## a probabilistic proof to a quasi-Monte Carlo lemma

Posted in Books, Statistics, Travel, University life with tags , , , , , on November 17, 2014 by xi'an

As I was reading in the Paris métro a new textbook on Quasi-Monte Carlo methods, Introduction to Quasi-Monte Carlo Integration and Applications, written by Gunther Leobacher and Friedrich Pillichshammer, I came upon the lemma that, given two sequences on (0,1) such that, for all i’s,

$|u_i-v_i|\le\delta\quad\text{then}\quad\left|\prod_{i=1}^s u_i-\prod_{i=1}^s v_i\right|\le 1-(1-\delta)^s$

and the geometric bound made me wonder if there was an easy probabilistic proof to this inequality. Rather than the algebraic proof contained in the book. Unsurprisingly, there is one based on associating with each pair (u,v) a pair of independent events (A,B) such that, for all i’s,

$A_i\subset B_i\,,\ u_i=\mathbb{P}(A_i)\,,\ v_i=\mathbb{P}(B_i)$

and representing

$\left|\prod_{i=1}^s u_i-\prod_{i=1}^s v_i\right| = \mathbb{P}(\cap_{i=1}^s A_i) - \mathbb{P}(\cap_{i=1}^s B_i)\,.$

Obviously, there is no visible consequence to this remark, but it was a good way to switch off the métro hassle for a while! (The book is under review and the review will hopefully be posted on the ‘Og as soon as it is completed.)

## Principles of scientific methods [not a book review]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , on November 11, 2014 by xi'an

Mark Chang, author of Paradoxes in Scientific Inference and vice-president of AMAG Pharmaceuticals, has written another book entitled Principles of Scientific Methods. As was clear from my CHANCE review of Paradoxes in Scientific Inference, I did not find much appeal in this earlier book, even after the author wrote a reply (first posted on this blog and later printed in CHANCE). Hence a rather strong reluctance [of mine] to engage into another highly critical review when I received this new opus by the same author. [And the brainwave cover just put me off even further, although I do not want to start a review by criticising the cover, it did not go that well with the previous attempts!]

After going through Principles of Scientific Methods, I became ever more bemused about the reason(s) for writing or publishing such a book, to the point I decided not to write a CHANCE review on it… (But, having spent some Métro rides on it, I still want to discuss why. Read at your own peril!)

## Rivers of London [book review]

Posted in Books, Kids, Travel with tags , , , , , , , , , , , on October 25, 2014 by xi'an

Yet another book I grabbed on impulse while in Birmingham last month. And which had been waiting for me on a shelf of my office in Warwick. Another buy I do not regret! Rivers of London is delightful, as much for taking place in all corners of London as for the story itself. Not mentioning the highly enjoyable writing style!

“I though you were a sceptic, said Lesley. I though you were scientific”

The first volume in this detective+magic series, Rivers of London, sets the universe of this mix of traditional Metropolitan Police work and of urban magic, the title being about the deities of the rivers of London, including a Mother and a Father Thames… I usually dislike any story mixing modern life and fantasy but this is a definitive exception! What I enjoy in this book setting is primarily the language used in the book that is so uniquely English (to the point of having the U.S. edition edited!, if the author’s blog is to be believed). And the fact that it is so much about London, its history and inhabitants. But mostly about London, as an entity on its own. Even though my experience of London is limited to a few boroughs, there are many passages where I can relate to the location and this obviously makes the story much more appealing. The style is witty, ironic and full of understatements, a true pleasure.

“The tube is a good place for this sort of conceptual breakthrough because, unless you’ve got something to read, there’s bugger all else to do.”

The story itself is rather fun, with at least three levels of plots and two types of magic. It centres around two freshly hired London constables, one of them discovering magical abilities and been drafted to the supernatural section of the Metropolitan Police. And making all the monologues in the book. The supernatural section is made of a single Inspector, plus a few side characters, but with enough fancy details to give it life. In particular, Isaac Newton is credited with having started the section, called The Folly. Which is also the name of Ben Aaronovitch’s webpage.

