

When the liberals say TINA, There Is No Alternative, it is objectively true.   But it is a conditional truth.  Yes, it is objectively true that, when one has set up the frame of all the neoliberal structures I just mentioned, there are no longer alternatives, and the frame is designed precisely to rule them all out.  However, if there are no longer alternatives within the frame, there is always the alternative of changing the frame.

Nuit Debout - 1 (1)

Nuit debout at dusk, March 64, 2016

Economics as theology, as viewed by Chinese astrologers



Chinese armillary sphere, Ming Dynasty, from Wikimedia Commons

Readers who recall Joseph Stiglitz’s quip that “economics is really a religion” will not be surprised to find a scholar of Chinese religion drawing parallels between the dismal science’s contemporary prestige and that of imperial Chinese astrology, on the basis of the common dependence of the two disciplinary practices on sophisticated mathematical models.  Not that imperial China had a monopoly on astrological economics:

…take the extraordinary success of Evangeline Adams, a turn-of-the-20th-century astrologer whose clients included the president of Prudential Insurance, two presidents of the New York Stock Exchange, the steel magnate Charles M Schwab, and the banker J P Morgan. … when Adams was arrested in 1914 for violating a New York law against astrology, it was mathematics that eventually exonerated her. During the trial, her lawyer Clark L Jordan emphasised mathematics in order to distinguish his client’s practice from superstition, calling astrology ‘a mathematical or exact science’. Adams herself demonstrated this ‘scientific’ method by reading the astrological chart of the judge’s son. The judge was impressed: the plaintiff, he observed, went through a ‘mathematical process to get at her conclusions… I am satisfied that the element of fraud… is absent here.’

I’m quoting from an article by Alan Jay Levinovitz on the website (one of whose senior editors owes me a letter, if I’m not mistaken).   The common origins of mathematics and astrology are addressed at some length in Chapter 8 of MWA, but not to make a point about superstition.  The deference granted economics on the grounds of its sophisticated mathematical models, in spite of its “unearned empirical authority,” deserves sustained analysis as well as critique.   I refer you to the references in Levinovitz’s article.  Here are a few choice quotations:

The historian Caley Horan at the Massachusetts Institute of Technology described to me how computing technology made financial astrology explode in the 1970s and ’80s. ‘Within the world of finance, there’s always a superstitious, quasi-spiritual trend to find meaning in markets,’ said Horan. ‘Technical analysts at big banks, they’re trying to find patterns in past market behaviour, so it’s not a leap for them to go to astrology.’ In 2000, USA Today quoted Robin Griffiths, the chief technical analyst at HSBC, the world’s third largest bank, saying that ‘most astrology stuff doesn’t check out, but some of it does’.

Modern governments, universities and businesses underwrite the production of economic theory with huge amounts of capital. The same was true for li production in ancient China. The emperor – the ‘Son of Heaven’ – spent astronomical sums refining mathematical models of the stars. Take the armillary sphere, such as the two-metre cage of graduated bronze rings in Nanjing, made to represent the celestial sphere and used to visualise data in three-dimensions. As Morgan emphasises, the sphere was literally made of money. Bronze being the basis of the currency, governments were smelting cash by the metric ton to pour it into li. A divine, mathematical world-engine, built of cash, sanctifying the powers that be.

‘I’ve come to the position that there should be a stronger bias against the use of math,’ [NYU economist] Romer explained to me. ‘If somebody came and said: “Look, I have this Earth-changing insight about economics, but the only way I can express it is by making use of the quirks of the Latin language”, we’d say go to hell, unless they could convince us it was really essential. The burden of proof is on them.’

and a reminder that Stiglitz’s joke was already the title of a book long before the 2008 crash:

Romer is not the first to elaborate the mathiness critique. In 1886, an article in Science accused economics of misusing the language of the physical sciences to conceal ‘emptiness behind a breastwork of mathematical formulas’. More recently, Deirdre N McCloskey’s The Rhetoric of Economics (1998) and Robert H Nelson’s Economics as Religion (2001) both argued that mathematics in economic theory serves, in McCloskey’s words, primarily to deliver the message ‘Look at how very scientific I am.’


Is the mathematical hierarchy oppressive?

