July 05, 2015

1:48 PM | Inquiry, Signs, Relations • 1
Re: Michael Harris • A Non-Logical Cognitive Phenomenon Human spontaneous non-demonstrative inference is not, overall, a logical process.  Hypothesis formation involves the use of deductive rules, but is not totally governed by them;  hypothesis confirmation is a non-logical cognitive phenomenon:  … Continue reading →

July 04, 2015

6:25 AM | A non-logical cognitive phenomenon
This is from an early version of Chapter 7 and from my 2009 presentation on avatars at the conference Two Streams in the Philosophy of Mathematics organized by David Corfield and Brendan Larvor.  Some of the first half has been preserved on p. 215 and there is a hint of the remainder on p. 201.  […]

July 03, 2015

11:19 AM | Math Bits of the Week
Here and there: 1)  First, a fun little (economics) paradox over at Math-Frolic this morning: http://math-frolic.blogspot.com/2015/07/gladly-paying-110-for-dollar-bill.html 2)  Conway.... J-J-John  Conway!: ICYMI, last Monday I got to talk with Siobhan Roberts about her upcoming biography of John Conway: http://mathtango.blogspot.com/2015/06/siobhan-roberts-playing-with-geniuses.html ...and
4:01 AM | Larry Laudan: “When the ‘Not-Guilty’ Falsely Pass for Innocent”, the Frequency of False Acquittals (guest post)
Professor Larry Laudan Lecturer in Law and Philosophy University of Texas at Austin “When the ‘Not-Guilty’ Falsely Pass for Innocent” by Larry Laudan While it is a belief deeply ingrained in the legal community (and among the public) that false negatives are much more common than false positives (a 10:1 ratio being the preferred guess), […]

July 02, 2015

8:00 PM | Relations & Their Relatives : 13
Re: Peirce List Discussion • Helmut Raulien The facts about relational reducibility are relatively easy to understand and I included links to relevant discussions in my earlier survey of relation theory. The following article discusses relational reducibility and irreducibility in … Continue reading →
1:30 PM | Relations & Their Relatives : 12
Re: Peirce List Discussion • Jeffrey Brian Downard In viewing the structures of relation spaces, even such small dyadic cases as we’ve been exploring so far, no one need feel too nonplussed at the lack of obviousness in this realm.  … Continue reading →

July 01, 2015

7:58 AM | Macroeconomics is pure, not applied, mathematics
As the owl of Minerva spreads its wings over the future of the euro, I am reminded of what Joseph Stiglitz had to say about the scientificity of economics, as reported recently in this text by his Columbia colleague Akeel Bilgrami: Among disciplines, economics… is perhaps the worst offender in inuring itself against alternative frameworks […]
1:21 AM | Stapel’s Fix for Science? Admit the story you want to tell and how you “fixed” the statistics to support it!
Stapel’s “fix” for science is to admit it’s all “fixed!” That recent case of the guy suspected of using faked data for a study on how to promote support for gay marriage in a (retracted) paper, Michael LaCour, is directing a bit of limelight on our star fraudster Diederik Stapel (50+ retractions). The Chronicle of Higher Education just published an article by […]

June 30, 2015

3:00 PM | Relations & Their Relatives : 11
Re: Peirce List Discussion • Jeffrey Brian Downard In discussing the “combinatorial explosion” of dyadic relations that takes off already in passing from a universe of two elements to a universe of three elements, I made the following observation: Looking … Continue reading →

June 29, 2015

11:00 AM | Siobhan Roberts... Playing With Geniuses
 Math-Frolic Interview #33  “John Conway is, by any standard, a very remarkable man, and he well deserves a remarkable biography, which this book undoubtedly is. Siobhan Roberts expertly conjures up a genuine picture of the man and his amazing world.”   —Roger Penrose If you don't already know the name Siobhan Roberts it's probably just a matter of a little more time. She is an
3:00 AM | Relations & Their Relatives : 10
Re: Peirce List Discussion • Jim Willgoose Here is the series of blog posts on Chapter 3 (The Logic of Relatives) from Peirce’s 1880 “Algebra of Logic” up to the point where I left off on May Day. Preliminaries Selections … Continue reading →

June 28, 2015

2:00 PM | My Thematics • 2
Communication is so much harder Than mere invention or discovery. Will they have in mind what I have in mind? Will I find the signs?   Will I have the time? There is so much shadow there must be light!

June 27, 2015

8:59 PM | M.C. Escher’s visual inquiries
The Amazing World of MC Escher is a new exhibit at the Scottish National Gallery of Modern Art in Edinburgh. It will be there from June 27 to September 27. The exhibit prompted a nice piece on Escher in The Guardian. Author Steven Poole mentions, but does not much explore, the relationship between Escher’s work [...]
8:01 AM | Lateral influence
My attention has been drawn to the video of Alex Gamburd’s recent talk at the IHP on his joint work with Jean Bourgain and Peter Sarnak.  If I had been in town for the workshop, I would probably have attended, in which case I would have been struck, as have many of our colleagues, by […]

June 26, 2015

1:36 PM | Friday Math Mix
Bits of math from the week: 1)  Braess's Paradox from Brian Hayes and American Scientist: http://www.americanscientist.org/issues/pub/2015/4/playing-in-traffic 2)  If you haven't already read Jim Henle's "The Proof and the Pudding," this piece by Jim may spur you to do so: https://theconversation.com/mathematics-spaghetti-alla-carbonara-and-you-42650 3)  Evelyn Lamb on "Cantor's Leaky Tent" (
12:00 PM | My Thematics • 1
I miss the days when I’d spend my days And nights dreaming up mathematics …

