Econlinks: The applied maths edition

• Serious fight on evolutionary theory ground. The bulk of evolutionary theorists seem to be set on taking Nowak et al to the guillotine, but there is also a small minority of fans: among them, my former Tinbergen Institute colleague Matthijs van Veelen (see a picture of him from when he was older, wiser, sporting a big white beard; NB: yours truly is the junior black-and-yellow fellow at his left, learning on the job) and his co-authors have a nice correspondence in Nature supporting Novak et al. PS. Note also that one co-author of the controversial paper is Romanian mathematician Corina Tarnita (whom, allegedly, many girls would/should like to have as role model)
• The wave equation and tsunami propagation: a concise exposition by Terry Tao. Brings back nice memories of my maths classes at Utrecht University.
• Life arithmetic with (unavoidable?) implications: "Life is short. Have an affair".
• New chess strategies (more)? Now to the good guys: the latest (and seemingly, last) Amber chess tournament was clearly won by Aronian-- followed in the combined rankings by Carlsen and Anand: these three are in my view also the only consistent, long-run runners in the chess marathon. And related: Carlsen's bold decision to challenge a by-now-obsolete chess world championship format.  
• Greg Mankiw with the correct (and scary) budget arithmetic. 
• This is piece of cake, walk in the park: should have focused on predicting Burgundy 2011 vintage quality :-). But agreed, it was better than mine.
• A trip through a Mandelbox. Via Alex Tabarrok at MR.
• The science of stout foam. Or: the time of cheaper Guinness is nye! I confessed already that I had chosen a great Condrieu (relative to the other wines I had at Alinea, this was the one unforgettable) on St. Patrick's, but obviously I still fancy the good old Irish stout! 
• On continuous harmonic spaces (the original paper). Shows that consonance and dissonance  in music are to a considerable extent routed in nature and can be described/defined mathematically, beyond cultural or time relativism. We like it!

Econlinks: Of (visual) art, old and new

• The third and the seventh: imagination materialized or Alex Roman's computer generated art. Via Michael Nielsen. 
• Staying in CG: meet Julia Map, of Google ancestry. And since we're here, read how the fractals changed the world --which was in a way also part of the obituary to Father Fractal, Benoit Mandelbrot, who passed away a couple of months ago; see a better one from the Economist. My own brief memories of him: I met Mandelbrot at a workshop on economics with heterogenous agents (WEHIA) at Essex University, back in 2005. Before his keynote speech, he introduced himself in the following very humorous way (paraphrasing): "Hi, I am Benoit Mandelbrot. And I am not dead yet. [pause] I tell you that because I have just met somebody in the corridor who told me: 'OMG, you are Benoit Mandelbrot. I thought you were dead for a long time now' ". 
• Meet Jeremy Mayer, tamer of the typewriter. "I disassemble typewriters and then reassemble them into full-scale, anatomically correct human figures. I do not solder, weld, or glue these assemblages together- the process is entirely cold assembly. I do not introduce any part to the assemblage that did not come from a typewriter". 
• Back to the traditional, but impressively executed: meet Camille Seaman. From the "Last Iceberg series" statement: "Nick Cave once sang, 'All things move toward their end.' Icebergs give the impression of doing just that, in their individual way much as humans do; they have been created of unique conditions and shaped by their environments to live a brief life in a manner solely their own. Some go the distance traveling for many years slowly being eroded by time and the elements; others get snagged on the rocks and are whittled away by persistent currents. Still others dramatically collapse in fits of passion and fury."
• On the art of fiction: interview with Michel Houllebecq, born provocateur. Hat tip MR.
• And yes, she is back online (hopefully she is now here to stay)! Meet my friend Anna, talented photographer and undercover economist. 

Econlinks: Of Maths, Efficiency, and Language

• Terry Tao brief and informative on the 2010 Fields medalists (Le Monde est aussi très heureux et honoré pour Ngo et Villani, "deux facettes de l'école mathématique française"). Read also Tao's intro to the winners of the Nevanlinna, Gauss and Chern prizes.
  

