Archive: Science

Lynxes and lumps

Science ·· More from January 2012
I’ve been reading Robert Batterman’s Devil in the details, a book that packs a lot of punch in a relatively few pages. Among its themes is that of the universality of certain mathematical models. Universality is “the slightly pretentious way in which physicists denote identical behaviour in different systems” (Berry 1987:185, quoted in Batterman 13).
That requires some unpacking. Two systems exhibit “identical” behavior if that behavior can, under suitable redescription, be seen to instantiate the same mathematical system (I use the imprecise word ‘system’ rather than a more precise term because what is instantiated need not be, for example, the graph of a single equation). They are different if, as in the case of Berry’s own examples, they have different shapes, or if, as in some cases discussed by Batterman, they are made of different stuffs. We will see yet another sort of difference below.
Let me start instead with something simple: the directed graph or digraph. Family trees and citation networks instantiate that structure: draw an arrow from x to y if x is a progenitor of y or if y is cited by x. More interestingly, so-called “scale-free” networks, though arising in different real-world situations (different in the sense of being realized on quite different scales by quite different sorts of process), obey the same statistics (for example, the number of arrows entering a node—think of links to a site—obeys a power-law distribution): the probability of a node’s having n entering links is inversely proportional to some small power n k of n. Many nodes will have only a few entering links, and a very few will have many.
xerox web network
Source: J. Lamping, R. Rao. “The hyperbolic browser: a focus+context technique for visualizing large hierarchies”. Journal of Visual Languages and Computing 7 (1996) 33–55, fig. 14. See also here.


LinkJanuary 20, 2012

“Une trace impérissable de ces fugitives mélodies”

The earliest known recording of the human voice from which intelligible sound has been recovered was made by the French scientist Édouard-Léon Scott de Martinville on 9 April 1860—seventeen years before Edison’s first phonograph recording. It is a bit of “Au clair de la lune”.
On 20 April another recording, longer and with better fidelity, was made. Earlier recordings exist, but for lack of calibration they have not been converted. Scott calibrated his later recordings with a tuning fork of known pitch.
The recovery was carried out by First Sounds, a group devoted to preserving, recovering, and publishing old recordings.
Below is a sketch from Scott’s patent application (“brevet d’invention”), dated 25 Mar 1857.


LinkJanuary 10, 2012

On Rosenberg on Science

A quotation first:
“But what about other items on Professor Williamson’s list of disciplines it would be hard to count as science: history, literary theory? Can science and naturalistic philosophy do without them? This is a different question from whether people, as consumers of human narratives and enjoyers of literature, can do without them. The question naturalism faces is whether disciplines like literary theory provide real understanding.
“Naturalism faces these questions because it won’t uncritically buy into Professor Williamson’s ‘default assumption … that the practitioners of a well-established discipline know what they are doing, and use the … methods most appropriate for answering its questions.’ If semiotics, existentialism, hermeneutics, formalism, structuralism, post-structuralism, deconstruction and post-modernism transparently flout science’s standards of objectivity, or if they seek arbitrarily to limit the reach of scientific methods, then naturalism can’t take them seriously as knowledge.
“That doesn’t mean anyone should stop doing literary criticism any more than foregoing fiction. Naturalism treats both as fun, but neither as knowledge.”
Rosenberg starts here with a brief list: history, literary theory. He forgets history (after implying that all history is narrative history: so much for the Annales school and hundreds of other historians), and turns to “disciplines like literary theory”.
Then we get a seriously defective bit of non-argument. In form:
If A, then B.
Therefore B.
Here A = “semiotics etc. flout science’s standards or seek to limit the reach of scientific methods”, and B = “naturalism can’t take them seriously”.
No doubt Rosenberg holds A true. But it is bad manners in philosophy, even op-ed philosophy, to pretend you’ve proved or been granted a controversial premise that you haven’t gone one step toward proving.
Another point:


