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A NYT op-ed the other day,”How Medical Care Is Being Corrupted” (by Pamela Hartzband and Jerome Groopman, physicians on the faculty of Harvard Medical School), gives a good sum-up of what I fear is becoming the new normal, even under so-called “personalized medicine”. “It is obsolete for the doctor to approach each patient strictly as an individual; medical decisions should […]

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7:30 PM | Weekly Potpourri

Newest mathy grab-bag:
1) George Hart presents 4 mins. of an elliptic hyperboloid:
http://tinyurl.com/ndy2ovs
2) A MathMunch weekly wrap-up:
http://mathmunch.org/2014/11/16/grothendieck-circle-packing-and-string-art/
3) A couple more tributes to Grothendieck:
https://rjlipton.wordpress.com/2014/11/16/alexander-grothendieck-1928-2014/
http://www.thebigquestions.com/2014/11/17/the-generalist

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1:17 AM | Erich Lehmann: Statistician and Poet

Memory Lane 1 Year (with update): Today is Erich Lehmann’s birthday. The last time I saw him was at the Second Lehmann conference in 2004, at which I organized a session on philosophical foundations of statistics (including David Freedman and D.R. Cox). I got to know Lehmann, Neyman’s first student, in 1997. One day, I […]

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2:05 AM | Kalmár's Compleness Proof

Dana Scott's proof reminded commenter "fbou" of Kalmár's 1935 completeness proof. (Original paper in German on the Hungarian Kalmár site.) Mendelsohn's Introduction to Mathematical Logic also uses this to prove completeness of propositional logic. Here it is (slightly corrected):
We need the following lemma:
Let $v$ be a truth-value assignment to the propositional variables in $\phi$, and let $p^v$ be $p$ if $v(p) = T$ and $\lnot p$ if $v(p) = F$. If $v$ makes $\phi$ true, then \[p_1^v,
[…]

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2:47 PM | Category Theory, instalment #1

As I said in my last post, I’ve been following some lectures on category theory since the beginning of term. The only way of really nailing this stuff down is to write yourself some notes, work through the proofs, etc. Which I’ve been … Continue reading →

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Today is the birthday of Lucien Le Cam (Nov. 18, 1924-April 25,2000): Please see my updated 2013 post on him. Filed under: Bayesian/frequentist

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6:04 PM | Orientation through words and notation

I thought recently, again, about the relationship between the written word and mathematical notation, both being systems of marks that carry meaning. Both systems grow with usage, and both provide some steady refinement of what we are able to see. I’m not so much interested, here, in the relationship between mathematical proficiency and language proficiency, [...]

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12:15 AM | Dana Scott's Favorite Completeness Proof

Last week I gave my decision problem talk at Berkeley. I briefly mentioned the 1917/18 Hilbert/Bernays completeness proof for propositional logic. It (as well as Post's 1921 completeness proof) made essential use of provable equivalence of a formula with its conjunctive normal form. Dana Scott asked who first gave (something like) the following simple completeness proof for propositional logic:
We want to show that a propositional formula is provable from a standard axiomatic set-up iff it is
[…]

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There was a session at the Philosophy of Science Association meeting last week where two of the speakers, Greg Gandenberger and Jiji Zhang had insightful things to say about the “Law of Likelihood” (LL)[i]. Recall from recent posts here and here that the (LL) regards data x as evidence supporting H1 over H0 iff Pr(x; H1) > Pr(x; H0). On many accounts, […]

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4:36 PM | Lectures on the Epsilon Calculus

Back in 2009, I taught a short course on the epsilon calculus at the Vienna University of Technology. I wrote up some of the material, intending to turn them into something longer. I haven't had time to do that, but someone might find what I did helpful. So I put it up on arXiv:
http://arxiv.org/abs/1411.3629

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4:00 PM | Big Helping of Potpourri

