How November 2015 Treated My Mathematics Blog


So after a couple dismal months my ratings appear to be up. The number of page views and of visitors, in fact, seem to be at all-time highs. At least they’re at highs for the past twelve months. I would like to think that the depressed readings of September and October — 708 page views and 381 visitors; 733 page views and 405 visitors, respectively — are behind me. November saw 1,215 page views and 519 visitors.

Some of this is an accident. My humor blog got a tidal wave of readers courtesy The Onion AV Club. The AV Club wrote up a piece about the sad end of the comic strip Apartment 3-G, and I’ve written a shocking amount about the soap strip. They mentioned me. And as I’ve used my comic strip posts there to mention my Reading the Comics series here, some curious people followed along.

That said, I’m not sure how many of those readers were AV Club curiosity-seekers. A crude estimate suggests somewhere a little over two hundred were. So even discounting that something near a thousand regular-style reders came in and looked around, and that’s nice to see. It’s back up to about where the readership was before the mysterious dropoff, in July, that many suspect results from mobile devices being incorrectly read.

For the roster of countries, well, the top was the United States as always, with some 837 page views. The United Kingdom came in with 62. The Canada appears third at 50 views, and the Philippines next at 20. The Singapore and the Australia tie at 19.

Single-reader countries this past month were Algeria, Argentina, Belgium, Egypt, Finland, Israel, Jamaica, Malaysia, Mexico, Nigeria, Puerto Rico, Romania, Thailand, Turkey, and Vietnam. Belgium, Nigeria, and Thailand are repeats from October. No country’s on a three-month streak.

The Reading the Comics posts are as ever the most popular group and I’ve bundled them under the one category tag. But my Ramsey Theory question turned out to be slightly more popular than any of them in November. After grouping together all the comics posts, the most popular articles look like:

  1. Why Was Someone Upset With Ramsey Theory In 1979? a question about a dimly remembered Dear Abby-class question.
  2. Reading the Comics, an ongoing series.
  3. How October Treated My Mathematics Blog, and yes, I risk an endless loop by mentioning this here.
  4. How Many Trapezoids I Can Draw and goodness it’s nice to see the trapezoids turning up again.
  5. How Antifreeze Works, one of my little pointers to someone else’s interesting writing.

Nothing really dominated my search term queries this month. Some of the things that turned up were:

  • illustration of electromagnetic wave theory scientist comics strip
  • james clerk maxwell comics (I’m not sure I have any of these; this suggests I ought to be finding some.)
  • origin is the gateway to your entire gaming universe. (I’ve had this explained to me, but I forget what it means.)
  • places 1975 miles from charlotte nc (I know of none specifically 1,975 miles away.)
  • if i got 70 percent in all exams what grade do i need on final to pass course? (This I can help with.)

December starts with my blog here at 30,298 page views, and with 543 WordPress followers. I expect it’ll be overtaken in page views by my humor blog sometime soon.

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What People Did Like In My Mathematics Blog In September 2015


I got so busy with my self-pitying yesterday I never got around to talking about what was popular in September. Well, I mentioned: the six most popular posts in September were all Reading the Comics articles, which I’m pretty sure is the first time it’s swept the top of the charts. Also I think for the first time none of the top ten articles were reblogs of anything, nor were they trapezoid-counting.

For some reason the most popular Reading The Comics entry was one from April. The rest were all September posts, which makes more sense. Anyway, to avoid being boring I’ll skip listing the September Reading the Comics posts. I’ll jump to numbers six through ten for the popular-postings roundup:

The country sending me the greatest number of readers was, as ever, the United States, with 418 this time around, down from August’s 496. In second place this time was the Philippines, with 43, up from 26. Italy came in third, with 34, and I didn’t see that coming either. (They’d sent nine in August). Canada with 29 and Australia with 22 round out the top five and it’s kind of a relief to see them finally. Singapore sent eight page views, up from five. India sent five, down from 22. So it goes.