LinkSeptember 19, 2011

On magnets and lies, and checking sources

The historian’s attitude, when attempting to establish matters of fact, toward the sources, is one of tempered but universal skepticism. The same applies to the history of the present. For example:
Don’t depend on popularizations for your knowledge of neuroscience (see the previous item in this blog for a similar issue concerning the biology of sex). A recent headline in several newspapers and online sources reads something like this: “Magnetic Pulses To The Brain Make It Impossible To Lie”. Wow! That’s exciting! And scary too…
The only problem is, it’s false. The original study, which takes two minutes to retrieve if you have access to the journal (Behavioural Brain Research, Volume 225.1 (Nov 2011) 209-214; doi:10.1016/j.bbr.2011.07.028) states its main result as follows:
In our study we found support for the general hypothesis: rTMS targeted at DLPFC changed spontaneous truth-telling/lying rate in a task with no mock-criminal, guilty knowledge, or personally relevant information processing contexts being involved. Importantly, clear hemispheric differences were found. In principle, artificial inhibition of the sustained neuronal activation-states in left DLPFC and possibly the concomitant effect on the systems intimately associated with DLPFC decreases the willingness to tell the truth (more non-truthful answers produced) and/or increases the willingness to tell lies. Conversely, inhibitory rTMS effect on right DLPFC and possibly the concomitant secondary effect on the DLPFC-associated systems increases willingness to tell truth (more truthful answers produced) and/or decreases willingness (or capability) to lie.
[Acronyms unpacked: rTMS = repetitive transcranial (from outside through the skull) magnetic stimulation; DLPFC = dorsolateral prefrontal cortex.]
The authors carefully note the limitations of their study.
  • The effects of the magnetic stimulation may spread beyond the area adjacent to the coil; and so “ interpretations on causal effects of TMS exclusively through the TMS-targeted area should be taken with care”.
  • The dorsolateral prefrontal cortex has many functions, and in a complicated task like “spontaneous” lying more than one may be activated: because “perceptual stimuli had to be named and two response variants chosen and reversed from time to time, the number of possible neural mechanisms that influence readiness to lie in our task and their possible interactions remain too numerous at present” to be sorted out.
  • The spontaneity of the lying was limited to some unknown degree. Subjects were “instructed to name the colour correctly or just lie about it, naming the other colour that was not presented in this trial, being free to choose whether to lie or not”, but they were also told that only lying or only telling the truth would not be “good for the experiment”.
The upshot is that there is a positive correlation between spontaneous truth-telling and rTMS stimulation of the right dorsolateral prefrontal cortex; and between spontaneous lying and stimulation of the left DLPFC. That’s very interesting. But it’s far from what you would gather from the headlines and stories online.
The moral should be obvious. In matters of science, there is no substitute for reading the original studies. Science journalists, and for that matter popularizing philosophers, should be drawn upon cautiously. Moreover, the studies often present complexities and issues (as here) that summaries, especially of the ax-grinding sort, tend to omit.
I learned this long ago when reading studies on animal perception that were cited over and over in the philosophical literature on representation. It was clear that only a few people had read the original studies; everyone else drew on their predecessors’ summaries. When I read the original studies, I discovered not only mistakes in the summaries but also a world of fascinating work that the “poor diet of examples” in the literature had simply omitted. Insect senses in particular offered much food for thought, and I recommend it highly if you’re thinking about the origins of representation or defining sensory modalities.
Philosophers have done a better job in the last twenty years. A much broader range of scientific results is brought to bear on philosophical debate, and prejudices according to which doing so is somehow unphilosophical have waned. Experimental Philosophy even generates its own results. But it’s well worth remembering, both when doing philosophy and when judging scientific results of political import, that although a great deal of expertise is required to contribute to ongoing research, rather less is needed to acquire a basic understanding of the results of research, to understand their limitations, and to evaluate second-hand accounts.

LinkSeptember 9, 2011

Williamson on naturalism

Science ·· More from September 2011
Timothy Williamson opinionates on naturalism at the Times.
He starts with a pre-1960 view of physics and biology: considered at a “sufficiently abstract level”, they are hypothetico-deductive. (I’ll let other people deal with that.) Naturalism would then be the view that all that exists is what will be asserted to exist in a completed hypothetico-deductive science of everything.
Williamson’s next move is not to refute that claim; instead he argues that not all science is hypothetico-deductive. It seems to me that the naturalist can happily agree & yet still affirm that all that exists is what will be asserted to exist in a completed science of everything. The notion of a science, to be sure, must be clarified if that claim is to be clear, but Williamson seems to regard the project as hopeless. In other words: if science can’t be characterized as HD (and it can’t), then there is no adequate characterization of science, and so the naturalistic view fails to assert anything definite.
There cannot be an adequate philosophical characterization of science, it would seem, because to be scientific is to have the scientific spirit, a wild horse no theory can tame… (It’s idle to say that no theory can “replace” that spirit. My theory of aerodynamics won’t get me to New York either.) But why can’t there be a theory of curiosity, honesty, precision, and rigor (so much for formal logic, which spells out what it is to reason rigorously in mathematics)? The naturalist is going to hold—is bound to hold—that if there is such a thing as the scientific spirit, then it too must fall within the purview of science. Williamson’s argument hinges on a Romantic assertion of art against science which comes close to begging the question it wants to answer.

LinkSeptember 4, 2011 | Comments (0)

Brief answers from Mr. Science

Science · Society ·· More from July 2007
Today Mr. Science shows us one way to tell men from women.
Men get wrinkles as they age.
Daniel Craig, age 39
Women don’t.
Nicole Kidman, age 40
Source: Internet Movie Poster Awards via “The Photoshop Awards: Nicole Kidman in The Golden Compass”, Dlisted 16 Jul 2007, (Kidman, Craig). From posters for The Golden Compass.

LinkJuly 16, 2007

X-Rays for everybody

Bibliography · Science ·· More from August 2006
A hundred years ago, X-rays were supposed to be good for all sorts of things. Now we know better. In The X-ray Century, Perry Sprawls and Jack E. Petersen reproduce a series of reports on the discoveries of Roentgen and others in 1896 (start with the last page and work backwards). They include a summary of Edward Trevert’s Something about X-rays for Everybody, published in 1896.
Trevert’s full name was Edward Trevert Bubier. He wrote popular books on electricity and radio, including the Electro-therapeutic handbook, with full directions for home treatment of nearly all diseases that can be cured or relieved by the application of electricity (New York: Manhattan Electrical Supply Co., 1900) and The ABC of wireless telegraphy, a plain treatise on Hertzian wave signalling (Lynn, Mass.: Bubier Publishing, 1906).
Trevert’s work was reprinted by Medical Physics Publishing in 1988. The reprint is no longer available but second-hand copies can be found at Amazon and ABE.

LinkAugust 29, 2006

David Brooks on the emotions of boys and men

It’s time for a new stereotype: Right-wingers don’t know science. But they still make propaganda from what they think they know. Exhibit #1 is from Mark Liberman at LanguageLog:
Mark Liberman, “David Brooks, cognitive neuroscientist”, LanguageLog 12 Jun 2006.
—, “Are men emotional children?”, LanguageLog 24 Jun 2006.
David Brooks makes dubious use of neuroscience to argue that in order to increase reading among boys, they should be given Hemingway and the like, not Jane Austen.
In his first post Liberman looks at one paper, presumably representative, on the topic of sex differences in learning. The paper concludes that for pictures that aroused intense negative emotions, women’s memories were, in a group comparison, somewhat better than men’s.
Turhan Canli et al., “Sex differences in the neural basis of emotional memories”, PNAS 99.16 (6 Aug 2002).
Associated with that finding were differences in activation patterns in the brain. But those differences must be set against a background of community. The two sexes “share an extensive network of structures associated with attention, language, and motor control that are associated with emotional arousal”; and, as Liberman notes, if we could see the raw data we would likely find a great deal of variation among individuals.
Even more telling is a second post. Brooks’s source turns out to be Why gender matters by Leonard Sax. Sax grossly misinterprets a paper concerning responses to pictures of faces exhibiting various negative emotions.
Killgore, William D. S.; Oki, Mika; Yurgelun-Todd, Deborah A., "Sex-specific developmental changes in amygdala responses to affective faces," Neuroreport 12.2 (Feb 2001): 427-433.
He claims that “the locus [in male brains] of brain activity associated with negative emotion remains stuck in the the amygdala”. In girls responses to negative emotion are supposed to shift to cerebral cortex during adolescence, in boys they don’t. From Liberman’s careful examination it is apparent that the study by Killgore et al. proves very little. The samples are very small, and individual differences between members of the same sex come close to swamping supposed differences between the sexes. The paper certainly does not support the claims of Sax or Brooks.
Brooks admits to being scientifically illiterate. Sax has an M.D. He also has an agenda, which is to promote single-sex public schools. The National Association for Single Sex Public Education (NASSPE), which seems to consist in Sax and an assistant, advertises his book prominently. The NASSPE has regional meetings every year. The Northeast Conference is co-sponsored with a charter-school outfit, Victory Schools, and a Transformation Life Coach who has founded the Academy For Leadership and Transformation (which seems to be nothing other than the Coach herself). It will set you back $325 plus $165 for accommodations.
Single-sex education may be a good thing, although memories of high-school gym, admittedly a special case, suggest that it has its drawbacks. But misinterpreting science is not. And even if the conclusions of the paper by Killgore et al. had been correctly stated, the inferences Brooks wants to draw from them are far from being justified.