• Interesting interview of Michael Nielsen with Cameron Neylon on practical steps towards open science (and, as it turns out, on useful advice beyond that)
  

• Gelman (channelling Palko) on 'teaching yourself Mathematics' (that was better than his acting somewhat confused and perhaps too much as a-- his own--discipline zealot in commenting on Banerjee and Duflo's review)
  

• Landsburg on efficiency and honest goal stating in policy analysis (see also Reinhardt's NYT column that started Landsburg). And another critical instance/application of (in)efficiency, via Barro.
  

• Languages shaping the way we think (and why I would have no chances with geographic idioms like Guugu Yimithirr or truth-revealing languages like Matses)
  

• Last but not least: two ok obituaries for Tony Judt, one in The Economist and one in the NYRB.
  

Econlinks

• The top 100 global thinkers, according to Foreign Policy. With the usual caveats: some should clearly not be there, others are missing (even from the first 5 positions, say...) etc. Highly subjective, but well, a top...

• Terry Tao makes a nice and concise exposition of some of the most beautiful parts at the intersection of Mathematics and Theoretical Physics (oh, nostalgia...), including quick reviews of classical and quantum mechanics.

• Some super nice games/quizzes via Steve Landsburg. Indeed be careful, some are highly addictive. For instance, The Paradoxion Express.

• Probably London's very first Indian restaurant (related, earlier- 2nd bullet point). With thanks to Daniel!

• The way forward for art: private funding with the right incentives for donors/funders. I think this ought to work also for universities, including public European ones... which are notoriously bad at this task, as we all know (with the important caveat that, especially in these European universities, the persons in charge of alumni networks and the like should really be the brains and not the (sub)mediocrities-- which seems to be the default in a lot of such places, even beyond the obvious fact that these are typically people with more /a lot more spare time; perhaps they/we should understand/decide that this is too important a job to leave to those with time to "spare" on it...-- only the brains can attract other brains and...their money).

On Noncommutative Geometry, String Theory, and the EU vs. US academe

All this in a 2005 interview with Alain Connes, in Iran (initial link to the PDF of the interview via Tyler Cowen, on MR).

First, I think this is a very welcome, very open interview (several questions/comments are just great, congrats to the interviewers!) and it is extremely interesting to see the opinion of this great mathematician (inter alia, Fields Medalist in 1982) on a wide range of topics. The pros: I completely agree with Connes's view on the distinct (ir)relevance of String Theory for Mathematics and respectively, Physics. I also like his (humorous) detachment from being considered the guru of NCG (of which unfortunately I know currently epsilon, albeit once I was almost sure this is what I wanted to do...) and from the tendency of always looking for / looking up to the one mastermind, in general, in any (sub)discipline. So no more on those, read for yourselves in the transcript of the interview. What I don't quite agree with is summarized below:

• resources (money) in research are not important (Connes's context has to do with the large interest/funding in Bio-Mathematics; he actually says "nothing", which I take as far stronger than "not important":-)): to the extent that it shapes incentives, I think it is actually very important. Intrinsic motivation is (the most) relevant, but it is not everything. The marginal (very able-- let us simplify) scientist can be moved into one direction or another by means of designing proper (or improper; but then again, who is to decide what is proper/improper in the context: I think we ought to take the view that lots of money is being thrown in one direction, because there is a lot of interest in that particular direction) extrinsic rewards. That being said, I personally (also) think there are a lot more interesting things in/to Maths than Biomaths :-).
• the European academic system is better than the US one. Hmmm, this is an endless debate and, as always, the truth is probably somewhere in the middle. Inter alia, it goes back to whether you need/want tenure or not in the academe (see for instance such a debate I've earlier linked to, especially within Economics) and to what goals you expect researchers to meet. And this also goes beyond one or another discipline, although it is perhaps interesting to discuss it indeed in the light of fundamental Mathematics, given its very abstract nature. Now, Connes believes that a system such as the French CNRS (which possibly is in the process of changing since 2005, when this interview took place) is perfect for mathematicians working on extremely complicated issues, that take years and years and years, since they are insulated from being subjected to those "n publications" requirement per year and in general from the eternal harassment of frequently showing how you compare to your peers, something specific to the top US institutions (Connes dismisses that the US places are ultimately inherently better in producing top scientists, because they get all the top European people-- not (entirely) true and to a great extent working eventually against his thesis, e.g. need to justify preferences of those very high European achievers for the US places, but let us not get also into that). The potential problem (sacrifice), as acknowledged by Connes, is the cost of such a practice, given that a lot of people might end up not producing anything and that the vast majority of them will be very far from getting Fields Medals or similar recognition among their peers... I say that the main problem is who bears that cost, namely the taxpayers here; and the public (not all of them having the same goals as Connes or as the specific, minority, group of the scientists, in general) is justified in knowing and assessing (whenever it so pleases) where its money is going and what precisely it pays for (if the funding is private, all this discussion has a completely different flavour-- remark that the US top academic places are privately funded, while all European examples Connes mentiones are public institutions; in my view, this again tips the balance towards the US academia). Related, but extremely surprising, Connes seems to be nostalgic after the Soviet Union academic system, but I think he deeply confuses things-- anyway, let us just say for the sake of this brief post that, fortunately, France was never quite like the Soviet Union, despite its tendency to lean extreme left, particularly within its academe... As for the claim that the Soviets would have been far ahead US and everybody else, if their system remained in place, I guess we'll never know (though I have opposite priors). And I think it is better we don't... So I am rather dissapointed that one of my idols in Mathematics has/had (this was '05) such, hmm: uninformed, views. But then again, I've always thought Economics (Not Politics. Politics is just a surface, not relevant in the long run, ultimately all boils down to Economics-- really!) is far less intuitive than Mathematics or Theoretical Physics :-).
  

I am sure one can go on and on, but I trust the main ideas are all outlined above (read also between the lines).

Weekend Econlinks

• "Famous economists" easy quiz. In fact too easy, as presented, because you can see the questions before you start the clock. So, in order to seriously test yourselves, just start the clock and then read the questions (you have 3 minutes in total). Took me 1 min and 14 seconds to answer all questions correctly, because I needed three trials for one of them-- yes, yes, I admit I have not read at all that book :-). Cowen claims it took him only 49 seconds. By the way, in case you didn't know of it, here's a great resource on the history of economic thought.

• The Levitt vs. Heckman leitmotive (actually the rest of that Univ of Chicago Magazine article is more interesting; in general, I think people put too many resources into this sort of personalized academic fights). Earlier on the same topic (3rd bullet point). See also an essay on the economics-made-for-fun genre, kind of vague / unfocused, but some parts are well worth your time (such as the beginning summary of the books in this econ-made-for-fun area)

• The three (only?!) habits of highly irritating management gurus: very well written, welcome article from the Economist. We love it!

• A nice recap post of Terry Tao on the "no self-defeating object" argument in mathematical proofs.

• Kahn has an interesting argument, but I find him overly pessimistic. I also think Cowen is somewhat out of touch with what is really going on with academic Economics. Very briefly, here's what I think: nothing is amiss with the current direction of research in Economics (as long as these ideas/ forecasts do not turn into self-fulfilling prophecies...)

• Hwang got rather easily off this (un)scientific mess. The timeline of events and more. Sometimes the academe & research world in general are too forgiving, and wrong (/dangerous?) precedents are set.

• Battle of Agincourt (welcome) controversy.

• Best US cities for classical music, in '09. Worldwide, I would place London, Amsterdam and Vienna somewhere in top 5. Not sure about Tokyo yet, since I was for too little there (and still have to put my impressions on paper... well, blog).

• Pure selection of 100% go-getters, if you ask me.

• Don't forget about the Prediction Markets on the Romanian 2009 Presidential Elections-- some seem to be making already (fictitious) fortunes there! :-)

Econlinks

• A summary of the debate "What's wrong with macroeconomics?" The debate goes on.

• Terry Tao's presentation of Perelman's solution to Poincaré's conjecture. There are chances you still won't understand much, but this is way better than attempting to directly digest Perelman's original articles :-).