After many interruptions I finally finished reading all the comments on Piper Harron’s blog, especially the long exchange (62 comments) entitled “Why I do not talk about math.”  This extended dialogue is deeply educational, and not only for those interested in mathematics.  Repeatedly contributors attempt to demonstrate their good intentions in the name of an abstract universalism, and Harron replies, politely but firmly, pointing out how the form as well as the content of their intervention reflects a position of privilege that is not necessarily conscious.  The entire exchange serves to reinforce the point of Harron’s title, as I understand it, namely that the process of repeatedly pointing out the effect of what (in a different post) Harron calls “oppressive hierarchies” eventually becomes tiresome, if not oppressive.

Harron’s comments overlap with the subject of Chapter 2 of MWA, entitled “How I acquired charisma.”  The chapter is primarily an extended reflection on the hierarchical structure of contemporary mathematics, interspersed (for narrative purposes) with an ideal-typical Bildungsroman whose anti-hero — who for the sake of convenience was chosen to bear a strong resemblance to the author of the book —is conducted, through the apparently natural workings of this hierarchical structure, to a middle-management position (routinized charisma) within the hierarchy.  The original purpose of the chapter was not mainly to engage in social criticism — that’s the focus of (parts of) Chapters 9, 3, and 4 — but rather to formulate a philosophical thesis, a tentative answer to the question formulated by KD on Harron’s blog:

I have always wondered exactly who gets to decide what is “important” or “interesting.”

I take sociology to be the discipline whose role is to answer questions like this, to study how collective decisions by groups of human beings come to be construed as objective and natural, and the chapter has a number of references to the sociology of science, and a handful of references to the much smaller literature in sociology of mathematics.

KD’s question, however, is political rather than sociological, with the implication that those who “get to decide” are exercising power from which those who don’t “get to decide” are excluded.  In the context of Harron’s blog, it is understood that this exclusion is not legitimate — or rather, since legitimacy as such can only be determined within the social order, that the order itself deserves to be called into question; in other words, as Harron writes, “We Need a Revolution. Period.

In a chapter of The Princeton Companion to Applied Mathematics entitled “Mediated Mathematics:  Representations of Mathematics in Popular Culture and Why These Matter,” Heather Mendick has written about how this exclusion is reflected in popular culture:

…popular culture can include some and exclude others.  For example, while society confers on all a responsibility to become mathematically literate, it suggests that only a special few possess mathematical “ability.”  It overwhelmingly depicts this ability as belonging in white, male, middle-class, heterosexual bodies.

Popular culture is not exactly a mirror of the reality of the profession, but it’s uncomfortably close.  Harron wrote an unconventional thesis in part because she sees this exclusion as rooted in the norms of contemporary mathematical practice; as she wrote

I just think our criteria for “new” “contributions” are seriously flawed and counterproductive and marginalizing. any mathematician who cares about “diversity” needs to be willing to shatter current paradigms.

I have been unhappy with the use of the word “diversity” in this context ever since I learned how it entered American jurisprudence in Christopher Newfield’s book Unmaking the Public University:

…in [Justice Lewis] Powell’s diversity framework, diversity was the expression of an institution’s freedom to choose particularly attractive individuals, and was about ensuring this freedom for powerful institutions like… Harvard College.…Diversity acquired social influence not as a moderate mode in which to pursue racial equality but as an alternative to that pursuit.

But Harron, whose blog is called The Liberated Mathematician, obviously doesn’t have Powell’s framework in mind when she uses the word diversity, so I will leave that discussion for later.  Instead I will engage in utopian speculation, in order to address what I see as the more subversive implications of Harron’s call for “power^people.”  Suppose one could magically do away with all the barriers to participation in mathematics of underrepresented populations, all the forms of exclusion, that are conventionally seen as political.  Would mathematics still be hierarchical?  And if so, would it still be oppressive?

A long tradition sees mathematics, and the sciences more generally, as necessarily hierarchical.  MWA quotes Max Weber on p. 10:

“Democracy should be used only where it is in place,” wrote Max Weber in the  1920s.  “Scientific training …is the affair of an intellectual aristocracy, and we  should not hide this from ourselves.”

And just last year, Alain Badiou wrote

The mathematical aristocracy at the creative level is… the most restrictive of all possible aristocracies.  (Badiou, Éloge des mathématiques, p. 23)

Chapter 2 of MWA exhibits the operations of hierarchy both symbolically (the IBM Men of Modern Mathematics poster, as well as Figures 2.1, 2.2, and 2.3) and materially (the role of the journal system in what Terry Tao called “certifying… significance” and “designation”, see p. 36).