LinkJune 25, 2006

The things of nature

Science · Society ·· More from April 2006
Reading the piece by Sherry Turkle mentioned below got me thinking, as I have off and on for some time, about nature. In the work on nature and natures I did for Physiologia, it became clear to me that natura and its cognates, and before it physis and its cognates, were fighting words. Nature, generally speaking, is good, and non-nature or un-nature bad; but occasionally the polarities are reversed, and nature must be dominated or conquered, replaced by what Pascal was already calling the “second nature” of upbringing and education, or by the higher nature of the intellect, the super-nature of faith.


LinkApril 30, 2006


It’s Friday the 13th. Outside, near-blizzard conditions. Bad luck for someone, whatever the date. —Long ago, when Hollywood ruled the entertainment world, movies would open in the downtown palaces and then, weeks or months later, they would be relegated to the second-run houses in the neighborhoods (the “nabes”). Philosophical Fortnights is something like that.
I’m unlikely to be the first to alert anyone to the current outrage or today’s sin against reason. Time and energy don’t allow it, not to mention a lack of expertise. Perhaps it’s not so bad that some weblogs should be slow. Weblog software is biased toward an evanescent present, to instantaneous response: but instantaneous responses are by and large stock responses, as I. A. Richards called them. Questions at talks are often stock questions: they’re what you would ask if someone were to argue for materialism or consequentialism. We know the moves after all. That’s part of being an academic philosopher, part of being an original philosopher too. It’s not surprising that those weblogs that consist mostly in links to news items sometimes content themselves with more-or-less long-winded equivalents of mmm or yuck. Good for rallying the troops, not so good for real thinking.
That, in any case, is my excuse for pulling together, belatedly, a few things that have accumulated over the last month or so.
A school for atheists
French, of course. Athéisme, l’homme majuscule is in pure form that secular humanism which Bill O’Reilly thinks is going to take over the country, along with George Soros and the ACLU. Citations, biographies, humor, the Song of Songs, even a section of atheist apologetics. I’m pleased to see them noticing Paul Léautaud, whose literary journal is among the best I know of. Among the (not very well sourced) citations: “La seule foi qui me reste—et encore!—c’est la foi dans les dictionnaires”, which is reminiscent of Nietzsche’s remark about grammar.
Atheism is enjoying a bit of a vogue in France, with help of Michel Onfray’s Traité d’athéologie (2246648017: Amazon.fr, Chapitre) and the Cours accéléré d'athéisme by Antonio Lopez Campillo and Juan Ignacio Ferrera (2930390042: Amazon.fr, Chapitre). Atheism seems to me on the whole a shallower position than theism. That isn’t a criticism but an observation: once you’ve said there’s no God, there isn’t much more to say. What remains is to develop an ethics that rigorously avoids any appeal to the supersensible.
Tara Smith, an epidemiologist at the University of Iowa, is the author of Aetiology, a weblog on disease and public health issues, with occasional remarks on academic life. One entry in her old weblog, “This view of life”, caught my eye. Smith is drawn to biology by the variety of life, by the endless supply of puzzles it presents. Smith starts from an essay in the New York Times (registration required) by Olivia Judson, author of Dr. Tatiana’s sex advice to all creation. In biology, says Judson,
small facts add up to big pictures. For although Mother Nature’s infinite variety seems incomprehensible at first, it is not. The forces of nature are not random; often, they are strongly predictable.
For example, if you were to discover a new species and you told me that the male is much bigger than the female, I would tell you what the mating system is likely to be: males fight each other for access to females. Or if you discover that the male’s testicles make up a large part of his weight, I can tell you that the females in his species consort with several males at a time.
Suppose you find that a particular bacterium lives exclusively in the gullets of leeches and helps them digest blood. Then I can tell you how that bacterium’s genome is likely to differ from those of its free-living cousins; among other changes, the genome will be smaller, and it will have lost sets of genes that are helpful for living free but useless for living inside another being.
Creationism, I should note, hasn’t a prayer of explaining any of these relations. What interests me more is Smith’s final paragraphs:
Elsewhere online, I was involved in a discussion about evolution with a number of people with a host of different beliefs, from atheist to a self-described fundamentalist Christian. One Christian (who actually happens to be in seminary) stated his view on the topic:
And for me, there is something deeply spiritual about that idea, of connectedness to all of the planet on some level. I don’t find that evolution challenges my spirit; rather, learning more about how nature interconnects allows me to find more footing with my own life and walk with God.
This feeling of interconnection is something any of us can experience, regardless of our religious beliefs (or lack thereof). To steal a quote from Darwin, there is grandeur in this view of life—and I’m happy I evolved.
The seminarian offers a gloss on the fact of interconnectedness: it is “spiritual”, in a Kantian way—suggestive of ends (and of nature’s being ordered to ends) but in no way demonstrating them. The relation to God intimated in interconnection is the Spinozan relation of being “part of nature”, in necessary relation to the whole; at least that seems to me a more natural conclusion than orthodox theism. You may hold as Leibniz did that all of nature is related and still set God apart from nature as its transcendent cause, wholly distinct from created things by virtue of being perfect. Interconnectedness is ambiguously suggestive of both.
Returning to Athéisme, under the rubric “Science” I find this:
De tout temps l’hommeThrough all age man has posed questions about nature, life, himself… His need of knowledge is immense and ever-increasing. No sooner is one question resolve than another, ten others, emerge.
Religion was the first attempt to provide answers to those question, most often in the form of certainties whose source is a divine Revelation (as in the great monotheisms).
The use of rationality and the progressive liberation of thought from the empire of religion have permitted metaphysics to erect explanatory theories, based, it is true, on logical reasoning but purely speculative because inaccessible to experiment.
In the century of the Enlightenment, the sciences, entering their modern epoch, became aware of the impossibility, by reason of the limits themselves of the human condition, to acquire knowledge beyond experience and so of the vanity of the quest for the absolute.
Science, by its methods, its rigor, its humility (it does not claim to give immutable answers or certainties), its concrete and experimentally verifiable results, gives answers which are almost universally accepted (almost, because there still are creationists!). As the domains covered by science grow ever broader, religions and metaphysics are regularly obliged to reposition themselves with respect to it.
Human curiosity and interest in our surroundings are such that questions not yet resolved by science will not soon be exhausted. Religion and metaphysics, which feed on human ignorance, still have grist for their mills. The stubborn criticism of the “revealed” truths of religion or of the reified, deified abstractions of metaphysics, is a combat which cannot be avoided if humanity is really to take in its hands its destiny and render the world more human.
s’est posé des questions sur la nature, sur la vie, sur lui-même… Son besoin de connaissance est immense et va croissant. Dès qu’une question est résolue, une autre, dix autres surgissent.
La religion, la première, a tenté d’apporter des réponses à ces questions, le plus souvent sous forme de certitudes puisées dans une Révélation divine (cas des grands monothéismes).
L’usage de rationalité et la libération progressive de la pensée de l’emprise des religions ont permis à la métaphysique d’échafauder des théories explicatives, certes basées sur un raisonnement logique mais purement spéculatif car inaccessible à l’expérimentation.
Au siècle des “Lumières”, les sciences qui entraient dans leur époque moderne, ont pris conscience de l’impossibilité, en raison des limites mêmes de la condition humaine, d’acquérir des connaissances au-delà de l’expérience et donc de la vanité de la quête de l’absolu.
La science, par ses méthodes, sa rigueur, son humilité (elle ne prétend pas donner des réponses immuables ou des certitudes), ses résultats concrets et vérifiables expérimentalement, donne des réponses qui sont quasi universellement admises (quasi, car il existe encore des créationnistes !). Les domaines couverts par la science sont de plus en plus larges, ce qui oblige les religions et la métaphysique à se repositionner régulièrement par rapport à elle.
La curiosité et l’intérêt de l’homme pour ce qui l’entoure sont tels que les questions qui ne sont pas encore résolues par la science ne sont pas prêtes de s’épuiser. La religion et la métaphysique, qui se nourrissent de l’ignorance des hommes, ont encore du grain à moudre. La critique obstinée des vérités “révélées” par les religions ou des abstractions réifiées, puis déifiées par la métaphysique, est un combat indispensable pour que l’homme puisse réellement prendre entre ses mains sa destinée et rendre le monde plus humain.