• Here's Paul Graham's rule of thumb for recognizing (publishing) winners and losers: "When you see something that's taking advantage of new technology to give people something they want that they couldn't have before, you're probably looking at a winner. And when you see something that's merely reacting to new technology in an attempt to preserve some existing source of revenue, you're probably looking at a loser" . He's also got an entertaining piece on the cheeseburger of essay forms.

• "So long as you use a knife there's some love left" or a(nother) glimpse at Norman Mailer's life & oeuvre. Controversy might be his nickname, but Mailer is one embarassing omission of the Literature Nobel Prize Commitee.

• The Chess Dreamteam?

• "The paradox is this: it's best to engage with your opponents' strongest arguments--but your view of what their strongest arguments are is not necessarily their view." This quote (valuable on its own) is from a must-read post of Gelman on (strategic) citation practices.

(Many) Econlinks for the Weekend

• A nice, brief VoxEU note of Willem Buiter on negative nominal interest rates (and their potential desirability). Greg Mankiw also tackled the topic earlier.

• If you're at all into arithmetics (and not only) you might like this concise exposé on very big numbers (think Ackerman series, Busy Beavers and the like if you are dubious about what "very big" stands for in this context...). Inter alia, this reminds me that many many years ago :-), when I was starting highschool, one of my life goals was to prove the Goldbach conjecture. I guess meanwhile I started looking for easier life targets :-).

• We absolutely love Blonde Parades -- though I wouldn't necessarily ask a financial crisis as prerequisite :-).

• Harvard in BIG trouble?...

• Pacepa and the former Romanian car industry (that he does get at all WSJ editorial space I find rather amazing in the first place, that he uses it to give advice to the USA gov on the failed car companies is, well... just fantastic :-)...). Hmm, at least he's got an interesting "style", shifting the entire blame on his former superior(s)... There isn't much Economics in there of course, as he after all admits himself..., but I would have liked at least some more precision in the numbers (and no, "billions" in "The Oltcit project lost billions" is not what I would call a good approximation)

• This is the only bullet point connected to the "pathetic" label of this blogpost. Levitt oddly calls it "reasonably interesting" on Freakonomics (I also do not agree with all Levitt's further opinions on the apparent "macro problem", but well, I guess he is well versed in Macroeconomics to know it better :-)), but I find this Guardian editorial "interesting" only inasmuch it shows the difference in Economics education between the "Economics editor" (sic!) of The Guardian and other Economics editors at, say, WSJ, NYTimes, The Economist, or FT... Inter alia, I wouldn't pretend that everybody understands the work of Bonhomme and Robin forthcoming at the ReStud (or for that matter, any other work in a top 5 research journal within Economics, which perhaps is not aimed to really everybody?), but indeed from an "Economics editor" we would perhaps expect a little bit more that the appraisal "divorced from reality" (merely from reading the abstract and nothing further in the text, since else our author would have found plenty of "reality"...). But Economics à la The Guardian it is, now you know what to read :-).

• Who's a bigger villain for Development: Mugabe or Anopheles/ Sachs or Easterly...? I guess you ought to know by now what I think in this mater, but that should not stop you from making your own opinion :-).

• In a rather vague Reuters article Romania comes 3rd in a top of "new wine regions". A pity they do not mention any Romanian wine de facto in that top, since the variance in the quality of all wines produced in the above mentioned regions is... well, infinite.

• Interesting facts & thoughts by Dan Hamermesh on (incentive...) bonuses for papers with multiple co-authors. Should they be designed as function of 1/N or 1/SquareRoot(N), where N the number of co-authors etc.? Perhaps we should also know what other disciplines do, if anything, in this regard, in Economics indeed there seems to be a (very surprising) heterogeneity of such practices among various Departments/Institutes.

• It might be the first time ever..., but yes, the Historian won against the Economist (my good old friend Daniel, Harvard trained Historian of Science too, will surely be very pleased to hear this:-) ). I would never allow Paul Krugman in such competitions again, this is bad for the whole Econ field :-). The good thing though is that the Historian won with (the true) Economics arguments :-).

