## Le Monde puzzle [#849]

Posted in Books, Kids, R, Statistics with tags , , , , , on January 19, 2014 by xi'an

A straightforward Le Monde mathematical puzzle:

Find a pair (a,b) of integers such that a has an odd number d of digits larger than 2 and ab is written as 10d+1+10a+1. Find the smallest possible values of a and of b.

I ran the following R code

```d=3
for (a in 10^(d-1):(10^d-1)){
c=10^(d+1)+10*a+1
if (a*trunc(c/a)==c)
print(c(a,c))}
```

which produced a=137 (and b=83) as the unique case. For d=4, I obtained a=9091 and b=21, for d=6, a=909091, and b=21, for d=7, a=5882353 and b=27, while for d=5, my code did not return any solution. While d=8 took too long to run, a prime factor decomposition of 10⁹+1 leads to (with the schoolmath R library)

```> for (d in 3:10) print(c(d,prime.factor(10^(d+1)+1)))
[1]   3  73 137
[1]    4   11 9091
[1]    5  101 9901
[1]      6     11 909091
[1]       7      17 5882353
[1]     8     7    11    13    19 52579
[1]     9   101  3541 27961
[1]   10   11   11   23 4093 8779
```

which gives a=52631579 and b=29 for d=8 and also explains why there is no solution for d=5. The corresponding a has too many digits!

This issue of Le Monde Science&Médecine leaflet had more interesting entries, from one on “LaTeX as the lingua franca of mathematicians”—which presumably made little sense to any reader unfamiliar with LaTeX—to the use of “big data” tools (like news rover) to analyse data produce by the medias, to  yet another tribune of Marco Zito about the “five sigma” rule used in particle physics (and for the Higgs boson analysis)—with the reasonable comment that a large number of repetitions of an experiment is likely to exhibit unlikely events, and an also reasonable recommendation to support “reproduction experiments” that aim at repeating exceptional phenomena—, to a solution to puzzle #848—where the resolution is the same as mine’s, but mentions the principle of Dirichlet’s drawers to exclude the fact that all prices are different, a principle I had never heard off…

## Dennis Lindley (1923-2013)

Posted in Books, Statistics, University life with tags , , , , , , on December 16, 2013 by xi'an

Dennis Lindley most sadly passed away yesterday at the hospital near his home in Somerset. He was one of the founding fathers of our field (of Bayesian statistics), who contributed to formalise Bayesian statistics in a coherent theory. And to make it one with rational decision-making, a perspective missing in Jeffreys’ vision. (His papers figured prominently in the tutorials we gave yesterday for the opening of O’Bayes 250.) At the age of 90, his interest in the topic had not waned away: as his interview with Tony O’Hagan last Spring showed, his passionate arguing for the rationale of the Bayesian approach was still there and alive! The review he wrote of The Black Swan a few years ago also demonstrated he had preserved his ability to see through bogus arguments. (See his scathing “One hardly advances the respect with which statisticians are held in society by making such declarations” in his ripping discussion of Aitkin’s 1991 Posterior Bayes factors.) He also started this interesting discussion last year about the five standard deviations “needed” for the Higgs boson…  My personal email contacts with Dennis over the re-reading of Jeffreys’ book  were a fantastic experience as he kindly contributed by expanding on how the book was received at the time and correcting some of my misunderstanding. It is a pity I can no longer send him the (soon to come?) final version of my Jeffreys-Lindley paradox paper as I intended to do. The email thomasbayes@gmail.com will no longer answer our queries… I figure there will be many testimonies and shared memories of his contributions and life at the Bayes-250 conference tomorrow. Farewell, Dennis, and I hope you now explore the paths of a more coherent world than ours!

## how can we tell someone “be natural”? [#2]

Posted in Books, Kids, pictures, University life with tags , , , , , , , , , on November 17, 2013 by xi'an

Following my earlier high school composition (or, as my daughter would stress, a first draft of vague ideas towards a composition!), I came upon an article in the Science leaflet of Le Monde (as of October 25) by the physicist Marco Zito (already commented on the ‘Og): “How natural is Nature?“. The following is my (commented) translation of the column, I cannot say I understand more than half of the words or hardly anything of its meaning, although checking some Wikipedia entries helped (I wonder how many readers have gotten to the end of this tribune)

The above question is related to physics in that (a) the electroweak interaction scale is about the mass of Higgs boson, at which scale [order of 100GeV] the electromagnetic and the weak forces are of the same intensity. And (b) there exists a gravitation scale, Planck’s mass, which is the energy [about 1.2209×1019GeV] where gravitation [general relativity] and quantum physics must be considered simultaneously. The difficulty is that this second fundamental scale differs from the first one, being larger by 17 orders of magnitude [so what?!]. The difference is puzzling, as a world with two fundamental scales that are so far apart does not sound natural [how does he define natural?]. The mass of Higgs boson depends on the other elementary particles and on the fluctuations of the related fields. Those fluctuations can be very large, of the same order as Planck’s scale. The sum of all those terms [which terms, dude?!] has no reason to be weak. In most possible universes, the mass of this boson should thus compare with Planck’s mass, hence a contradiction [uh?!].

