Throughover the workshop in Chennai floated (!) the figure of Jean/André Ville, with his inequality generalising Markov’s, who invented martingales. He is not such a well-known figure in France—at least to me!—, despite having led a rather exceptional life, from being a visiting scholar in Berlin (in the Maison académique de Berlin, along with a certain Jean-Paul Sartre) and Vienna in the 1930s, to his wife being (in Berlin) one of the many (disposable and despised) lovers of JP Sartre (to whom an open-minded or clueless Ville later sent his thèse d’université on martingales and collectives, a much more substantial piece of work than the current PhD), to him working with German and Austrian mathematicians and logicians, such as Popper, Gödel, and Wald–who, what a coïncidence!, died in India from a plane crash in 1950 that had left from Chennai–and being impressed enough by the latter to passing an economics degree in the Sorbonne when back in Paris, establishing a minimax result for a zero-sum matrix game with two players, to his counter-example to von Mises’ kollectiv, to his nickname of the King of Counterexamples in the Viennese mathematics seminar, to him operating the first (Bull) computer at the Université de Paris. (Glenn Shafer wrote a detailed accounting of his youth, on which this post is based, up to his thesis defence but a few days from France mobilising for war–where his collegue Wolfgang Doeblin would kill himself the year after, to avoid capture–. With Bernard Bru, Edmond Malinvaud and Alain Trognon among the people who helped.) After the war, he worked several years as a prépa maths teacher before working for a French State electricity companion on signal theory and Monte Carlo methods, and then returning to Université de Paris as a professor in 1957.
Archive for Kurt Gödel
André ou Jean Ville (1910-1989)
Posted in Books, pictures, Travel, University life with tags 25w5482, Abraham Wald, Alain Trognon, André Ville, Andrey Markov, École Normale Supérieure, Berlin, Bernard Bru, BIRS-CMI, Bull computers, Chennai, Edmond Malinvaud, Emile Borel, George Darmois, Glenn Shafer, history of Monte Carlo, history of statistics, India, Jean Ville, Jean-Paul Sartre, Karl Popper, Kurt Gödel, martingales, Maurice Fréchet, minimax strategy, Monte Carlo methods, Paris, Paul Lévy, plane crash, Richard von Mises, signal theory, Simone de Beauvoir, Sorbonne, supermartingale, two-player game, Université de Paris, Vienna, Ville's inequality, Wolfgang Doeblin, WW II on August 12, 2025 by xi'anStories of your life and Others [book review]
Posted in Books, Kids, University life with tags 1950's, AI, alien intelligence, alternative reality, Amazing Stories, Babel tower, book review, calliagnosia, CHANCE, cover, eugenism, evolutionary biology, Genetics, golem, Kurt Gödel, linguistics, Nature, Pascal's wager, Philosophy of religions, steampunk, Ted Chiang, Victorian society on March 18, 2025 by xi'an
Just finished the book Stories of your life and Others by Ted Chiang, which like the later Exhalation I deeply enjoyed. The book was published in 2001, with some of its stories appearing as early as 1990, hence this book review is of little relevance when many reviews and commentaries have been published, including academic reviews. (No chance for CHANCE, then!)
“Perhaps you have not noticed that the lower classes are reproducing at a rate exceeding that of the nobility and gentry (…) Consequently, our nation would eventually drown in coarse dullards.” (p.186)
While the original cover seems to cater to old-fashion science-fictions books and magazine of the 1950’s, like Amazing Stories, the contents are much more philosophical than science-fiction-al, even when the universe (or the physical laws that) Chiang creates relies on elaborate construction based on science. (Same thing happens with Exhalation.) With a take on religions and their logical loopholes that I particularly enjoy, like Hell is the Absence of God, where the central character is no given the choice of Pascal’s wager. And the nonsense of attributing handicaps and hardships to dog’s testing impacted individuals, as well as the involuntary humour in the innocent casualties resulting from angels visiting Earth. Some stories I liked less, like Understand, about a superhuman emerging from drug tests since the end cannot keep up with the premises. But others I really appreciated, from Babel, set in a naïve (very medieval) version of the World, with a flat Earth and a solid sky. To Division by Zero, where a Gödelian mathematician pushes the impossibility theorem to ruin all of mathematics, and to the superb Seventy Two Letters, that mixes cybernetics, Kabbalists’ golem, genetics and eugenics, in a Victorian setting that could make it pass for a steampunk story, but I disagree with this label since the novella somewhat runs backwards by returning to a freedom of choice that trumps eugenic goals, while aligned with the Victorian perception of science. The same with Story of Your Life, about constructing communication channels with a perplexing if peaceful alien race, whose purpose for this attempt is never clear, which is not an issue with enjoying the built-up of an understanding, as well as the disrupted time-frame of the narration. Or even the short (Nature) story, The Evolution of Human Science, which reflects the very real concern that AI could take over research, into directions that would escape human understanding (not a good signal for i!). Leaving hermeneutics (of AI research) to humans. And the final Liking what you see, a clever variation on the issues of “lookism”, the “burden” of beauty, and an imagined condition called calliagnosia that makes people insensitive to beauty or lack thereof in a person.
