How October 2016 Treated My Mathematics Blog


I do try to get these monthly readership review posts done close to the start of the month. I was busy the 1st of the month, though, and had to fit around the End 2016 Mathematics A To Z. And then I meant to set this to post on Thursday, since I didn’t have anything else going that day, and forgot.

Readership Numbers:

The number of page views declined again in October, part of a trend that’s been steady since June. There were only 907 views, down a slight amount from September’s 922 or more significantly from August’s 1002. I’ll find my way back above a thousand in a month if I can. A To Z months are usually pretty good ones, possibly because of all the fresh posts reminding people I exist.

The number of unique visitors dropped to 536. There had been 576 in September, but then there were only 531 unique visitors in August, if you believe that sort of thing. The number of likes was 115, exactly the same as in September and slightly up from August’s 107. The number of comments rose to 24, up from September’s 20 and August’s 16. That’s certainly been helped by people making requests for the End 2016 Mathematics A To Z. But that counts too.

Popular Posts:

The most popular post of the month was a surprise to me and dates back to September of 2012, incredibly. I suspect someone on a popular web site linked to it and I never suspected. And the Reading the Comics posts were popular as ever.

I’ve been trying to limit these most-popular posts to just five pieces. But How Mathematical Physics Works was the next piece to make the top ten and I am proud of it, so there.

Listing Countries:

Where did my readers come from in October? All over, but mostly, from 46 particular countries. Here’s the oddly popular list of them:

Country Readers
United States 466
United Kingdom 78
Philippines 55
India 52
Canada 32
Germany 27
Austria 23
Puerto Rico 19
Australia 14
France 12
Slovenia 10
Spain 9
Brazil 7
Netherlands 7
Italy 6
New Zealand 5
Singapore 5
Denmark 4
Sweden 4
Bulgaria 3
Poland 3
Serbia 3
Argentina 2
European Union 2
Indonesia 2
Norway 2
Bahamas 1
Belgium 1
Czech Republic 1 (**)
Estonia 1 (*)
Finland 1
Greece 1
Ireland 1
Israel 1
Jamaica 1
Japan 1
Mexico 1
Portugal 1 (*)
Russia 1
Saudi Arabia 1
Slovakia 1
South Africa 1
Ukraine 1
United Arab Emirates 1
Uruguay 1
Zambia 1

Estonia and Portugal are on two-month streaks as single-read countries. The Czech Republic’s on a three-month streak so. Nobody’s on a four-month streak, not yet.

Search Term Non-Poetry:

Once again it wasn’t a truly poetic sort of month. But it was one that taught me what people are looking for, and it’s comics about James Clerk Maxwell. Look at these queries:

  • comic strips of the scientist maxwell
  • comics trip of james clerk maxwell
  • comics about maxwell the scientist
  • james clerk maxwell comics trip
  • log 10 times 10 to the derivative of 10000
  • problems with vinyl lp with too many grooves
  • comics about integers
  • comic strip in advance algebra

I admit I don’t know why someone sees James Clerk Maxwell as a figure for a comics trip. He’s famous for the laws of electromagnetism, of course. Also for great work in thermodynamics and statistical mechanics. Also for color photography. And explaining how the rings of Saturn could work. And for working out the physics of truss bridges, which may sound boring but is important. Great subject for a biography. Just, a comic?

Counting Readers:

November sees the blog start with 42,250 page views, from 17,747 unique visitors if you can believe that. I’m surprised the mathematics blog still has a higher view count than my humor blog has, just now. That one’s consistently more popular; this one’s just been around longer.

WordPress says I started November with 626 followers, barely up from October’s 624. If you have wanted to follow me, there’s a button on the upper-right corner of the blog for that, at least until I change to a different theme. Also if you know a WordPress theme that would work better for the kind of blog I write let me know. I have a vague itch to change things around and that always precedes trouble. Also you can follow me on Twitter, @Nebusj, or check that out to make sure I’m not one of those people who somehow is hard to Twitter-read.

According to the “Insights” tab my readership’s largest on Sundays, which makes sense. I’ve standardized on Sundays for the Reading the Comics essays. That gets 18 percent of page views, slightly more than one in seven views. The most popular hour is again 6 pm, I assume Universal Time. 14 percent of page views come in that hour. That’s the same percentage as last month and it must reflect when my standard posting hour is.

How September 2016 Treated My Mathematics Blog


I put together another low-key, low-volume month in September. In trade, I got a low readership: my lowest in the past twelve months, according to WordPress, and less than a thousand readers for the first time since May. Well, that’s a lesson to me about something or other.

Readership Numbers:

So there were only 922 page views around here, down from August’s 1,002 and July’s 1,057. The number of distinct readers rose, at least, to 575. There had been only 531 in August. But there were 585 in July, which is the sort of way it goes.

The number of likes rose to 115, which is technically up from August’s 107. It’s well down from July’s 177. There were 20 comments in September, up from August’s 16 yet down from July’s 33. I think this mostly reflects how many fewer posts I’ve been publishing. There were just eleven original posts in August and September, compared to, for example, July’s boom of 17. I am thinking about doing a new A To Z round to close out the year, which if past performance is any indication would bring me all sorts of readers as well as make me spend every day writing, writing, writing and hoping for any kind of mathematics word that starts with ‘y’.

Popular Posts:

I’m not surprised that my most popular post for September was a Reading the Comics post. With hindsight I realize it’s almost perfectly engineered for reliable readership. It’s about something light but lets me, at least in principle, bring up the whole spectrum of mathematics. That said I am surprised two of the most popular posts were stepped deep into Freshman Calculus, threatening to be inaccessible to casual readers. But then both of those posts started out when online friends needed help with their calculus work, so maybe it better matches stuff people need to know. The most-read articles around here in September were:

Listing Countries:

Country Readers
United States 808
India 53
Canada 46
United Kingdom 34
New Zealand 24
Australia 23
Germany 18
Philippines 17
France 9
Argentina 8
Spain 7
Singapore 6
Brazil 6
Kenya 5
Switzerland 5
Austria 3
Denmark 3
Indonesia 3
Italy 3
Netherlands 3
South Africa 3
Uruguay 3
Bulgaria 2
Croatia 2
Cyprus 2
Greece 2
Israel 2
Japan 2
Malaysia 2
Mexico 2
Norway 2
Puerto Rico 2
Sweden 2
Turkey 2
Costa Rica 1
Czech Republic 1 (*)
Estonia 1
European Union 1
Hong Kong SAR China 1
Hungary 1
Mauritius 1
Poland 1
Portugal 1
Romania 1
Taiwan 1

Czech Republic was the only single-reader country last month, and no country’s on a two- or more-month single-reader streak. European Union dropped from three page views so I don’t know what they’re looking for that they aren’t finding here.

Search Term Non-Poetry:

Nothing all that trilling among the search terms, although someone’s on a James Clerk Maxwell kick. Among things that brought people here in September were:

  • how many grooves on a record
  • james clerk maxwell comics strip
  • james clerk maxwell comics
  • james clerk maxwell comics stript about scientiest
  • james clerk maxwell comics streip photos
  • james clerk maxwell comics script scientist
  • record groove width in micrometers
  • example of comics strip of maxwell

Definitely have to commission someone to draw a bunch of James Clerk Maxwell comics.

Counting Readers:

October starts with the mathematics blog at 41,318 page views from 17,189 recorded distinct visitors. (The first year or so of the blog WordPress didn’t keep track of distinct visitors, though, or at least didn’t tell us about them.)

WordPress’s “Insights” tab tells me the most popular day for reading stuff here is Sunday, with 18 percent of page views coming then. Since that’s the designated day for Reading the Comics posts that doesn’t surprise me. The most popular hour is 6 pm, which gets 14 percent of readers in. That must be because I’ve set 6 pm Universal Time as the standard moment when new posts should be published.

WordPress says I start October with 624 total followers, up modestly from September’s 614 base. There’s a button on the upper-right corner to follow this blog on WordPress. Below that is a button to follow this blog by e-mail. And if you’d like you can follow me on Twitter too, where I try to do more than just point out I’ve posted stuff here. But also to not post so often that you wonder if or when I rest.

How, Arguably, Very Slightly Less Well April 2016 Treated My Mathematics Blog


So now to my review of readership statistics. I’d expected another strong month. If I’ve learned anything it’s that posting a lot of stuff regularly encourages readers. I got to have another month with more than 1,000 readers here. In fact, there were a neat 1,500 page views, according to WordPress. This is a bit lower than March’s 1,557 page views. But remember that March had one more day than April did, and so had one more article. April had an average of fifty page views per post. March had 50.226. That’s no appreciable difference, I figure. February had 949 page views, although with only 14 articles. (And so about 68 page views per article posted, somehow.)

The number of unique visitors, as WordPress makes them out, was up though. April saw 757 visitors, a record around these parts. March only had 734, and February a relatively skimpy 538.

The measurements that seem to reflect reader engagement were ambiguous as ever. The number of likes was 345, technically up from March’s 320, and well above February’s 201. The number of comments, though, was 55, plummeting from March’s 84 and February’s 66. Part of that is I didn’t have any good controversies like the Continued Fractions post this month. But writing articles that encourage conversations, especially conversations between commenters (it can’t all be me chatting with individuals), has never been a strength of mine and I do need to ponder ways to improve that.

Proud as I am of the A To Z series, I must face the facts: none of the essays was in my top five most-read articles for April. One does sneak in at sixth place so I’ll list the top six articles instead. I’m going to suppose that the series pretty much balances out. That is, few of the articles have reason to read that one instead of another post. What are most popular are Reading the Comics posts, my trapezoids thing, and a couple of pointers to other people’s writing. Well, we can’t all be stars; someone has to be the starmaker. Most read in April:

There’s not any interesting search terms this month. Well, all right, there’s “what is an inversly [sic] propotional [sic] dice”. But I don’t know what the searcher was looking for there. I got the traditional appearance of “origin is the gateway to your entire gaming universe.” And I got asked “what makes a basketball tournament exciting?” I don’t know, but I was able to give at least a non-perfectly-ridiculous measure of how interesting one might be.

And for the always-popular listing of countries? As is usual for some reason, the United States sent me the greatest number of page views: 863. India was second at 80, and Canada third at 61. Austria was next at 45, and the United Kingdom and Germany tied for 42.

Single-reader countries were Belarus, Botswana, China, Dominican Republic, European Union, Greece, Guatemala, Hungary, Kuwait, Poland, Portugal, Qatar, Réunion, Serbia, South Korea, and Switzerland. Again, European Union. I’ve said that before. China, European Union, and Greece were there last month too. The European Union is somehow on a five-month single-reader streak. At this point I have to think whoever is doing it is doing so on purpose and for a bit of a giggle.

The month begins with 36,256 page views total, from 14,273 recorded visitors. I’ve reportedly got 579 WordPress readers, up from the 573 at the start of April, despite putting the Follow This Blog icon in a more prominent location. Well, there were some nice stretches of people following each of several days in a row and that’s something. It also lists eleven followers by e-mail, up from ten last month. Again, it’s all something.

How February 2016 Treated My Mathematics Blog


Once again I spent a month not obsessing about the WordPress-gathered statistics day to day. It was somewhat soothing. But I wasn’t doing well in visiting and commenting on other people’s blogs, and I know that hurts my own readership. The economy of social media runs on sharing attention.

But it was still a decent month around here. The total number of page views dropped below a thousand again, to an official tally of 949. That’s below January’s 998 and December’s 954. It’s a higher readership per day, though. At this rate if February had 31 days there’d have been 1,014 page views. On the other hand, I published 14 things in February, compared to 13 in January. Is the proper correction not the length of the year but how much anyone reads any post?

Well, the number of unique visitors rose. It reached 538 in February, up from January’s 523 and December’s 449. This is a twelve-month high at least. I can’t find older statistics, but I imagine that’s got to be an all-time high, considering.

The number of likes held steady. Well, it dropped from 202 in January to 201 in February. I know better than to think that signifies anything. It’s down from December’s 245, but that’s surely staying right about average. The number of comments rose to 66, up from 53 in January and 56 in December. I think most of that would be people offering requests for the Leap Day Mathematics A To Z.

For a change my top-five articles of the month aren’t dominated by Reading the Comics essays. Well, number 1 and number 5 are, but in comparison that isn’t much at all. The rest of the top five is me pointing to other interesting stuff, which does imply that people like me as a curator more than they like me as an original popularizer. Well, the readership for “Ensembled”, getting at canonical and microcanonical ensembles and statistical mechanics, wasn’t bad. And the early returns for the Leap Day Mathematics A To Z are good too. They had a short time to be read. They were outranked by:

The roster of countries sending me readers was a bit odd this month. The United States was on top, as ever, with 562 page views going to it. I grant I’m in the United States, and post at times convenient to its schedule, and I write in an American idiom. But there’s a lot more English readers outside the United States than inside, and I rarely write about things of particular interest in the United States or disinterest outside. I’ve always wondered why my readership is so close to home.

And then India came in second this month, with 64 readers. I’m glad to see it fluttering up that high. I feel better being read that far from home. Canada, which is close to home but which I’ve only been to twice, changing planes, brought me 41 readers. Germany, which I’ve spent nearly two weeks in, sent 40. Hong Kong, which I’ve been to a fair number of times but always in changing airplanes, 33. I think this is the first time my top-five readership hasn’t been dominated by the United States and the British Commonwealth. (The United Kingdom was next in line, at 26 page views, and Australia 19 after that. And then there’s a whole bunch of countries in which English isn’t a primary language.)

