The Summer 2017 Mathematics A To Z: What I Learned


I’ve in the past done essays about what I’ve taken away from an A to Z project. Please indulge me with this.

Summer 2017 Mathematics A to Z, featuring a coati (it's kind of the Latin American raccoon) looking over alphabet blocks, with a lot of equations in the background.
Art courtesy of Thomas K Dye, creator of the web comic Newshounds. He has a Patreon for those able to support his work. He’s also open for commissions, starting from US$10.

The big thing I learned from the Summer 2017 A To Z, besides that it would have been a little better started two weeks earlier? (I couldn’t have started it two weeks earlier. July was a frightfully busy month. As it was I was writing much too close to deadline. Starting sooner would have been impossible.)

Category theory, mostly. Many of the topics requested had some category theory component. Next would be tensors and tensor-related subjects. This is exciting and dangerous. Neither’s a field I know well. Both are fields I want to know better. It’s a truism that to really learn an advanced subject you have to teach a course in it. That’s how I picked up what I know about signal processing and about numerical quantum mechanics. Still, it’s perilous, especially when I would realize the subject asked-for wasn’t what I faintly remembered had been asked for, and that I’d been composing an essay for in my head for a week already.

Also, scheduling. The past A To Z sequences were relatively low-stress things for me. I could get as many as six essays ahead of what I needed to post. That’s so comfortable a place to be. This time around, I was working much closer to deadline, with some pieces needing major rewriting as few as fifteen hours before my posting hour. More needed minor editing the day of posting. There’s several causes for this. But the biggest is that I wrote much longer this time. Past A To Z sequences could have at least a couple essays that were a few paragraphs. This time around I don’t think any piece came in at under a thousand words, and the default was getting to be around 1500 words. I don’t think I broke 2,000 words, but I came close.

That’s fine, because the essays came out great. This has been the A To Z sequence I’m proudest of, so far. They’re the ones that make me think my father’s ever-supportive assurance that I could put these into a book that people would give me actual money for can be right. Still, the combination of writing about stuff I had to research more first and writing longer pieces made the workload more than I’d figured on. When I get to doing this again — and I will, when the exhaustion’s faded enough from memory — I will need more lead time between asking for topics and starting to write. And will need to freeze topics farther in advance than I did this time. I still suspect my father’s too supportive to say I could get money for this. But it’s a less unrealistic thought than I had figured before.

Also learned: hire an artist! I got a better-banner-than-I-paid-for from Thomas K Dye for this series. His work added a snappy bit of visual appeal to my sentence heaps. I’d also gotten from him a banner for the Why Stuff Can Orbit sequence, which I mean to resume now that I have some more writing time. But the banners give a needed bit of unity to my writing, and the automatically-generated Twitter announcements of these posts, and that’s helped the look of the place. Something like nine-tenths of the people I know online are visual artists of one kind or another. (The rest are writers, my siblings, and my mother.) I should be making reasons to commission them. For example, if I want to describe something too complicated to do in words alone I should turn it over to them. Remember, I don’t do the few-pictures thing because I’m a good writer. It’s because I’m too lazy to make an illustration myself. A bit of money can be as good as effort.

Speaking of effort, between the A To Z essays and Reading the Comics posts, and a couple miscellaneous other pieces, I wrote five to six thousand words per week for two months. That’s probably not sustainable indefinitely, but a slightly lower pace? And for a specific big project? It’s good to know that’s something I can do, albeit possibly by putting this blog on hold.

Learned to my personal everlasting humiliation: I spelled “Klein Bottle” wrong. Fortunately, I only spelled it “Klien” in the title of the essay, so it sits there in my tweet publicizing the post and in the full-length URL to the post, forever. I’ll recover, I hope.

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How June 2017 Treated My Mathematics Blog


I’m a little behind my usual review of the month’s readership and what’s popular around here, but I have good reason for it: I was busy earlier this week. Expect to be busy next week, too. Really, it’s going to be a bit of a mad month so do please watch this spot next week when I unleash some extra madness on myself. Thank you.

So. Readers in June 2017: how many did I have? Disappointingly few of them, it turns out. Only 878, down from the 1029 in May and 994 in April. Heck, that’s not even close to what I had been running in previous months. Not sure what happened there. Maybe it’s everybody getting out of (US) schools and not needing comic strips read to them anymore. The number of unique visitors fell too, to 542 down from May’s 662 and April’s 696. It’s not a phenomenon related to the number of things posted, either; I had 13 posts in June versus 12 in May, and 13 in April, and 12 in March, which suggests that July I can take relatively easy, come to think of it. I finally had an uptick in the number of likes, at least, with that rising to 99 from the 78 of May and the 90 of April. I don’t think that’s statistically significant a difference, though. The number of comments also rose, but to only 13; that beats May’s 8, but April only had 16. Well, I have a scheme in mind to increase the number of comments too. You’ll know it when you see it. But, wow, a statistics page like that and I worry that I’ve passed my prime here.

The popular stuff around here was about what I’d expected: the count of grooves in a record, and a bunch of Reading the Comics posts. And then one of the supplemental pieces in my Why Stuff Can Orbit series, which was helped by Elke Stangl’s most gracious words about it. The top articles, since there was a three-way tie for fourth place:

Now the roster of the 52 countries that sent me readers in June, and how many each of them did. Spoiler: the United States tops the list.

Country Views
United States 472
Turkey 74
India 52
United Kingdom 40
Canada 38
Austria 23
Puerto Rico 17
Australia 16
Germany 15
Singapore 12
Brazil 11
China 9
France 7
Italy 7
Slovenia 7
Philippines 5
Norway 4
Spain 4
Switzerland 4
Argentina 3
Hong Kong SAR China 3
Israel 3
Netherlands 3
New Zealand 3
Russia 3
Sweden 3
Cambodia 2
Chile 2
Indonesia 2
Kenya 2
Malaysia 2
Poland 2
Saudi Arabia 2
South Africa 2
South Korea 2
Thailand 2
Azerbaijan 1
Bahrain 1
Bangladesh 1
Belgium 1 (*)
Colombia 1 (*)
Estonia 1
Ghana 1
Hungary 1
Ireland 1
Japan 1 (*)
Jordan 1
Macedonia 1
Mexico 1
Palestinian Territories 1
Portugal 1 (***)
Ukraine 1 (*)

I make that out as readers coming from 52 countries, same as in May and slightly more than there were in April. There were 16 single-reader countries in June, down from May’s 21 and up from April’s 10. Belgium, Colombia, Japan, and Ukraine have been single-reader countries for two months running now. Portugal is on a four-month single-reader streak. Hi, person from Portugal. I’m glad you like me a little bit. That’s better than not at all. I have no idea why I’m suddenly popular in Turkey.

The most popular day for posts was Sunday, with 18 percent of page views. That’s marginally up from 16 percent in May, but the same as April’s count. The most popular hour was 4 pm, when 14 percent of my page views came. I rather suspected that would happen; I tried moving the default posting time two hours earlier this past month and sure enough, the readers followed. People stop in here right after something’s posted or not much at all. Hm.

The mathematics blog started the month with 50,125 page views, so hey, finally broke 50,000! Nice. These came from something like 22,754 distinct viewers that WordPress is aware of existing.

WordPress’s report of what search terms people are looking for has collapsed into uselessness. About all it admits to people wanting in June, besides “unknown search terms”, were Jumble — I want it too, but can’t find a good source that just gives me the day’s puzzle in a static picture — and “concept of pythagorean theorem” and “short conversation to explain algebra”. The Pythagorean theorem I can do, but a short conversation to explain algebra? … Well, which kind of algebra? I suppose they don’t want the fun kinds. They never do.