Philosophies, Puzzles and Paradoxes [book review]
Posted in Books, pictures, Statistics, Travel, University life with tags A Treatise on Probability, Bayesian inference, Bill Reid, book review, British Columbia, Canada, cedar, CHANCE, David Hume, Enlightenment, epistemic probability, First Nations, frequentist confidence, Haida culture, Henri Poincaré, incompleteness theorem, jatp, John Maynard Keynes, Kurt Gödel, likelihood, Likelihood Principle, marginalisation paradoxes, Maurice Allais, Monty Hall problem, Museum of Anthropology, paradoxes, Philosophy of Science, prior selection, puzzle, raven, Significance, Tintin, UBC, University of British Columbia, Vancouver on May 25, 2024 by xi'an
Yudi Pawitan and Youngjo Lee have written a book that recently caught my attention within the CRC Press list of new publications. Because philosophy, puzzles, and paradoxes are definitely of interest to me (as shown by numerous entries in the ‘Og!). The subtitle of said book is A Statistician’s Search for Truth.
Reviews of the book are already available, with for instance Andrew Gelman stating that he disagrees “with much of this book, but it’s an entertaining and thought-provoking introduction to some challenging questions” or Stephen Senn starting the foreword with “This is a remarkable book: wide-ranging, ambitious, challenging and profound but also intriguing, fascinating and original.” (Senn is also cited within the book for his discussion of our revisit of Harold Jeffreys’ Theory of Probability.) Nice cover as well (albeit I could not trace the origin of it, inside or outside the book.)
The book is made of three parts, one on the philosophical approaches to truth, scientific discovery, deduction, and induction, a second one on probability theories, with philosophical motivations, Bayesian inference, and likelihood-based inference, and a third section on paradoxes. Given that both authors are senior authors who have contributed to likelihood inference throughout their career, incl. the books In All Likelihood and Generalized Linear Models with Random Effects, the likelihood approach is somewhat privileged against other statistical resolutions towards the resolution of the paradoxes, with a defence of confidence distributions and a chapter on epistemic confidence that mostly stems from recent papers by the authors, like Pawitan et al. (2023) and Lee and Lee (2023). I find the discussion therein somewhat unclear, esp. because the same notation Pr(.) is employed for different probability notions.
“Epistemic confidence is the objective measure of uncertainty that’s attached to single events, where the objectivity is based on a consensus of rational minds.” (p.197)
The philosophy part is following the (European) Enlightenment in producing more and more involved discussions on reason, knowledge and scientific discovery. This exploration is an easy read, as it does not delve particularly deeply in the arguments of Kant, Hume, or Popper. With the apparently unescapable mention of Gödel’s incompleteness theorem, including a sausage citation from Poincaré that reminded of that strip from Tintin in America:
which, most probably, he would have applied to Ais! Several sections about pseudo-rational attempts to demonstrate the existence of Dog could have been skipped as well.
The part of probability already considers paradoxes which, like the subsequent ones are mostly the consequence of using natural (and hence ambiguous) languages instead of mathematical descriptions—incl. the statement of the Likelihood Principle. It also discusses Keynes’ logical (or imprecise) probabilities, briefly if appropriately given the pessimistic views of young Keynes on the assessment of the probability of an event. Savage is privileged enough to enjoy an entire chapter discussing his 1950’s axioms leading to the existence of a (subjective) prior on “the states of the world”. This is followed by a chapter on Inverse probability (aka Bayesian statistics), where the authors consider Bayes’ 1763 Essay to have stayed mostly unnoticed till the beginning of the 20th Century, which sounds a somewhat subjective judgement. (And as uncovered by Steve Stiegler, the original title of the Essay was indeed intended as a reply to Hume.) A further if short chapter is dedicated to the search for the prior distribution. Which thus gives the misguided impression that there should exist such a thing, rather than acknowledging that Bayesian statements are relative to the prior measure. The remainder of the discussion on invariant and reference priors is however mostly standard. Except when falling for the marginalisation paradox when stating that a product of improper priors implies independence on p.144.