It was another hefty list of singe-reader countries in September: Argentina, Austria, Bangladesh, Bosnia and Herzegovina, Egypt, Greece, Indonesia, Japan, Nepal, Peru, Saudi Arabia, Senegal, Serbia, South Korea, St Lucia, Switzerland, Trinidad and Tobago, United Arab Emirates, and Uruguay.

Repeats on that list from August are Argentina, Bangladesh, Indonesia, Nepal, South Korea, and Switzerland. Nepal is on a three-month single-reader streak here.

There’s not much good in the search terms; nearly all of them were listed as “unknown”. Among the few that were known:

  • foxtrot maths 8 cartoon comic
  • 8 piece math joke comic strip
  • foxtrot maths 9 comic cartoon
  • origin is the gateway to your entire gaming universe
  • james clerk maxwell theory comics
  • comics strip james clerk maxwell

I feel like there’s a niche here and that I need to commission some comics about James Clerk Maxwell.

September ends with the page having had 28,350 views altogether, and some 10,346 visitors. There’s 518 people listed as WordPress followers which is an increase of one, though the Statistics Insights page says five people started following me. Well, I guess at least it’s upward, from the area code of Albany, New York, up to the area code of Lansing, Michigan. I wonder what state capitol has area code 519. There were fifteen postings in September, up from fourteen in August, down from twenty-four in July. (July had the trailing end of the Mathematics A To Z project.)

And let me encourage people again to consider the “Follow Blog via Email” link on the upper right of the page. Or if you have an RSS reader, https://nebusresearch.wordpress.com/feed/ will give you posts. My Twitter account is @Nebusj.

A Summer 2015 Mathematics A To Z: vertex (graph theory)


Vertex.

I mentioned graph theory several weeks back, when this Mathematics A To Z project was barely begun. It’s a fun field. It’s a great one for doodlers, and it’s one that has surprising links to other problems.

Graph theory divides the conceptual universe into “things that could be connected” and “ways they are connected”. The “things that could be connected” we call vertices. The “ways they are connected” are the edges. Vertices might have an obvious physical interpretation. They might, represent the corners of a cube or a pyramid or some other common shape. That, I imagine, is why these things were ever called vertices. A diagram of a graph can look a lot like a drawing of a solid object. It doesn’t have to, though. Many graphs will have vertices and edges connected in ways that no solid object could have. They will usually be ones that you could build in wireframe. Use gumdrops for the vertices and strands of wire or plastic or pencils for the edges.

Vertices might stand in for the houses that need to be connected to sources of water and electricity and Internet. They might be the way we represent devices connected on the Internet. They might represent all the area within a state’s boundaries. The Köningsburg bridge problem, held up as the ancestor of graph theory, has its vertices represent the islands and river banks one gets to by bridges. Vertices are, as I say, the things that might be connected.

“Things that might be connected” is a broader category than you might imagine. For example, an important practical use of mathematics is making error-detecting and error-correcting codes. This is how you might send a message that gets garbled — in sending, in transmitting, or in reception — and still understand what was meant. You can model error-detecting or correcting codes as a graph. In this case every possible message is a vertex. Edges connect together the messages that could plausibly be misinterpreted as one another. How many edges you draw — how much misunderstanding you allow for — depends on how many errors you want to be able to detect, or to correct.

When we draw this on paper or a chalkboard or the like we usually draw it as a + or an x or maybe a *. How much we draw depends on how afraid we are of losing sight of it as we keep working. In publication it’s often drawn as a simple dot. This is because printers are able to draw dots that don’t get muddied up by edges being drawn in or eraser marks removing edges.

My Math Blog Statistics, October 2014


So now let me go over the mathematics blog statistics for October. I’ll get to listing countries; people like that.

It was a good month in terms of getting people to read: total number of pages viewed was 625, up from 558, and this is the fourth-highest month on record. The number of unique visitors was up too, from 286 in September to 323 in October, and that’s the third-highest since WordPress started giving me those statistics. The views per visitor barely changed, going from 1.95 to 1.93, which I’m comfortable supposing is a statistical tie. I reached 18,507 total page views by the end of October, and maybe I’ll reach that nice round-ish 19,000 by the end of November.

The countries sending me the most visitors were the usual set: the United States with 393, the United Kingdom with 35, and Austria with 23. Curiously, Argentina sent me 20 readers, while Canada plummeted down to a mere nine. Did I say something wrong, up there? On the bright side my Indian readership has grown to nine, which is the kind of trend I like. Sending just a single reader this past month were Albania, Brazil, Denmark, Estonia, Finland, Indonesia, Japan, the Netherlands, Nicaragua, Norway, Poland, Saint Kitts and Nevis, Serbia, Spain, Sweden, Taiwan, Turkey, and the United Arab Emirates. Brazil, Estonia, Finland, the Netherlands, and Sweden were single-reader countries last month, and Finland and Sweden also the month before. I feel embarrassed by the poor growth in my Scandinavian readership, but at least it isn’t dwindling.

The most popular posts in October got a little bit away from the comics posts; the ones most often read were:

There weren’t any really great bits of search term poetry this month, but there were still some evocative queries that brought people to me, among them:

  • where did negative numbers come from
  • show me how to make a comic stip for rationalnumbers
  • desert island logarithm
  • herb jamaal math ludwig
  • in the figure shown below, Δabc and Δdec are right triangles. if de = 6, ab = 20, and be = 21, what is the area of Δdec?
  • origin is the gateway to your entire gaming universe.

That “origin is the gateway” thing has come up before. I stil don’t know what it means. I’m a little scared by it.

My Math Blog Statistics, September 2014


Since it’s the start of a new month it’s time to review statistics for the previous month, which gives me the chance to list a bunch of countries, which is strangely popular with readers. I don’t pretend to understand this, I just accept the inevitable.

In total views I haven’t seen much change the last several months: September 2014 looks to be closing out with about 558 pages viewed, not a substantial change from August’s 561, and triflingly fewer than July’s 589. The number of unique visitors has been growing steadily, though: 286 visitors in September, compared to 255 the month before, and 231 the month before that. One can choose to read this as the views per visitor dropping to 1.95, its lowest figure since March, but I’ll take it as more people finding things that interest them, at least.

As to what those things are — well, mostly it’s comic strip posts, which I suppose makes sense given that they’re quite accessible and often contain jokes people understand. The most popular articles for September 2014 were:

As usual the country sending me the greatest number of readers was the United States (347), with Canada (29), Austria (27), the United Kingdom (26), and Puerto Rico and Turkey (20 each) coming up close behind. My single-reader countries for September were Bahrain, Brazil, Costa Rica, Czech Republic, Estonia, Finland, Germany, Iceland, Jamaica, Kazakhstan, Malaysia, the Netherlands, Pakistan, Saudi Arabia, Slovenia, and Sweden. Finland, Germany, and Sweden were single-reader countries in August, too, but at least none of them were single-reader countries in July as well.

Among the search terms bringing people here the past month have been:

I got to my 17,882nd reader this month, a little short of that tolerably nice and round 18,000 readers. If I don’t come down with sudden-onset boringness, though, I’ll reach that in the next week or so, especially if I have a couple more days of twenty or thirty readers.

June 2014 In Mathematics Blogging


And with the start of July I look over how well the mathematics blog did in June and see what I can learn from that. It seems more people are willing to read when I post stuff, which is worth knowing, I guess. After May’s near-record of 751 views and 315 visitors I expected a fall, and, yeah, it came. The number of pages viewed dropped to 492, which is … well, the fourth-highest this year at least? And the number of unique visitors fell to 194, which is actually the lowest of this year. The silver lining is this means the views per visitor, 2.54, was the second-highest since WordPress started sharing those statistics with me, so, people who come around find themselves interested. I start the month at 16,174 views total and won’t cross 17,000 at that rate come July, but we’ll see what I can do. And between WordPress and Twitter I’m (as of this writing) at exactly 400 followers, which isn’t worldshaking but is a nice big round number. I admit thinking how cool it would be if that were 400 million but I’d probably get stage fright if it were.