“There was a poster (…) that said: `Keep Calm and Carry On’, which I thought was good advice.”

This quote is unvoluntarily funny in that it takes place in a cellar holding material from World War II. Except that the now invasive red and white poster was never distributed during the war… On the opposite it was pulped to save paper and the fact that a few copies survived is a sort of (minor) miracle. Hence a double anachronism in that it did not belong to a WWII room and that Peter Grant should have seen its modern avatars all over London.

“Have you ever been to London? Don’t worry, it’s basically  just like the country. Only with more people.”

The last part of the book is darker and feels less well-written, maybe simply because of the darker side and of the accumulation of events, while the central character gets rather too central and too much of an unexpected hero that saves the day. There is in particular a part where he seems to forget about his friend Lesley who is in deep trouble at the time and this does not seem to make much sense. But, except for this lapse (maybe due to my quick reading of the book over the week in Warwick), the flow and pace are great, with this constant undertone of satire and wit from the central character. I am definitely looking forward reading tomes 2 and 3 in the series (having already read tome 4 in Austria!, which was a mistake as there were spoilers about earlier volumes).

## how far can we go with Minard’s map?!

Posted in Books, Linux, pictures, Statistics, Travel with tags , , , , , , , , , , on October 13, 2014 by xi'an

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.

## Rogue Male [book review]

Posted in Books with tags , , , , , on October 4, 2014 by xi'an

When I was about to leave a library in Birmingham, I spotted a “buy one get one half-price” book on a pile next to the cashier. Despite a rather weird title, Geoffrey Household’s Rogue Male looked classic enough to rank with Graham Green’s Confidential Agent or Erskine Childers’ Riddle of the Sands or yet John Buchan’s 39 Steps… Not mentioning the early Eric Ambler novels. I mean, a classic British thriller with political ramifications and a central character exposed with shortcomings and doubts.  After reading the book last week, I am glad I impulsively bought it. Rogue Male is not a Greene’s novel and this for several reason: (a) it is much more nationalistic, to the point of refusing to contact English authorities for fear of exposing some official backup of the attempted assassination, while Greene seemed to lean more to the Left, (b) it is both less and more psychological, in that it (i) superbly describes the process of getting rogue, i.e. of being hunted and of cutting or trying to cut [some] human feelings to rely on animal instincts for survival but (ii) leaves the overall motivation for Hitler’s attempted assassination and for the hunt by Nazi secret agents mostly unspecified  (c) it involves a very limited number of characters, all of them men, (d) it leaves so much of the action at the periphery that this appears as a weakness of the book… Still, there are some features also found in Greene’s Confidential Agent like the character failing in his attempt and being nearly captured or killed in the ensuing hunt, or the inner doubts about the (un)ethical nature of the fight… (Actually, both Greene and Household worked for the British secret services.) The overall story behind Rogue Male is a wee bit shallow and often too allusive to make sense but the underground part with the final psychological battle is superb. Truly a classic!

## The Unimaginable Mathematics of Borges’ Library of Babel [book review]

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , on September 30, 2014 by xi'an

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.

## xkcd [interview & book]

Posted in Books, Kids, Statistics with tags , , , , , , , on September 14, 2014 by xi'an

Of interest for xkcd fans: What If?: Serious Scientific Answers to Absurd Hypothetical Questions is out! Actually, it is currently the #1 bestseller on amazon! (A physics book makes it to the top of the bestseller list, a few weeks after a theoretical economics book got there. Nice! Actually, a statistics book also made it to the top: Nate Silver’s The SIgnal and the Noise….) I did not read the book, but it is made of some of the questions answered by Randall Munroe (the father of xkcd) on his what if blog. In connection with this publication, Randall Munroe is interviewed on FiveThirtyEight (Nate Silver’s website), as kindly pointed out to me by Bill Jefferys. The main message is trying to give people a feeling about numbers, a rough sense of numeracy. Which was also the purpose of the guesstimation books.