Single-reader nations this time around were Argentina, Bangladesh, Barbados, Cambodia, European Union (not a nation), Indonesia, Italy, Japan, Malaysia, the Netherlands, Portugal, South Korea, Suriname, Swaziland, Sweden, and Ukraine. Bangladesh, the European Union, the Netherlands, and Sweden were there last month too. The European Union is on a three-month streak but still isn’t a nation. And I still don’t know what WordPress even means by that. Singapore sent me three page views, down from twelve the month before. Poland didn’t send me any readers, which is shockingly unpopular even for me.

Search terms bringing people here? I’m happy to provide some. Among those that turned up:

  • how many teapizoids can you get in a rectangle (what gets me is there were multiple hits for this misspelling)
  • what is happening to the toby comic by corey pandolph? (and that’s interesting: after years of being in reruns Pandolph has started writing new installments. The strip has picked up “eight years later”, which seems like about how long Toby, Robot Satan has been idle. I’m glad to see this strip resume.)
  • origin is the gateway to your entire gaming universe. (and why wouldn’t it be?)
  • math theory penguins (I was with you up to the word `penguins’)
  • are any coins unfair (no! But coin tosses can be)
  • population charlotte nc 1975 (I’d tried interpolating what it might have been back then; I’d meant to do a series of essays about different ways to interpolate data, and might again someday)
  • true almost verywhere (not waffling about true or false: “almost everywhere” is a term of art with a precise meaning)

The month starts with 33,200 page views in total, from a recorded 12,782 distinct viewers. I’m tempted to give a prize to whoever logs number 33,333. WordPress credits me with 566 WordPress.com followers. If you’re not sure whether you’re a follower, well, there’ a “Follow Blog via Email” button over on the right side of the page. And I realize I’m not sure where they do put a “Follow Blog on WordPress” button for people who’re logged in to WordPress already. Maybe I need to worry about that. I’m also on Twitter, as @Nebusj, and I’d be happy with being followed there too.

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 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.

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.

My Mathematics Blog Abbreviated Statistics, June 2015


So, that was a fairly successful month. For June this blog managed a record 1,051 pages viewed. That’s just above April’s high of 1,047, and is a nice rebound from May’s 936. I feel comfortable crediting this mostly to the number of articles I published in the month. Between the Mathematics A To Z and the rush of Reading The Comics posts, and a couple of reblogged or miscellaneous bits, June was my most prolific month: I had 28 articles. If I’d known how busy it was going to be I wouldn’t have skipped the first two Sundays. And i start the month at 25,871 total views.

It’s quite gratifying to get back above 1,000 for more than the obvious reasons. I’ve heard rumors — and I’m not sure where because most of my notes are on my not-yet-returned main computer — that WordPress somehow changed its statistics reporting so that mobile devices aren’t counted. That would explain a sudden drop in both my mathematics and humor blogs, and drops I heard reported from other readership-watching friends. It also implies many more readers out there, which is a happy thought.

Unfortunately because of my computer problems I can’t give reports on things like the number of visitors, or the views per visitor. I can get at WordPress’s old Dashboard statistics page, and that had been showing the number of unique visitors and views per visitor and all that. But on Firefox 3.6.16, and on Safari 5.0.6, this information isn’t displayed. I don’t know if they’ve removed it altogether from the Dashboard Statistics page in the hopes of driving people to their new, awful, statistics page or what. I also can’t find things like the number of likes, because that’s on the New Statistics page, which is inaccessible on browsers this old.

Worse, I can’t find the roster of countries that sent me viewers. I trust that when I get my main computer back, and can look at the horrible new statistics page, I’ll be able to fill that in, but for now — nothing. I’m sorry. I will provide these popular lists when I’m able.

I can say what the most popular posts were in June. As you might expect for a month dominated by the A-To-Z project, the five most popular posts were all Reading The Comics entries:

Finally after that some of the A To Z posts appear, with fallacy, and graph, and n-tuple the most popular of that collection.

Among the search terms bringing people here were:

  • real life problems involving laws of exponents comic strip (three people wanted them!)
  • if the circumference is 40,000,000 then what is the radius (why, one Earth-radius, of course) (approximately)
  • poster on mathematical diagram in the form of cartoon for ,7th class student
  • how to figure out what you need on a final to pass (you need to start sooner in the term)
  • how to count fish (count all the things which are not fish, and subtract that from the total number of all things, and there you go)
  • einstein vs pythagoras formula (do I have to take a side?)
  • origin is the gateway to your entire gaming universe.
  • big ben anthropomorphized (it’s not actually Big Ben, you know. The text is clear that it’s Big Ben’s Creature.)
  • wyoming rectangular most dilbert (are we having Zippy the Pinhead fanfiction yet?)

Sorry it’s an abbreviated report. Or, sry is abbrev rept, anyway. I’ll fill in what I can, when I can, and isn’t that true of all of us?

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.

How April 2015 Treated My Mathematics Blog


(I apologize if the formatting is messed up. For some reason preview is not working, and I will not be trying the new page for entering posts if I can at all help it. I will fix when I can, if it needs fixing.)

As it’s the start of the month I want to try understanding the readership of my blogs, as WordPress gives me statistics. It’s been a more confusing month than usual, though. One thing is easy to say: the number of pages read was 1,047, an all-time high around these parts for a single month. It’s up from 1,022 in March, and 859 in February. And it’s the second month in a row there’ve been more than a thousand readers. That part’s easy.

The number of visitors has dropped. It was down to 389 in April, from a record 468 in March and still-higher 407 in April. This is, if WordPress doesn’t lead me awry, my fifth-highest number of viewers. This does mean the number of views per visitor was my highest since June of 2013. The blog had 2.69 views per visitor, compared to 2.18 in March and 2.11 in February. It’s one of my highest views-per-visitor on record anyway. Perhaps people quite like what they see and are archive-binging. I approve of this. I’m curious why the number of readers dropped so, though, particularly when I look at my humor blog statistics (to be posted later).

I’m confident the readers are there, though. The number of likes on my mathematics blog was 297, up from March’s 265 and February’s 179. It’s the highest on record far as WordPress will tell me. So readers are more engaged, or else they’re clicking like from the WordPress Reader or an RSS feed. Neither gets counted as a page view or a visitor. That’s another easy part. The number of comments is down to 64, from March’s record 93, but March seems to have been an exceptional month. February had 56 comments so I’m not particularly baffled by April’s drop.

May starts out with 23,884 total views, and 472 people following specifically through WordPress.

It’s a truism that my most popular posts are the trapezoids one and the Reading The Comics posts, but for April that was incredibly true. Most popular the past thirty days were:

  1. How Many Trapezoids I Can Draw.
  2. Reading The Comics, April 10, 2015: Getting Into The Story Problem Edition.
  3. Reading The Comics, April 15, 2015: Tax Day Edition.
  4. Reading The Comics, April 20, 2015: History Of Mathematics Edition.
  5. Reading The Comics, March 31, 2015: Closing Out March Edition.

I am relieved that I started giving all these Comics posts their own individual “Edition” titles. Otherwise there’d be no way to tell them apart.

The nations sending me the most readers were, as ever, the United States (662), Canada (82), and the United Kingdom (47), with Slovenia once again strikingly high (36). Hong Kong came in with 24 readers, Italy 23, and Austria a mere 18. Elke Stangl’s had a busy month, I know.

This month’s single-reader countries were Czech Republic, Morocco, the Netherlands, Puerto Rico, Romania, Taiwan, and Vietnam. Romania’s the only one that sent me a single reader last month. India bounced back from five readers to six.

Among the search terms bringing people to me were no poems. Among the interesting phrases were:

  • what point is driving the area difference between two triangles (A good question!)
  • how do you say 1,898,600,000,000,000,000,000,000,000 (I almost never do.)
  • is julie larson still drawing the dinette set (Yes, to the best of my knowledge.)
  • jpe fast is earth spinning? (About once per day, although the answer can be surprisingly difficult to say! But also figure about 465 times the cosine of your latitude meters per second, roughly.)
  • origin is the gateway to your entire gaming universe. (Again, I don’t know what this means, and I’m a little scared to find out.)
  • i hate maths 2015 photos (Well, that just hurts.)
  • getting old teacher jokes (Again, that hurts, even if it’s not near my birthday.)
  • two trapezoids make a (This could be a poem, actually.)
  • how to draw 2 trapezoids (I’d never thought about that one. Shall have to consider writing it.)

I don’t know quite what it all means, other than that I need to write about comic strips and trapezoids more somehow.

How My Mathematics Blog Was Read, For January 2015


And after reaching 20,000 views on the final day of December, 2014, could I reach 21,000 views by the end of January? Probably I could have, but in point of fact I did not. I am not complaining, though: I finished the month with 20,956 page views all told, after a record 944 pages got viewed by somebody, somewhere, for some reason. This is a record high for me, going well past the 831 that had been the January 2013 and December 2014 (tied) record. And likely I’ll reach 21,000 in the next couple days anyway.

According to WordPress, this was read by 438 distinct visitors, reading 2.16 views per visitor on average. That isn’t quite a record: January 2013 remains my high count for visitors, at 473, but it’s still, all told, some pretty nice numbers especially considering I don’t think I had my best month of blog-writing. I can’t wait to get some interesting new topics in here for February and see that they interest absolutely nobody.

The new WordPress statistics page is still awful, don’t get me wrong, but it has been getting a little bit better, and it does offer some new data I couldn’t gather easily before. Among them: that in January 205 I received 197 likes overall — a high for the past twelvemonth, which is as far as I can figure out how to get it, and up from 128 in December — and 51 comments, up from December 29, and also a high for the twelvemonth.

The three countries sending me viewers were, once again, the big three of the United States (594), Canada (56), and the United Kingdom (52), with Austria sending in 32 viewers, and Germany and Argentina ending 22 each. And India, for a wonder sent me a noticeable-to-me 18 readers, although on a per capita basis that still isn’t very many, I admit.

There was a bumper crop of single-reader countries, though, up from last month’s six: Belgium, Estonia, Finland, Greece, Hungary, Indonesia, Iraq, Japan, Kuwait, Libya, Mexico, Paraguay, Slovakia, and the United Arab Emirates each found only one person viewing anything around here. Greece and Mexico are repeats from December.

This month’s most popular articles were mostly comic strip posts, although they were a pretty popular set; none of these had fewer than 35 views per, which feels high to me. The top posts of the last 30 days, then, were:

  1. Reading the Comics, January 6, 2015: First of the Year Edition, in which I included drawing a sloppy `2′ as a snoring `Z’ as somehow connected to mathematics.
  2. Reading the Comics, January 24, 2015: Many, But Not Complicated Edition, which includes an explanation for why margins of errors on surveys are always like three or four percent.
  3. Reading the Comics, January 11, 2015: Standard Genres And Bloom County Edition, in which I reveal my best guess for Jon Bon Jovi’s shorts size in the late 80s.
  4. 20,000: My Math Blog’s Statistics, because my narcissism is apparently quite popular?
  5. Reading the Comics, January 17, 2015: Finding Your Place Edition, where, again, I can flog that thing about a watch as a compass.
  6. How Many Trapezoids I Can Draw, which also reveals how many trapeziums I think are different in interesting ways.
  7. A bit more about Thomas Hobbes, and his attempt to redefine the very nature of mathematics, which didn’t succeed in quite the way he wanted.

Among the interesting search terms that brought people here the past month have been ([sic] on all of them):

  • science fiction and trapazoids (Somebody should totally write the definitive SFnal treatment of trapezoids, I agree.)
  • food. stotagre nebus (I feel strangely threatened by this.)
  • a group of student offer at least one of mathematics,physics, and statistcs , 14 of them offer mathematics, 12 offer physics,and 16 offer statistics.7 offer statistics and maths 6 offer maths and physics, 4 offer physics and statistics only, while 5 offer all the three subject (Help?)
  • hiw to draw diffrent trameziums
  • soglow otto radio (Pretty sure I used to listen to that back on WRSU in my undergrad days.)
  • if a calendar has two consecutive months with friday the 13th which would they be (February and March, in a non-bissextile — that is, non-leap — year)
  • how to measure a christmas tree made of triangles and trapeziums (I would use a tape measure, myself)

So if I would summarize January 2015 in my readership here, I would say: tramezium?

My Math Blog Statistics, November 2014


October 2014 was my fourth-best month in the mathematics blog here, if by “best” we mean “has a number of page views”, and second-best if by “best” we mean “has a number of unique visitors”. And now November 2014 has taken October’s place on both counts, by having bigger numbers for both page views and visitors, as WordPress reveals such things to me. Don’t tell October; that’d just hurt its feelings. Plus, I got to the 19,000th page view, and as of right now I’m sitting at 19,181; it’s conceivable I might reach my 20,000th viewer this month, though that would be a slight stretch.

But the total number of page views grew from 625 up to 674, and the total number of visitors from 323 to 366. The number of page views is the highest since May 2014 (751), although this is the greatest number of visitors since January 2014 (473), the second month when WordPress started revealing those numbers to us mere bloggers. I like the trends, though; since June the number of visitors has been growing at a pretty steady rate, although steadily enough I can’t say whether it’s an arithmetic or geometric progression. (In an arithmetic progression, the difference between two successive numbers is about constant, for example: 10, 15, 20, 25, 30, 35, 40. In a geometric progression, the ratio between two successive numbers is about constant, for example: 10, 15, 23, 35, 53, 80, 120.) Views per visitor dropped from 1.93 to 1.84, although I’m not sure even that is a really significant difference.

The countries sending me the most readers were just about the same set as last month: the United States at 458; Canada recovering from a weak October with 27 viewers; Argentina at 20; Austria and the United Kingdom tied at 19; Australia at 17; Germany at 16 and Puerto Rico at 14.