• Average citation rates by field (through Ad Astra). One trend not emphasized in the article's discussion following the table is that in some fields the citation impact is very low on the short run (1-3 years), but increases much faster over the the longer run (8-10 years). This is why for instance Economics gets a higher average citation impact than Mathematics or Computer Science overall, though in the short run (eg, the two years span that the Thomson ISI citation ranks are typically constructed on) is equally "de-cited". Consider switching to Molecular Biology if you're after citations :-).

Econlinks

• McCloskey and Ziliak vs. Hoover and Siegler, from the (very welcome, long overdue...) statistician's perspective. Gelman has extremely interesting points and I agree with most of them, except that I think (and he partially admits...) he does not know much (euphemism...) about the rational addiction & co literature, so let us leave that point out, shall we (in any case it is not related to the matter at hand)...

• Massively collaborative mathematics (via Terry Tao). I count myself an idealist when it comes to such ideas, just as the author of this post, and there are some well argumented points therein, but... my more recent economics background takes me back to earth. So here's one main reason (there are others, linked particularly to the nature of problem chosen to be solved by way of such "massive collaboration") why I think this will not work out (in Maths or any other science, for that matter, Econ included): the costs (particularly time and effort to follow such discussions, not to mention trusting the person-- if at all-- to monitor it all etc) would far outweigh the benefits. Unless the persons participating are far more efficient than the average (in time management & co) and, perhaps crucially, are not concerned with career building any longer... Somebody like Terry Tao perhaps, to keep it to Maths, though he does not seem overenthusiastic either :-).

• Monty Python should get Honorary PhDs in Economics. Their idea is already better than Radiohead's marketing experiment; hence, we have high expectations for even more daring moves in this direction, within the arts & entertainment world and beyond.

• Nature editorial on a "scientific responsibility index". I think some of these indices do not have to do so much with the aggregate, such as a country/nation dimension (for instance, it is in my opinion almost ridiculous to claim that researchers from/in a certain country ought to feel in any way tarnished by other co-national researchers'--could be from other fields, other times etc-- lack of ethics, and thus by an eventual 'country science ethics index'...), but otherwise the article is on the right track... Via Razvan, on Ad Astra.

• The so much en vogue Bailout Game.

• George Soros, with an interesting (and financially very informative) FT article entitled "The game changer" (plus an account of how well his own financial operations fared). Obviously I do not agree with all his points, for instance one paragraph I do not fancy is the following: "As it is, both the uptick rule and allowing short-selling only when it is covered by borrowed stock are useful pragmatic measures that seem to work well without any clear-cut theoretical justification." In fact, I think it is precisely because we do not have clear-cut justifications and lent ourselves too much to "pragmatic" experimentation, of whatever kind, is why we ended up here. One new such 'pragmatic' rule is not necessary better than a previous such 'pragmatic' rule :-). Thanks to Paul for the link!

Econlinks

• "First -- Chill -- then Stupor -- then the letting go": a historical perspective on the market, starting with the Great Crash

• What would Milton Friedman say about the current financial crisis? And he wouldn't be wrong.

• Here's an excellent answer if you ever wondered why people are interested in finding prime numbers with tens of millions of digits. And a nice exposition of the Lucas-Lehmer test for Mersenne primes by Terry Tao, to whom I owe also the previous link.

• "If Krugman were not too valuable to the profession for his own work, we should appoint him to a permanent position as the translator of economics journals into English." This is from Avinash Dixit's appraisal of Paul Krugman's work many years ago, when Krugman won the John Bates Clark medal. Very actual also as motivation for Krugman's winning the Nobel this year. And here's somebody who has actually bet on Krugman winning in 2008.

• Bill Easterly excellent on the dangers of developping countries learning the wrong lessons from this crisis.

Econlinks today

• Problems of Interplanetary and Interstellar Trade. Indeed, somebody had to start researching on this topic, at some point :-). Here's the part I like best in the concluding remarks: "Perhaps, the establishment of a solar system monetary union would permit the free flow of capital [...]"

• Giuseppe Bertola on why offshoring and immigrant employment are good, using the Italian context. Link to the VoxEU article, link to the background research paper.