The paradoxes examined in the final part are Allais’ (an alumni of Lycée Lakanal!), and Ellsberg’s, avatars of the Saint Petersburg paradox and referring to failing to adhere to rational decision-making and not in the least to statistics. Conjunction and inclusion “fallacious fallacies”, which are central to Kahneman’s Thinking fast and slow bestseller, and attributed to reasoning in terms of likelihood rather than of probability (without accounting for multiple testing on p.228). A whole if short chapter on the Monty Hall and three prisoners paradoxes, another predictable occurrence in a book on reasoning paradoxes. Again mostly a matter of poor wording, plus relying on the choice of an underlying probability model, for which the authors again follow a likelihood approach, the number of the prize door or of the freed prisoner being the parameter. Kyburg’s (very weak) lottery paradox and related forensic paradoxes, concluding with the rejection of judgements based solely on probability reasoning. Hempel’s paradox of the ravens, a priori unrelated with statistical evidence, but turned into one by squeezing in some sampling models. Finishing with the (envelope) exchange paradox, where the authors refuse to put a prior on the unknown parameter but end up with a solution equivalent to adopting a Jeffreys prior.
In conclusion, this attempt at connecting statistical inference and philosophy, probability concepts and rational decision making, paradoxes and modelling, within a single book is academically sound and overall enjoyable, if not outstanding or remarkable as it does not constitute a radical move away from existing analyses of those classical paradoxes. Furthermore, I find the paradoxes overwhelmingly distant from genuine statistical settings and involving a rather stretched notion of data. Still, methinks I will keep this book in my bookcase, rather than leaving it for the taking in the department coffee room!
As I was completing the book and getting towards writing this book review, I also noticed a two page blurb in Significance (May 2024 issue) written by the authors on their book. (which happens rather frequently with this magazine). Unsurprisingly, the contents provd mostly extracted from the preface and introduction With a nice ravens picture (in conjunction with the raven paradox).
[Disclaimer about potential self-plagiarism: this post or an edited version may eventually appear in my Books Review section in CHANCE.]
Number savvy [book review]
Posted in Books, Statistics with tags #ERCSyG, book review, Brave New World, Brussels, Bruxelles, Canada, Census, CHANCE, CRC Press, data, data market, data pooling, data privacy, demonstrations, ERC Synergy Grant, EU, European Research Council, European Union, Gödel Escher and Bach, GDPR, geography, Kurt Gödel, microdata, Nassim Taleb, Paris, prospect theory, savvy, Statistics Canada, survey, Taoism on March 31, 2023 by xi'an“This book aspires to contribute to overall numeracy through a tour de force presentation of the production, use, and evolution of data.”
Number Savvy: From the Invention of Numbers to the Future of Data
is written by George Sciadas, a statistician working at Statistics Canada. This book is mostly about data, even though it starts with the “compulsory” tour of the invention(s) of numbers and the evolution towards a mostly universal system and the issue of measurements (with a funny if illogical/anti-geographical confusion in “gare du midi in Paris and gare du Nord in Brussels” since Gare du Midi (south) is in Brussels while Gare du Nord (north) in in Paris). The chapter (Chap. 3) on census and demography is quite detailed about the hurdles preventing an exact count of a population, but much less about the methods employed to improve the estimation. (The request for me to fill the short form for the 2023 French Census actually came while I was reading the book!)
The next chapter links measurement with socio-economic notions or models, like unemployment rate, which depends on so many criteria (pp. 77-87) that its measurement sounds impossible or arbitrary. Almost as arbitrary as the reported number of protesters in a French demonstration! Same difficulty with the GDP, whose interpretation seems beyond the grasp of the common reader. And does not cover significantly missing (-not-at-random) data like tax evasion, money laundering, and the grey economy. (Nitpicking: if GDP got down by 0.5% one year and up by 0.5% the year after, this does not exactly compensate!) Chapter 5 reflects upon the importance of definitions and boundaries in creating official statistics and categorical data. A chapter (Chap 6) on the gathering of data in the past (read prior to the “Big Data” explosion) is preparing the ground to the chapter on the current setting. Mostly about surveys, presented as definitely from the past, “shadows of their old selves”. And with anecdotes reminding me of my only experience as a survey interviewer (on Xmas practices!). About administrative data, progressively moving from collected by design to available for any prospection (or “farming”). A short chapter compared with the one (Chap 7) on new data (types), mostly customer, private sector, data. Covering the data accumulated by big tech companies, but not particularly illuminating (with bar-room remarks like “Facebook users tend to portray their lives as they would like them to be. Google searches may reflect more truthfully what people are looking for.”)