Sending only one reader this month were: Belgium, Bermuda, Croatia, Estonia, Guatemala, Hong Kong, Italy, Lebanon, Malaysia, the Netherlands, Norway, Oman, the Philippines, Romania, Singapore, South Korea, and Sweden. (Really, Singapore? I’m a little hurt. I used to live there.) The countries repeating that from October were Estonia, the Netherlands, Norway, and Sweden; Sweden’s going on three months with just a single reader each. I don’t know what’s got me only slightly read in Scandinavia and the Balkans.

My most-read articles for November were pretty heavily biased towards the comics, with a side interest in that Pythagorean triangle problem with an inscribed circle. Elke Stangl had wondered about the longevity of my most popular posts, and I was curious too, so I’m including in brackets a note about the number of days between the first and the last view which WordPress has on record. This isn’t a perfect measure of longevity, especially for the most recent posts, but it’s a start.

As ever there’s no good search term poetry, but among the things that brought people here were:

  • trapezoid
  • how many grooves are on one side of an lp record?
  • origin is the gateway to your entire gaming universe.
  • cauchy funny things done
  • trapezoid funny
  • yet another day with no plans to use algebra

Won’t lie; that last one feels a little personal. But the “origin is the gateway” thing keeps turning up and I don’t know why. I’d try to search for it but that’d just bring me back here, leaving me no more knowledgeable, wouldn’t it?

Reading The Comics, September 24, 2014: Explained In Class Edition


I’m a fan of early 20th century humorist Robert Benchley. You might not be yourself, but it’s rather likely that among the humorists you do like are a good number of people who are fans of his. He’s one of the people who shaped the modern American written-humor voice, and as such his writing hasn’t dated, the way that, for example, a 1920s comic strip will often seem to come from a completely different theory of what humor might be. Among Benchley’s better-remembered quotes, and one of those striking insights into humanity, not to mention the best productivity tip I’ve ever encountered, was something he dubbed the Benchley Principle: “Anyone can do any amount of work, provided it isn’t the work he is supposed to be doing at the moment.” One of the comics in today’s roundup of mathematics-themed comics brought the Benchley Principle to mind, and I mean to get to how it did and why.

Eric The Circle (by ‘Griffinetsabine’ this time) (September 18) steps again into the concerns of anthropomorphized shapes. It’s also got a charming-to-me mention of the trapezium, the geometric shape that’s going to give my mathematics blog whatever immortality it shall have.

Bill Watterson’s Calvin and Hobbes (September 20, rerun) dodged on me: I thought after the strip from the 19th that there’d be a fresh round of explanations of arithmetic, this time including imaginary numbers like “eleventeen” and “thirty-twelve” and the like. Not so. After some explanation of addition by Calvin’s Dad,
Spaceman Spiff would take up the task on the 22nd of smashing together Mysterio planets 6 and 5, which takes a little time to really get started, and finally sees the successful collision of the worlds. Let this serve as a reminder: translating a problem to a real-world application can be a fine way to understand what is wanted, but you have to make sure that in the translation you preserve the result you wanted from the calculation.

Joe has memorized the odds for various poker hands. Four times four, not so much.
Rick Detorie’s One Big Happy for the 21st of September, 2014. I confess ignorance as to whether these odds are accurate.

It’s Rick DeTorie’s One Big Happy (September 21) which brought the Benchley Principle to my mind. Here, Joe is shown to know extremely well the odds of poker hands, but to have no chance at having learned the multiplication table. It seems like something akin to Benchley’s Principle is at work here: Joe memorizing the times tables might be socially approved, but it isn’t what he wants to do, and that’s that. But inspiring the desire to know something is probably the one great challenge facing everyone who means to teach, isn’t it?

Jonathan Lemon’s Rabbits Against Magic (September 21) features a Möbius strip joke that I imagine was a good deal of fun to draw. The Möbius strip is one of those concepts that really catches the imagination, since it seems to defy intuition that something should have only the one side. I’m a little surprise that topology isn’t better-popularized, as it seems like it should be fairly accessible — you don’t need equations to get some surprising results, and you can draw pictures — but maybe I just don’t understand the field well enough to understand what’s difficult about bringing it to a mass audience.

Hector D. Cantu and Carlos Castellanos’s Baldo (September 23) tells a joke about percentages and students’ self-confidence about how good they are with “numbers”. In strict logic, yes, the number of people who say they are and who say they aren’t good at numbers should add up to something under 100 percent. But people don’t tend to be logically perfect, and are quite vulnerable to the way questions are framed, so the scenario is probably more plausible in the real world than the writer intended.

Steve Moore’s In The Bleachers (September 23) falls back on the most famous of all equations as representative of “something it takes a lot of intelligence to understand”.

My Math Blog Statistics, August 2014


So, August 2014: it’s been a month that brought some interesting threads into my writing here. It’s also had slightly longer gaps in my writing than I quite like, because I’d just not had the time to do as much writing as I hoped. But that leaves the question of how this affected my readership: are people still sticking around and do they like what they see?

The number of unique readers around here, according to WordPress, rose slightly, from 231 in July to 255 in August. This doesn’t compare favorably to numbers like the 315 visitors in May, but still, it’s an increase. The total number of page views dropped from 589 in July to 561 in August and don’t think that the last few days of the month I wasn’t tempted to hit refresh a bunch of times. Anyway, views per visitor dropped from 2.55 to 2.20, which seems to be closer to my long-term average. And at some point in the month — I failed to track when — I reached my 17,000th reader, and got up to 17,323 by the end of the month. If I’m really interesting this month I could hit 18,000 by the end of September.

The countries sending me the most readers were, in first place, the ever-unsurprising United States (345). Second place was Spain (36) which did take me by surprise, and Puerto Rico was third (30). The United Kingdom, Austria, and Canada came up next so at least that’s all familiar enough, and India sent me a nice round dozen readers. I got a single reader from each of Argentina, Belgium, Brazil, Finland, Germany, Hong Kong, Indonesia, Latvia, Mexico, Romania, Serbia, South Korea, Sweden, Thailand, and Venezuela. The only country that also sent me a single reader in July was Hong Kong (which also sent a lone reader in June and in May), and going back over last month’s post revealed that Spain and Puerto Rico were single-reader countries in July. I don’t know what I did to become more interesting there in August but I’ll try to keep it going.

The most popular articles in August were:

I fear I lack any good Search Term Poetry this month. Actually the biggest search terms have been pretty rote ones, eg:

  • trapezoid
  • barney and clyde carl friedrich comic
  • moment of inertia of cube around the longest diagonal
  • where do negative numbers come from
  • comic strip math cube of binomials

Actually, Gauss comic strips were searched for a lot. I’m sorry I don’t have more of them for folks, but have you ever tried to draw Gauss? I thought not. At least I had something relevant for the moment of inertia question even if I didn’t answer it completely.

In the Overlap between Logic, Fun, and Information


Since I do need to make up for my former ignorance of John Venn’s diagrams and how to use them, let me join in what looks early on like a massive Internet swarm of mentions of Venn. The Daily Nous, a philosophy-news blog, was my first hint that anything interesting was going on (as my love is a philosopher and is much more in tune with the profession than I am with mathematics), and I appreciate the way they describe Venn’s interesting properties. (Also, for me at least, that page recommends I read Dungeons and Dragons and Derrida, itself pointing to an installment of philosophy-based web comic Existentialist Comics, so you get a sense of how things go over there.)

https://twitter.com/saladinahmed/status/496148485092433920

And then a friend retweeted the above cartoon (available as T-shirt or hoodie), which does indeed parse as a Venn diagram if you take the left circle as representing “things with flat tails playing guitar-like instruments” and the right circle as representing “things with duck bills playing keyboard-like instruments”. Remember — my love is “very picky” about Venn diagram jokes — the intersection in a Venn diagram is not a blend of the things in the two contributing circles, but is rather, properly, something which belongs to both the groups of things.

https://twitter.com/mathshistory/status/496224786109198337

The 4th of is also William Rowan Hamilton’s birthday. He’s known for the discovery of quaternions, which are kind of to complex-valued numbers what complex-valued numbers are to the reals, but they’re harder to make a fun Google Doodle about. Quaternions are a pretty good way of representing rotations in a three-dimensional space, but that just looks like rotating stuff on the computer screen.

Daily Nous

John Venn, an English philosopher who spent much of his career at Cambridge, died in 1923, but if he were alive today he would totally be dead, as it is his 180th birthday. Venn was named after the Venn diagram, owing to the fact that as a child he was terrible at math but good at drawing circles, and so was not held back in 5th grade. In celebration of this philosopher’s birthday Google has put up a fun, interactive doodle — just for today. Check it out.

Note: all comments on this post must be in Venn Diagram form.

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July 2014 in Mathematics Blogging


We’ve finally reached the kalends of August so I can look back at the mathematics blog statistics for June and see how they changed in July. Mostly it’s a chance to name countries that had anybody come read entries here, which is strangely popular. I don’t know why.

Since I’d had 16,174 page views total at the start of July I figured I wasn’t going to cross the symbolically totally important 17,000 by the start of August and what do you know but I was right, I didn’t. I did have a satisfying 589 page views (for a total of 16,763), which doesn’t quite reach May’s heights but is a step up from June’s 492 views. The number of unique visitors as WordPress figures it was 231, up from June’s 194. That’s not an unusually large or small number of unique visitors for this year, and it keeps the views per visitor just about unchanged, 2.55 as opposed to June’s 2.54.

July’s most popular postings were mostly mathematics comics ones — well, they have the most reader-friendly hook after all, and often include a comic or two — but I’m gratified by what proved to be the month’s most popular since I like it too:

  1. To Build A Universe, and my simple toy version of an arbitrarily old universe. This builds on In A Really Old Universe and on What’s Going On In The Old Universe, and is followed by Lewis Carroll And My Playing With Universes, also some popular posts.
  2. Reading the Comics, July 3, 2014: Wulff and Morgenthaler Edition, I suppose because WuMo is a really popular comic strip these days.
  3. Reading the Comics, July 28, 2014: Homework in an Amusement Park Edition, I suppose because everybody likes amusement parks these days.
  4. Reading the Comics, July 24, 2014: Math Is Just Hard Stuff, Right? Edition, I suppose because people like thinking mathematics is hard these days.
  5. Some Things About Joseph Nebus, because I guess I had a sudden onset of being interesting?
  6. Reading the Comics, July 18, 2014: Summer Doldrums Edition, because summer gets to us all these days.

The countries sending me the most readers this month were the United States (369 views), the United Kingdom (43 views), and the Philippines (24 views). Australia, Austria, Canada, and Singapore turned up well too. Sending just a single viewer this month were Greece, Hong Kong, Italy, Japan, Norway, Puerto Rico, and Spain; Hong Kong and Japan were the only ones who did that in June, and for that matter May also. My Switzerland reader from June had a friend this past month.

Among the search terms that brought people to me this month:

  • comics strips for differential calculus
  • nebus on starwars
  • 82 % what do i need on my finalti get a c
  • what 2 monsters on monster legends make dark nebus

  • (this seems like an ominous search query somehow)
  • the 80s cartoon character who sees mathematics equations
  • starwars nebus
    (suddenly this Star Wars/Me connection seems ominous)
  • origin is the gateway to your entire gaming universe
    (I can’t argue with that)

Reading the Comics, July 28, 2014: Homework in an Amusement Park Edition


I don’t think my standards for mathematics content in comic strips are seriously lowering, but the strips do seem to be coming pretty often for the summer break. I admit I’m including one of these strips just because it lets me talk about something I saw at an amusement park, though. I have my weaknesses.

Harley Schwadron’s 9 to 5 (July 25) builds its joke around the ambiguity of saying a salary is six (or some other number) of figures, if you don’t specify what side of the decimal they’re on. That’s an ordinary enough gag, although the size of a number can itself be an interesting thing to know. The number of digits it takes to write a number down corresponds, roughly, with the logarithm of a number, and in the olden days a lot of computations depended on logarithms: multiplying two numbers is equivalent to adding their logarithms; dividing two numbers, subtracting their logarithms. And addition and subtraction are normally easier than multiplication and division. Similarly, raising one number to a power becomes multiplying one number by the logarithm of another, and multiplication is easier than exponentiation. So counting the number of digits in a number might be something anyway.

Steve Breen and Mike Thompson’s Grand Avenue (July 25) has the kids mention something as being “like going to an amusement park to do math homework”, which gives me a chance to share this incident. Last year my love and I were in the Cedar Point amusement park (in Sandusky, Ohio), and went to the coffee shop. We saw one guy sitting at a counter, with his laptop and a bunch of papers sprawled out, looking pretty much like we do when we’re grading papers, and we thought initially that it was so very sad that someone would be so busy at work that (we presumed) he couldn’t even really participate in the family expedition to the amusement park.

And then we remembered: not everybody lives a couple hours away from an amusement park. If we lived, say, fifteen minutes from a park we had season passes to, we’d certainly at least sometimes take our grading work to the park, so we could get it done in an environment we liked and reward ourselves for getting done with a couple roller coasters and maybe the Cedar Downs carousel (which is worth an entry around these parts anyway). To grade, anyway; I’d never have the courage to bring my laptop to the coffee shop. So I guess all I’m saying is, I have a context in which yes, I could imagine going to an amusement park to grade math homework at least.