Are these practices a relic of a more aristocratic period in the life of our species, and can we look forward to a future mathematics that is more inclusive, in the vision expressed by David Pimm and Nathalie Sinclair and quoted on p. 33 of MWA:

Asking “[I]n  what sense … can mathematics be considered a democratic regime…” open to all,  Pimm and Sinclair quote  … Henri Poincaré to the effect that “only  mathematicians are privy to the aesthetic sensibilities that enable” the decision of “what is worth studying.”  The article, published in a journal for educators, is  motivated by the “view that mathematics can do something for me in a  humanistic sense that repays the careful attention and deep engagement it may  require; one that may expose students to a fundamental sense and experience of  equality … and provide them with another sense of human commonality.”

Or is it the case, as Chapter 2 suggests, that “the content of mathematics is bound up … with a hierarchical charismatic structure”;  so that if Weber’s “intellectual aristocracy” lose control of the editorial boards of the “great journals” will mathematics be voided of its content and collapse into a sort of intellectual gray goo?

Philip Davis and Reuben Hersh, in The Mathematical Experience, famously claimed that “the typical working mathematician is a Platonist on weekdays and a formalist on Sundays.”  I would consider substituting “social constructivist” for “formalist” in that sentence; that would make clearer the unsettling radicalism implicit in Harron’s critique.  For my part, while my (routinized) charismatic bargain leaves me the freedom to be a social critic on the weekends, when I write things like this blog entry and Mathematics without Apologies, on weekdays I carry out my middle-level managerial tasks of maintaining the charismatic hierarchy — writing letters of recommendation, sitting on hiring committees, refereeing journal articles, all the “Traditional Rituals” (in the language of sociologist Bernard Gustin) without which the system would not be a system.  I’m a gatekeeper, in other words.  Not only that, I fulfill my functions with sincerity and commitment, and that should go without saying, otherwise my charisma would be unceremoniously withdrawn.

So am I contributing to the preservation of an oppressive system?  It’s easy to point to out that our professional autonomy is conditioned by one might call its limited sovereignty, the fact that (but this is one of the themes of Chapter 3) that we are dependent on Powerful Beings for the external goods without which the profession ceases to exist.  The Elsevier boycott of 2012 brought home to me just how little leverage we have, as mathematicians, over the profession’s material conditions, even those one might expect to be most dependent on our charismatic consent.  Our professional associations enjoy a fair amount of moral authority but lack the personnel, the organizational structure, the money, and the executive power to put up substantial resistance to the Powerful Beings on whom we depend.  Rereading the comments on Piper Harron’s blog, it occurs to me that the people to whom they are addressed, namely her readers, are not in a position to do much of anything about the issues raised there, beyond trying to answer questions like the one in this post’s title.

Alain Badiou bows down to mathematics


S’il existe une authentique Internationale, aujourd’hui, c’est bien celle des mathématiciens.

Alain Badiou, Éloge des mathématiques

When Alain Badiou, who is proud to call himself a Communist, claims that mathematicians represent the only authentic International (with a capital “I”), you know that, whatever the problem, he sees mathematics as part of the solution.   Badiou has written in Éloge des mathématiques that “the fundamental relation between philosophy and mathematics is a relation of reverence, if I may say so.  Something in philosophy bows down to mathematics.”

What, according to Badiou, is the purpose of philosophy?

I believe that philosophy has no other goal than this:  to allow anyone to apprehend, in the field of [his or her] vital experience, what is a happy orientation.  One could also say this:  to place at everyone’s disposal the certainty that the true life [vraie vie], that of a Subject freely oriented according to a true idea, is possible.

Mathematics contributes to this goal because the mathematical Subject’s orientation is free but disciplined:

…by virtue of their aesthetic force and of the invention they require, mathematics forces one to become a Subject whose freedom, far from being in opposition to discipline, demands it.  Indeed, when you work on a mathematical problem, the invention of the solution — and thus the creative freedom of the spirit — is not some sort of blind wandering, but is rather determined like a path always bordered in a way by the obligations of global coherence and of the rules of proof.  You accomplish your desire to find the solution not against rational law, but together with its help and its prohibitions at the same time.  Now that is what I began to think, in the first place with Lacan:  desire and law are not in opposition, they are dialectically identical.

Badiou’s secret mathematical love formula:  Desire = Law.  (Maybe someone can suggest a symbol for identity that is more dialectical than =?)  In a different formulation:

 Is there a happiness greater than [the pleasures that one finds in commerce]?  There’s the great question of philosophy.  Our societies, domesticated by Capital and fetishism of goods, answer:  no.  But philosophy, tenaciously and since the beginning, has labored to make us think that it exists.

