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Re: Frederik Stjernfelt • Natural Propositions Frederik, One small point that I find myself making on a periodic basis: I think it is better to describe Peirce’s take on logic as “non-psychologism” rather than “anti-psychologism”, the main thing being that … Continue reading →

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11:00 AM | Robin Williams Redux...

Now for something completely different (for MathTango)…
I've
written before how much I admire Cathy O'Neil's keen ability to touch
on varying topics over at her blog. Despite coming from a
mathematics academic background and titling her blog "Mathbabe,"
Cathy writes on a wide range of topics that rattle
around in her head. So I'll sorta take that cue today to veer off and relate an odd,

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5:34 PM | What we see when….

I recently listened to Krys Boyd’s interview with Peter Mendelsund, author of the new book What We See When We Read, on North Texas’ public radio. Mendelsund is an award-winning book jacket designer. The interview had the effect of connecting his thoughts about reading to thoughts that I have had about mathematics. It wasn’t immediately [...]

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An Assumed Law of Statistical Evidence (law of likelihood) Nearly all critical discussions of frequentist error statistical inference (significance tests, confidence intervals, p- values, power, etc.) start with the following general assumption about the nature of inductive evidence or support: Data x is better evidence for hypothesis H1 than for H0 if x are more probable under H1 than […]

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11:15 AM | Friday Wrap-up

Another week from the world of math:
1) Article touting the role of rote memorization in early math education:
http://tinyurl.com/lj759wd
2) Fawn Nguyen describes the beginning of her classroom school year, as perhaps only she can:
http://fawnnguyen.com/first-two-days-school/
3) LA Times op-ed on the gender-gap in mathematics:
http://www.latimes.com/opinion/op-ed/

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The focus of this conference is on different approaches to the foundationsof mathematics. The interaction between set-theoretic and category-theoreticfoundations has had significant philosophical impact, and represents a shiftin attitudes towards the philosophy of mathematics. This conference willbring together leading scholars in these areas to showcase contemporaryphilosophical research on different approaches to the foundations ofmathematics. To accomplish this, the conference has the […]

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12:19 PM | What’s the big deal with consistency?

(Cross-posted at NewAPPS)It is no news to anyone that the concept of consistency is a hotly debated topic in philosophy of logic and epistemology (as well as elsewhere). Indeed, a number of philosophers throughout history have defended the view that consistency, in particular in the form of the principle of non-contradiction (PNC), is the most fundamental principle governing human rationality – so much so that rational debate about PNC itself wouldn’t even be possible, as famously stated by
[…]

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MCMP Workshop "Bridges 2014"New York City, 2 and 3 Sept, 2014www.lmu.de/bridges2014The Munich Center for Mathematical Philosophy (MCMP) cordially invites you to "Bridges 2014" in the German House, New York City, on 2 and 3 September, 2014. The 2-day trans-continental meeting in mathematical philosophy will focus on inter-theoretical relations thereby connecting form and content of this philosophical exchange. The workshop will be accompanied by an open-to-public evening event with Stephan […]

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3:00 AM | C.S. Peirce • Syllabus • Selection 1

Selection from C.S. Peirce, “A Syllabus of Certain Topics of Logic” (1903) An Outline Classification of the Sciences 180. This classification, which aims to base itself on the principal affinities of the objects classified, is concerned not with all … Continue reading →

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"Arithmetic with fusions" (draft) is a joint paper with my graduate student Thomas Schindler (MCMP). The abstract is:In this article, the relationship between second-order comprehension and unrestricted mereological fusion (over atoms) is clarified. An extension $\mathsf{PAF}$ of Peano arithmetic with a new binary mereological notion of ``fusion'', and a scheme of unrestricted fusion, is introduced. It is shown that $\mathsf{PAF}$ interprets full second-order arithmetic, $Z_2$.Roughly […]

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I have been asked what I thought of some criticisms of the scientific relevance of philosophy of science, as discussed in the following snippet from a recent Scientific American blog. My title elicits the appropriate degree of ambiguity, I think. Quantum Gravity Expert Says “Philosophical Superficiality” Has Harmed Physics By John Horgan | August 21, 2014 | 14 “I interviewed […]