Wulff and Morgenthaler Truth Facts (July 25) makes a Venn diagram joke in service of asserting that only people who don’t understand statistics would play the lottery. This is an understandable attitude of Wulff and Morgenthaler, and of many, many people who make the same claim. The expectation value — the amount you expect to win some amount, times the probability you will win that amount, minus the cost of the ticket — is negative for all but the most extremely oversized lottery payouts, and the most extremely oversized lottery payouts still give you odds of winning so tiny that you really aren’t hurting your chances by not buying a ticket. However, the smugness behind the attitude bothers me — I’m generally bothered by smugness — and jokes like this one contain the assumption that the only sensible way to live is a ruthless profit-and-loss calculation to life that even Jeremy Bentham might say is a bit much. For the typical person, buying a lottery ticket is a bit of a lark, a couple dollars of disposable income spent because, what the heck, it’s about what you’d spend on one and a third sodas and you aren’t that thirsty. Lottery pools with coworkers or friends make it a small but fun social activity, too. That something is a net loss of money does not mean it is necessarily foolish. (This isn’t to say it’s wise, either, but I’d generally like a little more sympathy for people’s minor bits of recreational foolishness.)

Marc Anderson’s Andertoons (July 27) does a spot of wordplay about the meaning of “aftermath”. I can’t think of much to say about this, so let me just mention that Florian Cajori’s A History of Mathematical Notations reports (section 201) that the + symbol for addition appears to trace from writing “et”, meaning and, a good deal and the letters merging together and simplifying from that. This seems plausible enough on its face, but it does cause me to reflect that the & symbol also is credited as a symbol born from writing “et” a lot. (Here, picture writing Et and letting the middle and lower horizontal strokes of the E merge with the cross bar and the lowest point of the t.)

Berkeley Breathed’s Bloom County (July 27, rerun from, I believe, July of 1988) is one of the earliest appearances I can remember of the Grand Unification appearing in popular culture, certainly in comic strips. Unifications have a long and grand history in mathematics and physics in explaining things which look very different by the same principles, with the first to really draw attention probably being Descartes showing that algebra and geometry could be understood as a single thing, and problems difficult in one field could be easy in the other. In physics, the most thrilling unification was probably the explaining of electricity, magnetism, and light as the same thing in the 19th century; being able to explain many varied phenomena with some simple principles is just so compelling. General relativity shows that we can interpret accelerations and gravitation as the same thing; and in the late 20th century, physicists found that it’s possible to use a single framework to explain both electromagnetism and the forces that hold subatomic particles together and that break them apart.

It’s not yet known how to explain gravity and quantum mechanics in the same, coherent, frame. It’s generally assumed they can be reconciled, although I suppose there’s no logical reason they have to be. Finding a unification — or a proof they can’t be unified — would certainly be one of the great moments of mathematical physics.

The idea of the grand unification theory as an explanation for everything is … well, fair enough. A grand unification theory should be able to explain what particles in the universe exist, and what forces they use to interact, and from there it would seem like the rest of reality is details. Perhaps so, but it’s a long way to go from a simple starting point to explaining something as complicated as a penguin. I guess what I’m saying is I doubt Oliver would notice the non-existence of Opus in the first couple pages of his work.

Thom Bluemel’s Birdbrains (July 28) takes us back to the origin of numbers. It also makes me realize I don’t know what’s the first number that we know of people discovering. What I mean is, it seems likely that humans are just able to recognize a handful of numbers, like one and two and maybe up to six or so, based on how babies and animals can recognize something funny if the counts of small numbers of things don’t make sense. And larger numbers were certainly known to antiquity; probably the fact that numbers keep going on forever was known to antiquity. And some special numbers with interesting or difficult properties, like pi or the square root of two, were known so long ago we can’t say who discovered them. But then there are numbers like the Euler-Mascheroni constant, which are known and recognized as important things, and we can say reasonably well who discovered them. So what is the first number with a known discoverer?

Reading the Comics, June 11, 2014: Unsound Edition


I can tell the school year is getting near the end: it took a full week to get enough mathematics-themed comic strips to put together a useful bundle of them this time. I don’t know what I’m going to do this summer when there’s maybe two comic strips I can talk about per week and I have to go finding my own initiative to write about things.

Jef Mallet’s Frazz (June 6) is a pun strip, yeah, although it’s one that’s more or less legitimate for a word problem. The reason I have to say “more or less” is that it’s not clear to me whether, per Caulfield’s specification, the amount of ore lost across each Great Lake is three percent of the original cargo or three percent of the remaining cargo. But writing a word problem so that there’s only the one correct solution is a skill that needs development no less than solving word problems is, and probably if we imagine Caulfield grading he’d realize there was an ambiguity when a substantial number of of the papers make the opposite assumption to what he’d had in his mind.

Ruben Bolling’s Tom the Dancing Bug (June 6, and I believe it’s a rerun) steps into some of the philosophically heady waters that one gets into when you look seriously at probability, and that get outright silly when you mix omniscience into the mix. The Supreme Planner has worked out what he concludes to be a plan certain of success, but: does that actually mean one will succeed? Even if we assume that the Supreme Planner is able to successfully know and account for every factor which might affect his success — well, for a less criminal plan, consider: one is certain to toss heads at least once, if one flips a fair coin infinitely many times. And yet it would not actually be impossible to flip a fair coin infinitely many times and have it turn up tails every time. That something can have a probability of 1 (or 100%) of happening and nevertheless not happen — or equivalently, that something can have a probability of 0 (0%) of happening and still happen — is exactly analogous to how a concept can be true almost everywhere, that is, it can be true with exceptions that in some sense don’t matter. Ruben Bolling tosses in the troublesome notion of the multiverse, the idea that everything which might conceivably happen does happen “somewhere”, to make these impossible events all the more imminent. I’m impressed Bolling is able to touch on so much, with a taste of how unsettling the implications are, in a dozen panels and stay funny about it.

Enos cheats, badly, on his test.
Bud Grace’s The Piranha Club for the 9th of June, 2014.

Bud Grace’s The Piranha Club (June 9) gives us Enos cheating with perfectly appropriate formulas for a mathematics exam. I’m kind of surprised the Pythagorean Theorem would rate cheat-sheet knowledge, actually, as I thought that had reached the popular culture at least as well as Einstein’s E = mc2 had, although perhaps it’s reached it much as Einstein’s has, as a charming set of sounds without any particular meaning behind them. I admit my tendency in giving exams, too, has been to allow students to bring their own sheet of notes, or even to have open-book exams, on the grounds that I don’t really care whether they’ve memorized formulas and am more interested in whether they can find and apply the relevant formulas. But that doesn’t make me right; I agree there’s value in being able to identify what the important parts of the course are and to remember them well, and even more value in being able to figure out the area of a triangle or a trapezoid from thinking hard about the subject on your own.

Jason Poland’s Robbie and Bobbie (June 10) is looking for philosophy and mathematics majors, so, here’s hoping it’s found a couple more. The joke here is about the classification of logical arguments. A valid argument is one in which the conclusion does indeed follow from the premises according to the rules of deductive logic. A sound argument is a valid argument in which the premises are also true. The reason these aren’t exactly the same thing is that whether a conclusion follows from the premise depends on the structure of the argument; the content is irrelevant. This means we can do a great deal of work, reasoning out things which follow if we suppose that proposition A being true implies B is false, or that we know B and C cannot both be false, or whatnot. But this means we may fill in, Mad-Libs-style, whatever we like to those propositions and come away with some funny-sounding arguments.

So this is how we can have an argument that’s valid yet not sound. It is valid to say that, if baseball is a form of band organ always found in amusement parks, and if amusement parks are always found in the cubby-hole under my bathroom sink, then, baseball is always found in the cubby-hole under my bathroom sink. But as none of the premises going into that argument are true, the argument’s not sound, which is how you can have anything be “valid but not sound”. Identifying arguments that are valid but not sound is good for a couple questions on your logic exam, so, be ready for that.

Edison Lee fails to catch a ball because he miscalculates where it should land.
John Hambrock’s The Brilliant Mind of Edison Lee, 11 June 2014.

John Hambrock’s The Brilliant Mind of Edison Lee (June 11) has the brilliant yet annoying Edison trying to prove his genius by calculating precisely where the baseball will drop. This is a legitimate mathematics/physics problem, of course: one could argue that the modern history of mathematical physics comes from the study of falling balls, albeit more of cannonballs than baseballs. If there’s no air resistance and if gravity is uniform, the problem is easy and you get to show off your knowledge of parabolas. If gravity isn’t uniform, you have to show off your knowledge of ellipses. Either way, you can get into some fine differential equations work, and that work gets all the more impressive if you do have to pay attention to the fact that a ball moving through the air loses some of its speed to the air molecules. That said, it’s amazing that people are able to, in effect, work out approximate solutions to “where is this ball going” in their heads, not to mention to act on it and get to the roughly correct spot, lat least when they’ve had some practice.

Autocorrected Monkeys and Pulled Tea


The Twop Twips account on Twitter — I’m not sure how to characterize what it is exactly, but friends retweet it often enough — had the above advice about the infinite monkeys problem, and what seems to me correct advice that turning on autocorrect will get them to write the works of Shakespeare more quickly. And then John Kovaleski’s monkey-featuring comic strip Bo Nanas featured the infinite monkey problem today, so obviously I have to spend more time thinking of it.

It seems fair that monkeys with autocorrect will be more likely to hit a word than a monkey without will be. Let’s try something simpler than Shakespeare and just consider the chance of typing the word “the”, and to keep the numbers friendly let’s imagine that the keyboard has just the letters and a space bar. We’ll not care about punctuation or numbers; that’s what copy editors would be for, if anyone had been employed as a copy editor since 1996, when someone in the budgeting office discovered there was autocorrect.

Anyway, there’s 27 characters on this truncated keyboard, and if the monkeys were equally likely to hit any one of them, then, there’d be 27 times 27 times 27 — that is, 19,683 — different three-character strings they might hit. Exactly one of them is the desired word “the”. So, roughly, we would expect the monkey to get the word right one time in each 19,683 attempts at a three-character string. (We wouldn’t have to wait quite so long if we’ll accept the monkey as writing continuously and pluck out three characters in a row wherever they appear, but that’s more work than I feel like doing, and I doubt it would significantly change the qualitative results, of how much faster it’d be if autocorrect were on.)

But how many tries would be needed to hit a word that gets autocorrected to “the”? And here we get into the mysteries of the English language. I’d be surprised by a spell checker that couldn’t figure out “teh” probably means “the”. Similarly “hte” should get back to “the”. So we can suppose the five other permutations of the letters in “the” will be autocorrected. So there’s six different strings of the 19,683 possibilities that will get fixed to “the”. The monkey has one chance in 3280.5 of getting one of them and so, on average, the monkey can be expected to be right once in every 3281 attempts.

But there’s other typos possible: “thw” is probably just my finger slipping, and “ghe” isn’t too implausible either. At least my spell checker recognizes both as most likely meant to be “the”. Let’s suppose that a spell checker can get to the right word if any one letter is mistaken. This means that there are some 78 other three-character strings that would get fixed to “the”, for a total of 84 possible three-character strings which are either “the” or would get autocorrected to “the”. With that many, there’s one chance in a touch more than 234 that a three-character string will get corrected to “the”, and we have to wait, considering, not very long at all.

It gets better if two-character errors are allowed, but I can’t make myself believe that the spell check will turn “yje” into “the”, and that’s something which might be typed if you just had the right hand on the wrong keys. My checker hasn’t got any idea what “yje” is supposed to be anyway, so, one wrong letter is probably the limit.

Except. “tie” is one character wrong for “the” and no spell checker will protest “tie”. Similarly “she” and “thy” and a couple of other words. And it’d be a bit much to expect “t e” or “ he” to be turned back into “the” even though both are just the one keystroke off. And a spell checker would probably suppose that “tht” is a typo for “that”. It’s hard to guess how many of the one-character-off words will not actually be caught. Let’s say that maybe half the one-character-off words will be corrected to “the”; that’s still a pretty good 39 one-character misspellings, plus five permutations, plus the correct spelling or 45 candidate three-character strings for autocorrect to get. So our monkey has something like one chance in 450 of getting “the” in banging on the keyboard three times.

For four-letter words there are many more combinations — 531,441, if we just list the strings of our 27 allowed characters — but then there are more strings which would get autocorrected. Let’s say we want the string “thus”; there are 23 ways to arrange those letters in addition to the correct one. And there are 104 one-character-off strings; supposing that half of them will get us to “thus”, then, there’s 76 strings that get one to the desired “thus”. That’s a pretty dismal one chance in about 7,000 of typing one of them, unfortunately. Things get a little better if we suppose that some two-character errors are going to be corrected, although I can’t find one which my spell checker will accept right now, and if a single error and a transposition are viable.

With longer words yet there’s more chances for spell checker forgiveness: you can get pretty far off “accommodate” or “aneurysm” and still be saved by the spell checker, which is good for me as I last spelled “accommodate” correctly sometime in 1992, and I thought it looked wrong then.

So the conclusion has to be: you’ll get a bit of an improvement in speed by turning on autocorrect, for the obvious reason that you’re more likely to get one right out of 450 than you are to get one right out of 19,000. But it’s not going to help you very much; the number of ways to spell things so completely wrong that not even spell check can find you just grows far too rapidly to be helped. If I get a little bored I might work out the chance of getting a permutation-or-one-off for strings of different lengths.

And your monkey might be ill-served by autocorrect anyway. When I lived in Singapore I’d occasionally have teh tarik (“pulled tea”), black tea with sugar and milk tossed back and forth until it’s nice and frothy. It’s a fine drink but hard to write back home about because even if you get past the spell checker, the reader assumes the “teh” is a typo and mentally corrects for it. When this came up I’d include a ritual emphasis that I actually meant what I wrote, but you see the problem. Fortunately Shakespeare wrote relatively little about southeast Asian teas, but if you wanted to expand the infinite monkey problem to the problem of guiding tourists through Singapore, you’d have to turn the autocorrect off to have any hope of success.