• Our Moldavian neighbours are not too happy (if you are searching for the happiest Europeans instead, see here):

It was in Moldova that Weiner began to see, or, rather, failed to see, the building blocks that make a culture happy. "While I did meet some people I liked, Moldova is the least happy country on the planet," Weiner says. "People go to great lengths to see their neighbors fail. Completely seriously, it is a very morose place. I've never been so glad to leave a country."

• Pythagoras follow-up (well, almost...): Geometrical Music Theory (the shorter perspective, the longer report, both in a recent number of Science).

Quote for week 3rd to 9th of Feb '08

Mathematics is trivial, but I can’t do my work without it.

Richard Feynman

See the quote of the previous week.

The blue-eyed islanders puzzle

The morning pill: Terry Tao has just reminded me of the following famous logic puzzle. Obviously some of you have seen it before and might know the answer (disclaimer: I was confronted with this quite a while ago, in my first university year, as part of a challenge among Maths students), but many of you did not. Try to think about it on your own before checking the web for answers :-). Here's the puzzle in Tao's formulation:

There is an island upon which a tribe resides. The tribe consists of 1000 people, 100 of which are blue-eyed and 900 of which are brown-eyed. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and highly devout, and they all know that each other is also highly logical and highly devout.

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

One evening, he addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”.

What effect, if anything, does this faux pas have on the tribe?

If you give up (don't!) or simply want to check your reasoning, read Terry Tao's entire post and the subsequent comments. And if you still have problems understanding, you're welcome to drop a line :-).

Quote for week 13th to 19th of Jan '08

[...]The gift of early insight into chess or math or music is often also accompanied by a growing obsession with those activities, simply because of the wonders of connection and invention that unfold in the young mind. The world itself, with its more messy human interactions, its complicated histories, its emotional conflicts, can be put aside, and attention focused on an intricate bounded cosmos. Perhaps we should be grateful that such gifts are so rare, for if they were not, how many of us would prefer to remain cocooned in these glass-bead games? At least in mathematics and music, we may be grateful too that ultimately, with the coming of maturity, the world starts to put constraints on abstract play. Great music attains its power not simply through manipulation and abstraction, but by creating analogies with experience; music is affected by life, not cut off from it. Mathematics also comes up against the demands of the world, as the field opens up to understanding; early insights are tested against the full scale of what has been already been done and what yet remains undone. But chess, alone among this abstract triumvirate, is never tested or transformed. The only way expertise is ever tried is in victory or defeat. And if a player is as profoundly powerful as Mr. Fischer, defeat never creates a sense of limits. Seeing into a game and defeating an opponent — that defines the entire world.

Edward Rothstein, "Fischer vs. the World: A Chess Giant's Endgame"

Read the quote of the previous week.

What is good mathematics?

Read the answer by one of the most qualified persons to give an answer: Terence Tao.

Also: Tao's blog is for quite a while in my blogring, I hope you noticed that :-). Quite an interesting and welcome new idea there is that he'll be posting soon his notes on the graduate course "topics in ergodic theory".

Probability of being a serial killer: the case of Lucia de Berk

Here's a post on an extremely interesting story at the intersection of law, statistics and professional ethics in several disciplines. Inter alia, the issue has been covered in some of the best scientific journals. See for instance a). a report in the Science edition of the 16th of November (you need a subscription to access the PDF); b). a very good report on this case in Nature, January this year; you can read here that PDF (subscription free).

What is this about? One of the most interesting legal cases ever, involving multiple homicide, is now under review by the Supreme Court in the Netherlands. The case deals with the former trial of Lucia de Berk, a Dutch nurse, accused and sentenced to life imprisonment in spring 2003, for the alleged murder of seven hospital patients and the attempted murder on three others, in places where she had worked between 1999-2001. The issue is that there was never direct evidence to implicate De Berk (and she has always denied all accusations): she was condemned solely based on the fact that she happened to be always around when these patients died; basically the courts (an appeal court also upheld the initial verdict) decided that it was very unlikely, essentially only one chance in 342 million, according to the expert statistician who testified at the trial, that so many deaths could have occured accidentally while she was nearby.