The Insights panel thinks there are 666 WordPress.com followers to start the month. I can accept that. Not all of them seem to visit, but that might just be that they’re following me in their Readers rather than clicking individual links. I’ve given up on leaving a teaser of text out front and hiding the rest behind a click. That stuff might record, but nobody likes it, me included. If you’d like to follow this blog in your WordPress reader, there’s a little blue strip labelled “Follow nebusresearch” in the upper-right corner of the page. If you’d rather follow by e-mail, it’s under “Follow Blog Via Email” and don’t think I want a – in there. And I am on Twitter as well, as @Nebusj. That account sometimes gets into talking about non-mathematical stuff, including my humor blog which is a slightly more popular hangout, since I regularly explain what’s going on in the story strips. So if you looked at Mary Worth the last couple months and couldn’t figure out what the heck was going on, I can tell you: it’s CRUISE SHIPS. Only in more detail.

How May 2017 Treated My Mathematics Blog


The big news is that in May my mathematics blog crept back above a thousand page views. It had been a whole month since it had reached this threshold of purely imaginary significance. For what was a slow writing month — only twelve posts — marred by my computer dying and a nasty cold the final week, the numbers aren’t bad.

In May there were 1,029 pages viewed here. That’s up from April’s 994 and March’s 1,026. The number of unique visitors is down for the third month running, though, down to 662 from April’s 696 and March’s 699. The happy implication: people reading more posts as they visit. You know, liking my writing more.

Views and Visitors for my mathematics blog, January 2015 through May 2017 with as much June as there's been so far. It's all been kind of stable, rocking back and forth around 1,000 views and like 650 visitors per month, for the past year or so.
I still feel like trying to rig up some compensation for that bizarre event back in … September 2015, wasn’t it? … when suddenly everybody’s statistics everywhere dropped and we blamed it on them no longer counting mobile devices. But if that were so, surely they’ve put them back? There’s no way the non-mobile-device readership is growing fast enough that these numbers should be about stable.

I’d think, anyway. There were 78 posts liked in May, down from April’s 90 and March’s 85. Not to pout or anything but WordPress does tell me that in June 2015 there were 518 likes around here and I can’t think, gosh, what was different then? … Well, it was one of my A To Z months, with posts 28 days of the month, and that usually encourages cross-reading. The number of comments just cratered, though: there were only 8 all month, down from 16 in April and 15 in May. Clearly I’m failing to encourage conversation and I don’t know how to turn that around.

The low comments count does confirm something for me, though. I switched the way I cross-link to posts here so that I use the full URLs for articles instead of the wp.me tinyURLs. The full URLs create trackback links and are regarded as comments that need approval from me, but they clearly don’t count as comments in the monthly totals. Since I like the trackback links — I fool myself into thinking people use them to learn about related subjects — I’ll stick with that. I had shifted so as not to confound my comment counts on these statistics pages.

According to Insights the most popular day for reading stuff was Thursday, with 16 percent of page views then. In April Sunday was the busiest day again with 16 percent of page views; in March it was 18 percent, on Tuesdays. I may give up on tracking this; obviously, each day is about equally likely to be the most popular. The most popular reading time was the hour of 6 pm, with 11 percent of page views coming before 7 pm. In April the same hour got 11 percent of page views again. In March it got 12 percent. I might experiment with the designated posting hour to find a more popular time, but obviously most people are going to read right after the thing is published.

So what was popular writing around here in April? I don’t want to say I knew this would happen, but one of the top five posts was one for which I wrote eleven words, and which I predicted to myself would be among the motnh’s top posts.

  1. How Many Grooves Are On A Record’s Side? People want simple answers to their questions.
  2. Reading the Comics, May 27, 2017: Panels Edition and I’m surprised this took the lead in the month’s Reading the Comics races, given how little time it had to do it.
  3. How Many Trapezoids I Can Draw as see above comment about people wanting answers
  4. Theorem Thursday: The Jordan Curve Theorem which I was thinking about at the mall on Thursday. Something or other made me think of it and how much I liked my description of how you prove the theorem.
  5. Dabbing and the Pythagorean Theorem which, really, I should do more like given how popular this kind of post is.

Now the roster of the 52 countries that sent me readers in May, and how many each of them did. Spoiler: the United States tops the list.

Country Views
United States 658
Canada 40
United Kingdom 38
Australia 28
Italy 23
India 19
Singapore 15
Slovenia 13
Turkey 13
Spain 12
South Africa 11
Austria 10
Switzerland 10
Denmark 7
Mexico 7
New Zealand 7
Puerto Rico 7
Philippines 6
Brazil 5
Oman 5
Russia 5
Sweden 5
Germany 4
Chile 3
France 3
Netherlands 3
Bangladesh 2
European Union 2
Indonesia 2
Pakistan 2
Peru 2
Argentina 1 (*)
Bahamas 1
Belgium 1
Colombia 1
Czech Republic 1
Finland 1 (**)
Iceland 1
Israel 1
Japan 1
Nigeria 1
Poland 1
Portugal 1 (**)
Saudi Arabia 1
Slovakia 1
Sri Lanka 1
St. Kitts & Nevis 1
Taiwan 1
US Virgin Islands 1
Ukraine 1
Uruguay 1
Venezuela 1

There had been 45 countries sending readers in April and 56 in March. European Union makes its big return.

There were 21 single-reader countries in May, way up from April’s 10 but still down from March’s 26. Argentina was a single-reader country in April also. Finland and Portugal have been single-reader countries for three months.

The month starts with 49,247 page views from some 22,212 logged distinct visitors since WordPress started telling us about those. WordPress tells me also there are 662 followers on WordPress, people who’ve gone and clicked the ‘Follow On WordPress’ button at the top right of the page in the hopes that I’ll follow back and increase their readership count. We all know how the game works.

And then what are popular search terms bringing folks here? What you’d expect given the most popular posts.

  • comics conversation
  • how many grooves are on typical record or cd ? how they are arranged?
  • origin is the gateway to your entire gaming universe.
  • peacetips football prediction
  • only yestetday dividing fractions
  • animated rolling dice 7

Plus some 146 unknown search terms. I’d be interested to know what those are too.

Well, thanks all of you for being around for this. I hope it’s a good month ahead.

You know, the arrangement of CDs is probably an interesting subject. I love that sort of technical-detail stuff too. It’s probably only slightly mathematics but I bet I can find a pretext to include it here. If someone’s interested.

What I Learned Doing The End 2016 Mathematics A To Z


The slightest thing I learned in the most recent set of essays is that I somehow slid from the descriptive “End Of 2016” title to the prescriptive “End 2016” identifier for the series. My unscientific survey suggests that most people would agree that we had too much 2016 and would have been better off doing without it altogether. So it goes.

The most important thing I learned about this is I have to pace things better. The A To Z essays have been creeping up in length. I didn’t keep close track of their lengths but I don’t think any of them came in under a thousand words. 1500 words was more common. And that’s fine enough, but at three per week, plus the Reading the Comics posts, that’s 5500 or 6000 words of mathematics alone. And that before getting to my humor blog, which even on a brief week will be a couple thousand words. I understand in retrospect why November and December felt like I didn’t have any time outside the word mines.

I’m not bothered by writing longer essays, mind. I can apparently go on at any length on any subject. And I like the words I’ve been using. My suspicion is between these A To Zs and the Theorem Thursdays over the summer I’ve found a mode for writing pop mathematics that works for me. It’s just a matter of how to balance workloads. The humor blog has gotten consistently better readership, for the obvious reasons (lately I’ve been trying to explain what the story comics are doing), but the mathematics more satisfying. If I should have to cut back on either it’d be the humor blog that gets the cut first.

Another little discovery is that I can swap out equations and formulas and the like for historical discussion. That’s probably a useful tradeoff for most of my readers. And it plays to my natural tendencies. It is very easy to imagine me having gone into history than into mathematics or science. It makes me aware how mediocre my knowledge of mathematics history is, though. For example, several times in the End 2016 A To Z the Crisis of Foundations came up, directly or in passing. But I’ve never read a proper history, not even a basic essay, about the Crisis. I don’t even know of a good description of this important-to-the-field event. Most mathematics history focuses around biographies of a few figures, often cribbed from Eric Temple Bell’s great but unreliable book, or a couple of famous specific incidents. (Newton versus Leibniz, the bridges of Köningsburg, Cantor’s insanity, Gödel’s citizenship exam.) Plus Bourbaki.

That’s not enough for someone taking the subject seriously, and I do mean to. So if someone has a suggestion for good histories of, for example, how Fourier series affected mathematicians’ understanding of what functions are, I’d love to know it. Maybe I should set that as a standing open request.

In looking over the subjects I wrote about I find a pretty strong mix of group theory and real analysis. Maybe that shouldn’t surprise. Those are two of the maybe three legs that form a mathematics major’s education. So anyone wanting to understand mathematicians would see this stuff and have questions about it. (There are more things mathematics majors learn, but there are a handful of things almost any mathematics major is sure to spend a year being baffled by.)

The third leg, I’d say, is differential equations. That’s a fantastic field, but it’s hard to describe without equations. Also pictures of what the equations imply. I’ve tended towards essays with few equations and pictures. That’s my laziness. Equations are best written in LaTeX, a typesetting tool that might as well be the standard for mathematicians writing papers and books. While WordPress supports a bit of LaTeX it isn’t quite effortless. That comes back around to balancing my workload. I do that a little better and I can explain solving first-order differential equations by integrating factors. (This is a prank. Nobody has ever needed to solve a first-order differential equation by integrating factors except for mathematics majors being taught the method.) But maybe I could make a go of that.

I’m not setting any particular date for the next A-To-Z, or similar, project. I need some time to recuperate. And maybe some time to think of other running projects that would be fun or educational for me. There’ll be something, though.

Reading the Comics, September 3, 2016: Summer Vacation Edition


I quite like doing Reading The Comics posts. I do feel sometimes like I’m repeating myself; how much is there to say about a comic where the student gives a snarky response to a story problem? Or where someone bakes a pie to talk about circles? And sometimes I worry that I’m slacking, since there’s not much to explain in what a spray of algebraic symbols mean, or would mean if they were perfectly rendered.

But I do like the feel of playing to an audience. Cartoonists call out topics and I do my best to say something interesting about them. It means I do not know whether I’ll be saying something about game theory or infinitely large sets or the history of numerals or the ability of birds to count in any given week. I have to be on top of a wide range of topics, or figure a way to get on top quickly. Some weeks it’ll be very busy; some weeks it’ll be quiet. It makes for fun, varied challenges.

This week Comic Strip Master Command sent me nothing. None of the comics I read, from Comics Kingdom, from Gocomics.com, and a couple of other miscellaneous things I read from long habit (like Joe Martin’s comics, or the Jumble puzzle), addressed any mathematics topics. I do not know the last time I had a subject drought like this. Certainly it’s been a while.

Mathematics has gotten a few cameos. Rick Stromoski’s Soup To Nutz almost got on point with a useful mnemonic for remembering which are odd and which are even numbers. Tony Rubino and Gary Markstein’s Daddy’s Home and Mark Tatulli’s Heart of the City both have “mathematics is so hard” as excuses for jokes. But that isn’t really about mathematics. Any subject people hated would do.

Comic strips work under an astounding set of constraints. They have to be incredibly compact, they have to carry their point in text and illustration, and the ones that appear in newspapers have to appeal to a broad audience in a way even television shows barely need to anymore. Given this, some stock jokes might well be essential. I couldn’t fault comic strip artists for using them. Similarly I don’t mind when a cartoonist uses a pile of scribbles for a mathematical concept, or even if they get an idea simplified to the point of being wrong. They’re amazing pieces of art to have at all. If I can make something educational of them that’s great, but that’s my adding to what they do.

So I’m just assuming Comic Strip Master Command wanted me to have a week off and that this doesn’t reflect any hard feelings between me and any cartoonists. We’ll know this time next week if there’s real trouble.

Finally, What I Learned Doing Theorem Thursdays


Here’s the index to the stuff I posted on them.

The biggest thing I learned from my Theorem Thursdays project was: don’t do this for Thursdays. The appeal is obvious. If things were a little different I’d have no problem with Thursdays. But besides being a slightly-read pop-mathematics blogger I’m also a slightly-read humor blogger. And I try to have a major piece, about seven hundred words that are more than simply commentary on how a comic strip’s gone wrong, ready for Thursday evenings my time.

That’s all my doing. It’s a relic of my thinking that the humor blog should run at least a bit like a professional syndicated columnist’s, with a fixed deadline for bigger pieces. While I should be writing more ahead of deadline than this, what I would do is get to Wednesday realizing I have two major things to write in a day. I’d have an idea for one of them, the mathematics thing, since I would pick a topic the previous Thursday. And once I’ve picked an idea the rest is easy. (Part of the process of picking is realizing whether there’s any way to make seven hundred words about something.) But that’s a lot of work for something that’s supposed to be recreational. Plus Wednesdays are, two weeks a month, a pinball league night.

So Thursday is right out, unless I get better about having first drafts of stuff done Monday night. So Thursday is right out. This has problems for future appearances of the gimmick. The alliterative pull is strong. The only remotely compelling alternative is Theorems on the Threes, maybe one the 3rd, 13th, and 23rd of the month. That leaves the 30th and 31st unaccounted for, and room for a good squabble about whether they count in an “on the threes” scheme.

There’s a lot of good stuff to say about the project otherwise. The biggest is that I had fun with it. The Theorem Thursday pieces sprawled into for-me extreme lengths, two to three thousand words. I had space to be chatty and silly and autobiographic in ways that even the A To Z projects don’t allow. Somehow those essays didn’t get nearly as long, possibly because I was writing three of them a week. I didn’t actually write fewer things in July than I did in, say, May. But it was fewer kinds of things; postings were mostly Theorem Thursdays and Reading the Comics posts. Still, overall readership didn’t drop and people seemed to quite like what I did write. It may be fewer but longer-form essays are the way I should go.

Also I found that people like stranger stuff. There’s an understandable temptation in doing pop-mathematics to look for topics that are automatically more accessible. People are afraid enough of mathematics. They have good reason to be terrified of some topic even mathematics majors don’t encounter until their fourth year. So there’s a drive to simpler topics, or topics that have fewer prerequisites, and that’s why every mathematics blogger has an essay about how the square root of two is irrational and how there’s different sizes to infinitely large sets. And that’s produced some excellent writing about topics like those, which are great topics. They have got the power to inspire awe without requiring any warming up. That’s special.

But it also means they’re hard to write anything new or compelling about if you’re like me, and in somewhere like the second hundred billion of mathematics bloggers. I can’t write anything better than what’s already gone about that. Liouville’s Theorem? That’s something I can be a good writer about. With that, I can have a blog personality. It’s like having a real personality but less work.

As I did with the Leap Day 2016 A To Z project, I threw the topics open to requests. I didn’t get many. Possibly the form gave too much freedom. Picking something to match a letter, as in the A to Z, gives a useful structure for choosing something specific. Pick a theorem from anywhere in mathematics? Something from algebra class? Something mentioned in a news report about a major breakthrough the reporter doesn’t understand but had an interesting picture? Something that you overheard the name of once without any context? How should people know what the scope of it is, before they’ve even seen a sample? And possibly people don’t actually remember the names of theorems unless they stay in mathematics or mathematics-related fields. Those folks hardly need explained theorems with names they remember. This is a hard problem to imagine people having, but it’s something I must consider.

So this is what I take away from the two-month project. There’s a lot of fun digging into the higher-level mathematics stuff. There’s an interest in it, even if it means I write longer and therefore fewer pieces. Take requests, but have a structure for taking them that makes it easy to tell what requests should look like. Definitely don’t commit to doing big things for Thursday, not without a better scheme for getting the humor blog pieces done. Free up some time Wednesday and don’t put up an awful score on Demolition Man like I did last time again. Seriously, I had a better score on The Simpsons Pinball Party than I did on Demolition Man and while you personally might not find this amusing there’s at least two people really into pinball who know how hilarious that is. (The games have wildly different point scorings. This like having a basketball score be lower than a hockey score.) That isn’t so important to mathematics blogging but it’s a good lesson to remember anyway.

How July 2016 Treated My Mathematics Blog


I’m not unhappy. Of course not; I can find something cheery to say about whatever my readership in a given month was like. But for a month in which I spent nearly two weeks away from my normal Internet routines of visiting blog friends and belatedly answering comments and the like it wasn’t bad at all.

Readership Numbers:

So there were 1,057 page views in July. That’s down from June’s 1,099, but only a touch, and it’s up from May’s 981. And it’s above a thousand which makes me feel secure about being at least tolerated in these parts. The number of unique visitors was down to 585 from June’s 598 and May’s 627. But the June-to-July drop I can’t imagine is significant.

The number of likes rose to 177, from June’s 155 and May’s 133. I can’t hide it: I’m hoping for 199 in August and I don’t know where it’ll go from there. Comments were down a touch to 33, from June’s 39. But some of that is my failing to respond to other people because I was away. My own comments should count, shouldn’t they?

I am considering making one of those big changes and switching away from the theme — “P2 Classic” — that I have. I like its look, especially that it lets comments appear on the front page around here. But I’ve realized that the theme is a disaster on mobile devices. I don’t want to be needlessly difficult.

At the top of my WordPress theme is a box saying, 'Hi, Joseph. Whatcha up to?' encouraging me to make quick little informal posts which I never ever do.
I don’t know, worrying about what I should post? I’m sorry, I can’t use a slangy informal posting mechanism like this. I’m far too pompous. Also you have no idea how disorienting it is to have this image on my page.

Also while it’s got a nice friendly “Whatcha up to?” panel up top for me, to quickly add a post, I have never used it except when I wanted to search for something and the cursor was in the wrong field. If someone knows of an updated P2 Classic that you can read on a hand phone please let me know. I’d be glad for it.

Popular Posts:

To posts! The most popular stuff around here in July was a fair split between Reading the Comics posts and Theorem Thursday posts, plus a note that something I started back in May would too be returning. I hope to get to that soon again, maybe this week. That’s also comforting. They’re the things I put the most effort into and I’m glad people like them and don’t find much terribly wrong about them. The top five articles in July according to WordPress were:

Listing Countries:

What countries like me? … You know what? Bullet lists are so reportedly popular I’ll just try listing everybody and we’ll see what that does for drumming up interest. Readership by country, per WordPress’s data, were:

Country Readers
United States 616
Canada 57
India 52
United Kingdom 36
Philippines 30
Australia 27
Germany 26
Slovenia 22
Singapore 20
Austria 15
Brazil 15
Spain 13
Thailand 11
Pakistan 10
Puerto Rico 7
Indonesia 6
Ireland 6
Italy 6
Croatia 5
France 5
Hong Kong SAR China 5
New Zealand 5
Sweden 5
China 4
Mexico 4
South Korea 4
Finland 3
Greece 3
Portugal 3
Russia 3
Venezuela 3
Argentina 2
Czech Republic 2
European Union 2
Jordan 2
Netherlands 2
Norway 2
South Africa 2
United Arab Emirates 2
Belgium 1
Chile 1
Denmark 1
Dominican Republic 1
Ecuador 1
Latvia 1
Lithuania 1
Malaysia 1
Oman 1
Saudi Arabia 1
Serbia 1
Tunisia 1
Turkey 1
Ukraine 1 (*)

Ukraine is the only country to have been a single-reader country in June too. This is the nearest clean sweep I’ve noticed. The European Union reader, after seven months being alone, found a friend too. I hope they get along.

Search Term Non-Poetry:

Whew. It’s back.

  • origin is the gateway to your entire gaming universe.
  • what is the average number of grooves on one side of an lp record (if “1” doesn’t satisfy you)
  • arithmetic sequences and series joke 48 (the punch line I’d heard was “why did they laugh so much at 15,268?” “Well, you see, we’d never heard that one before!”)
  • example of convergent boundaries komiks stris (honestly now tempted to commission a comic strip artist just to do something about convergent boundaries.)
  • comics about arithmetic sequence / arithmetic sequence comics (probably I should also commission one about sequences)

Counting Readers:

If I have this right August started with the blog having had 39,394 page views — curse that leap second! — and 16,083 unique viewers. (Because the leap second would give time for one more page view, keeping me from 39,393. If there were a leap second, and if it were at the end of July instead of the end of June. Trust me, if you share a long sequence of assumptions with me then it’s funny.)

WordPress reports me as starting with 610 WordPress.com followers, which feels way up from the start of July’s 597. If you want to join me as a WordPress.com follower there ought to be a button in the upper-right corner, a bit below and to the right of my blog name and above the “Or Follow By Way Of RSS” tag. There’s also a Follow Blog Via Email option and don’t think it doesn’t bother me there’s no dash in E-mail there. More reasons to change the theme I suppose.

I’d wondered last month about WordPress reporting the most popular dates and times around here. So that’s why I moved my default posting time from 11 am Eastern to 2 pm Eastern. But just as in July the most popular day is Sunday (22 percent of page views). Comics posts I suppose. The most popular hour remains 3:00 pm (9 percent of page views). It kind of suggests the time of posting doesn’t matter to people. We’ll see, as I start trying 6 am or if I try something really wild like eleventy-q pm.

See you, I expect, tomorrow with comic strips.

What Did I Post On Theorem Thursdays?


Hi again folks. I don’t want you to think I forgot about my little blog here. I’ve just been off for a pretty major competitive-pinball event the past week and that and a visit to the Kennywood amusement park slurped up all my writing time. Should be recovered soon enough.

I’ll be back to posting original stuff soon enough, and to posting links to other people’s stuff. But for now I wanted to gather links to all the Theorem Thursday now that the project’s safely at its pre-announced conclusion. I’ve have thoughts about what it all meant soon, too.

Over June and July I put up rather extended posts about:

I do figure on returning to these long-form explanations of theorems, so that Mean Value Theorem and Fixed Point Theorem stuff shouldn’t be left dangling forever. I don’t know just when I will, though. I’ll discuss why that is in my “what-did-I-learn” post, when I have the chance.

Bourbaki and How To Write Numbers, A Trifle


So my attempt at keeping the Reading the Comics posts to Sunday has crashed and burned again. This time for a good reason. As you might have read between the lines on my humor blog, I spent the past week on holiday and just didn’t have time to write stuff. I barely had time to read my comics. I’ll get around to it this week.

In the meanwhile then I’d like to point people to the MathsByAGirl blog. The blog recently had an essay on Nicolas Bourbaki, who’s among the most famous mathematicians of the 20th century. Bourbaki is also someone with a tremendous and controversial legacy, one that I expect to touch on as I catch up on last week’s comics. If you don’t know the secret of Bourbaki then do go over and learn it. If you do, well, go over and read anyway. The author’s wondering whether to write more about Bourbaki’s mathematics and while I’m all in favor of that more people should say.

And as I promised a trifle, let me point to something from my own humor blog. How To Write Out Numbers is an older trifle based on everyone’s love for copy-editing standards. I had forgotten I wrote it before digging it up for a week of self-glorifying posts last week. I hope folks around here like it too.

Oh, one more thing: it’s the anniversary of the publishing of an admirable but incorrect proof of the four-color map theorem. It would take another century to get right. As I said Thursday, the five-color map theorem is easy. it’s that last color that’s hard.

Vacations are grand but there is always that comfortable day or two once you’re back home.

What I Learned Doing The Leap Day 2016 Mathematics A To Z


The biggest thing I learned in the recently concluded mathematics glossary is that continued fractions have enthusiasts. I hadn’t intended to cause controversy when I claimed they weren’t much used anymore. The most I have grounds to say is that the United States educational process as I experienced it doesn’t use them for more than a few special purposes. There is a general lesson there. While my experience may be typical, that doesn’t mean everyone’s is like it. There is a mystery to learn from in that.

The next big thing I learned was the Kullbach-Leibler Divergence. I’m glad to know it now. And I would not have known it, I imagine, if it weren’t for my trying something novel and getting a fine result from it. That was throwing open the A To Z glossary to requests from readers. At least half the terms were ones that someone reading my original call had asked for.

And that was thrilling. It gave me a greater feeling that I was communicating with specific people than most of the things that I’ve written, is the biggest point. I understand that I have readers, and occasionally chat with some. This was a rare chance to feel engaged, though.

And getting asked things I hadn’t thought of, or in some cases hadn’t heard of, was great. It foiled the idea of two months’ worth of easy postings, but it made me look up and learn and think about a variety of things. And also to re-think them. My first drafts of the Dedekind Domain and the Kullbach-Leibler divergence essays were completely scrapped, and the Jacobian made it through only with a lot of rewriting. I’ve been inclined to write with few equations and even fewer drawings around here. Part of that’s to be less intimidating. Part of that’s because of laziness. Some stuff is wonderfully easy to express in a sketch, but transferring that to a digital form is the heavy work of getting out the scanner and plugging it in. Or drawing from scratch on my iPad. Cleaning it up is even more work. So better to spend a thousand extra words on the setup.

But that seemed to work! I’m especially surprised that the Jacobian and the Lagrangian essays seemed to make sense without pictures or equations. Homomorphisms and isomorphisms were only a bit less surprising. I feel like I’ve been writing better thanks to this.

I do figure on another A To Z for sometime this summer. Perhaps I should open nominations already, and with a better-organized scheme for knocking out letters. Some people were disappointed (I suppose) by picking letters that had already got assigned. And I could certainly use time and help finding more x- and y-words. Q isn’t an easy one either.

Some More Mathematics Stuff To Read


And some more reasy reading, because, why not? First up is a new Twitter account from Chris Lusto (Lustomatical), a high school teacher with interest in Mathematical Twitter. He’s constructed the Math-Twitter-Blog-o-Sphere Bot, which retweets postings of mathematics blogs. They’re drawn from his blogroll, and a set of posts comes up a couple of times per day. (I believe he’s running the bot manually, in case it starts malfunctioning, for now.) It could be a useful way to find something interesting to read, or if you’ve got your own mathematics blog, a way to let other folks know you want to be found interesting.

Also possibly of interest is Gregory Taylor’s Any ~Qs comic strip blog. Taylor is a high school teacher and an amateur cartoonist. He’s chosen the difficult task of drawing a comic about “math equations as people”. It’s always hard to do a narrowly focused web comic. You can see Taylor working out the challenges of writing and drawing so that both story and teaching purposes are clear. I would imagine, for example, people to giggle at least at “tangent pants” even if they’re not sure what a domain restriction would have to do with anything, or even necessarily mean. But it is neat to see someone trying to go beyond anthropomorphized numerals in a web comic. And, after all, Math With Bad Drawings has got the hang of it.

Finally, an article published in Notices of the American Mathematical Society, and which I found by some reference now lost to me. The essay, “Knots in the Nursery:(Cats) Cradle Song of James Clerk Maxwell”, is by Professor Daniel S Silver. It’s about the origins of knot theory, and particularly of a poem composed by James Clerk Maxwell. Knot theory was pioneered in the late 19th century by Peter Guthrie Tait. Maxwell is the fellow behind Maxwell’s Equations, the description of how electricity and magnetism propagate and affect one another. Maxwell’s also renowned in statistical mechanics circles for explaining, among other things, how the rings of Saturn could work. And it turns out he could write nice bits of doggerel, with references Silver usefully decodes. It’s worth reading for the mathematical-history content.

How 2015 Treated My Mathematics Blog


Oh yeah, I also got one of these. WordPress put together a review of what all went on around here last year. The most startling thing to me is that I had 188 posts over the course of the year. A lot of that is thanks to the A To Z project, which gave me something to post each day for 31 days in a row. If I’d been thinking just a tiny bit harder I’d have come up with two more posts and made a clean sweep of June.

The unit of comparison for my readership this year was the Sydney Opera House. That’s a great comparison because everybody thinks they know how big an opera house is. It reminds me of a bit in Carl Sagan and and Ann Druyan’s Comet in which they compare the speed of an Oort cloud comet puttering around the sun to the speed of a biplane. We may have only a foggy idea how fast that is (I guess maybe a hundred miles per hour?) but it sounds nice and homey.

How December 2015 Treated My Mathematics Blog


I had expected December 2015 would see a decline in my readership. I didn’t have the spillover effect of my humor blog getting so much Apartment 3-G curiosity. The readership did drop, although not quite alarmingly. So let’s review that.

According to WordPress’s statistics page there were 954 views of these parts in December. That’s well down from November’s 3-G boosted 1,215. But it’s up from the 733 in October and 708 in September, and it’s the fifth highest of the past year. The number of unique visitors dropped, from 519 down to 449. That’s also up from October’s 405 and September’s 381. And it’s the fourth-highest of the past twelve months. There were fifteen posts in the month again, although I admit not all of them were really deep pieces. Some were just nagging people to read other things I’d written.

The reader-engagement data was up a tiny bit. The mathematics blog got back up to 245 likes in December, up from November’s 220 and October’s 244. It’s nowhere near the peaks of June (518), but June was the midst of the Summer A To Z glossary and that drew a lot of steady readers in. I should do another one. The number of comments rose to 56, up from November’s 37 and October’s 47. Again, that’s nowhere near June and July’s highs (114 and 100). But again, I didn’t have anything themed nearly so tightly going on.

I think that I could have had slightly better readership, and engagement, if I hadn’t gotten overwhelmed the last third of the month. I just stopped being able to go pay calls on other blogs, and leave comments and likes and whatnot to other writers. So I couldn’t reasonably expect folks to stop in here either. The weekly count of views and visitors certainly drops around then. But then most of the rest of western civilization also had a busy time in late December. But the holidays have mostly wrapped up, and I should be back to normal social-Internet stuff soon. I’d like to think I’ll be, anyway.

The most popular stuff around here — well, most of the popular articles were Reading the Comics series articles. I’ll just lump those together into one category if that’s all right by you. But the most popular stuff would be:

The countries sending me the most readers were nearly the usual set: the United States with 641 pages views, the United Kingdom with 50, the Canada with 45, the Germany with 27, and the India with 21. That’s my best India showing on record, I believe. Singapore sent me five page views.

Single-reader countries this time were Bahrain, Bangladesh, Belgium, Czech Republic, the European Union, Indonesia, Ireland, Lithuania, Nigeria, and Taiwan. I still don’t understand what the European Union is doing listed there. But Belgium and Nigeria are on three-month streaks there. Nobody’s on a four-month streak.

And among the interesting search terms to come up:

  • peppermint patty couldn’t solve the following math problems (most of them, really)
  • snoring jokes (my love would tell you my snoring is not a joke; it’s enough to rattle this house apart)
  • why are wizard of id classics being reprinted (well, they’re pretty solidly funny)
  • comic strip math problem solving algebra rae (I don’t know what the ‘rae’ is and assume it’s a cry of delight)
  • origin is the gateway to your entire gaming universe. (I think they’re just trying to creep my out now)
  • 22 decmber mathematics day topics (I believe that’s India’s national mathematics day. I don’t think I have any particularly interesting content for it, but I should maybe work on that)

I start the month of January with 553 total WordPress followers. And I start with 31,253 total page views and 11,721 total unique visitors as WordPress figures these things.

Reading the Comics, November 21, 2015: Communication Edition


And then three days pass and I have enough comic strips for another essay. That’s fine by me, really. I picked this edition’s name because there’s a comic strip that actually touches on information theory, and another that’s about a much-needed mathematical symbol, and another about the ways we represent numbers. That’s enough grounds for me to use the title.

Samson’s Dark Side Of The Horse for the 19th of November looks like this week’s bid for an anthropomorphic numerals joke. I suppose it’s actually numeral cosplay instead. I’m amused, anyway.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 19th of November makes a patent-law joke out of the invention of zero. It’s also an amusing joke. It may be misplaced, though. The origins of zero as a concept is hard enough to trace. We can at least trace the symbol zero. In Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers, Amir D Aczel traces out not just the (currently understood) history of Arabic numerals, but some of how the history of that history has evolved, and finally traces down the oldest known example of a written (well, carved) zero.

Tony Cochrane’s Agnes for the 20th of November is at heart just a joke about a student’s apocalyptically bad grades. It contains an interesting punch line, though, in Agnes’s statement that “math people are dreadful spellers”. I haven’t heard that before. It might be a joke about algebra introducing letters into numbers. But it does seem to me there’s a supposition that mathematics people aren’t very good writers or speakers. I do remember back as an undergraduate other people on the student newspaper being surprised I could write despite majoring in physics and mathematics. That may reflect people remembering bad experiences of sitting in class with no idea what the instructor was going on about. It’s easy to go from “I don’t understand this mathematics class” to “I don’t understand mathematics people”.

Steve Sicula’s Home and Away for the 20th of November is about using gambling as a way to teach mathematics. So it would be a late entry for the recent Gambling Edition of the Reading The Comics posts. Although this strip is a rerun from the 15th of August, 2008, so it’s actually an extremely early entry.

Ruben Bolling’s Tom The Dancing Bug for the 20th of November is a Super-Fun-Pak Comix installment. And for a wonder it hasn’t got a Chaos Butterfly sequence. Under the Guy Walks Into A Bar label is a joke about a horse doing arithmetic that itself swings into a base-ten joke. In this case it’s suggested the horse would count in base four, and I suppose that’s plausible enough. The joke depends on the horse pronouncing a base four “10” as “ten”, when the number is actually “four”. But the lure of the digits is very hard to resist, and saying “four” suggests the numeral “4” whatever the base is supposed to be.

Mark Leiknes’s Cow and Boy for the 21st of November is a rerun from the 9th of August, 2008. It mentions the holographic principle, which is a neat concept. The principle’s explained all right in the comic. The idea was first developed in the late 1970s, following the study of black hole thermodynamics. Black holes are fascinating because the mathematics of them suggest they have a temperature, and an entropy, and even information which can pass into and out of them. This study implied that information about the three-dimensional volume of the black hole was contained entirely in the two-dimensional surface, though. From here things get complicated, though, and I’m going to shy away from describing the whole thing because I’m not sure I can do it competently. It is an amazing thing that information about a volume can be encoded in the surface, though, and vice-versa. And it is astounding that we can imagine a logically consistent organization of the universe that has a structure completely unlike the one our senses suggest. It’s a lasting and hard-to-dismiss philosophical question. How much of the way the world appears to be structured is the result of our minds, our senses, imposing that structure on it? How much of it is because the world is ‘really’ like that? (And does ‘really’ mean anything that isn’t trivial, then?)

I should make clear that while we can imagine it, we haven’t been able to prove that this holographic universe is a valid organization. Explaining gravity in quantum mechanics terms is a difficult point, as it often is.

Dave Blazek’s Loose Parts for the 21st of November is a two- versus three-dimensions joke. The three-dimension figure on the right is a standard way of drawing x-, y-, and z-axes, organized in an ‘isometric’ view. That’s one of the common ways of drawing three-dimensional figures on a two-dimensional surface. The two-dimension figure on the left is a quirky representation, but it’s probably unavoidable as a way to make the whole panel read cleanly. Usually when the axes are drawn isometrically, the x- and y-axes are the lower ones, with the z-axis the one pointing vertically upward. That is, they’re the ones in the floor of the room. So the typical two-dimensional figure would be the lower axes.

How October Treated My Mathematics Blog


So, that wasn’t as bad as September. Last month I began my review of readership with the sad news I’d lost about a fifth of my readers from August. I haven’t got them all back yet. But the number of page views did rise to 733 in October. It’s just a bit over September’s 708, but that’s an improvement. That’s a good trend. But I do notice there was a little readership rise between July and August, and then the bottom dropped out. And 733 is still fewer than the number of readers my humor blog got from just people trying to figure out what the heck is wrong with the comic strip Apartment 3-G. (Nothing is happening in Apartment 3-G and the rumor is the strip’s been cancelled.)

The number of unique visitors rose, from 381 to 405. That’s only the eighth-highest result of the past twelve months. But it is only a little below the twelve-month average. (If you’d like to know: the 12-month mean number of visitors was 419.55, and standard deviation 39.715, so there you go. The median was 415.)

The number of likes rose again, from September’s absolutely unpopular 188 to a tolerable 244. That’s a little below the twelve-month mean (266.91) and twelve-month median (259), although given the standard deviation is 107.71 that’s hardly anything off the average.

The number of comments rose to 47, which looks good compared to September’s 25, but is nothing compared to the glory days of August and its 95 and the like. That’s farther below the twelve-month mean of 68.9 and median of 64 (standard deviation of 30), but, eh. I’ll take signs of hope. I maybe need to publicize more of my better material, more often.

Countries sending me readers have been the United States with 387 page views, the United Kingdom with 55, the Canada with 48, the Austria with 33, and the Philippines with 25. India only offered fourteen page views; Singapore, nine. The European Union got listed with five.

Single-reader countries for October were Belgium, Czech Republic, Georgia, Lebanon, Lithuania, Nigeria, Norway, Pakistan, Paraguay, Qatar, Saudi Arabia, Switzerland, Taiwan, Thailand, Turkey, and Uruguay. Repeats from September on that list are Saudia Arabia and Uruguay. None of the countries are on a three-month streak.

Among the most popular posts the past month were, of course, Reading the Comics surveys. To avoid flooding the list of what’s popular I’ll just list the category for Comic Strips instead.

  1. Reading the Comics, an ongoing series.
  2. How Many Trapezoids I Can Draw which hasn’t made the top-five or top-ten in a couple months. Curious.
  3. The Set Tour, Part 6: One Big One Plus Some Rubble and I’m glad to see this series getting a little bit of love. I’m having more fun with this than I’ve had with anything since the Summer A To Z.
  4. Phase Equilibria and the usefulness of μ, a reblogged post that’s part of my attempt to get people to pay attention to statistical mechanics.
  5. The Kind Of Book That Makes Me Want To Refocus On Logic, talking about a book I liked. I should probably talk about books I like more.

The search terms were mostly the usual bunch: origin is the gateway to your entire gaming universe and otto soglow little king and how fast is earth spinning. Delighting me, although I haven’t got anything to answer it exactly, was +how to start a pinball league. I’ve picked up a couple things about how they work, but that’s kind of outside the mathematics field proper.

The Set Tour, Part 5: C^n


The next piece in this set tour is a hybrid. It mixes properties of the last two sets. And I’ll own up now that while it’s a set that gets used a lot, it’s one that gets used a lot in just some corners of mathematics. It’s got a bit of that “Internet fame”. In particular circles it’s well-known; venture outside those circles even a little, and it’s not. But it leads us into other, useful places.

Cn

C here is the set of complex-valued numbers. We may have feared them once, but now they’re friends, or at least something we can work peacefully with. n here is some counting number, just as it is with Rn. n could be one or two or forty or a hundred billion. It’ll be whatever fits the problem we’re doing, if we need to pin down its value at all.

The reference to Rn, another friend, probably tipped you off to the rest. The items in Cn are n-tuples, ordered sets of some number n of numbers. Each of those numbers is itself a complex-valued number, something from C. Cn gets typeset in bold, and often with that extra vertical stroke on the left side of the C arc. It’s handwritten that way, too.

As with Rn we can add together things in Cn. Suppose that we are in C2 so that I don’t have to type too much. Suppose the first number is (2 + i, -3 – 3*i) and the second number is (6 – 2*i, 2 + 9*i). There could be fractions or irrational numbers in the real and imaginary components, but I don’t want to type that much. The work is the same. Anyway, the sum will be another number in Cn. The first term in that sum will be the sum of the first term in the first number, 2 + i, and the first term in the second number, 6 – 2*i. That in turn will be the sum of the real and of the imaginary components, so, 2 + 6 + i – 2*i, or 8 – i all told. The second term of the sum will be the second term of the first number, -3 – 3*i, and the second term of the second number, 2 + 9*i, which will be -3 – 3*i + 2 + 9*i or, all told, -1 + 6*i. The sum is the n-tuple (8 – i, -1 + 6*i).

And also as with Rn there really isn’t multiplying of one term of Cn by another. Generally, we can’t do this in any useful way. We can multiply something in Cn by a scalar, a single real — or, why not, complex-valued — number, though.

So let’s start out with (8 – i, -1 + 6*i), a number in C2. And then pick a scalar, say, 2 + 2*i. It doesn’t have to be complex-valued, but, why not? The product of this scalar and this term will be another number in C2. Its first term will the scalar, 2 + 2*i, multiplied by the first term in it, 8 – i. That’s (2 + 2*i) * (8 – i), or 2*8 – 2*i + 16*i – 2*i*i, or 2*8 – 2*i + 16*i + 2, or 18 + 14*i. And then its second term will be the scalar 2 + 2*i multiplied by the second term, -1 + 6*i. That’s (2 + 2*i)*(-1 + 6*i), or 2*(-1) + 2*6*i -2*i + 2*6*i*i. And that’s -2 + 12*i – 2*i -12, or -14 + 10*i. So the product is (18 + 14*i, -14 + 10*i).

So as with Rn, Cn creates a “vector space”. These spaces are useful in complex analysis. They’re also useful in the study of affine geometry, a corner of geometry that I’m sad to admit falls outside what I studied. I have tried reading up on them on my own, and I run aground each time. I understand the basic principles but never quite grasp why they are interesting. That’s my own failing, of course, and I’d be glad for a pointer that explained in ways I understood why they’re so neat.

I do understand some of what’s neat about them: affine geometry tells us what we can know about shapes without using the concept of “distance”. When you discover that we can know anything about shapes without the idea of “distance” your imagination should be fired. Mine is, too. I just haven’t followed from that to feel comfortable with the terminology and symbols of the field.

You could, if you like, think of Cn as being a specially-delineated version of R2*n. This is just as you can see a complex number as an ordered pair of real numbers. But sometimes information is usefully thought of as a single, complex-valued number. And there is a value in introducing the idea of ordered sets of things that are not real numbers. We will see the concept again.


Also, the heck did I write an 800-word essay about the family of sets of complex-valued n-tuples and have Hemingway Editor judge it to be at the “Grade 3” reading level? I rarely get down to “Grade 6” when I do a Reading the Comics post explaining how Andertoons did a snarky-word-problem-answers panel. That’s got to be a temporary glitch.

How September 2015 Treated My Mathematics Blog


So, well, that was disappointing. My readership was off in September. The month saw the fewest page views since November of 2014. The number of unique visitors was only back to about what it was in June of 2015, though, which is less alarming. Still, I can’t fault WordPress’s suspect statistics, not without inconsistency. My humor blog saw its highest readership on record and if I accept that, I have to accept the other.

The humor blog readership I understand. I started explaining what the heck was going on in Apartment 3-G and it’s been really baffling for a long while now because nothing has been going on since February, maybe March at the latest. You can see how that attracts eager readers.

But here’s the sad numbers count: there were 708 views on the mathematics blog in September, down from 909 in August and 863 in July. And well done from June’s record of 1,051.

The number of unique visitors was 381, down from August’s 506 and July’s 415. June had only 367 unique visitors, but that was part of the big Summer 2015 Mathematics A To Z project. That’s probably why more people were reading, too.

I can’t even point to signs of reader engagement. The number of likes was down to 188, compared to August’s 282 and July’s 381. Extrapolating, November should see me get a negative number of likes. Comments are even worse: after three months in a row of about a hundred comments each there were only 25 in September.

So as I say, disappointing. I can think of a few things I did differently in September. The most obvious is that I didn’t have the time I needed to go around to other mathematics blogs and pay visits. I can’t fault people not coming around to me when I don’t come around to them. And I can admit that September didn’t have the richest diversity of postings. A lot of it was Reading the Comics posts, which are fun but I admit also prone to sameness. On the other hand, those are the most popular posts too. I haven’t found a new project that engages my imagination the way the A To Z did, although I think the Set Tour has promise.

I would also put some blame on WordPress’s Publicize, which they keep making worse and worse. See, Publicize announces new posts to Twitter and whatever other social media networks you have linked to it. And in the old days of, like, May, it just worked. By default it posted the name of the article and a wp.me shortened link. If you wanted to customize this you could hit an ‘edit’ button and the article name and wp.me shortened link were there at the start, and it was easy to add a short sentence to tell people what’s happening.

But in June they stopped with the wp.me shortened links; instead it shows as much of the full URL as fits in the Twitter 140-character limit after whatever text you enter. And last month they made it worse. It’ll give the article name as a suggested default publicity post, but you have to copy-paste or retype the name to get even that. The message WordPress is sending is, clearly, ‘stop using Publicize’, although what they have as a substitue is unclear.

I suspect what they mean for us to do is use the new modernized article-entry page. The trouble is, the page is awful. It might be salvageable, or something I could get used to, in time. But it’s also this very watery and Ajax-dependent thing that assumes you have fast, reliable Internet. And I don’t. I have AT&T, which has no interest in providing high-speed Internet to my neighborhood and possibly my city. They aren’t even willing to pretend they mean to bring it in anytime soon. We’d dump them happily but the only alternative right now is Kabletown and goodness knows that’s a recipe for disaster. I suspect AT&T and Kabletown have decided not to compete for the Lansing, Michigan, market and we’re stuck between awful we know and awful we know we’d flee to.

Anyway, my suspicion is that the equivalent of Publicize for the newfangled WordPress add-a-post page works better. But that is blaming WordPress for my own laziness; there’s no reason I couldn’t put in the post and wp.me link and a clear #math tag so people know what they’re getting into. It just seemed like too much work. I suppose for a week or two I should try changing just that and see if there’s an appreciable difference.

I’m sorry to turn all this into a round of crankiness, especially when I can think of easy things I should be doing to get better results. I’m just sulking. It’ll pass.

My Mathematics Blog’s July 2015 Statistics, Plus Their Implications


Start of the month, so, it’s time to review my readership numbers. July was not as busy a month as June. I expected that. With the wrap-up of the A To Z glossary there were fewer posts in July than in June, and one can expect people to come to read posts. There weren’t that many fewer — 24 posts in July, versus 28 in June — but every bit counts.

So the number of page views dropped from 1,051 in June to 863 in July. The number of unique visitors rose, though, from 367 up to 415. The 415 visitors equals that in May. Is this a matter of just fewer posts? Perhaps. The number of views per posting dropped from 37.5 in June to 36.0 in July; that seems near enough identical. The number of unique visitors per posting rose from 13.1 in June to 17.3 in July, though.

What makes this interesting is these ratios for May. That month had 936 views, 415 visitors, and a scant twelve posts published. That implies 78 views per post, and 34.6 viewers per post. This seems to suggest the best readership-per-effort involvement is not necessarily daily.

The number of Likes received was down, too, from 518 in June to 382 in July. That’s my second-best on record, though. The number of likes per posting dropped from 18.5 to 16.0, which still seems probably about the same. The May ratio was 21.6 likes per posting. The number of comments dropped insignificantly, from 114 in June to 100 in July. The comments-per-posting rose from 4.1 to 4.2, no way a meaningful change. Though, still, in May, with 84 comments and twelve posts, I had a comments-per-posting ratio of 7.

This might suggest I’m best off posting every other day, or maybe even every third day, rather than going for a daily or near-daily schedule.

The greatest number of visitors came as ever from the United States, with 502. Canada sent the next-greatest number, 61 viewers. The United Kingdom came in third at 41. Italy was fourth, at 39 views, and the Philippines 37. I’m glad to have these readers, though I don’t know what’s got me interested in Italy and the Philippines. India sent me 14 viewers, down from June’s 15. Nobody’s listed as being from the European Union, although individual countries within it have a bunch of readers.