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2:30 PM | ¿Shifting Paradigms? • 4

Re: Harvey Friedman • Foundational Crisis? 2014 Aug 22 Shock and surprise are relative to a prior state of belief. The belief that mathematics reduces to logic, and that of a purely deductive sort from given axioms, seems to be … Continue reading →

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4:00 PM | ¿Shifting Paradigms? • 3

Re: Harvey Friedman • Good Math 2014 Aug 17 Speaking of mathematics in the context of “general intellectual activity” brings to mind Raymond Wilder’s take on “mathematics as a cultural system”. I would like to keep that in mind, if … Continue reading →

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11:00 AM | Another Friday Collection

From this week's wonderful world of math:
1) Shortly, after last week's potpourri came out the 113th Carnival of Mathematics went up; if by any chance you missed it, a lot more mathy links there:
http://www.walkingrandomly.com/?p=5537
2) I've referenced this research before, but just last week NPR covered findings that indicate winners of the Fields Medal (and other prizes) actually lowers

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In the first part of this post, I considered the challenge to decision theory from what L. A. Paul calls epistemically transformative experiences. In this post, I'd like to turn to another challenge to standard decision theory that Paul considers. This is the challenge from what she calls personally transformative experiences. Unlike an epistemically transformative experience, a personally transformative experience need not teach you anything new, but it does change you in […]

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(Cross-posted at NewAPPS)Mathematics has been much in the news recently, especially with the announcement of the latest four Fields medalists (I am particularly pleased to see the first woman, and the first Latin-American, receiving the highest recognition in mathematics). But there was another remarkable recent event in the world of mathematics: Thomas Hales has announced the completion of the formalization of his proof of the Kepler conjecture. The conjecture: “what is the best way to stack
[…]

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1:43 PM | Model theory without tears?

Ah well, you win some and you lose some. I was writing for months about recursive ordinals and proof theory with a view to a short-ish book. And now, quite a way in, I realise that I have to go … Continue reading →

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Despite the fact that Fisherians and Neyman-Pearsonians alike regard observed significance levels, or P values, as error probabilities, we occasionally hear allegations (typically from those who are neither Fisherian nor N-P theorists) that P values are actually not error probabilities. The denials tend to go hand in hand with allegations that P values exaggerate evidence against […]

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5:06 PM | Bohemian gravity

Tim Blais, a McGill University physics student made this really great a capella version of "Bohemian Rhapsody", called "Bohemian Gravity", with physics lyrics explaining superstring theory, like "Manifolds must be Kahler!" (lyrics here).Another article on this.

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12:00 PM | Forest Primeval → Riffs & Rotes

Re: Shifting Paradigms? • (1) • (2) • (3) • (4) • (5) Prompted by the discussion of Catalan numbers on the Foundations Of Math List, I dug up a few pieces of early correspondence and later discussions that bear … Continue reading →

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10:32 AM | Reinstatement

M-Phi readers may or may not have paid attention to the bizarre events during the last twelve months, over which I was initially dismissed by the University of Oxford, and smeared with lies in the national press. I described some of this in a statement Prof. Leiter put up on 26 March 2014:From late 2013, Oxford proceeded with a prosecution, involving failures of due process and proportionality, despite the support I received from my College and several members of the Faculty. The prosecution
[…]

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6:34 PM | Friday Bonanza

ICYMthem:
1) Fun li'l anecdote about topologist Egbert Rudolf van Kampen from MathOverflow.net last week:
http://mathoverflow.net/questions/178104/a-topologist-is-not-a-mathematician-a-small-question
2) New popular statistics (…I know, that sounds like an oxymoron! ;-)) book out from Gary Smith, "Standard Deviations":
http://tinyurl.com/poefeew
(haven't read it, but it's from a professor at

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I have never eaten Vegemite---should I try it? I currently have no children---should I apply to adopt a child? In each case, one might imagine, whichever choice I make, I can make it rationally by appealing to the principles of decision theory. Not according to L. A. Paul. In her rich and fascinating new book, Transformative Experience, Paul issues two challenges to orthodox decision theory---they are based upon examples such as these.(In this post and the next, I'd like […]

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10:44 AM | Worlds Without Domain

An article "Worlds Without Domain" arguing against the idea that possible worlds have domains. The abstract is: "A modal analogue to the "hole argument" in the foundations of spacetime is given against the conception of possible worlds having their own special domains".