And then enters this apparently massive probabilistic argument:

If you ask passerbys to select a number each between two large bounds, like – 10000 and 10000, it is very unlikely to obtain exactly zero as the sum of those numbers. So if you observe zero as the sum, you will consider the result is not «natural» [I'd rather say that the probabilistic model is wrong]. The physicists’ reasoning so far was «Nature cannot be unnatural. Thus the problem of the mass of Higgs’ boson must have a solution at energy scales that can be explored by CERN. We could then uncover a new and interesting  physics». Sadly, CERN has not (yet?) discovered new particles or new interactions. There is therefore no «natural» solution. Some of us imagine an unknown symmetry that bounds the mass of Higgs’ boson.

And a conclusion that could work for a high school philosophy homework:

This debate is typical of how science proceeds forward. Current theories are used to predict beyond what has been explored so fat. This extrapolation works for a little while, but some facts eventually come to invalidate them [sounds like philosophy of science 101, no?!]. Hence the importance to validate through experience our theories to abstain from attributing to Nature discourses that only reflect our own prejudices.

This Le Monde Science leaflet also had a short entry on a meteorite called Hypatia, because it was found in Egypt, home to the Alexandria 4th century mathematician Hypatia. And a book review of (the French translation of) Perfect Rigor, a second-hand biography of Grigory Perelman by Martha Gessen. (Terrible cover by the way, don’t they know at Houghton Mifflin that the integral sign is an elongated S, for sum, and not an f?! We happened to discuss and deplore with Andrew the other day this ridiculous tendency to mix wrong math symbols and greek letters in the titles of general public math books. The title itself is not much better, what is imperfect rigor?!)  And the Le Monde math puzzle #838

## Monte Carlo workshop (Tage 1 & 2)

Posted in Statistics, Travel, University life with tags , , , , , , , , , , on February 21, 2013 by xi'an

Gathering with simulators from other fields (mostly [quantum] physicists) offers both the appeal of seeing different perspectives on simulation and the diffiulty of having to filter alien vocabulary and presentation styles (generally assuming too much background from the audience). For instance; while the first talk on Tuesday by Gergely Barnaföldi about using GPUs for simulation was quite accessible, showing poor performances of the (CPU based) Mersenne twister., when using Dieharder as the evaluator. (This was in comparison with GPU-based solutions.) This provided an interesting contrapoint to the (later) seminar by Frederik James on random generators. (Of course, I did have some preliminary background on the topic.)

On the opposite, the second talk by Stefan Schäfer involved hybrid Monte Carlo methods but it took a lot of efforts (for me) to translate back to my understanding of the notion, gathered from this earlier Read Paper of Girolami and Calderhead, with the heat-bath and leapfrog algorithms. One extreme talk in this regard was William Lester’s talk on Wednesday morning on quantum Monte Carlo and its applications in computational chemistry where I could not get past the formulas! Too bad because it sounded quite innovative with notions like variational Monte Carlo and diffusion Monte Carlo… Nice movies, though. On the other hand, the final talk of the morning by Gabor Molnar-Saska on option pricing was highly pedagogical, defining everything and using simple examples as illustrations. (It certainly did not cure my misgivings about modelling the evolution of stock prices via pre-defined diffusions like Black-and-Scholes’, but the introduction was welcome, given the heterogeneity of the audience.) Both talks on transportation problems were also more accessible (maybe because they involved no pysics!)

The speakers in the afternoon sessions of Wednesday also made a huge effort to bring the whole audience up-to-date about their topic, like protein folding and high-energy particle physics (although everyone knows about the Higgs boson nowadays!). And ensemble Kalman filters (x2). In particular, Andrew Stuart did a great job with his simulation movies. Even the final talk about path-sampling for quantum simulation was mostly understandable, at least the problematic of it.  Sadly, at this stage, I still cannot put a meaning on “quantum Monte Carlo”… (Incidentally, I do not think my own talk reached much of the audience, missing convincing examples I did not have time to present:)

## statistics do not always lie

Posted in Books, Statistics, University life with tags , , , , , , , , on December 16, 2012 by xi'an

Le Monde weekend edition science leaflet (Le Monde[wes] from now on!) had several interesting entries this weekend. One was a blurb by Cédric Villani with the above title. Or in French “Les statistiques ne sont pas toujours des mensonges“. This most communicant of our Fields Medalists focussed on two recent scientific news to conclude about the relevance of statistics (herein considered as one of the mathematical sciences!) in scientific discoveries: the validation of the significance of the observations connected with the Higgs Boson and the invalidation of the significance of the Séralini et al. experiments on Monsanto genetically modified maize NK603. Villani actually reproduces the erroneous and quasi-universal interpretation of the statistical analysis of the Higgs Boson as establishing its existence with a probability of .999999, as already discussed in an earlier post. (The whole issue was discussed on the ISBA forum, following Dennis Lindley’s call.) I also mentioned the Monsanto experiment in an earlier post last month, experiment whose publication was surrounded by hyper mediatisation and later controversy, while being validated by the Elsevier journal Food and Chemical Toxicology.

Another interesting entry was the blurb of Marco Zito, physicist in CEA, on another Fields Medalist, Laurent Schwartz, the mathematician who formalised Dirac deltas into the theory of distributions. He first recalls his discovery of Schwartz’s wonderful Théorie des Distributions that I read with fascination in the early 1980’s. (And that most surprisingly does not seem to have been translated in English…) He then discusses the personality of Laurent Schwartz, as described in the wonderful A Mathematician Grappling with His Century, his autobiography where he describes his political involvement against the French war in Algeria, esp. about the disappearance and murder by torture of the young mathematician Maurice Audin. Laurent Schwartz was actually excluded a few years from the faculty at École Polytechnique for this involvement…