👓 Additional thoughts on the Ted Hill paper | Timothy Gowers

Read Additional thoughts on the Ted Hill paper by Timothy Gowers (Gowers's Weblog)
First, I’d like to thank the large number of commenters on my previous post for keeping the discussion surprisingly calm and respectful given the topic discussed. In that spirit, and to try t…

The analysis here makes me think there might be some useful tidbits hiding in the 300+ comments of his prior article. I wish I had the time to dig back into it.

Highlights, Quotes, Annotations, & Marginalia

Our prehistoric ancestors were not doing higher mathematics, so we would need to think of some way that being on the spectrum could have caused a man at that time to become highly attractive to women.  

One needs to remember that it isn’t always the men that themselves need to propagate the genes directly (ie, they don’t mate with someone to hand their genes down to their progeny directly). Perhaps a man on the autism spectrum, while not necessarily attractive himself, has traits which improve the lives and fitness of the offspring of his sister’s children? Then it’s not his specific genes which are passed on as a result, but those of his sister’s which have a proportion of his genes since they both share their parent’s genes in common.
September 19, 2018 at 03:35PM

variability amongst males  

Does it need to be a mate-related thing? Why not an environmental one. I seem to recall that external temperature had a marked effect on the sexual selection within alligator populations such that a several degree change during gestation would swing the sex proportion one way or another. Could these effects of environment have caused a greater variability?

Further, what other factors may be at play? What about in sea horse populations where males carry the young? Does this make a difference?
September 19, 2018 at 03:41PM

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👓 Has an uncomfortable truth been suppressed? | Timothy Gowers

Read Has an uncomfortable truth been suppressed? by Timothy Gowers (Gowers's Weblog)
Update to post, added 11th September. As expected, there is another side to the story discussed below. See this statement about the decision by the Mathematical Intelligencer and this one about the…

I agree in large part with his assessment, and do so in part based on Ted Hill’s Quillette article and not having read the actual paper yet.

I will say that far more people have now either heard about or read Hill’s paper than would have ever otherwise been aware of it had it actually gone ahead and actually been published and kept up. This is definitely an academic case of the Barbara Streisand effect, though done somewhat in reverse.

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🔖 [1809.05923] What is Applied Category Theory? by Tai-Danae Bradley

Bookmarked [1809.05923] What is Applied Category Theory? by Tai-Danae BradleyTai-Danae Bradley (arxiv.org)

This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and compositionality), two constructions (monoidal categories and decorated cospans) and two examples (chemical reaction networks and natural language processing) within the field. [PDF]

hat tip:

See also Notes on Applied Category Theory

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🎧 “Malcolm Gladwell’s 12 Rules for Life” Season 3 Episode 7 | Revisionist History

Listened “Malcolm Gladwell's 12 Rules for Life” Season 3 Episode 7 by Malcolm Gladwell from Revisionist History

"Crucial life lessons from the end of hockey games, Idris Elba, and some Wall Street guys with a lot of time on their hands."

Revisionist History wades into the crowded self-help marketplace, with some help with from a band of math whizzes and Hollywood screenwriters. It's late in a hockey game, and you're losing. When should you pull your goalie? And what if you used that same logic when a bad guy breaks into your house and holds your entire family hostage? We think the unthinkable, so you don’t have to.

Why one should be a bit more disagreeable and “pull the goalie”.

Pulling the Goalie: Hockey and Investment Implications on SSRN.

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👓 Election Update: Democrats’ Chances In The 13 Romney-Clinton Districts | Five Thirty Eight

Read Election Update: Democrats’ Chances In The 13 Romney-Clinton Districts by Nathaniel Rakich (Five Thirty Eight)
Welcome to our Election Update for Thursday, Sept. 13! The biggest update: We now have a Senate forecast to go with our House forecast! The “Classic” version of the Senate forecast currently gives Democrats a 1 in 3 chance of flipping the upper chamber. Meanwhile, the “Classic” version of our House forecast hasn’t really changed much since yesterday: Democrats still have a 5 in 6 chance of winning control. Across thousands of simulations, Democrats’ average gain was 39 seats.
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👓 Why Le’Veon Bell Might Make More Money If He Ends His Holdout Now | Five Thirty Eight

Read Why Le’Veon Bell Might Make More Money If He Ends His Holdout Now by Josh Hermsmeyer (Five Thirty Eight)
Last weekend, Steelers running back Le’Veon Bell sat out the first game of the regular season rather than play under the NFL franchise tag. Slated to earn $14.5 million in guaranteed money in 2018, Bell loses out on $855,529 each week he fails to report. The franchise tag would make Bell the third highest paid running back in the NFL this season — but only if he actually plays. Around the league, there is a wide range of speculation on how long Bell’s holdout will last. ESPN’s Adam Schefter reports that his sources believe Bell could be back by the end of September, while others note his holdout could conceivably last through Week 10.
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👓 Statement by Amie Wilkinson addressing unfounded allegations. | Amie Wilkinson

Read Statement by Amie Wilkinson addressing unfounded allegations. by Amie Wilkinson (math.uchicago.edu)
This statement addresses some unfounded allegations about my personal involvement with the publishing of Ted Hill's preprint "An evolutionary theory for the variability hypothesis" (and the earlier version of this paper co-authored with Sergei Tabachnikov). As a number of erroneous statements have been made, I think it's important to state formally what transpired and my beliefs overall about academic freedom and integrity. I first saw the publicly-available paper of Hill and Tabachnikov on 9/6/17, listed to appear in The Mathematical Intelligencer. While the original link has been taken down, the version of the paper that was publicly available on the arxiv at that time is here. I sent an email, on 9/7/17, to the Editor-in-Chief of The Mathematical Intelligencer, about the paper of Hill and Tabachnikov. In it, I criticized the scientific merits of the paper and the decision to accept it for publication, but I never made the suggestion that the decision to publish it be reversed. Instead, I suggested that the journal publish a response rebuttal article by experts in the field to accompany the article. One day later, on 9/8/17, the editor wrote to me that she had decided not to publish the paper. I had no involvement in any editorial decisions concerning Hill's revised version of this paper in The New York Journal of Mathematics. Any indications or commentary otherwise are completely unfounded. I would like to make clear my own views on academic freedom and the integrity of the editorial process. I believe that discussion of scientific merits of research should never be stifled. This is consistent with my original suggestion to bring in outside experts to rebut the Hill-Tabachnikov paper. Invoking purely mathematical arguments to explain scientific phenomena without serious engagement with science and data is an offense against both mathematics and science.

A response to an article I read the other day in Quillette.

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🔖 Equilibrium points in n-person games by John Nash | PNAS

Bookmarked Equilibrium points in n-person games by John F. Nash Jr. (PNAS 36 (1) 48-49; https://doi.org/10.1073/pnas.36.1.48)

One may define a concept of an n-person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n-tuple of pure strategies, one strategy being taken for each player. For mixed strategies, which are probability distributions over the pure strategies, the pay-off functions are the expectations of the players, thus becoming polylinear forms in the probabilities with which the various players play their various pure strategies.

Any n-tuple of strategies, one for each player, may be regarded as a point in the product space obtained by multiplying the n strategy spaces of the players. One such n-tuple counters another if the strategy of each player in the countering n-tuple yields the highest obtainable expectation for its player against the n − 1 strategies of the other players in the countered n-tuple. A self-countering n-tuple is called an equilibrium point.

The correspondence of each n-tuple with its set of countering n-tuples gives a one-to-many mapping of the product space into itself. From the definition of countering we see that the set of countering points of a point is convex. By using the continuity of the pay-off functions we see that the graph of the mapping is closed. The closedness is equivalent to saying: if P1, P2, … and Q1, Q2, …, Qn, … are sequences of points in the product space where Qn → Q, Pn → P and Qn counters Pn then Q counters P.

Since the graph is closed and since the image of each point under the mapping is convex, we infer from Kakutani’s theorem1 that the mapping has a fixed point (i.e., point contained in its image). Hence there is an equilibrium point.

In the two-person zero-sum case the “main theorem”2 and the existence of an equilibrium point are equivalent. In this case any two equilibrium points lead to the same expectations for the players, but this need not occur in general.

Communicated by S. Lefschetz, November 16, 1949

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👓 What Did Ada Lovelace’s Program Actually Do? | Two Bit History

Read What Did Ada Lovelace's Program Actually Do? (twobithistory.org)
In 1843, Ada Lovelace published the first nontrivial program. How did it work?

Interesting that he indicates what may have been one of the first published computer code bugs.

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👓 ‘Hard Day’s Night’: A Mathematical Mystery Tour | NPR

Read 'Hard Day's Night': A Mathematical Mystery Tour (NPR | Weekend Edition Saturday)
The jangly opening chord of The Beatles' hit "A Hard Day's Night" is one of the most recognizable in pop music. Maybe it sounds like nothing more than a guitarist telling his bandmates, "Hey, we're doing a song here, so listen up." But for decades, guitarists have puzzled over exactly how that chord was played.
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👓 A Songwriting Mystery Solved: Math Proves John Lennon Wrote ‘In My Life’ | NPR

Read A Songwriting Mystery Solved: Math Proves John Lennon Wrote 'In My Life' (NPR | Weekend Edition Saturday)

Over the years, Lennon and McCartney have revealed who really wrote what, but some songs are still up for debate. The two even debate between themselves — their memories seem to differ when it comes to who wrote the music for 1965's "In My Life."

Mathematics professor Jason Brown spent 10 years working with statistics to solve the magical mystery. Brown's the findings were presented on Aug. 1 at the Joint Statistical Meeting in a presentation called "Assessing Authorship of Beatles Songs from Musical Content: Bayesian Classification Modeling from Bags-Of-Words Representations."

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👓 Make Your Daughter Practice Math. She’ll Thank You Later. | New York Times

Read Opinion | Make Your Daughter Practice Math. She’ll Thank You Later. (nytimes.com)
The way we teach math in America hurts all students, but it may be hurting girls the most.
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👓 abc News | Peter Woit

Read abc News by Peter WoitPeter Woit (math.columbia.edu)
The last couple months I’ve heard reports from several people claiming that arithmetic geometers Peter Scholze and Jakob Stix had identified a serious problem with Mochizuki’s claimed proof of the abc conjecture. These reports indicated that Scholze and Stix had traveled to Kyoto to discuss this with Mochizuki, and that they were writing a manuscript, to appear sometime this summer. It seemed best then to not publicize this here, better to give Mochizuki, Scholze and Stix the time to sort out the mathematics and wait for them to have something to say publicly. Today though I saw that Ivan Fesenko has put out a document entitled Remarks on Aspects of Modern Pioneering Mathematical Research.

Peter definitely predicted the Fields medal for Peter Scholze here.

The intrigue of this case is quite interesting. Take a look at some of the comments on these posts. Some border on religious zealotry, and even this when I know Peter heavily curates his comments section to make them useful.

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🔖 Gems And Astonishments of Mathematics: Past and Present | Dr. Mike Miller at UCLA Extension

Bookmarked Gems And Astonishments of Mathematics: Past and Present (UCLA Continuing Education)

Mathematics has evolved over the centuries not only by building on the work of past generations, but also through unforeseen discoveries or conjectures that continue to tantalize, bewilder, and engage academics and the public alike.  This course, the first in a two-quarter sequence, is a survey of about two dozen problems—some dating back 400 years, but all readily stated and understood—that either remain unsolved or have been settled in fairly recent times.  Each of them, aside from presenting its own intrigue, has led to the development of novel mathematical approaches to problem solving.  Topics to be discussed include (Google away!): Conway’s Look and Say Sequences, Kepler’s Conjecture, Szilassi’s Polyhedron, the ABC Conjecture, Benford’s Law, Hadamard’s Conjecture, Parrondo’s Paradox, and the Collatz Conjecture.  The course should appeal to devotees of mathematical reasoning and those wishing to keep abreast of recent and continuing mathematical developments.

Suggested prerequisites: Some exposure to advanced mathematical methods, particularly those pertaining to number theory and matrix theory.

Tuesday 7:00PM - 10:00PM
Location: UCLA
Instructor: Michael Miller
MATH X 451.44 | 362773
Fee: $453.00

I’ve been waiting with bated breath to see what Dr. Miller would be offering in the evenings at UCLA Extension this Fall and Winter quarters. The wait is over, though it’ll be a few days before we can register.

If you’re interested in math at all, I hope you’ll come join the 20+ other students who follow everything that Mike teaches. Once you’ve taken one course from him, you’ll be addicted.

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