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10:10 PM | Egon Pearson’s Heresy

Today is Egon Pearson’s birthday: 11 August 1895-12 June, 1980. E. Pearson rejected some of the familiar tenets that have come to be associated with Neyman and Pearson (N-P) statistical tests, notably the idea that the essential justification for tests resides in a long-run control of rates of erroneous interpretations–what he termed the “behavioral” rationale of tests. In an […]

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1:31 AM | Blog Contents: June and July 2014

Blog Contents: June and July 2014* (6/5) Stephen Senn: Blood Simple? The complicated and controversial world of bioequivalence (guest post) (6/9) “The medical press must become irrelevant to publication of clinical trials.” (6/11) A. Spanos: “Recurring controversies about P values and confidence intervals revisited” (6/14) “Statistical Science and Philosophy of Science: where should they meet?” (6/21) […]

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4:01 AM | Winner of July Palindrome: Manan Shah

Winner of July 2014 Contest: Manan Shah Palindrome: Trap May Elba, Dr. of Fanatic. I fed naan, deli-oiled naan, deficit an affordable yam part. The requirements: In addition to using Elba, a candidate for a winning palindrome must have used fanatic. An optional second word was: part. An acceptable palindrome with both words would best an acceptable palindrome with just […]

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The CogSci 2014 Proceedings have been posted and there are a number of links to interesting papers. Here are some math-related investigations: A neural network model of learning mathematical equivalence The Psychophysics of Algebra Expertise: Mathematics Perceptual Learning Interventions Produce Durable Encoding Changes Two Plus Three is Five: Discovering Efficient Addition Strategies without Metacognition Modeling [...]

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11:15 AM | Friday Potpourri

Another week's-worth of schtuff:
1) Sue VanHattum has started a new "Math Mama's Gazette" for students and teachers. First issue here:
http://mathmamawrites.blogspot.com/2014/08/math-mamas-gazette-issue-number-one.html
2) Stephen Stigler's 7 pillars of statistics:
http://blogs.sas.com/content/iml/2014/08/05/stiglers-seven-pillars-of-statistical-wisdom/
3) The fifth run of Keith Devlin's "

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Memory Lane: August 6, 2013. My initial post on JSM13 (8/5/13) was here. Nate Silver gave his ASA Presidential talk to a packed audience (with questions tweeted[i]). Here are some quick thoughts—based on scribbled notes (from last night). Silver gave a list of 10 points that went something like this (turns out there were 11): […]

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Quando ho condiviso il tweet qui sotto, non mi ero reso ancora conto del nome che avevo appena letto, eppure avrebbe dovuto suonarmi un campanello nella testa. Continuano i riconoscimenti internazionali per la #matematica dell'Universita' della #Calabria pic.twitter.com/JHIWaVlVGu— Gianluigi Filippelli (@ulaulaman) August 18, 2014Poi dopo è successo che sono andato a ricontrollare (che poi i campanelli magari suonano e semplicemente la suoneria è così bassa che non la senti, […]

Nash, J. (1950). Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, 36 (1) 48-49. DOI: 10.1073/pnas.36.1.48

Nash J. (1951). Non-Cooperative Games, The Annals of Mathematics, 54 (2) 286-295. DOI: http://dx.doi.org/10.2307/1969529

Gottlob G., Greco G. & Scarcello F. (2003). Pure Nash equilibria, Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge - TARK '03, 215-230. DOI: http://dx.doi.org/10.1145/846241.846269