What happens now is that the 2003 sentence is being challenged by several scientists who signed a petition to re-open the case (this is what the Supreme Court needs to decide on, after last months a justice department panel indeed recommended that the case be reopened). Richard Gill, a Leiden University mathematician and organizer of the petition, states that the previous conclusion, leading to the condemnation of De Berk, is based on "every statistical mistake in the book". Gill and others concluded that the previous statistical testimony was based on an incorrect analysis and that in fact the probability estimated earlier, of 1 in 342 million, is in fact as low as 1 in 48 or even 1 in 5, which are very unlikely to meet the criterion of "beyond reasonable doubt" needed for a criminal conviction. Here's the website of Gill dedicated to this case (with his detailed discussion of the statistical aspects in this case here and Gill's synopsis/reconstruction of the case + other interesting details here). There is even a whole book criticizing De Berk's conviction on scientific procedure, by Ton Derksen , a philosopher of science from the University of Nijmegen. Mark Buchanan, who wrote about the case in Nature (see the link above) summarizes the legal essence of the argument this way: "The court needs to weigh up two different explanations: murder or coincidence. The argument that the deaths were unlikely to have occurred by chance (whether 1 in 48 or 1 in 342 million) is not that meaningful on its own - for instance, the probability that ten murders would occur in the same hospital might be even more unlikely. What matters is the relative likelihood of the two explanations. However, the court was given an estimate for only the first scenario."

This is certainly not an easy case, despite the fact that it is not the first one that might involve wrong statistical evidence in a criminal sentence (the Nature report linked above also mentions another high profile case involving misuse of statistics, the case of Sally Clark, from 1999, in Britain). My opinions are the following. Firstly, I strongly believe that the Dutch Supreme Court has more than sufficient basis to re-open De Berk's case and carefully re-analyse all the previous evidence (I've obviously signed the petition as well). Further, one can only hope that a wrong verdict is overturned swiftly in De Berk's case, should the petitioners be right (and then I wouldn't want to be in the place of the 'expert statistician' who testified to start with, although it is true, as can be read on Gill's discussion, that this expert "always insisted that his analysis only showed that the observed coincidence could not be due to pure chance, not that Lucia caused the the deaths"; moreover, this expert himself wants the case to be reopen; but the scientific flaws would still be there, if the petitioners are right.). More generally, one can only hope that science will be used with the greatest care in any legal processes, especially criminal ones, given the extreme emotions and stakes typically involved (but not only: science has to be done properly, anytime, anywhere, anyway...).

The song of the day: "Finite Simple Group (of Order Two)", by the Klein Four Group

Fantastic, simply fantastic! Maths, music (nod bad at all), fun and-- the sine qua non-- love, at work, together: I've just relived my entire college life :-). Never heard of the guys before, but they've surely got all my votes. The excellent lyrics of today's song are pasted below, for future reference... More songs and lyrics on the Klein Four Group's website.

Many thanks, Ana!

Finite Simple Group (of order two)
A Klein Four original by Matt Salomone

The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true

But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two

I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two

Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense

I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two

I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")

I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.

Check out the previous songs in my "song of the day" category (with the caveat that most of them are less hilarious than this one :-)).

Econlinks for 13-05-'07

• an excellent (wide-audience targeted) article on the upside of income inequality, by Gary Becker and Kevin Murphy. Greg Mankiw also writes about it (and singles out exactly the fragment I wanted to single out).

• a clear KO administered by Steven Levitt to some 'journalist' who tried to criticise him and made a mess of himself, rather... That was nice (don't upset Levitt if you're not a pro and particularly don't do it if you have no clue what you're talking about...), but I think Levitt is wasting his time with answering such nonsense in such detail, and he'd rather give some reactions to the interesting part of the criticisms raised, for instance, by Rubinstein (Rust and Heckman are other heavyweights that criticised Levitt in the past). I summarized a bit of all that on this blog, a while ago.

