Ian Stewart on Black-Scholes

The influential mathematician and writer Ian Stewart has a short article in a recent Guardian that considers the idea that the Black-Scholes model of option pricing contributed to the financial collapse. (Thanks to Ole Hjortland for the link.) As I summarized things back in October 2009, the derivation of the central partial differential equation is quite accessible, and involves the sorts of idealizations that we'd be happy to make in most other areas of science. In my book I discuss the case of Long-Term Capital Management (LTCM) and the ways in which its trading strategies appear to have been misled by the mathematical model itself. One dimension of the problem is noted by Stewart:

Any mathematical model of reality relies on simplifications and assumptions. The Black-Scholes equation was based on arbitrage pricing theory, in which both drift and volatility are constant. This assumption is common in financial theory, but it is often false for real markets. The equation also assumes that there are no transaction costs, no limits on short-selling and that money can always be lent and borrowed at a known, fixed, risk-free interest rate. Again, reality is often very different.

In particular, the volatility estimate based on recent trading history will be reliably too low when a market enters a new period of instability and resulting higher volatility. If traders miss this change, then they will see what look like ideal arbitrage opportunities. This is what mostly what sunk LTCM and seems to underlie many more recent failures as well.

How Widely Known is Broad's Anticipation of Jackson's Knowledge Argument?

As part of my seminar on emergence and reduction we spent two weeks reviewing the classic discussions of Mill and Broad, along with McLaughlin's helpful paper "The Rise and Fall of British Emergentism." One interesting feature of these early discussions that McLaughlin relegates to his interesting footnotes is the perennial appeal to qualia. In particular, it is striking to come across the following passage from Broad's 1925 The Mind and its Place in Nature:

We have no difficulty in conceiving and adequately describing determinate possible motions which we have never witnessed and which we never shall witness. We have merely to assign a determinate direction and a determinate velocity. But we could not possibly have formed the concept of such a colour as blue or such a shade as sky-blue unless we had perceived instances of it, no matter how much we had reflected on the concept of Colour in general or on the instances of other colours and shades which we had seen. It follows that, even when we know that a certain kind of secondary quality (e.g., colour) pervades or seems to pervade a region when and only when such and such a kind of microscopic event (e.g., vibrations) is going on within the region, we still could not possibly predict that such and such a determinate event of the kind (e.g., a circular movement of a certain period) would be connected with such and such a determinate shade of colour (e.g., sky-blue). The trans-physical laws are then necessarily of the emergent type.

This should remind anyone of Jackson's famous Knowledge argument involving the physicist Mary who knows the correct physical theory of color, but who lacks color experiences. I would not say that the arguments are identical, of course. Jackson is arguing against physicalism, while Broad is arguing against what he calls mechanism. But both physicalism and mechanism have reductive implications, and the appeal to color experience in both cases to block this sort of reduction is quite similar.
This made me wonder how widely known this sort of overlap is, and if there are obvious antecedents that Broad is drawing on. Brie Gertler notes in her Encyclopedia of Philosophy article on the Knowledge argument that "Arguments in the same spirit had appeared earlier (Broad 1925, Robinson 1982)". And one finds a section on the Knowledge argument in Kent Gustavsson's entry on Broad in the Stanford Encyclopedia of Philosophy. Broad is also noted in the entry on the Knowledge argument by Martine Nida-Rümelin. So, maybe it is well-known.
It appears to me that Broad is drawing on the obvious chapter in Mill's Logic, especially Mill's remark that "from no knowledge of the properties of those substances could we ever predict that it [the tongue] could taste, unless gelatine or fibrin could themselves taste; for no elementary fact can be in the conclusion, which was not in the premises" (Bk. III, ch. vi, section 1). Indeed this style of argument could perhaps be traced back to Locke's Essay and God's power to superadd the power of thinking to matter (Bk. IV, ch. III, section 6).
Update (Feb. 13): Chalmers has drawn my attention to two prominent discussions of Broad's knowledge argument: Stoljar's introduction to There's Something About Mary and Chalmers' own "Consciousness and its Place in Nature".

Babies are Newtonians?

Following an earlier post noting the apparent Bayesian tendencies of babies, we now have word for fellow University of Missouri professor Kristy vanMarle that babies have innate knowledge of Newtonian physics.
From the Yahoo News summary "Infants Grasp Gravity with Innate Sense of Physics":

"We believe that infants are born with expectations about the objects around them, even though that knowledge is a skill that's never been taught," Kristy vanMarle, an assistant professor of psychological sciences at the University of Missouri, said in a statement. "As the child develops, this knowledge is refined and eventually leads to the abilities we use as adults."
To come to this conclusion, vanMarle and her colleague, Susan Hespos, a psychologist at Northwestern University, reviewed infant cognition research conducted over the last 30 years. They found that infants already have an intuitive understanding of certain physical laws by 2 months of age, when they start to track moving objects with both eyes consistently and can be tested with eye-tracking technology.
For instance, at this age they understand that unsupported objects will fall (gravity) and hidden objects don't cease to exist. In one test, researchers placed an object inside of a container and moved the container; 2-month-old infants knew that the hidden object moved with the container.
This innate "physics" knowledge only grows as the infants experience their surroundings and interact more with the world. By 5 months of age, babies understand that solid objects have different properties than noncohesive substances, such as water, the researchers found.

Note: Regular readers will notice that I have given into the Google/Blogger renovations and opted for the white background. Also, I have enabled mobile formatting for easy access to this blog on mobile devices.

Journal for the History of Analytical Philosophy: Update

About a year ago I posted an announcement of the launch of a new, open-access, peer-reviewed journal devoted to the history of analytic philosophy. I am pleased to report that 2 articles and 1 substantial book review have already appeared:
James Pearson, Distinguishing WV Quine and Donald Davidson
Francesco Orsi, David Ross, Ideal Utilitarianism, and the Intrinsic Value of Acts
Kevin Klement, Review: Gregory Landini, Russell. London and New York, Routledge 2011.
Interested readers are encouraged to subscribe to the journal's Facebook page for news and updates on new articles. Our goal is to publish articles as soon as possible after they have been through our review process.
Update (Feb. 19): The journal also has an RSS feed that will list recent articles.

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: