The Fat Tech Cat Diet

This got me thinking about the things that live inside my phone.

Like much of the world, I seem to live in a permanent state of vexation about technology, privacy, and how to survive in a world where so many access points are guarded by hungry algorithm crunching data trolls. This is not a new anxiety for me, I’ve blogged here before about some of the privacy concerns of smart cities, the privacy choices made by Apple in the past, and even the benevolent hackers protecting us.  But technology moves on, and the fat cats of the tech sector seem to be getting fatter on a steady diet of user data. 

Well this certainly doesn’t inspire confidence.

This topic has been especially hot on my mind this summer, because in an unexpected move (precipitated by this) I switched from an iPhone to a phone with an Android operating system and have been questioning the implications to my privacy ever since.

I mean, wow, I’ve had to click “I Agree” to a whole lot of things the last month.

But as it (shockingly) turns out, it doesn’t quite matter whether I agree or not.  A report from the Associated Press revealed that Google apps store a time-stamped register your locations, even when you specifically turn off location services.  So, for example, even if your “location history” is turned off, every time your gmail app pings a tower, the time and location is saved in your history.  That’s frustrating.

So maybe you think it’s smarter to use an iPhone and stay away from Google’s proprietary apps.  Well, I have bad news for you.  Apple, who has always differentiated itself by loudly proclaiming its commitment to locking up all of your private data inside your phone that it can’t be touched even by the engineers at Apple, has a new (as of iOS10) privacy scheme.  And the math around it doesn’t look very good.  The scheme is called differential privacy, and in a nutshell, Apple now sends all of your local data back to the mothership, but mixes it with enough noisy data that (in theory) your data could never be tied back to you personally.  This is an opt-in scheme, and when you agree to it, you are agreeing to a data sharing budget of epsilon per day.  That is, there is an upper bound, epsilon, to the amount of data they will harvest each day.

However, mathematicians have shown that even for a fixed epsilon, the amount of privacy being lost is not really something to be proud of, in fact they show that the amount of privacy you can lose each day is unbounded.  A post from Andy Greenberg at Wired gives a good rundown on some of the research that has been done on the shortcomings of the algorithm.

What also really bugs me about this, is how apparently nonchalant Apple is about dealing with the criticism.  I mean, I’m torn.  On the one hand, Google is standing there out in the open with its grabby robot hands taking all of my data and I can’t stop them.  And in some sense, Apple is doing the same thing but just pretending it isn’t.  

Cathy O’Neil, the longtime blogger and now frequent contributor to Bloomberg has done a lot of writing about big tech companies and their questionable algorithm practices.  Recently, O’Neil wrote about a set of proposals from Mark Warner regarding data privacy.  Specifically, what the government might do to limit who gets to access your data and what they get to do with it.   For the algorithms that have big control over your life, Warner recommends a system of algorithm auditing by human (because in case you missed it, algorithm bias is a very real thing). Most recently, she wrote about what Zuckerberg and his fellow cats can do to reel in the powerful and dangerous beast they’ve created.

What motivates your personal decisions on privacy?  Do you think about what operating system you use and does it vex you every day?  Let me know in the comments, or as usual I’ll be tweeting from my underground bunker @extremefriday.

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Musings on a Mathematician’s Duties

Diver figurines on fruit

Come with me to take a dive into the abc conjecture and the ethical duties of mathematicians! Image courtesy of HaPe_Gera via Flickr CC.

As I mentioned in my last post, I wish a genie would grant me thorough understanding of the proof Shinichi Mochizuki proposed for the abc conjecture. Much of this wish is motivated by a desire for the divisive debate to be settled concerning the more than 500 page text. Last year, it was announced that Go Yamashita had written a summary of Mochizuki’s proposed proof, but that summary was still 294 pages and didn’t settle debates about Mochizuki’s potential proof.

In July, Ivan Fesenko, who has organized conferences on the inter-universal Teichmüller(IUT) theory that underlies Mochizuki’s proposed proof, released a document titled “Remarks on Aspects of Modern Pioneering Mathematical Research,” which heavily focuses on Mochizuki’s IUT theory and the abc conjecture.

Continue reading

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On Math Anxiety

Just below the placid surface is an infinite wellspring of anxiety. Image courtesy of Christopher Michel via Flickr CC.

Math anxiety is so real.  We’ve always kind of known it, but a study confirmed it in 2017. By reading the brain functioning of math anxious and math non-anxious people while performing simple arithmetic problems, the research shows that people are better at automatic problem solving when the parts of their brains associated with math anxiety aren’t activated.  So that feeling you get when someone asks you to quickly multiply two numbers and you just stare at them, tearing up, like a sad deer in headlights…that’s real. 

So we know it’s real.  And we know that a lot lot lot of people feel it (disclaimer, sometimes I have really had bad math anxiety…sometimes math still makes me cry) but that doesn’t change the fact that everyone has to get through some amount of math education.  This means we need to teach math in a way that minimizes the stimulation of that anxious brain and maximizes the release of those glorious math fueled dopamines. 

Stan Yoshinobu, who writes The IBL Blog, published a collection of student voices on math anxiety. The student voices will likely sound familiar to you, and what doesn’t surprise me at all is the the fact that the quotes Yoshinobu collected come for college students but I’ve heard the same words coming from the mouths of people 50 years removed from formal education.  People carry that anxiety with them forever and it’s so intense

This is bad situation, since studies have also shows that math anxiety is contagious; math anxious parents pass on their attitudes and mindsets to their children and perpetuate the problem even with the best of intentions.  Also, a recent study of elementary school teachers showed the impact of mindset on student outcomes. Teachers with a growth mindset produce more successful students.

As a way to mitigate the anxiety, Yoshinobu blogged about the iceberg diagram for recognizing and addressing student anxiety. In the post, he points out some of the nonverbal and non-obvious ways that student anxiety manifests and how they can be addressed.  One point he brings up is the interplay between math anxiety and other attitudes, beliefs, and mindsets that can inhibit learning.  Looming large among them is stereotype threat, the idea that people “like you” aren’t good at math so you won’t be either.

An interview with one of the authors of the 2017 study, Sian Bailock, also discusses stereotype threat and how to avoid introducing it to children.  Bailock’s research focuses on the various types of situations —  whether in math, sports, or life — that can “rob us of the cognitive horsepower that we need to succeed.”

Whether you’re teaching university level abstract algebra, or helping your kid add fractions at the kitchen table, the anxiety can be just below the surface — yours or theirs, depending on your own level of mathematical trauma.  This semester I’m going to try and pay more attention to student buy-in and intentional mindset conditioning throughout the semester.  So I’m curious, what sort of exercises do you do at the beginning, middle, end of the semester to help improve attitudes and beliefs in your classes?  Let me know here in the comments, or on Twitter @extremefriday.  

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What Wish Would You Ask a Math Genie to Grant?

Genie figurines with a magic lamp

Credit: Image via Flickr CC Brian Neudorff

“If a genie offered to give you a thorough understanding of one theorem, what theorem would you choose?” blogger John D. Cook recently asked on his @AnalysisFact Twitter account. Responses ranged from the names of theorems to questions about the genie’s potential trickery to creative ways of gaining insights beyond an understanding of one theorem.

Cook summarized the results on his blog. In an interview conducted over email, he answered my questions about his genie idea. (The following interview has been edited for length and clarity.) Continue reading

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Welcome To The Blog

Our new blogger takes a walk with her service dog Delilah.

If you’re new to the blog, welcome. We are the Blog on Math Blogs, your premier destination for blog reviews, tours of the mathematical blogosphere and all the cool math stuff that lives on the internet (omg there’s so much of it this internet thing is never-ending). And beginning next month we’ll be joined by a new co-editor, Rachel Crowell!

Just like Evelyn and me, Rachel is part of the proud lineage of AAAS-AMS Mass Media Fellows. Every summer the AMS sponsors one mathematician to work at at a mass media news desk. Something like NPR, Wired, Scientific American, or in Rachel’s case, the Oregonian. It’s good for science and it’s good for the world, since I’m sure we can agree there should always be more mathematicians everywhere all the time. But it’s also a really great experience for anyone with a technical background interested in writing, as Rachel was when she applied. Over the years the AMS has collected essays on the experiences of past fellows.

After studying math at the University of Missouri, Rachel was the 2015 fellow working at the Oregonian in Portland, Oregon, where she was part of the storytelling team. She wrote a bunch of articles while she was there, including a lot of coverage for the local science going on at the universities around Portland. Since then Rachel has been writing for the AMS Math in the Media blog, as well as freelancing at other venerable science news purveyors.

Rachel writes for Science News for Students, a super resource for plain english science articles about all sorts of current research, scientific and mathematical. Rachel wrote a fun piece about different jobs that use geometry to study motion, from crash test dummies to video game design.

She’s also been writing for the millennial focused PBS affiliate site Over there she was working on some really fun Buzzfeed style quizzes, like “Which Top New Species of 2018 Are You?” I’m the Swire’s Snailfish. Depressing since this makes me the top predator among bottom feeders. Not exactly how I prefer to self-identify.

Rachel has a soft spot for applied math, and likes thinking how different types of math affect our day-to-day life. She’s also really into the craft of science and math writing, and wants to share more resources for people who want to get in on that.

I asked Rachel about her ideas for the blog moving forward, and she said she really wants to talk to you, the bloggers and readers and citizens of the internet, to cover your blogs and your interests. If you have ideas for Rachel or a blog you’d like to share, she encourages you to reach out by email (racheljcrowell at gmail dot com) or you can find her on Twitter @writesRCrowell.

And of course you can always find me on Twitter @extremefriday.

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Return Of The Bots

A picture of a stealth bomber. Image via Flickr CC @BowiTheBoxer

Bots have been getting some extra love on the internet these days, particularly in the form of the I Forced A Bot meme. So I thought it would be a good time to revisit all things bot, neural network and AI.

First, let’s take a moment to discuss and debunk the I Forced A Bot meme. The general gist is that a bot sucks in 1,000 hours of X, trains a neural network and then recreates X, usually to hilarious effect, something like this one below.

The meme is said to have started with a piece of Harry Potter fanfic that was written using a predictive text keyboard trained on the Harry Potter books — plus a little bit of human intervention — and released on Twitter by @BotnikStudios.

Hilarious, sure, but this meme really started to pique my interest when Janelle Shane, AI researcher and chief blogger at AIweirdness, chimed in to explain what makes these memes so different from actual content generated by a machine learning algorithm. One comment that Shane makes is that it’s really hard for bots trained on neural nets to do things like write scripts and recipes because they have very short memories. For example, a bot that writes a recipe will forget the ingredients by the time it gets to the preparation instructions. And in stories or commercials, this would mean great difficulty in recalling characters and making any kind of meaningful narrative arc.

These bots — and the so-called deep learning algorithms — typically work by processing training data over and over again to improve their understanding of the data, essentially by performing increasingly better pattern matching. But as Shane and many others have long pointed out, these types of algorithms are typically very bad a learning common sense. We’ve all heard the one about how changing a single pixel can cause the neural net to confuse a dog with a stealth bomber. For a great down-to-earth overview of how deep learning works and why in fact it’s essential that deep learning algorithms have such selective memories, check out this piece by Natalie Wolchover for Quanta.

Shane has blogged about lots of strangely funny constructions that can come out of trained neural nets. For example, what sort of halloween costumes might a neural network come up with if it was fed the inventories of costume warehouses? Or what nail polish colors do you get when you feed existing polish colors into a neural network trained on heavy metal band names?

Machine learning made another appearance in entertainment news this summer when the pop singer Taryn Southern was called out for using AI to write her music. To me it sounds more like she wrote the piece collaboratively with some AI software, which I think is pretty cool.

We’ve covered some aspects of bot-ism and neural networks here on the blog before. Evelyn Lamb posted about the Best of the Bots, and I wrote about The Neural Net That Predicts Sexual Orientation.

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Some Math for Wedding Season

Here’s a wedding I went to where I was thinking about optimal seating charts the whole time. Photo courtesy of Sam Carleton.

It’s that time of year when happy friend and family gather to celebrate the entry of two singletons into forever tuple-dom. That inevitable mapping from the set of people into the set of pairs of people, with its ever changing domain…*sigh*…what a special time.

If you’re the one planning the wedding you’ll be happy to know that there are several mathematical solutions to writing the seating chart. One of them is presented on the SAS Operations Research Blog. You’ll also be happy to know that there’s some data been crunched on what it takes to be an upper-crust wedding.

A few years ago the techie blogger Todd Schneider wrote an N-gram analysis of the New York Times Wedding Section based on a data set he built at An N-gram analysis is a tool used a lot in computational linguists and probability. It scans a text (or a corpus of texts!) for a fixed string or set of strings with length N. In this examples the strings are words that you might find in a NYT wedding announcement.

This controversial section of the paper has historically been grist for some annoyed gripes that it keeps showing the same Episcopalian Yale graduates from Greenwich, Connecticut. A while back The Atlantic had an article on the odds of getting into the New York Times wedding section. If you’re vying for a spot, you may want to adjust your strategy accordingly.

But back to the N-grams. Schneider uses this tool to search for trends in the NYT wedding announcements by searching common surnames, alma mater, religious affiliations, and employers. From Schneider’s analysis he determined that brides are getting older, episcopalianism is on the decline, and investment banking doesn’t have the same cache that it once did. But don’t take his word for it, you can do your own wedding N-gram searches at weddingcrunchers, for example I just found that Uber, Lyft, and Taxicab show up surprisingly frequently. How romantic.

