Archive for the Travel Category
Like many others, I discovered Minard’s map of the catastrophic 1812 Russian campaign of Napoleon in Tufte’s book. And I consider it a masterpiece for its elegant way of summarising some many levels of information about this doomed invasion of Russia. So when I spotted
Apart from the trivia about familial connection with the Russian campaign and the Berezina crossing which killed one of his direct ancestors, his great-great-grandfather, along with a few dozen thousand others (even though this was not the most lethal part of the campaign), he brings different perspectives on the meaning of a map and the quantity of information one could or should display. This is not unlike other attempts at competiting with Minard, including those listed on Michael Friendly’s page. Incl. the cleaner printing above. And the dumb pie-chart… A lot more can be done in 2013 than in 1869, indeed, including the use of animated videos, but I remain somewhat sceptical as to the whole purpose of the book. It is a beautiful object, with wide margins and nice colour reproductions, for sure, alas… I just do not see the added value in work. I would even go as far as thinking this is an a-statistical approach, namely that by trying to produce as much data as possible into the picture, he forgets the whole point of the drawing which is I think to show the awful death rate of the Grande Armée along this absurd trip to and from Moscow and the impact of temperature (although the rise that led to the thaw of the Berezina and the ensuing disaster does not seem correlated with the big gap at the crossing of the river). If more covariates were available, two further dimensions could be added: the proportions of deaths due to battle, guerilla, exhaustion, desertion, and the counterpart map of the Russian losses. In the end, when reading I learned more about the history surrounding this ill-planned military campaign than about the proper display of data towards informative and unbiased graphs.
While it took quite a while (!), with several visits by three of us to our respective antipodes, incl. my exciting trip to Melbourne and Monash University two years ago, our paper on ABC for state space models was arXived yesterday! Thanks to my coauthors, Gael Martin, Brendan McCabe, and Worapree Maneesoonthorn, I am very glad of this outcome and of the new perspective on ABC it produces. For one thing, it concentrates on the selection of summary statistics from a more econometrics than usual point of view, defining asymptotic sufficiency in this context and demonstrated that both asymptotic sufficiency and Bayes consistency can be achieved when using maximum likelihood estimators of the parameters of an auxiliary model as summary statistics. In addition, the proximity to (asymptotic) sufficiency yielded by the MLE is replicated by the score vector. Using the score instead of the MLE as a summary statistics allows for huge gains in terms of speed. The method is then applied to a continuous time state space model, using as auxiliary model an augmented unscented Kalman filter. We also found in the various state space models tested therein that the ABC approach based on the marginal [likelihood] score was performing quite well, including wrt Fearnhead’s and Prangle’s (2012) approach… I like the idea of using such a generic object as the unscented Kalman filter for state space models, even when it is not a particularly accurate representation of the true model. Another appealing feature of the paper is in the connections made with indirect inference.
This is a book I carried away from JSM in Boston as the Oxford University Press representative kindly provided my with a copy at the end of the meeting. After I asked for it, as I was quite excited to see a book linking Jorge Luis Borges’ great Library of Babel short story with mathematical concepts. Even though many other short stories by Borges have a mathematical flavour and are bound to fascinate mathematicians, the Library of Babel is particularly prone to mathemati-sation as it deals with the notions of infinite, periodicity, permutation, randomness… As it happens, William Goldbloom Bloch [a patronym that would surely have inspired Borges!], professor of mathematics at Wheaton College, Mass., published the unimaginable mathematics of Borges’ Library of Babel in 2008, so this is not a recent publication. But I had managed to miss through the several conferences where I stopped at OUP exhibit booth. (Interestingly William Bloch has also published a mathematical paper on Neil Stephenson’s Cryptonomicon.)
Now, what is unimaginable in the maths behind Borges’ great Library of Babel??? The obvious line of entry to the mathematical aspects of the book is combinatorics: how many different books are there in total? [Ans. 10¹⁸³⁴⁰⁹⁷...] how many hexagons are needed to shelf that many books? [Ans. 10⁶⁸¹⁵³¹...] how long would it take to visit all those hexagons? how many librarians are needed for a Library containing all volumes once and only once? how many different libraries are there [Ans. 1010⁶...] Then the book embarks upon some cohomology, Cavalieri’s infinitesimals (mentioned by Borges in a footnote), Zeno’s paradox, topology (with Klein’s bottle), graph theory (and the important question as to whether or not each hexagon has one or two stairs), information theory, Turing’s machine. The concluding chapters are comments about other mathematical analysis of Borges’ Grand Œuvre and a discussion on how much maths Borges knew.
So a nice escapade through some mathematical landscapes with more or less connection with the original masterpiece. I am not convinced it brings any further dimension or insight about it, or even that one should try to dissect it that way, because it kills the poetry in the story, especially the play around the notion(s) of infinite. The fact that the short story is incomplete [and short on details] makes its beauty: if one starts wondering at the possibility of the Library or at the daily life of the librarians [like, what do they eat? why are they there? where are the readers? what happens when they die? &tc.] the intrusion of realism closes the enchantment! Nonetheless, the unimaginable mathematics of Borges’ Library of Babel provides a pleasant entry into some mathematical concepts and as such may initiate a layperson not too shy of maths formulas to the beauty of mathematics.