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Posts

May 22, 2015

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Re: Ken Regan • The Shapes of Computations There are several issues of computation shape and proof style that raise their heads already at the ground level of boolean functions and propositional calculus. The dimensions I have found most prominent … Continue reading →
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Another quirky, weekly compilation of math bits that I didn't cover at Math-Frolic: 1)  The latest "Carnival of Mathematics" with all its festivities is ready-and-waiting (it includes the infinite Kolakoski sequence which sort of semi-blew my mind!): http://solvemymaths.com/2015/05/17/carnival-of-mathematics-122/ 2)   Not exactly math, but survey research...a fun, longish read from the '

May 20, 2015

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The Hyperuniverse Programme, launched in 2012, and currently pursued within a Templeton-funded research project at the Kurt Gödel Research Center in Vienna, aims to identify and philosophically motivate the adoption of new set-theoretic axioms.The programme intersects several topics in the philosophy of set theory and of mathematics, such as the nature of mathematical (set-theoretic) truth, the universe/multiverse dichotomy, the alternative conceptions of the set-theoretic multiverse, the […]
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"How To Bake Pi" by Eugenia Cheng [In Britain, this book goes under the title, "Cakes, Custard and Category Theory," a title I prefer!]  An intrinsic hazard of reviewing media, be it movies, TV, plays, music, books etc., is that 'expectations' play a significant role in any judgment. I like Eugenia Cheng's new book, "How To Bake Pi," and recommend it, and believe it will be on my year-end
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[After a delay, let’s continue …!] In the second half of Chapter 2 of his book, Burgess first turns to discuss some opponents of the project of rigorization when conceived as the project of regimenting mathematics into standard set theory. We … Continue reading →
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The comments on this post have taken a technical turn.  I will eventually have to consult a local homotopy theorist to figure out what’s going on.  In the meantime, I need to think about what I’m going to say at tomorrow’s event at the venerable bookstore that has reportedly become an obligatory stop for Russian […]

May 19, 2015

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2nd part of the double header: Society for Philosophy and Psychology (SPP): 41st Annual meeting SPP 2015 Program Wednesday, June 3rd 1:30-6:30: Preconference Workshop on Replication in the Sciences, organized by Edouard Machery 1:30-2:15: Edouard Machery (Pitt) 2:15-3:15: Andrew Gelman (Columbia, Statistics, via video link) 3:15-4:15: Deborah Mayo (Virginia Tech, Philosophy) 4:15-4:30: Break 4:30-5:30: Uri Simonshon (Penn, […]
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Voevodsky at the IAS on September 25, 2010, courtesy of the IAS Just short of two weeks after Siobhan Roberts published her article in nautil.us about Voevodsky and Univalent Foundations, it was Kevin Hartnett’s turn at Quanta, with an article entitled Will Computers Redefine the Roots of Math? I didn’t do justice to Roberts’s article […]

May 18, 2015

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This is a Survey of previous blog and wiki posts on the Theme One Program that I worked on all through the 1980s. The aim of the project was to develop fundamental algorithms and data structures to support an integrated … Continue reading →
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Jacob Lurie has done all of us an immense favor by posting a comment on the “No Comment” post, explaining why he chose to respond in that way, and sharing his thoughts on the hope, expressed twice on this blog, that HOTT/UF might provide a quicker route to his results on higher categories (obtained at […]

May 17, 2015

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This is a Survey of earlier blog and wiki posts on the Semiotic Theory Of Information.  All my projects are exploratory in essence but this line of inquiry is more open-ended than most.  The question is: What is information and how … Continue reading →
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Math-Frolic Interview #31 "Penelope Maddy is the candy-store kid of metaphilosophical logic and maths. She’s stocked up with groovy thoughts about the axioms of mathematics, about what might count as a good reason to adopt one, about mathematical realism, about Gödel’s intuitions, naturalism, second philosophy, Hume and Quine, world-word connections, about where mathematical objectivity
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A new joint paper…. “Error statistical modeling and inference: Where methodology meets ontology” Aris Spanos · Deborah G. Mayo Abstract: In empirical modeling, an important desiderata for deeming theoretical entities and processes as real is that they can be reproducible in a statistical sense. Current day crises regarding replicability in science intertwines with the question […]