Greco, G. & Scarcello, F. (2009). On the complexity of constrained Nash equilibria in graphical games, Theoretical Computer Science, 410 (38-40) 3901-3924. DOI: 10.1016/j.tcs.2009.05.030

Goldstone, R. & Janssen, M. (2005). Computational models of collective behavior, Trends in Cognitive Sciences, 9 (9) 424-430. DOI: 10.1016/j.tics.2005.07.009

Beni G. (1993). Swarm Intelligence in Cellular Robotic Systems, Robots and Biological Systems: Towards a New Bionics?, NATO ASI Series Volume 102 703-712. DOI: http://dx.doi.org/10.1007/978-3-642-58069-7_38

Bonabeau E., Dorigo M. & Theraulaz G. (2000). Inspiration for optimization from social insect behaviour, Nature, 406 (6791) 39-42. DOI: http://dx.doi.org/10.1038/35017500

Citation

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Quando ho condiviso il tweet qui sotto, non mi ero reso ancora conto del nome che avevo appena letto, eppure avrebbe dovuto suonarmi un campanello nella testa. Continuano i riconoscimenti internazionali per la #matematica dell'Universita' della #Calabria pic.twitter.com/JHIWaVlVGu— Gianluigi Filippelli (@ulaulaman) August 18, 2014Poi dopo è successo che sono andato a ricontrollare (che poi i campanelli magari suonano e semplicemente la suoneria è così bassa che non la senti, […]

Nash, J. (1950). Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, 36 (1) 48-49. DOI: 10.1073/pnas.36.1.48

Nash J. (1951). Non-Cooperative Games, The Annals of Mathematics, 54 (2) 286-295. DOI: http://dx.doi.org/10.2307/1969529

Gottlob G., Greco G. & Scarcello F. (2003). Pure Nash equilibria, Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge - TARK '03, 215-230. DOI: http://dx.doi.org/10.1145/846241.846269

Greco, G. & Scarcello, F. (2009). On the complexity of constrained Nash equilibria in graphical games, Theoretical Computer Science, 410 (38-40) 3901-3924. DOI: 10.1016/j.tcs.2009.05.030

Goldstone, R. & Janssen, M. (2005). Computational models of collective behavior, Trends in Cognitive Sciences, 9 (9) 424-430. DOI: 10.1016/j.tics.2005.07.009

Beni G. (1993). Swarm Intelligence in Cellular Robotic Systems, Robots and Biological Systems: Towards a New Bionics?, NATO ASI Series Volume 102 703-712. DOI: http://dx.doi.org/10.1007/978-3-642-58069-7_38

Bonabeau E., Dorigo M. & Theraulaz G. (2000). Inspiration for optimization from social insect behaviour, Nature, 406 (6791) 39-42. DOI: http://dx.doi.org/10.1038/35017500

Citation

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Zur Jahrtausendwende hatte das Clay-Institut jeweils 1 Million Dollar für sieben mathematische Probleme ausgelobt, von denen in der Zwischenzeit erst eines (die Poincaré-Vermutung) gelöst wurde. Manjul Bhargava, frischgebackener Fields-Medaillist, hat heute auf dem ICM eine 66,48-prozentige Lösung eines weiteren Millionenproblems – der Birch-Swinnerton-Dyer-Vermutung – vorgestellt, die ihm freilich keine 66,48% des Millionenpreises einbringen wird… Es…

Manjul Bhargava, Christopher Skinner & Wei Zhang (2014). A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture, ArXiv, arXiv: 1407.1826v2

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Un gruppo di fisici che studiano la meccanica dei fluidi ha iniziato una proficua collaborazione con Kara Maki riguardo lo studio dinamico delle "pellicole" di lacrime. Il modello, sviluppato in tre articoli che hanno preceduto il lavoro conclusivo, soprattutto sperimentale, è così descritto: all'interno della pellicola lacrimale, le dinamiche del fluido sono governate dalle equazioni incomprimibili di Navier-Stokes insieme con la conservazione di massa ed energia. Alla superficie libera
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Miller A., Carchman R., Long R. & Denslow S.A. La Crosse viral infection in hospitalized pediatric patients in Western North Carolina., Hospital pediatrics, (26) PMID: 24313031

