The unplanned impact of mathematics (Nature)

Peter Rowlett has assembled, with some other historians of mathematics, seven accessible examples of how theoretical work in mathematics led to unexpected practical applications. His discussion seems to be primarily motivated by the recent emphasis on the "impact" of research, both in Britain and in the US:

There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won't have the right piece of seemingly pointless mathematics to hand.

For philosophers, the most important example to keep in mind, I think, is the last one, offered by Chris Linton: the role of Fourier series in promoting the later "rigorization" of math:

In the 1870s, Georg Cantor's first steps towards an abstract theory of sets came about through analysing how two functions with the same Fourier series could differ.

Rowlett has a call for more examples on the BSHM website. Hopefully this will convince some funding agencies that immediate impact is not a fair standard!

Revised SEP Entry: Mathematical Explanation

The Stanford Encyclopedia Entry on "Mathematical Explanation" has just been updated and revised. Thanks to Paolo Mancosu for this important resource!

Babies are Bayesians?

From the abstract of a recent paper in Science:

When 12-month-old infants view complex displays of multiple moving objects, they form time-varying expectations about future events that are a systematic and rational function of several stimulus variables. Infants’ looking times are consistent with a Bayesian ideal observer embodying abstract principles of object motion. The model explains infants’ statistical expectations and classic qualitative findings about object cognition in younger babies, not originally viewed as probabilistic inferences.

Group Selection Explains "Why We Celebrate a Killing"?

In an otherwise thoughtful piece in the New York Times on the reactions to Bin Laden's killing, Jonathan Haidt throws in a weird flourish

There’s the lower level at which individuals compete relentlessly with other individuals within their own groups. This competition rewards selfishness.

But there’s also a higher level at which groups compete with other groups. This competition favors groups that can best come together and act as one. Only a few species have found a way to do this. ...

Early humans found ways to come together as well, but for us unity is a fragile and temporary state. We have all the old selfish programming of other primates, but we also have a more recent overlay that makes us able to become, briefly, hive creatures like bees. Just think of the long lines to give blood after 9/11. Most of us wanted to do something — anything — to help.

So,

last week’s celebrations were good and healthy. America achieved its goal — bravely and decisively — after 10 painful years. People who love their country sought out one another to share collective effervescence. They stepped out of their petty and partisan selves and became, briefly, just Americans rejoicing together.

The claim seems to be that the origins of these reactions in group selection means that displaying these reactions now is "good and healthy" because group selection benefits groups? Not the best argument, I would say.

Periodical Cicadas Invade Missouri!

Those interested in mathematical explanations of physical phenomena should take note: May 15th is the predicted date for the emergence of swarms of the "Great Southern Brood" of cicadas, whose life cycle is 13 years. More details are provided by the Columbia Missourian:

Periodical cicadas survive on a strategy of satiating their predators. They emerge in such large numbers that there will always be some left over to reproduce. After a while, predators get tired of eating the cicadas and leave them alone.

“If you walked outside and found the world swarming with Hershey Kisses, eventually you would get so sick of Hershey Kisses that you would never ever want to eat them again,” Kritsky said.

The mathematical explanation answers the question: why is their life cycle a prime number?

Why I Will Not Boycott Synthese

Yesterday Brian Leiter posted a long entry on his blog discussing the dispute surrounding a special issue of Synthese on "Evolution and Its Rivals". Leiter mentions several concerns, and I encourage anyone interested in the issue to read over what he has posted.

The main problem he identifies is that journal editors inserted the following preface to the special issue:

Statement from the Editors-in-Chief of SYNTHESE

This special issue addresses a topic of lively current debate with often strongly expressed views. We have observed that some of the papers in this issue employ a tone that may make it hard to distinguish between dispassionate intellectual discussion of other views and disqualification of a targeted author or group.

We believe that vigorous debate is clearly of the essence in intellectual communities, and that even strong disagreements can be an engine of progress. However, tone and prose should follow the usual academic standards of politeness and respect in phrasing. We recognize that these are not consistently met in this particular issue. These standards, especially toward people we deeply disagree with, are a common benefit to us all. We regret any deviation from our usual standards.

Johan van Benthem

Vincent F. Hendricks

John Symons

Editors-in-Chief / SYNTHESE

This insertion was made over the objections of the guest editors of the special issue.

Leiter calls for a boycott of the journal:

I would urge all philosophers to stop submitting to Synthese; to withdraw any papers they have submitted at Synthese; and to decline to referee for Synthese until such time as the editors acknowledge their error, and make appropriate amends.

Based on what I can find out about this, a boycott seems unwarranted. The editors of Synthese have elected to dramatically expand the number of issues they publish, and this has involved a proliferation of special issues where much of the editorial work is delegated to guest editors. Full disclosure: I am currently co-editing one such issue now. So, for me, the issue concerns the propriety of the journal editors inserting a preface over the objections of the guest editors. I believe that the journal editors should be allowed to exercise their judgment on such an issue. Of course, others might have acted differently. But the editors of the journal are ultimately responsible for the articles printed in the journal, and for this reason they should not be expected to delegate all questions about a special issue to the guest editors.

For Leiter, the issue seems to be related to debates about intelligent design. I would concede that a pattern of behavior which suggested that the editors were advocating for intelligent design at the expense of competing views would be disturbing and might warrant a boycott of the journal. However, there does not seem to be any such pattern, and a boycott would damage not only the editors, but also the many contributors whose articles meet the high standards of scholarship of a leading philosophy journal.

New Book: Scientific Structuralism

Alisa Bokulich and Peter Bokulich have edited a helpful new volume with the title Scientific Structuralism, as part of the Boston Studies in the Philosophy of Science. There are nine contributions, which approach structuralism in the philosophy of science from a variety of perspectives: ontological, epistemic, representational and even in connection with structural explanation.

Here is the table of contents:

STRUCTURAL REALISM: A NEO-KANTIAN PERSPECTIVE, Michela Massimi
IN DEFENCE OF ONTIC STRUCTURAL REALISM, Steven French and James Ladyman
STRUCTURALIST APPROACHES TO PHYSICS: OBJECTS, MODELS, AND MODALITY, Katherine Brading
MATHEMATICAL STRUCTURAL REALISM, Christopher Pincock
STRUCTURAL EMPIRICISM, AGAIN, Otávio Bueno
STRUCTURAL REALISM: CONTINUITY AND ITS LIMITS, Ioannis Votsis
STRUCTURALISM ABOUT SCIENTIFIC REPRESENTATION, Martin Thomson-Jones
ONTIC STRUCTURAL REALISM AS A METAPHYSICS OF OBJECTS, Michael Esfeld and Vincent Lam SCIENTIFIC EXPLANATION AND SCIENTIFIC STRUCTURALISM, Mauro Dorato and Laura Felline

Some readers should be able to access the book online here.