May 16, 2015

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I read a short article on scientificamerican.com reporting on a recent advance in the investigation of the neural systems that support navigation, or our sense of direction.  When I did some follow-up on the individual who led the study, I was surprised to find another interesting collaboration between scientists and artists. While the collaboration was [...]
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In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many … Continue reading →
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It’s time to add René Thom’s discordant voice to this chorus.  The title of this post is taken from his article La Science Malgré Tout in the 1973 edition of Encyclopaedia Universalis, and more recently from the epigraph of an article by Alain Chenciner entitled Le vrai, le faux, l’insignifiant [The true, the false, the […]

May 15, 2015

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some maths from the week: 1)  The 2015 topic for the FQXi annual essay contest was "Trick or Truth: the Mysterious Connection Between Physics and Mathematics." Peruse the entries here: http://fqxi.org/community/forum/category/31424?sort=community 2)  Another interview with Cedric Villani: http://www.huffingtonpost.com/2015/05/07/cedric-villani-mathematic_n_7223966.html 3)  Just another lesson
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A few years ago I began a sketch on the Precursors of Category Theory, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. This post is … Continue reading →

May 14, 2015

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This is a Survey of previous blog and wiki posts on Inquiry Driven Systems, material that I plan to refine toward a more compact and systematic treatment of the subject. Elements Prospects for Inquiry Driven Systems Introduction to Inquiry Driven … Continue reading →

May 13, 2015

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A number of people have very kindly sent corrections to the last version of Notes on Category Theory. There are a number of possibly confusing typos and also a downright wrong proof. Embarrassing. So here’s a “maintenance upgrade”, hopefully making … Continue reading →
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“No Comment” was Jacob Lurie’s reaction when the panel of Breakthrough Prize laureates was asked, at last November’s Breakthrough Prize Symposium at Stanford, what they thought of the “prospects for the Univalent Foundations program and whether that is a contender for changing” foundations of mathematics.  The other panelists had deferred to Lurie, in some amusement; […]

May 11, 2015

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This is a Survey of previous blog and wiki posts on Differential Logic, material that I plan to develop toward a more compact and systematic account. Elements Differential Logic : Introduction Differential Propositional Calculus Applications Differential Logic and Dynamic Systems … Continue reading →
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Giving pause...: Over the weekend Mike Lawler, posted about two items ("two incredible descriptions of what it is like to do math research") he wished he had seen in graduate school in order to maintain his avid prior enthusiasm for math (one is a Numberphile interview with Ken Ribet, and the other is Cedric Villani's current book, "Birth of a Theorem"): http://tinyurl.com/q355eyo The post

May 10, 2015

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This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing … Continue reading →
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As you will very probably have already seen, The Open Logic Project (a team of serious and good people) has now made available an early public version open-source collaborative logic text, somewhat ploddingly called the Open Logic Text.  There are two things to … Continue reading →

May 09, 2015

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Stephen Senn Head of Competence Center for Methodology and Statistics (CCMS) Luxembourg Institute of Health Double Jeopardy?: Judge Jeffreys Upholds the Law “But this could be dealt with in a rough empirical way by taking twice the standard error as a criterion for possible genuineness and three times the standard error for definite acceptance”. Harold […]

May 08, 2015

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Msc Kvetch on my Rejected Posts blog.Filed under: frequentist/Bayesian, msc kvetch, rejected post
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Some mathiness you might've missed: 1)  More and more of these 'traveling salesman'-like algorithm stories are showing up in the popular press: http://tinyurl.com/oslersw 2)  John McGowan reviews (and recommends) "Statistics Done Wrong: The Woefully Complete Guide" by Alex Reinhart: http://math-blog.com/2015/05/04/review-of-statistics-done-wrong-the-woefully-complete-guide/ 3)  Spurious
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