Manifestos tend to be heaps of unargued commonplaces. This one is no exception. The threefold division—religion, metaphysics, science—is straight from Auguste Comte. It’s as if the anthropology and history of science of the last sixty years had never existed. But let’s consider just one claim more closely: that “religion and metaphysics feed upon the ignorance of men”.
This is meant to be an objection. But the ground of the objection cannot be merely that religion and metaphysics address matters on which we are ignorant. Science does too. Nor can it be even that they take up questions that science does not, unless you take a hard positivist line and rule out such questions as meaningless. But ethics, for one, is not meaningless, even though at least part of its subject matter lies outside the range of questions science can address.
The objection isn’t really to disciplines that inquire into matters not (yet) addressed by science, but to the methods that religion and metaphysics use to answer them: revelation and speculation. Consider speculation—“raisonnement inaccessible à l’expérimentation”. It’s not easy to find a metaphysics that has no relation to experience; and I’m not sure what a metaphysical “experiment” would be. The authors seem to be running together two sorts of claim:
  • (i) The claim, Kantian in spirit, that certain questions—summarized by the phrase “the quest for the absolute”—cannot even in principle be settled by appeal to experience;
  • (ii) The claim that only experiment, and not just experience generally, yields genuine knowledge.
The second is more restrictive than the first. How much more depends on the definition of “experiment”. Too narrow a definition will consign history to the flames. I’m not sure that (ii) can be made plausible except by defining ‘experiment’ merely as some sort of test to which experience is essential. But then (ii) is effectively equivalent to (i).
Concerning (i): Kant’s position, in brief, is that reason itself demands that we move from the conditioned (e.g. a determinate region of space) to the unconditioned (space without limits). This is not the result of some argumentum ad ignorantiam but a product of reflection on what being conditioned presupposes. Kant himself did not so much rule out metaphysics as put it in its place: the Ideas of metaphysics (God, space, time, the harmonious unity of the laws of nature) have no role in the determination of the objects of thought, and thus no role in science; nevertheless they remain indispensable to thought and even to science, as conditions on the conversion of experience into knowledge that cannot be proved from experience itself (nor applied to it, as the categories are).
What I’m summarizing is the murkiest part of the Critique of pure reason. Opinions differ, to say the least, on what Kant was up to and whether he succeeded. Still what I’ve said is enough to show that the Kantian claim (i) need not commit you to a combat with religion or metaphysics. Indeed if you want to revive the “warfare between science and theology” (historically a dubious notion, I should note), it would seem that you must either argue that outside science there is no knowledge or else grant that religion does have testable consequences that science can refute.
The critique of dubious religious or metaphysical claims is a worthwhile project. I don’t think it is well served by dubious history or question-begging arguments.
Briefly noted
  • The neuroscience of regret:
    From Cosma Shalizi’s Three-toed sloth.— Nathalie Camille, Giorgio Coricelli, Jerome Sallet, Pascale Pradat-Diehl, Jean-René Duhamel and Angela Sirigu, “The involvement of the orbitofrontal cortex in the experience of regret”, Science 305 (2004): 1167--1170. Punchline: “The orbitofrontal cortex has a fundamental role in mediating the experience of regret”. There is a comment by David Eagleman (308 (27 May 2005):1260) and a response by the authors.
  • The neuroscience of intuition:
    From Neurotopia.— One class of neuron, known as Van Economo neurons, resides in the fronto-insular cortex and the anterior cingulate cortex. Those two areas of the brain are “active during social situations”, when we’re assessing other people’s beliefs and desires; they also process “the conscious monitoring of visceral activity”. As Neurotopia notes, the expression “gut feeling” may have some truth to it.
  • Old fogies still have it in ’em:
    From Postclassic. —At least some old fogies. Old Masters and Young Geniuses by David Galenson distinguishes two kinds of artist: the experimental artist and the conceptual innovator. The innovator is at his or her best under 40; experimenters reach their peak at 40 or later. (Galenson is an economist at Chicago.)

LinkJanuary 14, 2006