But maybe you’re not married yet, and maybe you are a hopeless romantic hoping to meet that special someone in a taxi cab. Then what you need to consider is the stable marriage problem. This stable marriage problem asks for a way for find a stable pairing between two equally sized sets, say a set of men and a set of women (sorry this one’s a bit hetero/cis normative) given that all the people in each set have ordered preferences. There’s a solution to this problem, and that is the Gale-Shapley algorithm. That is, there is a pairing in which each person is paired with a person who they prefer and who prefers them and neither partner has the option for a “better” pairing. This is good news if you’re looking for an optimal partner (because who isn’t?) and it seems that you can run your Tinder game sort of like the Gale-Shapley algorithm.

Otherwise, PunkRockOR has you covered with a roundup of operations research models for finding love.

If you need me, I’ll be the one loitering around the wedding cake. Oh, and I’m for hire to write mathematically themed MOH and Best Man speeches. You can find me on Twitter @extremefriday.

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Some Revelations In My Tech Free Adventure

On the ferry to Dar Es Salaam, contemplating pedagogy, accessibility, transportation, supply chain management and sunsets. Photo Courtesy of Frank Neikes.

I’m still in Tanzania, still with limited access to technology resources, so I wanted to take this post to share with you a few technology-free mathematical revelations I’ve had during my time here.

First, the pedagogical revelation. I’m teaching a Complex Analysis course to a group of 150 non-native english speakers in an acoustically challenging space. Imagine a large hall made of concrete, with lots of metal crossbeams running widthwise, and open air windows that allow all the noise in from outside and allow all of my careful words to escape into the schoolyard.

It has never been put in such stark relief how I take for granted my ability (and the ability in others!) to hear well and understand me when I speak. I have a great great deal of difficulty both hearing and understanding students when they ask questions, due to barriers of a linguistic and acoustic nature. And I’m constantly worried that they can’t hear or understand me. It’s completely changed the speed and cadence with which I deliver a lecture and engage with student questions. And it has really gotten me thinking, how many non-native english speaking or hard of hearing students have I had in my career who could have benefited from this?

It reminded me of this important microphone related PSA I read on Twitter a few weeks ago from writer @SarahPinsker. She wrote, “Abandoning the mic at a panel/ reading causes an accessibility issue for audience members. Even if you ask “y’all can hear me?” you don’t know if there’s someone with hearing loss who came out for you & has now been put in the uncomfortable position of speaking out or losing out.” I will never again eschew a microphone and dismissively say “It’s ok, I have a loud voice.” Although, to be honest, I never would have done that in the first place.

The AMS Inclusion/Exclusion blog has done some great coverage on accessibility concerns in mathematics, including ableism and inclusive pedagogy. If you’re interested in getting in on some of these conversation, I’ve found that Piper Harron’s Twitter feed is often full of thoughtful and nuanced takes on the subject.

The other revelation I’ve had is more mathematical in nature, and it involves what makes math interesting to humans, and it’s occurred to me that there are two main camps (feel free to fight me on this one, I’m not committed to this idea). There are the math-is-beauty-and-beauty-is-math-and-we-should-learn-number-theory-because-it’s-written-into-the-very-bones-of-our-being types, call then Type A. And there are the math-is-money-and-we-should-learn-complex-analysis-because-it-will-help-us-become-engineers-so-we-can-build-big-things-and-get-money, call them Type E.

I’ve been a Type A for most of my life, and I think that most of my students have been Type A as well. People who are just drawn to the wonder and beauty of it all. But suddenly I’m seeing a world full of nails, and math is the hammer, and I’m wondering if maybe my students were really Type E all along and maybe I wasn’t paying close enough attention. And I’m wondering if maybe I’m not also secretly a Type E…

It’s not that I think these two types necessarily need to exist in conflict with one another, nor are they necessarily mutually exclusive. And it’s not as simple as just a pure/applied split, because of course we all know that all math is eventually applied math. I’ve just noticed that math means different things to different people, and that’s pretty amazing. It’s the ultimate multitool. Whether you coming at math from hardcore operations research like PunkRockOR or mathematical essentials like From Fish to Infinity, there is an entry point for everyone.

My job as a lecturer is just to find out people’s preferred point of entry and guide them there. And my job as a mathematician, I guess it to make really good math regardless of which Type I belong to.

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Teaching Offline

The campus at Marian University College (Maruco) in Bagamoyo.