Reading the Comics, June 4, 2014: Intro Algebra Edition


I’m not sure that there is a theme to the most recent mathematically-themed comic strips that I’ve seen, all from GoComics in the past week, but they put me in mind of the stuff encountered in learning algebra, so let’s run with that. It’s either that or I start making these “edition” titles into something absolutely and utterly meaningless, which could be.

Marc Anderson’s Andertoons (May 30) uses the classic setup of a board full of equation to indicate some serious, advanced thinking going on, and then puts in a cute animal twist on things. I don’t believe that the equation signifies anything, but I have to admit I’m not sure. It looks quite plausibly like something which might turn up in quantum mechanics (the “h” and “c” and lambda are awfully suggestive), so if Anderson made it up out of whole cloth he did an admirable job. If he didn’t make it up and someone recognizes it, please, let me know; I’m curious what it might be.

Marc Anderson reappears on the second of June has the classic reluctant student upset with the teacher who knew all along what x was. Knowledge of what x is is probably the source of most jokes about learning algebra, or maybe mathematics overall, and it’s amusing to me anyway that what we really care about is not what x is particularly — we don’t even do ourselves any harm if we call it some other letter, or for that matter an empty box — but learning how to figure out what values in the place of x would make the relationship true.

Jonathan Lemon’s Rabbits Against Magic (May 31) has the one-eyed rabbit Weenus doing miscellaneous arithmetic on the way to punning about things working out. I suppose to get to that punch line you have to either have mathematics or gym class as the topic, and I wouldn’t be surprised if Lemon’s done a version with those weight-lifting machines on screen. That’s not because I doubt his creativity, just that it’s the logical setup.

Eric Scott’s Back In The Day (June 2) has a pair of dinosaurs wondering about how many stars there are. Astronomy has always inspired mathematics. After one counts the number of stars one gets to wondering, how big the universe could be — Archimedes, classically, estimated the universe was about big enough to hold 1063 grains of sand — or how far away the sun might be — which the Ancient Greeks were able to estimate to the right order of magnitude on geometric grounds — and I imagine that looking deep into the sky can inspire the idea that the infinitely large and the infinitely small are at least things we can try to understand. Trying to count stars is a good start.

Steve Boreman’s Little Dog Lost (June 2) has a stick insect provide the excuse for some geometry puns.

Brian and Ron Boychuk’s The Chuckle Brothers (June 4) has a pie shop gag that I bet the Boychuks are kicking themselves for not having published back in mid-March.

The Math Blog Statistics, May 2014


And on to the tracking of how my little mathematics blog is doing. As readership goes, things are looking good — my highest number of page views since January 2013, and third-highest ever, and also my highest number of unique viewers since January 2013 (unique viewer counts aren’t provided for before December 2012, so who knows what happened before that). The total number of page views rose from 565 in April to 751, and the number of unique visitors rose from 238 to 315. This is a remarkably steady number of views per visitor, though — 2.37 rising to 2.38, as if that were a significant difference. I passed visitor number 15,000 somewhere around the 5th of May, and at number 15,682 right now that puts me on track to hit 16,000 somewhere around the 13th.

As with April, the blog’s felt pretty good to me. I think I’m hitting a pretty good mixture of writing about stuff that interest me and finding readers who’re interested to read it. I’m hoping I can keep that up another month.

The most popular articles of the month — well, I suspect someone was archive-binging on the mathematics comics ones because, here goes:

  1. How Many Trapezoids I Can Draw, which will be my memorial
  2. Reading the Comics, May 13, 2014: Good Class Problems Edition, which was a tiny bit more popular than …
  3. Reading the Comics, May 26, 2014: Definitions Edition, the last big entry in the Math Comics of May sequence.
  4. Some Things About Joseph Nebus is just my little biographic page and I have no idea why anyone’s even looking at that.
  5. Reading the Comics, May 18, 2014: Pop Math of the 80s Edition is back on the mathematics comics, as these things should be,
  6. Reading the Comics, May 4, 2014: Summing the Series Edition and what the heck, let’s just mention this one too.
  7. The ideal gas equation is my headsup to a good writer’s writings.
  8. Where Does A Plane Touch A Sphere? is a nicely popular bit motivated by the realization that a tangent point is an important calculus concept and nevertheless a subtler thing than one might realize.

I think without actually checking this is the first month I’ve noticed with seven countries sending me twenty or more visitors each — the United States (438), Canada (39), Australia (38), Sweden (31), Denmark (21), and Singapore and the United Kingdom (20 each). Austria came in at 19, too. Sixteen countries sent me one visitor each: Antigua and Barbuda, Colombia, Guernsey, Hong Kong, Ireland, Italy, Jamaica, Japan, Kuwait, Lebanon, Mexico, Morocco, Norway, Peru, Poland, Swaziland, and Switzerland. Morocco’s the only one to have been there last month.

And while I lack for search term poetry, some of the interesting searches that brought people here include:

  • working mathematically comics
  • https://nebusresearch.wordpress.com/ [ They’ve come to the right place, then. ]
  • how do you say 1898600000000000000000000000 in words [ I never do. ]
  • two trapezoids make a [ This is kind of beautiful as it is. ]
  • when you take a trapeziod apart how many trangles will you have?
  • -7/11,5/-8which is greter rational number and why
  • origin is the gateway to your entire gaming universe. [ This again is rather beautiful. ]
  • venn diagram on cartoons and amusement parks [ Beats me. ]

Reading the Comics, May 26, 2014: Definitions Edition


The most recent bunch of mathematics-themed comics left me feeling stumped for a theme. There’s no reason they have to have one, of course; cartoonists, as far as I know, don’t actually take orders from Comic Strip Master Command regarding what to write about, but often they seem to. Some of them seem to touch on definitions, at least, including of such ideas as the value of a quantity and how long it is between two events. I’ll take that.

Jef Mallet’s Frazz (May 23) does the kid-resisting-the-question sort of joke (not a word problem, for a change of pace), although I admit I didn’t care for the joke. I needed too long to figure out how the meaning of “value” for a variable might be ambiguous. Caulfield kind of has a point about mathematics needing to use precise words, but the process of making a word precise is a great and neglected part of mathematical history. Consider, for example: contemporary (English-language, at least) mathematicians define a prime number to be a counting number (1, 2, 3, et cetera) with exactly two factors. Why exactly two factors, except to rule out 1 as a prime number? But then why rule that 1 can’t be a prime number? As an idea gets used and explored we get a better idea of what’s interesting about it, and what it’s useful for, and can start seeing whether some things should be ruled out as not fitting a concept we want to describe, or be accepted as fitting because the concept is too useful otherwise and there’s no clear way to divide what we want from what we don’t.

I still can’t buy Caulfield’s proposition there, though.

Steve Boreman’s Little Dog Lost (May 25) circles around a bunch of mathematical concepts without quite landing on any of them. The obvious thing is the counting ability of animals: the crow asserts that crows can only count as high as nine, for example, and the animals try to work out ways to deal with the very large number of 2,615. The vulture asserts he’s been waiting for 2,615 days for the Little Dog to cross the road, and wonders how many years that’s been. The first installment of the strip, from the 26th of March, 2007, did indeed feature Vulture waiting for Little Dog to cross the road, although as I make it out there’s 2,617 days between those events.

At a guess, either Boreman was not counting the first and the last days of the interval between March 26, 2007, and May 25, 2014, or maybe he forgot the leap days. Finding how long it is between dates is a couple of kinds of messes, first because it isn’t necessarily clear whether to include the end dates, and second because the Gregorian calendar is a mess of months of varying lengths plus the fun of leap years, which include an exception for century years and an exception to the exception, making it all the harder. My preferred route for finding intervals is to not even try working the time out by myself, and instead converting every date to the Julian date, a simple serial count of the number of dates since noon Universal Time on the 1st of January, 4713 BC, on the Julian calendar. Let the Navy deal with leap days. I have better things to worry about.

Samson’s Dark Side Of The Horse (May 26) sees Horace trying to count sheep to get himself to sleep; different ways of denoting numbers confound him. I’m not sure if it’s known why counting sheep, or any task like that, is useful in getting to sleep. My guess would be that it just falls into the sort of activity that can be done without a natural endpoint and without demanding too much attention to keep one awake, while demanding enough attention that one isn’t thinking about the bank account or the noise inside the walls or the way the car lurches two lanes to the right every time one taps the brake at highway speeds. That’s a guess, though.

Tom Horacek’s Foolish Mortals (May 26) uses the “on a scale of one to ten” standard for something that’s not usually described so vaguely, and I like the way it teases the idea of how to measure things. The “scale of one to ten” is logically flawed, since we have no idea what the units are, how little of something one represents or how much the ten does, or even whether it’s a linear scale — the difference between “two” and “three” is the same as that between “three” and “four”, the way lengths and weight work — or a logarithmic one — the ratio between “two” and “three” equals that between “three” and “four”, the way stellar magnitudes, decibel sound readings, and Richter scale earthquake intensity measure work — or, for that matter, what normal ought to be. And yet there’s something useful in making the assessment, surely because the first step towards usefully quantifying a thing is to make a clumsy and imprecise quantification of it.

Dave Blazek’s Loose Parts (May 26) kind of piles together a couple references so a character can identify himself as a double major in mathematics and theology. Of course, the generic biography for a European mathematician, between about the end of the Western Roman Empire and the Industrial Revolution, is that he (males most often had the chance to do original mathematics) studied mathematics alongside theology and philosophy, and possibly astronomy, although that reflects more how the subjects were seen as rather intertwined, and education wasn’t as specialized and differentiated as it’s now become. (The other generic mathematician would be the shopkeeper or the exchequer, but nobody tells jokes about their mathematics.)

And, finally, Doug Savage’s Savage Chickens (May 28) brings up the famous typing monkeys (here just the one of them), and what really has to be counted as a bit of success for the project.

Reading the Comics, May 18, 2014: Pop Math of the 80s Edition


And now there’ve suddenly been enough mathematics-themed comics for a fresh collection of the things. If there’s any theme this time around it’s to mathematics I remember filtering into popular culture in the 80s: the Drake Equation (which I, at least, first saw in Carl Sagan’s Cosmos and found haunting), and the Rubik’s Cube, which pop mathematics writers in the early 80s latched onto with an eagerness matched only by how they liked polyominoes in the mid-70s, and the Mandelbrot Set, which I think of as a mid-to-late 80s thing because that’s when it started covering science-oriented magazine covers and the screens of IBM PS/2’s being used by the kids in the math and science magnet programs.

Incidentally, this time around I’ve tried to include the Between Friends that I talk about, because I’m not convinced the link to its Comics Kingdom home site will last indefinitely. Gocomics.com seems to keep links from expiring, even for non-subscribers, but I’m curious whether it would be better-liked if I included images of the strips I talk about? I’m fairly confident that this is fair use, as I talk about mathematical subjects inspired by the strips, but I don’t know whether people care much about saving a click before reading my attempts to say something, anything, about a kid given a word problem about airplanes that he answers in a flippant manner.

Wulff and Morgenthaler’s WuMo (May 15) features Professor Rubik, “five minutes after” inventing what he’s famous for. Ernö Rubik really is a Professor (of architecture, at the Budapest College of Applied Arts when he invented his famous cube), and was interested in the relationships of things in space and of objects moving in space. The Rubik’s Cube is of interest mathematically because it offers a great excuse to introduce group theory to the average person. Group theory is, among other things, a way of studying structures that look like arithmetic but that aren’t necessarily on numbers. Rotations work very much like the addition of numbers, at least, the modular addition (where if a result is less than zero, or greater than some upper bound, you add or subtract that upper bound until the result is back in range), and the Rubik’s Cube offers several interacting sets of things to rotate, so that the groups represented by it are fascinatingly complex.

Though the cube was invented in 1974 it didn’t become an overwhelming phenomenon until 1979, and then much of the early 80s was spent in people making jokes about how frustrating they found it and occasionally buying books that were supposed to tell you how to solve it, but you couldn’t after all. Then there was a Saturday morning cartoon about the cube which I watched because I had horrible, horrible, horrible taste in cartoons as a kid. Anyway, it turns out that if you played it perfectly you could solve any Rubik’s Cube in no more than twenty steps, although this wasn’t proven until 2010. I confess I usually just give up around step 35 and take the cube apart. Don’t watch the cartoon.

Eric the Circle (May 17), this entry by “Designroo”, features Eric in the midst of the Mandelbrot Set. The Mandelbrot Set, basis for two-thirds of all the posters on the walls in the mathematics department from 1986 through 2002, was discovered by Benoît Mandelbrot in one of those triumphs of numerical computing. It’s not hard to describe how to make it — it’s only a little more advanced than the pastime of hitting a square root or a square button on a calculator and watching numbers dwindle to zero or grow infinitely large — but the number of calculations that need to be done to see it mean it’d never have been discovered before there were computers to do the hard work, of calculation and of visualization.

Among the neat things about the Mandelbrot set are that it does have inlets that look like circles, and it has an infinite number of them: if you zoom in closely at any point on the boundary of the Mandelbrot set you’ll find a not-quite-perfect replica of the original set, with the big carotid shape and the budding circles on the edges, over and over, inexhaustibly.

Bill Amend’s FoxTrot (May 17, rerun) asks why there aren’t geometry books on tape. It’s not quite an absurd question: in principle, geometry is a matter of deductive logic, and is about the relationship between ideas we call “points” and “lines” and “angles” and the like. Pictures are nice to have, as appeals to intuition, but our intuition can be wrong, and pictures can lead us astray, as any optical illusion will prove. And yet it’s so very hard to do away with that intuition. We may not know a compelling reason why the things we draw on sheets of paper should correspond to the results of logical, deductive reasoning that ought to be true whether drawn or not and whether, for that matter, a universe existed or not, but seeing representations of the relationships of geometric objects seems to help nearly everyone understand them better than simply knowing the reasons they should have those relationships.