June 25, 2015

5:12 PM | Notation
Mike Shulman has kept the promise he made a few weeks ago by writing a post on the n-category café speculating on the reasons HoTT, as a proposed foundation for mathematics, is in practice closely associated  to computer formalization, even though there is no necessary connection between the two. Shulman’s post is comprehensive; he does […]
3 years ago… MONTHLY MEMORY LANE: 3 years ago: June 2012. I mark in red three posts that seem most apt for general background on key issues in this blog.[1]  It was extremely difficult to pick only 3 this month; please check out others that look interesting to you. This new feature, appearing the last week of each month, began at the blog’s 3-year […]

June 23, 2015

7:11 PM | A very brief, incomplete, and stopgap account of women in medieval logic
This afternoon Catarina commented on FB about the glaring lack of women logicians in the currently-being-edited Cambridge Companion to Medieval Logic. It's a topic that I've recently bumped heads with myself when trying to tread the line between encouraging my department to draw their curricula from a wide variety of sources, not just in terms of gender but also in terms of time and geography, while also ensuring that no rigorous quota for women authors was instituted as departmental policy, […]
4:52 PM | How to explain homotopy theory to a number theorist
(Although I tried to make this an impersonal account of an ideal-typical state of affairs, this will actually be semi-autobiographical.  Readers are asked to pretend not to notice.) I missed my chance to learn homotopy theory as a student but on three occasions made half-hearted attempts to make up the gap in my understanding.  The […]

June 21, 2015

1:29 PM | What does the Mona Lisa have in common with a leopard?
Seen on a kiosk today in Paris.  Here is the bottom half of the poster: I don’t actually know the answer to the question.  Nor to the second-order question, namely why would anyone buy a collection of books in order to answer the first question.

June 20, 2015

12:10 PM | This is what charisma looks like, part 3: Is mathematics democratic?
This post is a series of scattered thoughts in reaction to a  comment by Mike Shulman dated May 26: I don’t really know whether there are more democratic methods of organizing mathematics that would be as or more effective than the current dependence on charismatic leaders; it seems related to the search for alternative models […]

June 19, 2015

3:25 PM | Eminem’s math envy
This is what you see if you search for If Eminem was a math guy on the internet. License undetermined, owner apparently www.teachpi.org Olivier Fouquet, a number theorist at Orsay, wrote a few weeks ago to point out some rap lyrics I might have wanted to include in Chapter 8.  Eminem reveals his own math […]
3:00 PM | Relations & Their Relatives : 9
Re: Peirce List Discussion • Helmut Raulien In discussing Peirce’s concept of a triadic sign relation that exists among objects, signs, and interpretant signs the question arises whether any of the classes so related are classes by themselves, that is, … Continue reading →
1:00 PM | Linkfest
... 51 years ago, this weekend, three young civil rights workers, James Chaney, Andrew Goodman, and Michael Schwerner were brutally murdered during an ill-fated trip to Mississippi. In light of the past week's further solemn events in the American South, I feel a need to reach back momentarily to this mid-60's tribute from Paul Simon to Andy Goodman: ------------------------------------------

June 18, 2015

7:00 PM | Can You change Your Bayesian prior? (i)
This is one of the questions high on the “To Do” list I’ve been keeping for this blog.  The question grew out of discussions of “updating and downdating” in relation to papers by Stephen Senn (2011) and Andrew Gelman (2011) in Rationality, Markets, and Morals.[i] “As an exercise in mathematics [computing a posterior based on the client’s prior probabilities] […]

June 17, 2015

10:00 AM | Mathematical pleasure as a means of resisting dominant economic power
That’s one of the recurring themes of MWA, but it took a Lecturer in Writing at Case Western Reserve to notice it and to put it into words.  I haven’t been able to express it so succinctly and directly, in part for the reasons outlined in the last paragraph of this post, but also because, […]

June 14, 2015

5:13 PM | Some statistical dirty laundry: The Tilberg (Stapel) Report on “Flawed Science”
I had a chance to reread the 2012 Tilberg Report* on “Flawed Science” last night. The full report is now here. The discussion of the statistics is around pp. 17-21 (of course there was so little actual data in this case!) You might find it interesting. Here are some stray thoughts reblogged from 2 years ago… […]

June 13, 2015

8:06 PM | Collective behavior: flocks, magnets, neurons and mathematics
The analysis of collective behavior is quickly becoming cross-disciplinary.  I wrote a few years ago about a study that analyzed the coordination of starling flocks. That post was based on the work of Thierry Mora and William Bialek, presented in their paper Are Biological Systems Poised at Criticality. The paper was published in the Journal [...]

June 12, 2015

1:00 PM | Weekly Links
Math-related stuff you might've missed: 1)  From "Better Explained," one of the best learning sites on the Web, some discussion of the importance of intuition in learning: http://betterexplained.com/articles/intuition-isnt-optional/ 2)  "Futility Closet," succinctly, on Erdös et.al.'s 'friendship theorem": http://www.futilitycloset.com/2015/06/06/the-friendship-theorem/ 3)  86th edition of
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