...First off, biggest news of the week was the death of Alexander Grothendieck on Thursday, which I referenced (with links) in my Math-Frolic post earlier this morning:
http://math-frolic.blogspot.com/2014/11/to-thine-own-self-be-true-legend-passes.html
Otherwise, bunch-of-links from the week:
1) A post from RJ Lipton on Stanislaw Ulam and an unproved conjecture:
http://

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9:32 AM | In memoriam: Alexander Grothendieck

By Catarina Dutilh NovaesAlexander Grothendieck, who is viewed by many as the greatest mathematician of the 20th century, has passed away yesterday after years of living in total reclusion. (To be honest, I did not even know he was still alive!) He was a key figure in the development of the modern theory of algebraic geometry, among others, but to philosophers and logicians he is perhaps best known as one of the major forces behind the establishment of category theory as a new foundational […]

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The Colbert ReportGet More: Daily Show Full Episodes,Indecision Political Humor,The Colbert Report on FacebookH/T Tina Eliassi-Rad (And comments that pick on Tao for (sort of) calling 27 a prime will be summarily deleted.)

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One year ago I reblogged a post from Matt Strassler, “Nature is Full of Surprises” (2011). In it he claims that [Statistical debate] “often boils down to this: is the question that you have asked in applying your statistical method the most even-handed, the most open-minded, the most unbiased question that you could possibly ask? It’s not asking whether […]

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3:04 PM | ❦ Pyramus & Thisbe ❦

It’s all about love And the knots thereof I have known beauty I’ll bring it to you Jon Awbrey • 12 Nov 2014

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The NY Times Magazine had a feature on the Amazing Randi yesterday, “The Unbelievable Skepticism of the Amazing Randi.” It described one of the contestants in Randi’s most recent Million Dollar Challenge, Fei Wang: “[Wang] claimed to have a peculiar talent: from his right hand, he could transmit a mysterious force a distance of three feet, […]

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4:56 AM | Frankl, My Dear : 11

Re: Dick Lipton & Ken Regan • (1) • (2) Let’s take a moment from the differential analysis of the proposition in Example 1 to form a handy compendium of the results obtained so far. Example 1 (1) Enlargement Map of … Continue reading →

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We had an excellent discussion at our symposium yesterday: “How Many Sigmas to Discovery? Philosophy and Statistics in the Higgs Experiments” with Robert Cousins, Allan Franklin and Kent Staley. Slides from my presentation, “Statistical Flukes, the Higgs Discovery, and 5 Sigma” are posted below (we only had 20 minutes, but much came out in the discussion). Even the challenge I […]

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Peircers, The concept of continuity that Peirce highlights in his synechism is a logical principle that is somewhat more general than the concepts of either mathematical or physical continua. Peirce’s concept of continuity is better understood as a concept of … Continue reading →

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8:30 PM | Potpourri

Some links from the week (potpourri links and blog posts may decrease somewhat as I'm busy with other Web stuff through end-of-year):
1) Mike Lawler offered up a bunch of fun math examples from the week in this post:
http://mikesmathpage.wordpress.com/2014/11/03/fun-math-that-i-saw-this-week/
2) The mathematics of falling objects results in tragedy:
http://wavefunction.fieldofscience.com/

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15th CONGRESS OF LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE (CLMPS 2015)University of Helsinki, Finland, 3-8 August 2015http://clmps.helsinki.fiSubmission deadline: 30 November 2014The Congress of Logic, Methodology and Philosophy of Science (CLMPS) is organized every four years by the Division of Logic, Methodology and Philosophy of Science (DLMPS). The Philosophical Society of Finland, the Academy of Finland Centre of Excellence in the Philosophy the Social Sciences (TINT) and the Division […]

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4:48 AM | Frankl, My Dear : 10

Re: Dick Lipton & Ken Regan • (1) • (2) (5) Figure 5 shows the 14 terms of the difference map as arcs, arrows, or directed edges in the venn diagram of the original proposition There are two types of arcs, … Continue reading →

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10:20 PM | Frankl, My Dear : 9

“It doesn’t matter what one does,” the Man Without Qualities said to himself, shrugging his shoulders. “In a tangle of forces like this it doesn’t make a scrap of difference.” He turned away like a man who has learned renunciation, … Continue reading →