For Badiou, although mathematics is not for everyone, it does offer a “model, limited but convincing, of the possible dialectical relation between the finiteness of the individual who works and strays, and the infinity of the Subject who has understood a universal truth.”

I have underlined many more sentences in my copy of  Éloge des mathématiques and could go on quoting them, explaining both my agreements and disagreements.  But the few passages translated above should give a sense of his aims.  Readers who are only familiar with philosophy of mathematics in the analytic tradition will probably find this all baffling, but you should bear in mind that Badiou sees philosophy not as a series of footnotes to science but rather, in the spirit of the ancient Greeks, as an accompaniment in the search for happiness and the vraie vie.   Mathematics plays a central role because, as Badiou sees it, philosophy only became possible with the development of systematic mathematical reasoning.

Here is the list of Badiou’s New York appearances last December (and a few from previous years).  Can you find the word “mathematics?”

Alain Badiou, “The Fundamental Contradictions of the Contemporary World”

Monday, December 15, 2014 – 6:00pm

Location: East Gallery, Buell Hall (Maison Francaise)

Event Category: Talks

Eminent French philosopher Alain Badiou will deliver a public lecture on the topic of the fundamental contradictions of the contemporary world.
Alain Badiou is a philosopher, playwright, novelist and political activist. Heis professor emeritus at the École Normale Supérieure in Paris and continues to teach seminars at the Collège International de Philosophie and the European Graduate School. Trained as a mathematician, Alain Badiou is one of the most original French philosophers today. His philosophy seeks to expose and make sense of the potential of radical innovation (revolution, invention, transfiguration) in every situation. In addition to several novels, plays and political essays, he has published a number of major philosophical works, including Theory of the Subject, Being and Event, Being and Event II: Logics of Worlds and Being and Event III: The Immanence of Truths (forthcoming).

Below is his December program in NYC:

December 13th, at 6pm

He will be at the Miguel Abreu Gallery for the book launch of the English translation of Gilles Châtelet’s To Live and Think Like Pigs, for which he wrote the foreword.

Miguel Abreu Gallery, 36 Orchard Street, New York, NY 10002.

(Gilles Châtelet obtained a Ph.D. in mathematics before he went on to a career in philosophy; more about him in future posts.)


December 13th, at 7 pm:

He will participate in a lecture-performance entitled “A Dialogue Between A Chinese Philosopher And A French Philosopher” at The Educational Alliance.

The Educational Alliance, Manny Cantor Center, 197 East Broadway, New York, NY 10002


December 15th, at 6 pm: 

Badiou will give a presentation entitled “The fundamental contradictions of the contemporary world”, at the Maison Française of Columbia University.

Maison Française of Columbia University, 515 West 116th Street, New York, NY 10027

December 16th, at 6 pm:

On the occasion of the US publication of his book, The Age of the Poets: And Other Writings on Twentieth-Century Poetry and Prose, he will give a talk about “Literature and Onthology” at the Maison Française of NYU.

Maison Française of NYU, 16 Washington Mews, New York, NY 10003


December 17th, at 7 pm:

He will be at the Jack Tilton Gallery to lead a discussion entitled “Some considerations about contemporary art”.


Literature and Philosophy: Roman/Romanesque

Alain Badiou in dialogue
with Emily Apter

Thursday, December 10, 2015, 7:00 p.m.

A New French Philosophy Event, co-sponsored by the departments of French and Comparative Literature

ALAIN BADIOU is a philosopher, playwright, and author. His books include Logics of Worlds; Being and Event; Theory of the Subject; The Century and a host of treatises and manifestos on aesthetics, Arab Spring, love, and, most recently, mathematics.

EMILY APTER teaches in the departments of French and Comparative Literature at NYU. She co-edited a collection of Badiou’s essays on literature with Bruno Bosteels (Verso, 2014), and is currently completing a book on “unexceptional politics.”

You should not be reading this!


Jean-Michel Kantor is concerned that “the American intellectual world is … closed to European (French /CNRS) ideas,” and that readers of this blog, especially American intellectuals, have not had the opportunity to read what Michael Blay has written about blogs and other forms of electronic communication.  The proof that you are closed to French/CNRS ideas is that you are still reading this blog, and even the quotation on the back cover of Blay’s book has not yet convinced you to stop.  At Kantor’s request, I am therefore making the pages he selected from the book available so you can decide whether or not to overcome your click-addiction and devote fingers like the ones (presumably Kantor’s) pictured in the photocopies to slower and more ethical activities.