Maki K.L., Braun R.J., Henshaw W.D. & King-Smith P.E. (2010). Tear film dynamics on an eye-shaped domain I: pressure boundary conditions., Mathematical medicine and biology : a journal of the IMA, 27 (3) 227-254. PMID: 20064825

Maki K.L., Braun R.J., Ucciferro P., Henshaw W.D. & King-Smith P.E. (2010). Tear film dynamics on an eye-shaped domain. Part 2. Flux boundary conditions, Journal of Fluid Mechanics, 647 361-390. DOI: http://dx.doi.org/10.1017/s002211200999382x

Maki K.L., Braun R.J. & P. E. King-Smith (2008). An overset grid method for the study of reflex tearing, Mathematical Medicine and Biology, 25 (3) 187-214. DOI: http://dx.doi.org/10.1093/imammb/dqn013

Citation

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Un gruppo di fisici che studiano la meccanica dei fluidi ha iniziato una proficua collaborazione con Kara Maki riguardo lo studio dinamico delle "pellicole" di lacrime. Il modello, sviluppato in tre articoli che hanno preceduto il lavoro conclusivo, soprattutto sperimentale, è così descritto: all'interno della pellicola lacrimale, le dinamiche del fluido sono governate dalle equazioni incomprimibili di Navier-Stokes insieme con la conservazione di massa ed energia. Alla superficie libera […]

Miller A., Carchman R., Long R. & Denslow S.A. La Crosse viral infection in hospitalized pediatric patients in Western North Carolina., Hospital pediatrics, (26) PMID: 24313031

Maki K.L., Braun R.J., Henshaw W.D. & King-Smith P.E. (2010). Tear film dynamics on an eye-shaped domain I: pressure boundary conditions., Mathematical medicine and biology : a journal of the IMA, 27 (3) 227-254. PMID: 20064825

Maki K.L., Braun R.J., Ucciferro P., Henshaw W.D. & King-Smith P.E. (2010). Tear film dynamics on an eye-shaped domain. Part 2. Flux boundary conditions, Journal of Fluid Mechanics, 647 361-390. DOI: http://dx.doi.org/10.1017/s002211200999382x

Maki K.L., Braun R.J. & P. E. King-Smith (2008). An overset grid method for the study of reflex tearing, Mathematical Medicine and Biology, 25 (3) 187-214. DOI: http://dx.doi.org/10.1093/imammb/dqn013

Citation

rmathematicus tweeted: @rmathematicus

RT @JPBarlow: Men used to ask, "Why buy a cow when milk's so cheap?" Now women ask, "Why buy an entire pig just to get a little sausage?"

2014-09-02 06:05:12

rmathematicus tweeted: @rmathematicus

RT @DrGaryRivett: CFP: Social Networks, 1450-1850: An interdisciplinary conference at the University of Sheffield, 16-17 July 2015 See: htt…

2014-09-02 06:01:34

MindAfterMath tweeted: @MindAfterMath

2014-09-02 05:51:05

michiexile tweeted: @michiexile

RT @caseyjohnston: a woman's password should be like her skirt: long as hell, like with a 40 foot train, otherwise you're asking for it, am…

2014-09-02 05:45:33

michiexile tweeted: @michiexile

RT @scalzi: *Explains something to daughter, who is unmoved*
Wife: You just mansplained that to her.
Me (offended): I did not! I DADSPLAIN…

2014-09-02 05:23:45

ricardosaenz tweeted: @ricardosaenz

The Man Who Knew The Man Who Knew Infinity http://t.co/iEtQeojZT0 vía @amermathsoc

2014-09-02 05:23:05

fawnpnguyen tweeted: @fawnpnguyen

2014-09-02 04:43:00

fawnpnguyen recommended Look Ma, No Zero!

2014-09-02 04:27:44

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