The notion of learning geometry without drawings takes one fairly close to the Bourbaki project, the famous/infamous early 20th century French mathematical collective that tried to work out the logical structure of all mathematics on a purely formal, reasoned basis without any appeals to diagrams or physical intuition at all. It was an ambitious, controversial, and fruitful program that got permanently tainted because following from it was the “New Math”, an attempt at mathematics educational reform of the 60s and 70s which crashed hard against the problem that parents will only support educational reform that doesn’t involve teaching a thing in ways different from how they learned it.

Sondra Bell-Lundy's _Between Friends_, 18 May 2014: mothers draw a Venn Diagram.
Sondra Bell-Lundy’s _Between Friends_, 18 May 2014: mothers draw a Venn Diagram.

Sandra Bell-Lundy’s Between Friends (May 18) brings up my old nemesis of Venn Diagrams, although it gets them correct.

T Lewis and Michael Fry’s Over The Hedge (May 18) showcases the Drake Equation, a wonderful bit of reasoning that tries to answer the question of “how many species capable of interstellar communication are there”, considering that we only have evidence for at most one. It’s a wonderful bit of word-problem-type reasoning: given what we do know, which amounts mostly to how many stars there are, how can we work out what we would like to know? Frank Drake, astronomer, and co-designer of the plaque on Pioneers 10 and 11, made some estimates of what factors are relevant in going from what we do know to what we would like to know, and how they might relate. When Drake first published the equation only the number of stars could be reasonably estimated; today we can also add a good estimate of how likely a star is to have planets, and a fair estimate of how likely a planet is to be livable. The other steps are harder to estimate. But the process Drake used, of evaluating what he would need to know in order to give an answer, is still strong: there may be things about the equation which are wrong — factors that interact in ways not previously considered, for example — but it divides a huge problem into a series of smaller ones that can, hopefully, be studied and understood in pieces and through this process be turned into knowledge.

And finally, Jeff Harris’s Shortcuts (May 18), a kid’s activity/information panel, spends a half-a-comics-page talking about numbers and numerals. It’s a pretty respectable short guide to numbers and their representations, including some of the more famous number-representation schemes.

Reading the Comics, May 13, 2014: Good Class Problems Edition


Someone in Comic Strip Master Command must be readying for the end of term, as there’s been enough comic strips mentioning mathematics themes to justify another of these entries, and that’s before I even start reading Wednesday’s comics. I can’t say that there seem to be any overarching themes in the past week’s grab-bag of strips, but, there are a bunch of pretty good problems that would fit well in a mathematics class here.

Darrin Bell’s Candorville (May 6) comes back around to the default application of probability, questions in coin-flipping. You could build a good swath of a probability course just from the questions the strip implies: how many coins have to come up heads before it becomes reasonable to suspect that something funny is going on? Two is obviously too few; two thousand is likely too many. But improbable things do happen, without it signifying anything. So what’s the risk of supposing something’s up when it isn’t? What’s the risk of dismissing the hints that something is happening?

Mark Anderson’s Andertoons (May 8) is another entry in the wiseacre schoolchild genre (I wonder if I’ve actually been consistent in describing this kind of comic, but, you know what I mean) and suggesting that arithmetic just be done on the computer. I’m sympathetic, however much fun it is doing arithmetic by hand.

Justin Boyd’s Invisible Bread (May 9) is honestly a marginal inclusion here, but it does show a mathematics problem that’s correctly formed and would reasonably be included on a precalculus or calculus class’s worksheets. It is a problem that’s a no-brainer, really, but that fits the comic’s theme of poorly functioning.

Steve Moore’s In The Bleachers (May 12) uses baseball scores and the start of a series. A series, at least once you’re into calculus, is the sum of a sequence of numbers, and if there’s only finitely many of them, here, there’s not much that’s interesting to say. Each sequence of numbers has some sum and that’s it. But if you have an infinite series — well, there, all sorts of amazing things become possible (or at least logically justified), including integral calculus and numerical computing. The series from the panel, if carried out, would come to a pair of infinitely large sums — this is called divergence, and is why your mathematician friends on Facebook or Twitter are passing around that movie poster with a math formula for a divergent series on it — and you can probably get a fair argument going about whether the sum of all the even numbers would be equal to the sum of all the odd numbers. (My advice: if pressed to give an answer, point to the other side of the room, yell, “Look, a big, distracting thing!” and run off.)

Samson’s Dark Side Of The Horse (May 13) is something akin to a pun, playing as it does on the difference between a number and a numeral and shifting between the ways we might talk about “three”. Also, I notice for the first time that apparently the little bird sometimes seen in the comic is named “Sine”, which is probably why it flies in such a wavy pattern. I don’t know how I’d missed that before.

Rick Detorie’s One Big Happy (May 13, rerun) is also a strip that plays on the difference between a number and its representation as a numeral, really. Come to think of it, it’s a bit surprising that in Arabic numerals there aren’t any relationships between the representations for numbers; one could easily imagine a system in which, say, the symbol for “four” were a pair of whatever represents “two”. In A History Of Mathematical Notations Florian Cajori notes that there really isn’t any system behind why a particular numeral has any particular shape, and he takes a section (Section 96 in Book 1) to get engagingly catty about people who do. I’d like to quote it because it’s appealing, in that way:

A problem as fascinating as the puzzle of the origin of language relates to the evolution of the forms of our numerals. Proceeding on the tacit assumption that each of our numerals contains within itself, as a skeleton so to speak, as many dots, strokes, or angles as it represents units, imaginative writers of different countries and ages have advanced hypotheses as to their origin. Nor did these writers feel that they were indulging simply in pleasing pastimes or merely contributing to mathematical recreations. With perhaps only one exception, they were as convinced of the correctness of their explanations as are circle-squarers of the soundness of their quadratures.

Cajori goes on to describe attempts to rationalize the Arabic numerals as “merely … entertaining illustrations of the operation of a pseudo-scientific imagination, uncontrolled by all the known facts”, which gives some idea why Cajori’s engaging reading for seven hundred pages about stuff like where the plus sign comes from.

Reading the Comics, May 4, 2014: Summing the Series Edition


Before I get to today’s round of mathematics comics, a legend-or-joke, traditionally starring John Von Neumann as the mathematician.

The recreational word problem goes like this: two bicyclists, twenty miles apart, are pedaling toward each other, each at a steady ten miles an hour. A fly takes off from the first bicyclist, heading straight for the second at fifteen miles per hour (ground speed); when it touches the second bicyclist it instantly turns around and returns to the first at again fifteen miles per hour, at which point it turns around again and head for the second, and back to the first, and so on. By the time the bicyclists reach one another, the fly — having made, incidentally, infinitely many trips between them — has travelled some distance. What is it?

And this is not hard problem to set up, inherently: each leg of the fly’s trip is going to be a certain ratio of the previous leg, which means that formulas for a geometric infinite series can be used. You just need to work out what the lengths of those legs are to start with, and what that ratio is, and then work out the formula in your head. This is a bit tedious and people given the problem may need some time and a couple sheets of paper to make it work.

Von Neumann, who was an expert in pretty much every field of mathematics and a good number of those in physics, allegedly heard the problem and immediately answered: 15 miles! And the problem-giver said, oh, he saw the trick. (Since the bicyclists will spend one hour pedaling before meeting, and the fly is travelling fifteen miles per hour all that time, it travels a total of a fifteen miles. Most people don’t think of that, and try to sum the infinite series instead.) And von Neumann said, “What trick? All I did was sum the infinite series.”

Did this charming story of a mathematician being all mathematicky happen? Wikipedia’s description of the event credits Paul Halmos’s recounting of Nicholas Metropolis’s recounting of the story, which as a source seems only marginally better than “I heard it on the Internet somewhere”. (Other versions of the story give different distances for the bicyclists and different speeds for the fly.) But it’s a wonderful legend and can be linked to a Herb and Jamaal comic strip from this past week.

Paul Trap’s Thatababy (April 29) has the baby “blame entropy”, which fits as a mathematical concept, it seems to me. Entropy as a concept was developed in the mid-19th century as a thermodynamical concept, and it’s one of those rare mathematical constructs which becomes a superstar of pop culture. It’s become something of a fancy word for disorder or chaos or just plain messes, and the notion that the entropy of a system is ever-increasing is probably the only bit of statistical mechanics an average person can be expected to know. (And the situation is more complicated than that; for example, it’s just more probable that the entropy is increasing in time.)

Entropy is a great concept, though, as besides capturing very well an idea that’s almost universally present, it also turns out to be meaningful in surprising new places. The most powerful of those is in information theory, which is just what the label suggests; the field grew out of the problem of making messages understandable even though the telegraph or telephone lines or radio beams on which they were sent would garble the messages some, even if people sent or received the messages perfectly, which they would not. The most captivating (to my mind) new place is in black holes: the event horizon of a black hole has a surface area which is (proportional to) its entropy, and consideration of such things as the conservation of energy and the link between entropy and surface area allow one to understand something of the way black holes ought to interact with matter and with one another, without the mathematics involved being nearly as complicated as I might have imagined a priori.

Meanwhile, Lincoln Pierce’s Big Nate (April 30) mentions how Nate’s Earned Run Average has changed over the course of two innings. Baseball is maybe the archetypical record-keeping statistics-driven sport; Alan Schwarz’s The Numbers Game: Baseball’s Lifelong Fascination With Statistics notes that the keeping of some statistical records were required at least as far back as 1837 (in the Constitution of the Olympic Ball Club of Philadelphia). Earned runs — along with nearly every other baseball statistic the non-stathead has heard of other than batting averages — were developed as a concept by the baseball evangelist and reporter Henry Chadwick, who presented them from 1867 as an attempt to measure the effectiveness of batting and fielding. (The idea of the pitcher as an active player, as opposed to a convenient way to get the ball into play, was still developing.) But — and isn’t this typical? — he would come to oppose the earned run average as a measure of pitching performance, because things that were really outside the pitcher’s control, such as stolen bases, contributed to it.

It seems to me there must be some connection between the record-keeping of baseball and the development of statistics as a concept in the 19th century. Granted the 19th century was a century of statistics, starting with nation-states measuring their populations, their demographics, their economies, and projecting what this would imply for future needs; and then with science, as statistical mechanics found it possible to quite well understand the behavior of millions of particles despite it being impossible to perfectly understand four; and in business, as manufacturing and money were made less individual and more standard. There was plenty to drive the field without an amusing game, but, I can’t help thinking of sports as a gateway into the field.

Creator.com's _Donald Duck_ for 2 May 2014: Ludwig von Drake orders his computer to stop with the thinking.

The Disney Company’s Donald Duck (May 2, rerun) suggests that Ludwig von Drake is continuing to have problems with his computing machine. Indeed, he’s apparently having the same problem yet. I’d like to know when these strips originally ran, but the host site of creators.com doesn’t give any hint.

Stephen Bentley’s Herb and Jamaal (May 3) has the kid whose name I don’t really know fret how he spent “so much time” on an equation which would’ve been easy if he’d used “common sense” instead. But that’s not a rare phenomenon mathematically: it’s quite possible to set up an equation, or a process, or a something which does indeed inevitably get you to a correct answer but which demands a lot of time and effort to finish, when a stroke of insight or recasting of the problem would remove that effort, as in the von Neumann legend. The commenter Dartpaw86, on the Comics Curmudgeon site, brought up another excellent example, from Katie Tiedrich’s Awkward Zombie web comic. (I didn’t use the insight shown in the comic to solve it, but I’m happy to say, I did get it right without going to pages of calculations, whether or not you believe me.)

However, having insights is hard. You can learn many of the tricks people use for different problems, but, say, no amount of studying the Awkward Zombie puzzle about a square inscribed in a circle inscribed in a square inscribed in a circle inscribed in a square will help you in working out the area left behind when a cylindrical tube is drilled out of a sphere. Setting up an approach that will, given enough work, get you a correct solution is worth knowing how to do, especially if you can give the boring part of actually doing the calculations to a computer, which is indefatigable and, certain duck-based operating systems aside, pretty reliable. That doesn’t mean you don’t feel dumb for missing the recasting.

Rick Detorie's _One Big Happy_ for 3 May 2014: Joe names the whole numbers.

Rick DeTorie’s One Big Happy (May 3) puns a little on the meaning of whole numbers. It might sound a little silly to have a name for only a handful of numbers, but, there’s no reason not to if the group is interesting enough. It’s possible (although I’d be surprised if it were the case) that there are only 47 Mersenne primes (a number, such as 7 or 31, that is one less than a whole power of 2), and we have the concept of the “odd perfect number”, when there might well not be any such thing.

The Math Blog Statistics, April 2014


Another month’s gone by and the statistics about viewership were pretty gratifying for April 2014. But I’m feeling awfully good about the place, because I’ve felt more gratified by the mathematics blog lately. It’s felt to me like there’ve been more comments and more interaction the past couple weeks, and it’s felt like it’s getting closer to supporting a community, which is thrilling, if not exactly measurable given what WordPress shares with me.

In March 2014, according to last month’s statistics survey, there were 453 views from 257 distinct viewers. That jumped pretty noticeably this month to 565 views, albeit from 235 distinct viewers, a views-per-visitor jump from 1.76 to 2.40. I suspect there’s some archive-bingers, and I’m happy to give anyone that thrill. It’s my greatest viewer count since June 2013, and the fourth-highest since December 2012 when WordPress started sharing statistics on unique visitors. I also noted at the start of April that while I’d reached 14,000 visitors in March I’d need a stroke of luck to reach 15,000 in April. I came close: the month topped out with my 14,931st view.

