X

Posts

November 23, 2014

+
It is one of the rules of my system of general harmony, that the present is big with the future, and that he who sees all sees in that which is that which shall be. Leibniz • Theodicy Re: Dick … Continue reading →

November 22, 2014

+
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  “It is obsolete for the doctor to approach each patient strictly as an individual; medical decisions should […]

November 21, 2014

+
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
+
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 […]

November 19, 2014

+
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, […]

November 18, 2014

+
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 →
+
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

November 17, 2014

+
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, [...]
+
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 […]

November 15, 2014

+
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, […]

November 14, 2014

+
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
+
...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://
+
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 […]
+
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.)

November 13, 2014

+
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 […]

November 12, 2014

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

November 11, 2014

+
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, […]
+
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 →

November 09, 2014

+
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 […]
+
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 →

November 07, 2014

+
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/

November 05, 2014

+
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 […]
+
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 →

November 03, 2014

+
“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 →

November 01, 2014

+
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 […]

October 31, 2014

+
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
+
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 […]
+
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 →

October 30, 2014

+
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 →

October 29, 2014

+
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 →