How the pandemic has shaped our future: from the built environment, to the way we work, to the way we learn.

With vaccinations underway, we’re edging closer and closer to the end of the pandemic. This week, On The Media looks at how the pandemic has shaped what’s possible for the future — from the built environment to the way we work to the way we learn.

1. Sam Kling [@SamKling2], American Council of Learned Societies public fellow, on whether cities like New York were bound to become hubs for disease. Listen.

2. Vanessa Chang [@vxchang], lecturer at California College of the Arts, explains how pandemics of the past have been instrumental in shaping architecture; Mik Scarlet [@MikScarlet] delineates the social model of disability; and Sara Hendren [@ablerism], author of What Can A Body Do?: How We Meet the Built World, describes how the wisdom of people with disabilities can inform the redesign our post-pandemic world. Listen.

3. OTM reporter Micah Loewinger [@micahloewinger] tells the story of how distance learning saved his friend's life. Listen.

Read Postdoctoral position in HoTT at Johns Hopkins University by Emily Riehl (Homotopy Type Theory)

The Department of Mathematics at Johns Hopkins University solicits applications for one two-year postdoctoral fellowship beginning Summer 2021 (with some flexibility in the start and end dates). Th…

The ergodic hypothesis is a key analytical device of equilibrium statistical mechanics. It underlies the assumption that the time average and the expectation value of an observable are the same. Where it is valid, dynamical descriptions can often be replaced with much simpler probabilistic ones — time is essentially eliminated from the models. The conditions for validity are restrictive, even more so for non-equilibrium systems. Economics typically deals with systems far from equilibrium — specifically with models of growth. It may therefore come as a surprise to learn that the prevailing formulations of economic theory — expected utility theory and its descendants — make an indiscriminate assumption of ergodicity. This is largely because foundational concepts to do with risk and randomness originated in seventeenth-century economics, predating by some 200 years the concept of ergodicity, which arose in nineteenth-century physics. In this Perspective, I argue that by carefully addressing the question of ergodicity, many puzzles besetting the current economic formalism are resolved in a natural and empirically testable way.

↬ Kevin Marks retweet (2020-12-15) of 
↬ Simon Wardley @swardley in Simon Wardley on Twitter: “Anyway, this is a fabulous paper – The ergodicity problem in economics – … well worth the read.” / Twitter (2020-12-15 04:12)

Ergodic theory is a forbiddingly technical branch of mathematics. ❧

From the New York Times-bestselling author of How Not to Be Wrong, himself a world-class geometer, a far-ranging exploration of the power of geometry, which turns out to help us think better about practically...

From the New York Times-bestselling author of How Not to Be Wrong, himself a world-class geometer, a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything
How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play chess, and why is learning chess so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry.
For real. If you're like most people, geometry is a sterile and dimly-remembered exercise you gladly left behind in the dust of 9th grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps, only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. OK, it is geometry, but only a tiny part, a border section that has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.
Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word geometry, from the Greek, has the rather grand meaning of measuring the world. If anything, that's an undersell. Geometry doesn't just measure the world - it explains it. Shape shows us how.

Some reviews of Luca's previous books"This book is like a magnificent suspension bridge, linking the science of the human brain to the practical craft of applying it in everyday life. I loved it." – Rory Sutherland, Ogilvy's Vice Chairman“A SUPERB book […] by one of the profound thinkers in our field [behavioral economics].” – Michal G. BartlettWhat's ergodicity, and why it matters?"The Most Important Property to Understand in Probability, in Life, in Anything." – Nassim Nicholas Taleb on ergodicity."I think the most under-rated idea is ergodicity." – David Perell, author.Is ergodicity the most important concept in decision-making and behavioral sciences? (Yes.)Is it relevant for you in your daily life? (Yes.)Is it possible to explain it so simply that a grandma or a high-schooler can understand it? (Yes.)Even if they know nothing about maths? (Yes.)That's because ergodicity is an important idea with so many practical applications. Sadly, most books describe it in a very technical way, making it inaccessible to most people.In this short book, 6-times author Luca Dellanna describes ergodicity as simply as possible. You will read stories about how not knowing about it destroyed his cousin’s career as a skier, or how misunderstanding it caused additional deaths during the pandemic. You will learn how to spot situations in which ergodicity matters and the three strategies to react appropriately.The book is approximately 166 pages long, of which 143 are pure content and the rest tables of content, etc.This page sells the eBook / Kindle version. Around mid-November, the paperback version will become available on Amazon and in selected stores (e.g., most Barnes & Noble).Who is this book for?This book is for readers interested in growing themselves, their career, or their business, and who want to learn about ergodicity and its practical applications without having to understand its mathematical foundation. No mathematical knowledge is required, only a high-school level understanding of English.Readers who want to master the theory and mathematical foundation of ergodicity are better off reading a more formal manuscript. This book is not a substitute for it, but a complement.You might also be interested in my second Roam book, on management (link).About the authorLuca Dellanna is the author of 7 books. He is a researcher in complexity science and emergent behaviors, and an operational excellence consultant. He spoke at Nudgestock and regularly teaches management workshops and risk management courses.His personal website is Luca-Dellanna.com and his Twitter is @DellAnnaLuca.What you will getBy purchasing this book, you will receive all of the following:PDF version.ePub version (compatible with Apple Books & other eBook readers).mobi version (Kindle)Moreover, you will get added to my mailing list, where I frequently publish essays that do not make it into books.The Roam versionThis book is also available as a Roam Research graph.Roam is a website that shows content in an interconnected way, a bit like Wikipedia. Reading the book this way will allow you to go back and forth content at your pace and following your interests."Ten minutes in, and I'm already questioning whether I'll want to read another non-fiction book *not* published in Roam format. How fascinating and so very valuable. Thank you Luca Dellanna" – Conor M. Ogle (link)Important: reading the Roam version requires a pre-existing Roam subscription, which is not included in this bundle.If you purchase the Roam version, you will receive the eBook in 3 formats (PDF, Kindle, and ePub) and the Roam version (as an editable .json export of the book) and a document suggesting how to import the Roam book and use it and the option to email me to request access to a live, read-only version of the book.Patron's supportThank you very much for your support, it helps me spending more time on my research.I will also add your name as a Patron in the acknowledgment section of the future editions of the book.Some more reviews of Luca's books“Luca’s book was so helpful to my work. Opened my eyes up to some more reasons why change is so hard.” – Chris Murman"A thoughtfully written book in very straightforward language." – A.L. PeeveyYou can find more reviews on the pages of my other books, such as this one.

This could be interesting as an overview to recommend

It's fairly often that I see a tweet that sums to something like "I find <prevalent concept> super hard" or "everybody's bad at <prevalent concept>, nobody really gets it" and I think it's worth discussing who and what this serves to accomplish

— shelley (@codebytere) September 11, 2020

This, but also and specifically for mathematics! We need to normalize the idea that math is easy.

In mathematics, the tombstone, halmos, end-of-proof, or Q.E.D. symbol "∎" (or "□") is a symbol used to denote the end of a proof, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "quod erat demonstrandum", meaning "which was to be demonstrated". In magazines, it is one of the various symbols used to indicate the end of an article. In Unicode, it is represented as character U+220E ∎ END OF PROOF (HTML ∎). Its graphic form varies, as it may be a hollow or filled rectangle or square.

I want to get started with #indieweb what is the easiest way to do that? Esp wrt syndication tools

— the big cauchy/cosh(y) couch (@fourierfiend) September 10, 2020

Hello fellow mathematician!

There are lots of ways to syndicate content, some dependent on which platform(s) you’re using and where you’re syndicating to/from. Your best bet is to swing by the IndieWeb Dev chat and ask that very question.

Theorem: Syndication is easy.

Proof: “It’s easy to show” (I’m waving my hands here) that there are a lot of assumptions and baggage that go with the word “easiest.”   ∎

I’ve personally found there’s generally an inverse relationship between ease/simplicity of syndication and control over exact display for most platforms. You could go low-fi and pipe your feed into something like IFTTT/Zapier  for cross-posting all the way up to customized integration with available APIs for each platform. Many take a middle-of-the-road approach that I notice Jeremy recommended as I’m writing this.

The cross-posting wiki page will give you some useful terminology and definitions which may help you decide on how to syndicate what/where. Based on the context of the URL in your Twitter profile, the IndieWeb wiki pages for static site generator and syndication will give you some ideas and options to think about and explore. 

Some of the pages about specific static site generators will give you some code and ideas for how to implement syndication. For example Max Böck has an article Indieweb pt1: Syndicating Content to Twitter, which is Eleventy and Twitter specific, but which could likely be modified for your purposes. SSGs may have some specific peculiarities for syndication that I’m not as familiar with coming from the more dynamic side of the fence.

Since you indicate a language preference for your current site, there’s also a page for Flask with a few users noted there. You might ask Fluffy (usually around in chat) for some advice as I know she syndicates to a few platforms and may have some ideas or even tools/code to share from the Flask perspective.

Q.E.D., right!?

(p.s.: Great Twitter handle!)

Hagoromo chalk has developed a cult following among mathematicians. When the company went out of business, chaos ensued.

I’ve read this same sort of article in other venues in the past, but closer to the revival of the company. This seems to have cropped up again because the original owner of the Japanese company has passed away in the last month.

The Society for Mathematical Biology - e-Conference 2020.
August 17 - 20, 2020

OK when I can't even figure out how to send a viewer to the top of the page, it's time to get up and go for a ride. #indieweb blues

— Cognitively_Accessible_Math (@geonz) August 6, 2020

IndieWeb, cycling, math, AND OER! I’m in… 

How was I not following @geonz before?!

a fast way to write and share mathematics

Bookmarked Lecture Notes by Arun Debray (web.ma.utexas.edu)

I LATEXed up lecture notes for many of the classes I have taken; feel free to read through them or use them to review. If you find a mistake or typo, please let me know. If you want to look over the .tex source for any of these notes, please send me an email.

A great set of LaTeXed notes from a variety of coursework.

via Rama Kunapuli.

Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

earlier draft available on arXiv

Module 4: -- Edward Frenkel: Harmonic Analysis

Module 1: -- Edward Frenkel: The Continents of Mathematics

Module 3: -- Edward Frenkel: Galois Groups

Module 2: -- Edward Frenkel: Symmetry and Unification

I find myself seeing some immediate and excellent historical examples in Dr. Ibram X. Kendi‘s book Stamped from the Beginning. In chapter nine of the book he discusses the variety and flavors of racism espoused by Thomas Jefferson in his book Notes on the State of Virginia (1785), which would become the most  consumed American nonfiction book until well into the mid-nineteenth century.

Shortly afterward Samuel Stanhope Smith countered portions of Jefferson’s racist ideas in the 1787 annual oration to the august American Philosophical Society. This annual lecture was already one of the most heralded scholarly lectures in America and was attended by the wealthy and elite leaders and thinkers in the country. The lecture would be published as the influential Essay on the Causes of Variety of Complexion and Figure in the Human Species. 

Samuel Stanhope Smith joined those preeminent intellectuals in Boston’s American Academy of Arts and Sciences and Philadelphia’s American Philosophical Society in attacking polygenesists, in reviving climate theory in America. His scholarly defense of scripture was quickly printed in Philadelphia, in London, and in Lord Kames’s back-yard, Edinburgh. By the time he sat down in Princeton’s presidential chair in 1795, he had amassed an international scholarly reputation.

So in just a few pages Kendi lays out some serious evidence of the direct spread of a wide variety of racist ideas by not only by the academic elite, but the leaders of multiple influential universities and scientific and philosophical institutions in America. The reverberating echos of these wrongs are still haunting us today. They still need to be addressed and righted. We need to use our moral alembic and distill these racist ideas out of science in America.

Lest one wonder about the influence of Samuel Stanhope Smith’s essay, I’ll note that Noah Webster cited Smith directly in Webster’s 1828 Dictionary in the definition of philosophy. The citation was from  Smith’s second edition of his Essay on the Causes of Variety of Complexion and Figure in the Human Species (1810). The quote as given: “True religion, and true philosophy must ultimately arrive at the same principle.”

We’re obviously still seeking both true religion and true philosophy.

While you’re thinking about #shutdownSTEM on June 10th and long thereafter, I recommend you spend some time sitting with the ideas that have been handed down to us and question them closely, for this is what science and philosophy are all about. If you find you can’t do that hard work–and it is hard, then perhaps read a bit of Dr. Kendi’s excellent and ardent text Stamped from the Beginning.

An unsolved conjecture, and a clever topological solution to a weaker version of the question.

Mathematics Research Reports is a journal run for and by mathematicians, committed to the mission of providing high-quality scientific content, while adhering to the principles of Fair Open Access. This includes being freely available for a scientific audience worldwide, with no author publication charges, thanks to support from the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University. This journal publishes research announcements of significant advances in all branches of mathematics, short complete papers of original research (up to about 15 journal pages), and review articles (up to about 30 journal pages). All articles should be designed to communicate their contents to a broad mathematical audience and should meet high standards for mathematical content and clarity. All papers are reviewed, and the entire Editorial Board must approve the acceptance of any paper. Founded by members of the editorial board of Electronic Research Announcements in Mathematical Sciences (published by the American Institute of Mathematical Sciences and preceded by Electronic Research Announcements of the American Mathematical Society), Mathematics Research Reports is owned and operated by its editorial board, and supported by senior editors drawn from among former editors of both Electronic Research Announcements in Mathematical Sciences and Electronic Research Announcements of the American Mathematical Society.

From time to time academic journals undergo an interesting process of fission. Typically as a result of some serious dissatisfaction, the editorial board resigns en masse to set up a new journal, t…

there’s nothing like knowing that you’re going to have to justify your decision to a bunch of mathematicians. ❧

Annotated on May 20, 2020 at 10:05AM

A bit of Googling will reveal people who’ve already written some code to quickly download them all in bulk as well. I’m happy with doing things manually as there’s only a handful of the 8GB of textbooks I’m interested in.

Browsing through, I’ll note a few that look interesting and which foodies like my friend Jeremy Cherfas may enjoy. (Though I suspect he’s likely read them already, but just in case…)

• Food Analysis, ed. S. Suzanne Nielsen
• Food Analysis Laboratory Manual by S. Suzanne Nielsen
• Brewing Science: A Multidisciplinary Approach by Michael Mosher and Kenneth Trantham
• Food Fraud Prevention: Introduction, Implementation, and Management by John W. Spink

New update on Math3ma: I’m delighted to share that this summer I’ll begin as a postdoctoral researcher at X, formerly Google X, the Moonshot Factory, in Mountain View, CA. (I’ll work remotely until travel is safe again.) I am *thrilled* for the future! https://t.co/e20ivNYNjp

— Tai-Danae Bradley (@math3ma) April 18, 2020

He made profound contributions to number theory, coding theory, probability theory, topology, algebra and more — and created games from it all. He died of the coronavirus.

My PhD thesis “At the Interface of Algebra and Statistics” is now on the arXiv! https://t.co/7IwEu8wqQC It uses basic tools in quantum physics to explore mathematical structure that's both algebraic & statistical. Curious? See my new 10m video on YouTube!! https://t.co/zOtBtGeQVK pic.twitter.com/U8X622mtse

— Tai-Danae Bradley (@math3ma) April 14, 2020

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.