The most popular articles of the past thirty days were:

  1. How Dirac Made Every Number, the answer to that puzzle of how to construct any counting number using precisely four 2’s and ordinary operations (it’s a forehead slapper once you’ve seen it)
  2. Reading the Comics, April 27, 2014: The Poetry of Calculus Edition, as everyone wants to see some calculus poetry
  3. Can You Be As Clever As Dirac For A Little Bit in which that Dirac puzzle was laid out and the rules given
  4. How Many Trapezoids I Can Draw, always with the trapezoids
  5. Reading the Comics, April 21, 2014: Bill Amend In Name Only Edition, which includes a bundle of a lot of mathematics comics from Bill Amend’s FoxTrot in case you need some

The countries sending me the most viewers were the United States (294), Canada (65), Denmark (29), Austria (27), and the United kingdom (26), and I count nine countries sending me at least ten views each, which I think is a record but I haven’t been keeping track of that number. Sending me a single viewer each were Belgium, Brazil, Ecuador, Finland, Greece, Hungary, Malaysia, Morocco, Oman, Sweden, and Venezuela. Belgium, Brazil, Hungary, and Sweden were single-country viewers last month, and Hungary’s got a three-month single-viewer streak going. So, ah, hi, whoever that is in Hungary. Apparently nobody has ever visited me from Honduras.

Once again there’s a shortage of search term poetry, but there were some fair queries the past month, including:

Reading the Comics, April 27, 2014: The Poetry of Calculus Edition


I think there are enough comic strips for another installment of this series, so, here you go. There are a couple comics once again using mathematics, and calculus particularly, just to signify that there’s something requiring a lot of brainpower going on, which is flattering to people who learned calculus well enough, at the risk of conveying a sense that normal people can’t hope to become literate in mathematics. I don’t buy that. Anyway, there were comics that went in other directions, which is why there’s more talk about Dutch military engineering than you might have expected for today’s entry.

Mark Anderson’s Andertoons (April 22) uses the traditional blackboard full of calculus to indicate a genius. The exact formulas on the board don’t suggest anything particular to me, although they do seem to parse. I wouldn’t be surprised if they turned out to be taken from a textbook, possibly in fluid mechanics, that I just happen not to have noticed.

Piers Baker’s Ollie and Quentin (April 23, rerun) has Ollie and Quentin flipping a coin repeatedly until Quentin (the lugworm) sees his choice come up. Of course, if it is a fair coin, a call of heads or tails will come up eventually, at least if we carefully define what we mean by “eventually”, and for that matter, Quentin’s choice will surely come up if he tries long enough.

Continue reading “Reading the Comics, April 27, 2014: The Poetry of Calculus Edition”

Reading the Comics, April 21, 2014: Bill Amend In Name Only Edition


Recently the National Council of Teachers of Mathematics met in New Orleans. Among the panelists was Bill Amend, the cartoonist for FoxTrot, who gave a talk about the writing of mathematics comic strips. Among the items he pointed out as challenges for mathematics comics — and partly applicable to any kind of teaching of mathematics — were:

  • Accessibility
  • Stereotypes
  • What is “easy” and “hard”?
  • I’m not exactly getting smarter as I age
  • Newspaper editors might not like them

Besides the talk (and I haven’t found a copy of the PowerPoint slides of his whole talk) he also offered a collection of FoxTrot comics with mathematical themes, good for download and use (with credit given) for people who need to stock up on them. The link might be expire at any point, note, so if you want them, go now.

While that makes a fine lead-in to a collection of mathematics-themed comic strips around here I have to admit the ones I’ve seen the last couple weeks haven’t been particularly inspiring, and none of them are by Bill Amend. They’ve covered a fair slate of the things you can write mathematics comics about — physics, astronomy, word problems, insult humor — but there’s still interesting things to talk about. For example:

Continue reading “Reading the Comics, April 21, 2014: Bill Amend In Name Only Edition”

Reading the Comics, April 1, 2014: Name-Dropping Monkeys Edition


There’s been a little rash of comics that bring up mathematical themes, now, which is ordinarily pretty good news. But when I went back to look at my notes I realized most of them are pretty much name-drops, mentioning stuff that’s mathematical without giving me much to expand upon. The exceptions are what might well be the greatest gift which early 20th century probability could give humor writers. That’s enough for me.

Mark Anderson’s Andertoons (March 27) plays on the double meaning of “fifth” as representing a term in a sequence and as representing a reciprocal fraction. It also makes me realize that I hadn’t paid attention to the fact that English (at least) lets you get away with using the ordinal number for the part fraction, at least apart from “first” and “second”. I can make some guesses about why English allows that, but would like to avoid unnecessarily creating folk etymologies.

Hector D Cantu and Carlos Castellanos’s Baldo (March 27) has Baldo not do as well as he expected in predictive analytics, which I suppose doesn’t explicitly require mathematics, but would be rather hard to do without. Making predictions is one of mathematics’s great applications, and drives much mathematical work, in the extrapolation of curves and the solving of differential equations most obviously.

Dave Whamond’s Reality Check (March 27) name-drops the New Math, in the service of the increasingly popular sayings that suggest Baby Boomers aren’t quite as old as they actually are.

Rick Stromoski’s Soup To Nutz (March 29) name-drops the metric system, as Royboy notices his ten fingers and ten toes and concludes that he is indeed metric. The metric system is built around base ten, of course, and the idea that changing units should be as easy as multiplying and dividing by powers of ten, and powers of ten are easy to multiply and divide by because we use base ten for ordinary calculations. And why do we use base ten? Almost certainly because most people have ten fingers and ten toes, and it’s so easy to make the connection between counting fingers, counting objects, and then to the abstract idea of counting. There are cultures that used other numerical bases; for example, the Maya used base 20, but it’s hard not to notice that that’s just using fingers and toes together.

Greg Cravens’s The Buckets (March 30) brings out a perennial mathematics topic, the infinite monkeys. Here Toby figures he could be the greatest playwright by simply getting infinite monkeys and typewriters to match, letting them work, and harvesting the best results. He hopes that he doesn’t have to buy many of them, to spoil the joke, but the remarkable thing about the infinite monkeys problem is that you don’t actually need that many monkeys. You’ll get the same result — that, eventually, all the works of Shakespeare will be typed — with one monkey or with a million or with infinitely many monkeys; with fewer monkeys you just have to wait longer to expect success. Tim Rickard’s Brewster Rockit (April 1) manages with a mere hundred monkeys, although he doesn’t reach Shakespearean levels.

But making do with fewer monkeys is a surprisingly common tradeoff in random processes. You can often get the same results with many agents running for a shorter while, or a few agents running for a longer while. Processes that allow you to do this are called “ergodic”, and being able to prove that a process is ergodic is good news because it means a complicated system can be represented with a simple one. Unfortunately it’s often difficult to prove that something is ergodic, so you might instead just warn that you are assuming the ergodic hypothesis or ergodicity, and if nothing else you can probably get a good fight going about the validity of “ergodicity” next time you play Scrabble or Boggle.

The Math Blog Statistics, March 2014


It’s the start of a fresh month, so let me carry on my blog statistics reporting. In February 2014, apparently, there were a mere 423 pages viewed around here, with 209 unique visitors. That’s increased a bit, to 453 views from 257 visitors, my second-highest number of views since last June and second-highest number of visitors since last April. I can make that depressing, though: it means views per visitor dropped from 2.02 to 1.76, but then, they were at 1.76 in January anyway. And I reached my 14,000th page view, which is fun, but I’d need an extraordinary bit of luck to get to 15,000 this month.

March’s most popular articles were a mix of the evergreens — trapezoids and comics — with a bit of talk about March Madness serving as obviously successful clickbait:

  1. How Many Trapezoids I Can Draw, and again, nobody’s found one I overlooked.
  2. Calculating March Madness, and the tricky problem of figuring out the chance of getting a perfect bracket.
  3. Reading The Comics, March 1, 2014: Isn’t It One-Half X Squared Plus C? Edition, showing how well an alleged joke will make comic strips popular.
  4. Reading The Comics, March 26, 2014: Kitchen Science Department, showing that maybe it’s just naming the comics installments that matters.
  5. What Are The Chances Of An Upset, which introduces some of the interesting quirks of the bracket and seed system of playoffs, such as the apparent advantage an eleventh seed has over an eighth seed.

There’s a familiar set of countries sending me the most readers: as ever the United States up top (277), with Denmark in second (26) and Canada in third (17). That’s almost a tie, though, as the United Kingdom (16), Austria (15), and the Philippines (13) could have taken third easily. I don’t want to explicitly encourage international rivalries to drive up my page count here, I’m just pointing it out. Singapore is in range too. The single-visitor countries this past month were the Bahamas, Belgium, Brazil, Colombia, Hungary, Mexico, Peru, Rwanda, Saudi Arabia, Spain, Sri Lanka, Sweden, Syria, and Taiwan. Hungary, Peru, and Saudi Arabia are the only repeat visitors from February, and nobody’s got a three-month streak going.

There wasn’t any good search-term poetry this month; mostly it was questions about trapezoids, but there were a couple interesting ones:

So, that’s where things stand: I need to get back to writing about trapezoids and comic strips.

Reading the Comics, March 26, 2014: Kitchen Science Department


It turns out that three of the comic strips to be included in this roundup of mathematics-themed strips mentioned things that could reasonably be found in kitchens, so that’s why I’ve added that as a subtitle. I can’t figure a way to contort the other entries to being things that might be in kitchens, but, given that I don’t get to decide what cartoonists write about I think I’m doing well to find any running themes.

Ralph Hagen’s The Barn (March 19) is built around a possibly accurate bit of trivia which tries to stagger the mind by considering the numinous: how many stars are there? This evokes, to me at least, one of the famous bits of ancient Greek calculations (for which they get much less attention than the geometers and logicians did), as Archimedes made an effort to estimate how many grains of sand could fit inside the universe. Archimedes had apparently little fear of enormous numbers, and had to strain the Greek system for representing numbers to get at such enormous quantities. But he was an ingenious reasoner: he was able to estimate, for example, the sizes and distances to the Moon and the Sun based on observing, with the naked eye, the half-moon; and his work on problems like finding the value of pi get surprisingly close to integral calculus and would probably be a better introduction to the subject than pre-calculus courses are. It’s quite easy in considering how big (and how old) the universe is to get to numbers that are really difficult to envision, so, trying to reduce that by imagining stars as grains of salt might help, if you can imagine a ball of salt eight miles across.

Continue reading “Reading the Comics, March 26, 2014: Kitchen Science Department”

Reading The Comics, March 17, 2014: After The Ides Edition


Rather than wait to read today’s comics I’m just going to put in a fresh entry going over mathematical points raised in the funny pages. This one turned out to include a massive diversion into the wonders of the ancient Roman calendar, which is a mathematical topic, really, although there’s no calculations involved in it just here.

Bill Hinds’s Cleats (March 7, rerun) calls on one of the common cultural references to percentages, the idea of athletes giving 100 percent efforts. (Edith is feeling more like an 80 percent effort, or less than that.) The idea of giving 100 percent in a sport is one that invites the question, 100 percent of what; granting that there is some standard expectable effort made, then, even the sports reporting cliche of giving 110 percent is meaningful.
Cleats continued on the theme the next day, as Edith was thinking more of giving about 79 percent of 80 percent, and it’s not actually that hard to work out in your head what percent that is, if you know anything about doing arithmetic in your head.

Jef Mallet’s Frazz (March 14) was not actually the only comic strip among the roster I normally read to make a Pi Day reference, but I think it suffices as the example for the whole breed. I admit that I feel a bit curmudgeonly that I don’t actually care about Pi Day. I suppose that as a chance for people to promote the idea of learning mathematics, and maybe attach it to some of the many interesting things to be said about mathematics using Pi as the introductory note the idea is fine, but just naming a thing isn’t by itself a joke. I’m told that Facebook (I’m not on it) was thick with people posting photographs of pies, which is probably more fun when you think of it than when you notice everybody else thought of it too. Anyway, organized Pi Day events are still pretty new as Internet Pop Holidays go. Perhaps next year’s comics will be sharper.

Jenny Campbell’s Flo and Friends (March 15) comes back to useful mental arithmetic work, in this case in working out a reasonable tip. A twenty-percent tip is, mercifully, pretty easy to remember just as what’s-her-name specifies. (I can’t think of the kid’s name and there’s no meet-our-cast page on the web site. None of the commenters mention her name either, although they do make room to insult health care reform and letting students use calculators to do arithmetic, so, I’m sorry I read that far down too.) But as ever you need to make sure the process is explained clearly and understood, and Tina needed to run a sanity check on the result. Sanity checks, as suggested, won’t show that your answer is right, but they will rule out some of the wrong ones. (A fifteen percent tip is a bit annoying to calculate exactly, but dividing the original amount by six will give you a sixteen-and-two-thirds percent tip, which is surely close enough, especially if you round off to a quarter-dollar.)

Steve Breen and Mike Thompson’s Grand Avenue (March 15) has the kids wonder what are the ides of March; besides that they’re the 15th of the month and they’re used for some memorable writing about Julius Caesar it’s a fair thing not to know. They derive from calendar-keeping, one of the oldest useful applications of mathematics and astronomy. The ancient Roman scheme set three special dates in the month: the kalends, which seem to have started as the day of the new moon as observed in Rome; the nones, when the moon was at its first quarter; and the ides, when the moon was full.