If one thing defined June it was “good grief but there’s a lot of mathematics comics”, which I attributed to Comic Strip Master Command ordering cartoonists to clear the subject out before summer vacation. It does mean the top five posts for June are almost comically lopsided, though:

Now, that really is something neat about triangles in the post linked above so please do read it. What I’m not clear about is why the June 16th comics post was so extremely popular; it’s nearly twice as viewed as the runner-up. If I were sure what keyword is making it so popular I’d do more with that.

Now on to the international portion of this contest: what countries are sending me the most visitors? Of course the United States comes in first, at 336 views. Denmark finished second with 17, and there was a three-way tie for third as Australia, Austria, and the United Kingdom sent sixteen each. (Singapore and Canada came in next with nine each.) I had a pretty nice crop of single-reader countries this month: Argentina, Bosnia and Herzegovina, Cambodia, Egypt, Ghana, Hong Kong, Indonesia, Japan, Paraguay, Saudi Arabia, Switzerland, and Thailand. Hong Kong, Japan, and Switzerland are repeats from last month and nobody’s got a three-month streak going.

Among the interesting search terms to bring people to me:

  • names for big numbers octillion [ happy to help? ]
  • everything to need to know about trapezoids [ I’m going to be the world’s authority on trapezoids! ]
  • what does the fact that two trapezoids make a parallelogram say about tth midline [ I have some ideas but don’t want to commit to anything particular ]
  • latching onto you 80 version [ I … think I’m being asked for lyrics? ]
  • planet nebus [ I feel vaguely snarked upon, somehow ]
  • origin is the gateway to your entire gaming universe [ … thank you? ]
  • nebus student job for uae [ Um … I guess I can figure out a consulting fee or something if you ask? ]

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.

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”

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.)

Reading the Comics, January 20, 2014


I’m getting to wonder whether cartoonists really do think about mathematics only when schools are in session; there was a frightening lull in mathematics-themed comic strips this month and I was getting all ready to write about something meaningful like how Gaussian integration works instead. But they came around, possibly because the kids went back to school and could resist answering word problems about driving places so they can divide apples again.

Carla Ventresca and Henry Beckett’s On A Claire Day (January 3) really just name-drops mathematics, as a vaguely unpleasant thing intruding on a conversation, even though Paul’s just dropped in a bit of silliness that, if I’m not reading it wrongly, is tautological anyway. There’s a fair question at work here, though: can “how good” a person is be measured? Obviously, it can’t if nobody tries; but could they succeed at all?

It sounds a bit silly, but then, measuring something like the economic state of a nation was not even imagined until surprisingly recently: most of the economic measures we have postdate World War II. One can argue whether they’re measuring what they are supposed to represent well, but there’s not much dispute about the idea that economic health could be measured anymore. When Assistant Secretary of State for the Truman administration, James Webb — later famous for managing NASA during the bulk of the Space Race — tried to get foreign relations measured in a similar way, though the idea was mocked as ridiculous (the joke was apparently something along the lines of a person rushing in to announce “Bulgaria is down two points!”, which is probably funnier if you haven’t grown up playing Civilization-style grand strategy games), and he gave up on that fight in favor of completing a desperately needed reorganization of the department.

I don’t know how I would measure a person’s goodness, but I could imagine a process of coming up with some things that could be measured, and trying them out, and seeing how well the measurements match what it feels they should be measuring. This is all probably too much work for a New Year’s Resolution, but it might get someone their thesis project.