Single-reader countries for July were: Albania, Chile, Czech Republic, Denmark, Egypt, Estonia, Greece, Mexico, Nepal, Norway, Portugal, Serbia, and the United Arab Emirates. Czech Republic is the only country that was also a single-viewer country last month.

The most popular posts over July were, if we can trust WordPress’s statistics:

  1. Reading the Comics, April 20, 2015: History of Mathematics Edition
  2. Reading the Comics, July 4, 2015: Symbolic Curiosities Edition
  3. Reading the Comics, July 24, 2015: All The Popular Topics Are Here Edition
  4. Reading the Comics, July 19, 2015: Rerun Comics Edition
  5. A Summer 2015 Mathematics A To Z: tensor
  6. Lewis Carroll Tries Changing The Way You See Trigonometry
  7. A Summer 2015 Mathematics A To Z: ring

There’s no search term poetry again, alas, although a few things came up. Among them:

  • bloom county 2015 (something I don’t think I ever mentioned, but six people came here looking for it)
  • susan from between friends (Between Friends is one of the comic strips regularly featured around here)
  • origin is the gateway to your entire gaming universe.
  • comics strip for sum of difference of two binomials (are there any?)
  • chain rule card sort (not sure what this means, but I’m intrigued)
  • math statistics of the 80s (again, not sure what this means)

I start the month with a total of 26,734 views, and alongside that 1,946 comments. I expect the 2,000th comment to come sometime in August. I’m curious what it’ll be.

And then to remind people to read my blog, in a post on my blog. There’s this “Follow Blog via Email” link that, at least in the P2 Classic theme I’m using right now, is over on the upper right of the page. You can do that. If you have an RSS reader, https://nebusresearch.wordpress.com/feed/ will give you posts. https://nebusresearch.wordpress.com/comments/feed/ will give you comments, although that’s got to be a baffling feed. And my regular old Twitter account is @Nebusj. Thanks for existing and all that.

What I Learned Doing The A To Z Project


So now I’ve had the chance to rest a little and recover from the Summer 2015 Mathematics A To Z Project. I’d been inspired to it by Sue Archer and her Doorway Between Worlds blog. I had piggybacked on her discussing the word “into” with a description of its mathematical use.

The first thing I learned is that it’s easy to write several week’s worth of essays in a big session if I have a clear idea what they’re all to be about. That left me feeling good. I do worry when I go several days without anything fresh or more than the reblog of someone’s interesting pictures. I like sharing someone else’s interesting pictures too, mind you. I just know it’s not work on my part to share them. Also when I had to travel a while in May and June, and when my computer was out for repairs, I didn’t have to scramble to do anything.

Another is that I liked the format, which had me jumping around several concentrations of mathematics. It also had me jump from common enough levels into math-major stuff all the way to grad school stuff. I particularly liked trying to introduce graduate-level mathematics in tolerably clear English and in around a thousand words. Helping me out here was the Hemmingway Editor, which attempts to judge how complicated one’s writing is. It’s in favor of shorter, clearer sentences with fewer adverbs and no uses of the word “very”. I can’t agree with everything it judges. It’s a computer, after all. But writing about advanced subjects while watching how complicated my sentences came out has helped my prose style.

Something else I’ve learned from this is that there’s a taste for pop-mathematics about more advanced topics. It’s easy to suppose that people who never studied, or never liked studying, mathematics are most likely to read about the easy stuff. That’s probably not quite so. Probably what people really want is to feel like they’re being let in on the cool stuff. Mathematics has a lot of cool stuff. A lot of it requires a long running start, though. For example, I couldn’t talk about a ring until I’d described what a group was. So that essay felt like it was taking forever to get started while I wrote it. I don’t know how it felt to people reading it. The z-transform, similarly, has a lot that’s neat about it, but it took a while to get there. I hope it stayed promising long enough for people to stick through it.

My terror throughout writing all 26 entries was that I was about to say something really, obviously stupid, and that a flock of mathematicians would descend on me. Scorn and semiprofessional humiliation would follow. I’m still a bit worried, although nobody’s said anything too bad to me yet.

The project was quite good for my readership. Between the A to Z essays, Reading the Comics posts, occasional other essays, and reblogs, I went a solid thirty days with something new posted every day. That’s surely why June was my most-read month here ever. And why July, though having fewer posts, was still pretty well-read. I confess I’m disappointed and a bit surprised I never hit the “Freshly Pressed” lottery with any of these. But that’s just the natural envy any writer has. Everybody else always seems to be more successful.

I’d like to do a similar thematically linked project. I might in a few months do another A to Z. I’m open to other themes, though, and would love to hear suggestions.

How May 2015 Treated My Mathematics Blog


For May 2015 I tried a new WordPress theme — P2 Classic — and I find I rather like it. Unfortunately it seems to be rubbish on mobile devices and I’m not WordPress Theme-equipped-enough to figure out how to fix that. I’m sorry, mobile readers. I’m honestly curious whether the theme change affected my readership, which was down appreciably over May.

According to WordPress, the number of pages viewed here dropped to 936 in May, down just over ten percent from April’s 1047 and also below March’s 1022. Perhaps the less-mobile-friendly theme was shooing people away. Maybe not, though: in March and April I’d posted 14 articles each, while in May there were a mere twelve. The number of views per post increased steadily, from 73 in March to just under 75 in April to 78 in May. I’m curious if this signifies anything. I may get some better idea next month. June should have at least 13 posts from the Mathematics A To Z gimmick, plus this statistics post, and there’ll surely be at least two Reading The Comics posts, or at least sixteen posts. And who knows what else I’ll feel like throwing in? It’ll be an interesting experiment at least.

Anyway, the number of unique visitors rose to 415 in May, up from April’s 389 but still below March’s 468. The number of views per visitor dropped to 2.26, far below April’s 2.68, but closer in line with March’s 2.18. And 2.26 is close to the normal count for this sort of thing.

The number of likes on posts dropped to 259. In April it was 296 likes and in March 265. That may just reflect the lower number of posts, though. Divide the number of likes by the number of posts and March saw an average of 18.9, April 21.14, and May 21.58. That’s all at least consistent, although there’s not much reason to suppose that only things from the current month were liked.

The number of comments recovered also. May saw 83 comments, up from April’s 64, but not quite back to March’s 93. That comes to, for May, 6.9 comments for each post, but that’s got to be counting links to other posts, including pingbacks and maybe the occasional reblogging. I’ve been getting chattier with folks around here, but not seven comments per post chatty.

June starts at 24,820 views, and 485 people following specifically through WordPress.

I’ve got a healthy number of popular posts the past month; all of these got at least 37 page views each. I cut off at 37 because that’s where the Trapezoids one came in and we already know that’s popular. More popular than that were:

I have the suspicion that comics fans are catching on, quietly, to all this stuff.

Now the countries report. The nations sending me at least twenty page views were the United States (476), the United Kingdom (85), Canada (65), Italy (53), and Austria (20).

Sending just a single reader were Belgium, Bulgaria, Colombia, Nigeria, Norway, Pakistan, Romania, and Vietnam. Romania is on a three-month single-reader streak; Vietnam, two. India sent me a mere two readers, down from six last month. The European Union sent me three.

And among the interesting search terms this past month were:

  • origin is the gateway to your entire gaming universe.
  • how to do a cube box (the cube is easy enough, it’s getting the boxing gloves on that’s hard)
  • popeye “computer king” (Remember that comic?)
  • google can you show me in 1 trapezoid how many cat how many can you make of 2 (?, although I like the way Google is named at the start of the query, like someone on Next Generation summoning the computer)
  • plato “divided line” “arthur cayley” (I believe that mathematics comes in on the lower side of the upper half of Plato’s divided line)
  • where did negative numbers originate from

Someday I must work out that “origin is the gateway” thing.