But by the time of Numa Pompilius, the second (traditional) King of Rome, who reformed the calendar around 713 BC, the lunar link was snapped, partly so that the calendar year could more nearly fit the length of the time it takes to go from one spring to another. (Among other things the pre-Numa calendar had only ten months, with the days between December and March not belonging to any month; since Romans were rather agricultural at the time and there wasn’t much happening in winter, this wasn’t really absurd, even if I find it hard to imagine living by this sort of standard. After Numa there were only about eleven days of the year unaccounted for, with the time made up, when it needed to be, by inserting an extra month, Mercedonius, in the middle of February.) Months then had, February excepted, either 29 or 31 days, with the ides being on the fifteenth day of the 31-day months (March, May, July, and October) and the thirteenth day of the 29-day months.

For reasons that surely made sense if you were an ancient Roman the day was specified as the number of days until the next kalend, none, or ide; so, for example, while the 13th of March would be the 2nd day before the ides of March, II Id Mar, the 19th of March would be recorded as the the the 14th day before the kalend of April, or, XIV Kal Apr. I admit I could probably warm up to counting down to the next month event, but the idea of having half the month of March written down on the calendar as a date with “April” in it leaves me deeply unsettled. And that’s before we even get into how an extra month might get slipped into the middle of February (between the 23rd and the 24th of the month, the trace of which can still be observed in the dominical letters of February in leap years, on Roman Catholic and Anglican calendars, and in the obscure term “bissextile year” for leap year). But now that you see that, you know why (a) the ancient Romans had so much trouble getting their database software to do dates correctly and (b) you get to be all smugly superior to anyone who tries making a crack about the United States Federal Income Tax deadline being on the Ides of April, since they never are.

(Warning: absolutely no one ever will be impressed by your knowledge of the Ides of April and their inapplicability to discussions of the United States Federal Income Tax. However, you might use this as a way to appear like you’re making friendly small talk while actually encouraging people to leave you alone.)

Tom Horacek’s Foolish Mortals (March 17), an erratically-published panel strip, calls on the legend of how mathematicians “usually” peak in their twenties. It’s certainly said of mathematicians that they do their most important work while young — note that the Fields Medal is explicitly given to mathematicians for work done when they were under forty years old — although I’m not aware of anyone who’s actually studied this, and the number of great mathematicians who insist on doing brilliant work into their old age is pretty impressive.

Certainly, for example, Newton began work on calculus (and optics and gravitation) when he was about 23, but he didn’t publish until he was about fifty. (Leibniz, meanwhile, started publishing calculus his way at about age 38.) It’s probably impossible to say what Leonhard Euler’s most important work was, but (for example) his equations describing inviscid fluids — which would be the masterpiece for anybody not Euler — he published when he was fifty. Carl Friedrich Gauss didn’t start serious work in electromagnetism until he was about 55 years old, too. The law of electric flux which Gauss worked out for that — which, again, would have been the career achievement if Gauss weren’t overflowing with them — he published when he was 58.

I guess that I’m saying is that great minds, at least, don’t necessarily peak in their twenties, or at least they have some impressive peaks afterwards too.

14,000


Sometime on Thursday, the 6th of March, it appears I registered my 14,000th visitor to the math blog here. WordPress believes it to be someone from either the United States, France, Germany, Canada, or Australia, which at least covers a respectable number of possible time zones. The number’s a nice, big, round one, which I admit is about all I can think of that’s particularly interesting about it; even Wikipedia figures the most likely things you’re looking for if you look for 14,000 anything is either the ISO specification or an asteroid discovered in March of 1993 and apparently not even named yet. (It’s designated 1993 FZ55.) Well, at least asteroid 15,000 has a name.

Stare too hard at any one statistic, though, and you’ll start to wonder how reliable it is; I know for example that multiple of those 14,000 page views were me, testing neurotically to see whether the WordPress statistics counter was actually registering page views (particularly in the earliest days, when I was less self-confident and was using tags worse). Surely my just loading a page to see if it registers shouldn’t count as an actual page view, but, how can WordPress tell the difference?

Taking the WordPress statistics as if they meant what they purport to mean, though, indicates that apparently the most interesting thing I ever did was forget how to show why the area of a trapezoid was the trapezoid formula. My most-read article of all time is How Many Trapezoids I Can Draw, which is still standing at six by the way; some of the other articles which went into that (like Setting Out to Trap A Zoid and How Do You Make A Trapezoid Right) are also in the top five. All that’s based around working out how to work out a formula for the area of a trapezoid and convince yourself it’s right. For some reason the Reading the Comics post from September 11, 2012 also made the cut (I suppose the date is boosting it there). The early post How Many Numbers Have We Named is also fairly reliably popular.

Some of the most popular from the past year have included Something Neat About Triangles — since that post is only two months old I figure it’s got a good future ahead of it — and Solving The Price Is Right’s “Any Number” Game, which maybe solves the game less than explains why it’s usually a pretty good one to watch. Also popular is Counting From 52 to 11,108, and Inder J Taneja’s fascinating project in producing numbers using the digits one through nine in ascending or descending order.

Reading the Comics, March 1, 2014: Isn’t It One-Half X Squared Plus C? Edition


So the subject line references here a mathematics joke that I never have heard anybody ever tell, and only encounter in lists of mathematics jokes. It goes like this: a couple professors are arguing at lunch about whether normal people actually learn anything about calculus. One of them says he’s so sure normal people learn calculus that even their waiter would be able to answer a basic calc question, and they make a bet on that. He goes back and finds their waiter and says, when she comes with the check he’s going to ask her if she knows what the integral of x is, and she should just say, “why, it’s one-half x squared, of course”. She agrees. He goes back and asks her what the integral of x is, and she says of course it’s one-half x squared, and he wins the bet. As he’s paid off, she says, “But excuse me, professor, isn’t it one-half x squared plus C?”

Let me explain why this is an accurately structured joke construct and must therefore be classified as funny. “The integral of x”, as the question puts it, has not just one correct answer but rather a whole collection of correct answers, which are different from one another only by the addition of a constant whole number, by convention denoted C, and the inclusion of that “plus C” denotes that whole collection. The professor was being sloppy in referring to just a single example from that collection instead of the whole set, as the waiter knew to do. You’ll see why this is relevant to today’s collection of mathematics-themed comics.

Jef Mallet’s Frazz (February 22) points out one of the grand things about mathematics, that if you follow the proper steps in a mathematical problem you get to be right, and to be extraordinarily confident in that rightness. And that’s true, although, at least to me a good part of what’s fun in mathematics is working out what the proper steps are: figuring out what the important parts of something you want to study should be, and what follows from your representation of them, and — particularly if you’re trying to represent a complicated real-world phenomenon with a model — whether you’re representing the things you find interesting in the real-world phenomenon well. So, while following the proper steps gets you an answer that is correct within the limits of whatever it is you’re doing, you still get to work out whether you’re working on the right problem, which is the real fun.

Mark Pett’s Lucky Cow (February 23, rerun) uses that ambiguous place between mathematics and physics to represent extreme smartness. The equation the physicist brings to Neil is the (time-dependent) Schrödinger Equation, describing how probability evolves in time, and the answer is correct. If Neil’s coworkers at Lucky Cow were smarter they’d realize the scam, though: while the equation is impressively scary-looking to people not in the know, a particle physicist would have about as much chance of forgetting this as of forgetting the end of “E equals m c … ”.

Hilary Price’s Rhymes With Orange (February 24) builds on the familiar infinite-monkeys metaphor, but misses an important point. Price is right that yes, an infinite number of monkeys already did create the works of Shakespeare, as a result of evolving into a species that could have a Shakespeare. But the infinite monkeys problem is about selecting letters at random, uniformly: the letter following “th” is as likely to be “q” as it is to be “e”. An evolutionary system, however, encourages the more successful combinations in each generation, and discourages the less successful: after writing “th” Shakespeare would be far more likely to put “e” and never “q”, which makes calculating the probability rather less obvious. And Shakespeare was writing with awareness that the words mean things and they must be strings of words which make reasonable sense in context, which the monkeys on typewriters would not. Shakespeare could have followed the line “to be or not to be” with many things, but one of the possibilities would never be “carport licking hammer worbnoggle mrxl 2038 donkey donkey donkey donkey donkey donkey donkey”. The typewriter monkeys are not so selective.

Dan Thompson’s Brevity (February 26) is a cute joke about a number’s fashion sense.

Mark Pett’s Lucky Cow turns up again (February 28, rerun) for the Rubik’s Cube. The tolerably fun puzzle and astoundingly bad Saturday morning cartoon of the 80s can be used to introduce abstract algebra. When you rotate the nine little cubes on the edge of a Rubik’s cube, you’re doing something which is kind of like addition. Think of what you can do with the top row of cubes: you can leave it alone, unchanged; you can rotate it one quarter-turn clockwise; you can rotate it one quarter-turn counterclockwise; you can rotate it two quarter-turns clockwise; you can rotate it two quarter-turns counterclockwise (which will result in something suspiciously similar to the two quarter-turns clockwise); you can rotate it three quarter-turns clockwise; you can rotate it three quarter-turns counterclockwise.

If you rotate the top row one quarter-turn clockwise, and then another one quarter-turn clockwise, you’ve done something equivalent to two quarter-turns clockwise. If you rotate the top row two quarter-turns clockwise, and then one quarter-turn counterclockwise, you’ve done the same as if you’d just turned it one quarter-turn clockwise and walked away. You’re doing something that looks a lot like addition, without being exactly like it. Something odd happens when you get to four quarter-turns either clockwise or counterclockwise, particularly, but it all follows clear rules that become pretty familiar when you notice how much it’s like saying four hours after 10:00 will be 2:00.

Abstract algebra marks one of the things you have to learn as a mathematics major that really changes the way you start looking at mathematics, as it really stops being about trying to solve equations of any kind. You instead start looking at how structures are put together — rotations are seen a lot, probably because they’re familiar enough you still have some physical intuition, while still having significant new aspects — and, following this trail can get for example to the parts of particle physics where you predict some exotic new subatomic particle has to exist because there’s this structure that makes sense if it does.

Jenny Campbell’s Flo and Friends (March 1) is set off with the sort of abstract question that comes to mind when you aren’t thinking about mathematics: how many five-card combinations are there in a deck of (52) cards? Ruthie offers an answer, although — as the commenters get to disputing — whether she’s right depends on what exactly you mean by a “five-card combination”. Would you say that a hand of “2 of hearts, 3 of hearts, 4 of clubs, Jack of diamonds, Queen of diamonds” is a different one to “3 of hearts, Jack of diamonds, 4 of clubs, Queen of diamonds, 2 of hearts”? If you’re playing a game in which the order of the deal doesn’t matter, you probably wouldn’t; but, what if the order does matter? (I admit I don’t offhand know a card game where you’d get five cards and the order would be important, but I don’t know many card games.)

For that matter, if you accept those two hands as the same, would you accept “2 of clubs, 3 of clubs, 4 of diamonds, Jack of spades, Queen of spades” as a different hand? The suits are different, yes, but they’re not differently structured: you’re still three cards away from a flush, and two away from a straight. Granted there are some games in which one suit is worth more than another, in which case it matters whether you had two diamonds or two spades; but if you got the two-of-clubs hand just after getting the two-of-hearts hand you’d probably be struck by how weird it was you got the same hand twice in a row. You can’t give a correct answer to the question until you’ve thought about exactly what you mean when you say two hands of cards are different.

February 2014’s Mathematics Blog Statistics


And so to the monthly data-tracking report. I’m sad to say that the total number of viewers dropped compared to January, although I have to admit given the way the month went — with only eight posts, one of them a statistics one — I can’t blame folks for not coming around. The number of individual viewers dropped from 498 to 423, and the number of unique visitors collapsed from 283 to 209. But as ever there’s a silver lining: the pages per viewer rose from 1.76 to 2.02, so, I like to think people are finding this more choice.

As usual the country sending me the most readers was the United States (235), with Canada in second (31) and Denmark, surprising to me, in third place (30). I suppose that’s a bit unreasonable on my part, since why shouldn’t Danes be interested in mathematics-themed comic strips, but, I’m used to the United Kingdom being there. Fourth place went to Austria (17) and I was again surprised by fifth place, Singapore (14), but happy to see someone from there reading, as I used to work there and miss the place, especially in the pits of winter. Sending me just a single reader each were: Albania, Argentina, Ecuador, Estonia, Ethiopia, Greece, Hungary, New Zealand, Peru, Saudia Arabia, South Korea, Thailand, United Arab Emirates, Uruguay, and Venezuela. Greece and South Korea are the only repeats from January 2013.

The most popular articles the past thirty days were:

  1. Reading The Comics, February 1, 2014, my bread-and-butter subject for the blog.
  2. How Many Trapezoids I Can Draw, which will be my immortal legacy.
  3. Reading The Comics, February 11, 2014: Running Out Pi Edition, see above, although now I’m trying out something in putting particular titles on things.
  4. The Liquefaction of Gases, Part I, referring to a real statistical mechanics post by CarnotCycle.
  5. I Know Nothing Of John Venn’s Diagram Work, my confession of ignorance, or at least of casualness in thought, in the use of a valuable tool.

The most interesting search terms bringing people to me the past month were “comics strip about classical and modern physics”, “1,898,600,000,000,000,000,000,000,000 in words”, and “how much could a contestant win on the $64.00 question”, which you’d superficially think would be a question you didn’t have to look up. (Of course, in the movie Take It Or Leave It, based on the radio quiz program, the amount of the gran jackpot is raised to a thousand dollars, for dramatic value. This is presumably not what the questioner was looking for.)