And if your fingers are not yet convinced of the virtues of slowness and don’t have time to read the three pages in French, here is a key excerpt, with (absent) punctuation as in the original:

“[…] choose slowness in order to recover the viewpoint of an actor of your existence by escaping the supposed virtues of the ever-faster and of acceleration that dispossess each of you of your existence by reducing it to unreflected behavior that is to say to ideologically conformist and learned behavior, to behaviors by means of which the totality of existence can enter into the productive field;”

Beneath the excessively long jargon-and-banality-packed phrasing — a clear sign that the author chose something other than slowness in pasting together this pamphlet — the reader may recognize one of the recurring themes of this blog, and of MWA:  namely, the resistance to reducing mathematics to its function in “the productive field.”  Although Blay concludes with a conclusion with which I believe I am in agreement, I am unable to detect anything resembling a persuasive argument in this excerpt, and, unlike Kantor, I remain convinced that it is possible to reason within the frame of a 250-1000 word blog entry.  For all I know, Blay may even agree with me.

Are your colleagues zombies?


No, I don’t mean that kind of zombie; you’d know it if they were.  No special philosophical training is required to detect Hollywood zombies; they are easily recognized by their facial expressions, gait, and characteristic behavior patterns.  The philosopher’s zombie, in contrast, is indistinguishable on grounds of physical appearance alone, and a dualist might want to argue that no material distinctions can be made between the zombies in your department and the rest of your colleagues.  What makes a zombie a legitimate object of philosophical inquiry is its (his?  hers?  eir?) absence of consciousness.  And today’s question is whether mathematical research requires consciousness, or whether it could just as well be left to zombies. If I were a philosopher of mind I’d consider it my professional duty to spend at least an hour every week imagining that my colleagues are all zombies, totally lacking in conscious experience, and introspecting about what, if anything, would be different about my professional and personal relations to them.  (And writing up the notes of my introspection for publication.)  No such duty weighs upon me as a mathematician, but I still recommend the exercise for the light it sheds on the question of mechanization of mathematics.  My colleagues may or may not think their colleagues are zombies, but those who profess a belief in a future in which the field is dominated by artificial intelligence are telling us that we may as well be, for all the difference it makes to mathematics. I was led to this train of thought by reading Andrew Smart’s Beyond Zero and One, subtitled Machines, Psychedelics, and Consciousness.  Chapter 7 of MWA is largely inspired by the notion that mathematics is neither invented nor discovered but is rather an altered state of consciousness, and to this end sought (without much success) to catalogue examples of mathematicians working creatively under the influence of mind-altering drugs.  Elsewhere I have described mathematics as a consensual hallucination, following the expression originally due to William Gibson.  But it had not occurred to me before reading Smart’s book to explore the more basic question of whether mathematics and consciousness necessarily have anything to do with one another.  Smart is writing about artificial intelligence, and about when, if ever,  consciousness will be attributed to computers.  His argument, which I think is original, is that altered states of consciousness are not merely coding errors but are inseparable from the very possibility of consciousness.  Thus he proposes to replace the Turing test for AI consciousness with a Turing-acid test, in which an AI would be tested for the ability to hallucinate as well as to display the normal attributes of consciousness. Colleagues who favor mechanization of mathematics should reflect upon this comment from Chapter 8 of Smart’s book:

…in order for a machine to have human consciousness and its own intuitions, the computer might also have to develop human-like biases and errors, even though these are the things we wish to eliminate by using robots to reason perfectly.

Since the expressed motivation for mechanization is precisely to eliminate the errors of human reasoning, it follows, if Smart is right, that the ideal mechanical mathematician will be unconscious.  Smart follows John Searle in his own account of the objectivity of mathematics:

Mathematics, like language, is observer-relative:  its mode of existence is ontologically subjective in that it depends on conscious agents for its existence.  But mathematics has epistemically objective truths.

If you accept this characterization of mathematics, then you have to agree that talk of zombie mathematicians is a category mistake, and that the machines that some of our colleagues expect to replace us on the near side of the singularity will necessarily be epistemically indistinguishable from human beings; in particular they will be conscious.  Thus we may be tempted to read the dialogue between Tim Gowers and C, the AI helper in his essay entitled Rough Structure and Classification as an account of an hallucination; but which of the two characters is hallucinating?

              (Image from Night of the Living Dead, public domain)


Update:  You may want to refer to this site for additional information on the title question.