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The biennial meeting of the Philosophy of Science Association (PSA) starts this week (Nov. 6-9) in Chicago, together with the History of Science Society. I’ll be part of the symposium: How Many Sigmas to Discovery? Philosophy and Statistics in the Higgs Experiments on Nov.8 with Robert Cousins, Allan Franklin, and Kent Staley. If you’re […]

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7:00 PM | End-of-week Potpourri

Links from the week:
1) Some puzzles from Presh Talwalkar started the week:
http://tinyurl.com/ntgfqpk
And some more puzzles here:
http://cavmaths.wordpress.com/puzzles-and-starters/
2) If you can't get enough of James Grime, Reddit did an AMA ('ask-me-anything') thread with him this week:
http://tinyurl.com/o75p57h
3) Evelyn Lamb told us about Euclid, geometry, and a possibly grumpy Omar

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5:32 PM | Oxford Gaol: Statistical Bogeymen

Memory Lane: 3 years ago. Oxford Jail (also called Oxford Castle) is an entirely fitting place to be on (and around) Halloween! Moreover, rooting around this rather lavish set of jail cells (what used to be a single cell is now a dressing room) is every bit as conducive to philosophical reflection as is exile on Elba! (It […]

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11:16 AM | Back to school …

Once upon a lifetime ago, I took Part III of the Maths Tripos. In fact, rather alarmingly, I started exactly fifty years ago this term. And it was tough. You had to aim to do over the year (the equivalent … Continue reading →

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5:20 PM | Frankl, My Dear : 8

Re: Dick Lipton & Ken Regan • (1) • (2) (4) Figure 4 shows the eight terms of the tacit extension as arcs, arrows, or directed edges in the venn diagram of the original proposition Each term of the tacit extension … Continue reading →

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5:48 PM | Frankl, My Dear : 7

Re: Dick Lipton & Ken Regan • (1) • (2) We continue with the differential analysis of the proposition in Example 1. Example 1 (1) A proposition defined on one universe of discourse has natural extensions to larger universes of discourse. … Continue reading →

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Josh Parsons (Oxford) has written a widely discussed post on "The LaTeX cargo cult," explaining why he discourages philosophy students from using LaTeX. He makes some interesting points. But what he has left out is the overarching principle that you should simply always use the best tool for the purpose at hand - and "best" should take into account lots of things: cost (in money and time you need to invest to become proficient in the use of the tool), ease of use, functionality, and the
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Winifred Edgerton Merrill fu la prima americana ad ottenere un dottorato in matematica presso la Columbia University nel 1886. Nella sua tesi sviluppò una rappresentazione geometrica degli infinitesimi in diversi sistemi di coordinate, utilizzando lo jacobiano per per derivare le trasformazioni tra gli integrali nei diversi sistemi.Tra matematica e astronomiaNata a Ripon, nel Wisconsin, il 24 settembre del 1862 da Emmet e Clara Edgerton, si trasferisce con la famiglia a New York intorno al […]

Kelly S.E. & Rozner S.A. (2012). Winifred Edgerton Merrill: "She Opened the Door", Notices of the American Mathematical Society, 59 (04) 504-512. DOI: http://dx.doi.org/10.1090/noti818

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Winifred Edgerton Merrill fu la prima americana ad ottenere un dottorato in matematica presso la Columbia University nel 1886. Nella sua tesi sviluppò una rappresentazione geometrica degli infinitesimi in diversi sistemi di coordinate, utilizzando lo jacobiano per per derivare le trasformazioni tra gli integrali nei diversi sistemi.Tra matematica e astronomiaNata a Ripon, nel Wisconsin, il 24 settembre del 1862 da Emmet e Clara Edgerton, si trasferisce con la famiglia a New York intorno al […]

Kelly S.E. & Rozner S.A. (2012). Winifred Edgerton Merrill: "She Opened the Door", Notices of the American Mathematical Society, 59 (04) 504-512. DOI: http://dx.doi.org/10.1090/noti818