Steve Moore’s In The Bleachers (January 14) comes back with a huge pile of equations standing as a big, complicated explanation for something. It doesn’t look to me like the description has much to do with describing balls bouncing, however, which is a bit of a disappointment given previous strips that name-drop Lev Landau or pull up implicit differentiation when they don’t need even need it. Maybe Moore wasn’t able to find something that looked good before deadline.

Bill Hinds’s Cleats (January 16, rerun) is just the sort of straightforward pun I actually more expect out of FoxTrot (see below).

Nate Frakes’s Break of Day (January 19) shows an infant trying to count sheep and concluding she’s too young to. Interesting to me is that the premise of the joke might actually be wrong: humans appear to have at least a rough sense of numbers, at least for things like counting and addition, from a surprisingly early age. This is a fascinating thing to learn about, both because it’s remarkable that humans should have a natural aptitude for arithmetic, and because of how difficult it is to come up with tests for understanding quantity and counting and addition that work on people with whom you can’t speak and who can’t be given instruction on how to respond to a test. Stanislas Dehaene’s The Number Sense: How The Mind Creates Mathematics describes some of this, although I’m hesitant to recommend it uncritically because I know I’m not well-read in the field. It’s somewhere to start learning, though.

Chip Sansom’s The Born Loser (January 20) could be the start of a word problem in translating from percentiles to rankings, and, for that matter, vice-versa. It’s convenient to switch a ranking to percentiles because that makes it easier to compare groups of different sizes. But many statistical tools, particularly the z-score, might be considered to be ways of meaningfully comparing the order of groups of different sizes that are nevertheless similar.

Bill Amend’s FoxTrot (January 20, rerun) is the reliable old figure-eight ice skating gag. I hope people won’t think worse of me for feeling that Droopy did it better.

T Lewis and Michael Fry’s Over The Hedge (January 20) uses a spot of the Fundamental Theorem of Calculus (rendered correctly) to stand in for “a really hard thought”. Calculus is probably secure in having that reputation: it’s about the last mathematics that the average person might be expected to take, and it introduces many new symbols and concepts that can be staggering (even the polymath Isaac Asimov found he just couldn’t grasp the subject), and so many of its equations are just beautiful to look at. The integral sign seems to me to have some graphic design sense that, for example, matrices or the polynomial representations of knots just don’t manage.

November 2013’s Statistics


Hi again. I was hesitant to look at this month’s statistics, as I pretty much fell off the face of the earth for a week there, but I didn’t have the chance to do the serious thinking that’s needed for mathematics writing. The result’s almost exactly the dropoff in readership I might have predicted: from 440 views in October down to 308, and from 220 unique visitors down to 158. That’s almost an unchanged number of views per visitor, 2.00 dropping to 1.95, so at least the people still interested in me are sticking around.

The countries sending me the most viewers were as ever the United States, then Austria (hi, Elke, and thank you), the United Kingdom and then Canada. Sending me a single visitor each were Bulgaria, Cyprus, Czech Republic, Ethiopia, France, Jordan, Lebanon, Nepal, New Zealand, Russia, Singapore, Slovenia, Switzerland, and Thailand. This is also a drop in the number of single-viewer countries, although stalwarts Finland and the Netherlands are off the list. Slovenia’s the only country making a repeat appearance from last month, in fact.

The most popular articles the past month were:

And I apologize for not having produced many essays the past couple weeks, and can only fault myself for being more fascinated by some problems in my day job that’ve been taking up time and mental energy and waking me in the middle of the night with stuff I should try. I’ll be back to normal soon, I’m sure. Don’t tell my boss.

Reading the Comics, November 13, 2013


For this week’s round of comic strips there’s almost a subtler theme than “they mention math in some way”: several have got links to statistical mechanics and the problem of recurrence. I’m not sure what’s gotten into Comic Strip Master Command that they sent out instructions to do comics that I can tie to the astounding interactions of infinities and improbable events, but it makes me wonder if I need to write a few essays about it.