The following Chapter 8 is somehow confusing in its defence of microdata, by which I understand keeping the raw data rather than averaging through summary statistics. Synthetic data is mentioned there, but without reference to a reference model, while machine learning makes a very brief appearance (p.222). In Chapter 9, (statistical) data analysis is [at last!] examined, but mostly through descriptive statistics. Except for a regression model and a discussion of the issues around hypothesis testing and Bayesian testing making its unique visit, albeit confusedly in-between references to Taleb’s Black swan, Gödel’s incompleteness theorem (which always seem to fascinate authors of general public science books!), and Kahneman and Tversky’s prospect theory. Somewhat surprisingly, the chapter also includes a Taoist tale about the farmer getting in turns lucky and unlucky… A tale that was already used in What are the chances? that I reviewed two years ago. As this is a very established parable dating back at least to the 2nd century B.C., there is no copyright involved, but what are the chances the story finds its way that quickly in another book?!
The last and final chapter is about the future, unsurprisingly. With prediction of “plenty of black boxes“, “statistical lawlessness“, “data pooling” and data as a commodity (which relates with some themes of our OCEAN ERC-Synergy grant). Although the solution favoured by the author is centralised, through a (national) statistics office or another “trusted third party“. The last section is about the predicted end of theory, since “simply looking at data can reveal patterns“, but resisting the prophets of doom and idealising the Rise of the (AI) machines… The lyrical conclusion that “With both production consolidation and use of data increasingly in the ‘hands’ of machines, and our wise interventions, the more distant future will bring complete integrations” sounds too much like Brave New World for my taste!
“…the privacy argument is weak, if not hypocritical. Logically, it’s hard to fathom what data that we share with an online retailer or a delivery company we wouldn’t share with others (…) A naysayer will say nay.” (p.190)
The way the book reads and unrolls is somewhat puzzling to this reader, as it sounds like a sequence of common sense remarks with a Guesstimation flavour on the side, and tiny historical or technical facts, some unknown and most of no interest to me, while lacking in the larger picture. For instance, the long-winded tale on evaluating the cumulated size of a neighbourhood lawns (p.34-38) does not seem to be getting anywhere. The inclusion of so many warnings, misgivings, and alternatives in the collection and definition of data may have the counter-effect of discouraging readers from making sense of numeric concepts and trusting the conclusions of data-based analyses. The constant switch in perspective(s) and the apparent absence of definite conclusions are also exhausting. Furthermore, I feel that the author and his rosy prospects are repeatedly minimizing the risks of data collection on individual privacy and freedom, when presenting the platforms as a solution to a real time census (as, e.g., p.178), as exemplified by the high social control exercised by some number savvy dictatures! And he is highly critical of EU regulations such as GDPR, “less-than-subtle” (p.267), “with its huge impact on businesses” (p.268). I am thus overall uncertain which audience this book will eventually reach.
[Disclaimer about potential self-plagiarism: this post or an edited version will potentially appear in my Books Review section in CHANCE.]
undecidable learnability
Posted in Books, Statistics, Travel, University life with tags academic journals, incompleteness theorem, Kurt Gödel, learnability, Nature Machine Intelligence, Robins-Wasserman paradox, Vapnik-Chervonenkis on February 15, 2019 by xi'an
“There is an unknown probability distribution P over some finite subset of the interval [0,1]. We get to see m i.i.d. samples from P for m of our choice. We then need to find a finite subset of [0,1] whose P-measure is at least 2/3. The theorem says that the standard axioms of mathematics cannot be used to prove that we can solve this problem, nor can they be used to prove that we cannot solve this problem.”
In the first issue of the (controversial) nature machine intelligence journal, Ben-David et al. wrote a paper they present a s the machine learning equivalent to Gödel’s incompleteness theorem. The result is somewhat surprising from my layman perspective and it seems to only relate to a formal representation of statistical problems. Formal as in the Vapnik-Chervonenkis (PAC) theory. It sounds like, given a finite learning dataset, there are always features that cannot be learned if the size of the population grows to infinity, but this is hardly exciting…
The above quote actually makes me think of the Robbins-Wasserman counter-example for censored data and Bayesian tail prediction, but I am unsure the connection is anything more than sheer fantasy..!
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