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Direi che oggi pomeriggio è stato un bel respirare, al Palazzo Brera. Cristina Lazzeroni dell'Università di Birmingham è venuta alle 18 (come avevo scritto nel post precedente) per raccontare del bosone di Higgs, del modello standard e di materia e antimateria. E' una sperimentale presso l'esperimento LHCb al CERN, l'esperimento dedicato proprio alla ricerca su uno dei grandi misteri dell'universo: perché in esso c'è un eccesso di materia (e d'altra parte se non fosse così, non ci sarebbe […]

Aaij R., B. Adeva, M. Adinolfi, C. Adrover, A. Affolder, Z. Ajaltouni, J. Albrecht, F. Alessio, M. Alexander & S. Ali & (2013). First Observation of CP Violation in the Decays of B_{s}^{0} Mesons, Physical Review Letters, 110 (22) DOI: http://dx.doi.org/10.1103/physrevlett.110.221601

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Per i I cieli di Brera, il 24 settembre (domani... scusate per il ritardo nell'annuncio...) alle 18 presso la Sala delle Adunanze dell'Istituto Lombardo nel Palazzo Brera sito in via Brera 28 (Milano), si terrà la conferenza La fisica delle particelle e il Large Hadron Collider: recenti sviluppi e questioni aperte: Cristina Lazzeroni ci introdurrà alla fisica delle particelle e agli studi fatti al Large Hadron Collider del Cern di Ginevra mettendo l’accento su recenti sviluppi come la
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Aad G., J. Abdallah, S. Abdel Khalek, O. Abdinov, R. Aben, B. Abi, S. H. Abidi, M. Abolins, O. S. AbouZeid & H. Abramowicz & (2014). Measurement of the Higgs boson mass from the $H\to \gamma \gamma $ and $H\to Z{Z}^{*}\to 4\ell $ channels in $pp$ collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector, Physical Review D, 90 (5) DOI: http://dx.doi.org/10.1103/physrevd.90.052004

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One of the exciting things about mathematical oncology is that thinking about cancer often forces me to leave my comfortable arm-chair and look at some actually data. No matter how much I advocate for the merits of heuristic modeling, when it comes to cancer, data-agnostic models take second stage to data-rich modeling. This close relationship […]

Gallaher, J. & Anderson, A.R. (2013). Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance., Interface Focus, 3 (4) 20130016. arXiv: 1305.0524v1

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MindAfterMath tweeted: @MindAfterMath

Hidden Markov Models: The Forward Algorithm http://t.co/pA3UeRO7vK #compsci #datascience #math #stem #mathchat

2014-11-23 06:45:07

DrMathochist tweeted: @DrMathochist

RT @vox_ebooks: Drone footage shows the incredible scale of the Miss America contest.

2014-11-23 06:20:12

AppreciateMath tweeted: @AppreciateMath

2014-11-23 05:39:55

profkeithdevlin tweeted: @profkeithdevlin

RT @TheTweetOfGod: Marriage should be between a man and a woman. Unless it's gay marriage.

2014-11-23 05:13:51

profkeithdevlin tweeted: @profkeithdevlin

RT @bcmillerKCCO: @RichardDawkins In Kenya, Al-Shabab gunmen slay 28 bus passengers who could not recite an Islamic creed http://t.co/rHgEb…

2014-11-23 05:13:37

CardColm tweeted: @CardColm

Surprise guest at end of 3 he #StevieWonder show: the irrepressible J. Monae. Core band 32 people. Over 45 in all! http://t.co/MluswPQTfL

2014-11-23 05:09:33

gaussianos tweeted: @gaussianos

RT @Edwmad: Una imagen vale más que mil palabras en la suma de una serie numérica http://t.co/GPcNrTBXu7 vía @gaussianos http://t.co/ITFID…

2014-11-23 04:53:45

fawnpnguyen tweeted: @fawnpnguyen

@ChrisHunter36 @j_lanier Duck!! You know, just... duck!

2014-11-23 04:46:45

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