Mathematics and Scientific Representation now available for Google preview

Despite not actually being in print, my forthcoming book can now be previewed on Google books here.

Mathematics and Scientific Representation book cover

My book Mathematics and Scientific Representation will soon be released. Here is the recently unveiled book cover:

More substantial discussions of the book's contents will be added here soon!

Classic Mr. Show: 24 is the highest number

Some inspiration to start the semester:

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.