• one very interesting piece of Paul Rubin in the Washington Post, on the link between evolution and (some) people's wrong opinions on immigration and trade. I cannot agree more with one of his conclusions: "A deeper understanding of economics is like reading- it must be taught". Via Greg Mankiw (though I can't really see this as 'Darwin versus Smith'...).

• an older entry of Bernard Salanié (who's recently decided to take a break from blogging: I hope it won't be for very long...) on Maths prodigy Terence Tao (you can read a short description of Tao's work- and of the other recent Fields medal laureates- that got him the recent Fields medal, in the March number of the Notices of the American Mathematical Society; in the same number there is also an interview with him and with the other two Fields medalists who did not decline the honour, like Perelman) . The bottom line is that you should take the Terence Tao Test (TTT) as well- and don't forget that he had solved it perfectly before he was 8 years old :-).

On why you need Maths for Economics and in general

Some young but very ambitious students (yeah, yeah, some of you are reading this post on my blog right now :-)) have been asking me why would they need to know Maths if they want to become economists (in industry or academia) and what Maths courses are most suitable for them and how much Maths would they actually use in practice anyway...

These are very interesting and very pertinent questions and obviously they were asked and answered before. By many, many times. I'll thefore select a few such answers for you, among those that I largely agree with. To start up, I am very lucky to be able to refer all of you to Greg Mankiw's detailed answers to the questions directly relating Maths to your further careers as economists. First, why do aspiring economists need Maths and second, which Maths courses are a minimum that you should plan to take. By the way, for those of you interested in doing a PhD in Economics, I'd take professor Mankiw's advice very seriously: "if you are thinking about a PhD program in economics, you are advised to take math courses until it hurts" :-).

And if you want something to complement the above - and, at the same time, a more general perspective on why a Maths education might be useful - I also recommend you to read Gian-Carlo Rota's "10 lessons of an MIT education" (it's not the MIT part that's important for my purpose here :-)) and I am referring in this case (there are also things among these 10 lessons that I do not fully agree with, but it's not time to voice my discontent with that :-)) particularly to his Lesson number 10, here's the relevant part: "Mathematics is still the queen of the sciences [...] When an undergraduate asks me whether he or she should major in mathematics rather than in another field that I will simply call X, my answer is the following: "If you major in mathematics, you can switch to X anytime you want to, but not the other way around."

For the last part of the questions above, on how much Maths would you actually use in practice beyond absurd requirements of some crazed professors :-): that largely depends on what you will actually do, whether you'll be working as an academic or as a consultant of some sort etc (Greg Mankiw already had a bit on this, at the links mentioned above). But that aside, a good Maths training will give you something potentially more important, whatever you'll be doing: it will enable you to think logically in whatever situations you will face (and that is what I'd call the 'qualitative' bonus of having done Maths), plus it will give you a technical basis and will allow you to rely on your own skills for most day-to-day computing, accounting, investing, issues (and that is what I'd label the 'quantitative' methodology advantage that comes with having learnt Maths): à propos, I recall here a pertinent citation attributed to Anatole France: "People who don't count won't count"... Furthermore, and this is more important than many think, once you did it properly and you understood it (in Maths you do not memorize- if you try that, you don't stand a chance- you need to understand, you need to get used to it...), you will always be able to know how and where to look for particular bits, whenever you need to apply them again (that was contained also within Rota's rules, if you read carefully, in his Lesson 3: By and large, "knowing how" matters more than "knowing what." ).

Scientific Breakthrough: Mapping E8

This definitely calls for celebration in the whole scientific community! Perseverance, a lot of patience, a team of 18 brilliant mathematicians and computer scientists, 64 Gb of RAM: the result is mapping E8, the largest among the exceptional simple Lie groups. Here's the press release of the American Institute of Mathematics. And here, some details of the computation. For a lot more information check the Atlas of Lie Groups and Representations.

Update (same day): the 18-people team involved in the breakthrough (Dan Ciubotaru, a Romanian, is one of the members)

Update 26th of March: Razvan Florian posted my note about Ciubotaru as news on Ad Astra. Science also had as news this fantastic breakthrough, on March 23rd.