I’m in Bagamoyo, Tanzania at the moment teaching two summer courses to a group of undergraduate students at Marian University College. This experience is different from my typical teaching experience along several dimensions. I am teaching Complex Analysis to a group of 150 students. This is a course I’ve never taught, and it’s a group of students 5 times the size of my typical class. In order to deliver a message to the entire class at once, I need to write the message on a piece of paper and pin it to the main bulletin board. Moreover, this is an entire room full of non-native english speakers learning a subject full of technically dense jargon. And to take my challenge to the next level, I have one whiteboard that’s roughly…well, it’s small (it’s about the size of what I would have in my office).

As a blogger the internet is obviously critically important to my productivity, and so much of my teaching and blogging inspiration comes from the #MTBoS. And as a professor I am naturally pre-occupied with using technology in the classroom. This is such a hot topic, anyone who has ever applied for a job, or tenure has given it at least passing thought. The AMS blog PhD Plus Epsilon has featured several posts on technology for teaching and here we’ve done a couple of posts on teaching with technology. But this visit has got me thinking about teaching without technology. What does a technology-less classroom look like, and what are the advantages?

Getting ready to learn some Complex Analysis.

While tech resources some almost impossible to get away from in US schools, a few years ago the New York Times profiled a screen-free school in Silicon Valley of all places So it must be possible. Several years ago the Chronicle of Higher Ed published an article about efforts to “teach naked.” That is, to teach without have the power of machines to lean on and hide behind and how this stands to benefit students.

One important incentive for pumping our classrooms full of technology is that technology is like a language and it’s important that students be fluent its the language of technology by the time they graduate. To this important point, the Remind Blog has a post about teaching digital literacy without actually using technology. Students can learn about blogging, commenting, and online etiquette through well moderated discussions, and hashtags on the blackboard can actually work just like #hashtags.

The Flip’d Blog gives several good suggestions for using a technology-less environment to capitalize on student engagement, including several links to studies supporting the merits of good old fashioned pen-and-paper note taking.

I gave my first quiz today in Complex Analysis and without any prior discussion, each student showed up with a pencil, a ruler, and a scientific calculator. I have to say, this warmed my heart, since straight lines make graphing so much lovelier and I often find myself smh at the primacy of the TI-83.

I hope they learn so much! Wish me luck!

Posted in Issues in Higher Education, Math Education | Tagged | 1 Comment

Summer Time is Puzzle Time

Courtesy of

It’s Mid-May, that means it time to put away your serious things and time to start thinking about (what else?) math puzzles!

Alexander Bogomolny, of CutTheKnotMath, has curated an amazing collection of math puzzles, problems, and interactive lessons. I always love to do geometry problems to get by brain working in the morning, and Bogomolny has plenty to spare. For example, this morning I picked up Two Equilateral Triangle on Sides of a Square. I solved it quickly, and then checked the (6 different!) solutions he gives on the page, all of which were different from my (sort of lame) approach.

Here I am in economy class, meanwhile he’s using quadrances and the triple spread formula. Bogomolny’s clear and varied solutions make me recall how much geometry has passed through my brain at one point or another, and also make the problems an interesting tool for exploring different math concepts in the classroom. He posts a lot of his problems to Twitter; you can follow him @CutTheKnotMath to get your daily dose of puzzles.

For the more tactile puzzlers among us, several people have sent me links to the infinity puzzle, which are “a new type of puzzle inspired by topological spaces that continuously tile.” There is a nice write up from some of the the makers at The Nervous System Blog, a blog about generative design. The puzzles are designed that they can be done right-side-up and upside-down and have no edges, but rather edge identifications.

Recently our friend of the blog, Mike Lawler from MikesMathPage, did a lesson in topology with his kids with the infinity puzzle as a jumping off point. Lawler and his crew determine the actual edge identification for their puzzle. Is it a Möbius strip? Is it a Klein bottle? Find out.

At the blog, Oliver Roeder curates a column called The Riddler, where really tricky but fun math problems are waiting to nerd snipe you. I particularly enjoyed the minimal urinal problem: what’s the minimum number urinals so that N people can optimally urinate? It’s much harder than it looked at first. This optimal urinal problem also showed up on the companion blag to xkcd a few years ago.

I appreciate that Roeder splits his riddles into Riddler Classic (to do while you’re on a long flight) and Riddler Express (to do while you eat breakfast). You might try the classic problem from a few weeks ago, which asked, how many decimal numbers are equal to the average of their digits?

Anyhow, if you’re headed to the beach, meeting friends for a beer, or just going for a walk in the woods, these puzzles are sure to delight everyone you meet, without exception. So definitely keep a few in your back pocket at all times, starting now. And please pass on worthy puzzles to me @extremefriday.

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