Gene Weingarten, Dan Weingarten, and David Clark’s Barney and Clyde (October 30) summons the classic “infinite monkeys” problem of probability for its punch line. The concept — that if you had something producing strings of letters at random (taken to be monkeys because, I suppose, it’s assumed they would hit every key without knowing what sensibly comes next), it would, given enough time, produce any given result. The idea goes back a long way, and it’s blessed with a compelling mental image even though typewriters are a touch old-fashioned these days.

It seems to have gotten its canonical formulation in Émile Borel’s 1913 article “Statistical Mechanics and Irreversibility”, as you might expect since statistical mechanics brings up the curious problem of entropy. In short: every physical interaction, say, when two gases — let’s say clear air and some pink smoke as 1960s TV shows used to knock characters out — mix, is time-reversible. Look at the interaction of one clear-gas molecule and one pink-gas molecule and you can’t tell whether it’s playing forward or backward. But look at the entire room and it’s obvious whether they’re mixing or unmixing. How can something be time-reversible at every step of every interaction but not in whole?

The idea got a second compelling metaphor with Jorge Luis Borges’s Library of Babel, with a bit more literary class and in many printings fewer monkeys.

Continue reading “Reading the Comics, November 13, 2013”

October 2013’s Statistics


It’s been a month since I last looked over precisely how not-staggeringly-popular I am, so it’s time again.
For October 2013 I had 440 views, down from September’s 2013. These came from 220 distinct viewers, down again from the 237 that September gave me. This does mean there was a slender improvement in views per visitor, from 1.97 up to 2.00. Neither of these are records, although given that I had a poor updating record again this month that’s all tolerable.

The most popular articles from the past month are … well, mostly the comics, and the trapezoids come back again. I’ve clearly got to start categorizing the other kinds of polygons. Or else plunge directly into dynamical systems as that’s the other thing people liked. October 2013’s top hits were:

  1. Reading the Comics, October 8, 2013
  2. How Many Trapezoids I Can Draw
  3. Reading the Comics, September 11, 2013
  4. From ElKement: On The Relation Of Jurassic Park and Alien Jelly Flowing Through Hyperspace
  5. Reading the Comics, September 21, 2013
  6. The Mathematics of a Pricing Game

The country sending me the most readers again was the United States (226 of them), with the United Kingdom coming up second (37). Austria popped into third for, I think, the first time (25 views), followed by Denmark (21) and at long last Canada (18). I hope they still like me in Canada.

Sending just the lone reader each were a bunch of countries: Bermuda, Chile, Colombia, Costa Rica, Finland, Guatemala, Hong Kong, Laos, Lebanon, Malta, Mexico, the Netherlands, Oman, Romania, Saudi Arabia, Slovenia, Sweden, Turkey, and Ukraine. Finland and the Netherlands are repeats from last month, and the Netherlands is going on at least three months like this.

Reading the Comics, October 26, 2013


And once again while I wasn’t quite looking we got a round of eight comic strips with mathematical themes to review. Some of them aren’t even about kids not understanding fractions, if you can imagine.

Jason Chatfield’s Ginger Meggs (October 14) does the usual confused-student joke. It’s a little unusual in having the subject be different ways to plot data, though, with line graphs, bar graphs, and scatter graphs being shown off. I think remarkable about this is that line graphs and bar graphs were both — well, if not invented, then at least popularized — by one person, William Playfair, who’s also to be credited for making pie charts a popular tool. Playfair, an engineer and economist of the late 18th and early 19th century, and I do admire him for developing not just one but multiple techniques for making complicated information easier to see.

Eric the Circle (October 16) breaks through my usual reluctance to include it — just having a circle doesn’t seem like it’s enough — because it does a neat bit of mathematical joking, in which a cube looks “my dual” in an octahedron. Duals are one of the ways mathematicians transform one problem into another, that usually turns out to be equivalent; what’s surprising is that often a problem that’s difficult for the original is easy, or at least easier, for the dual.

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Reading the Comics, October 8, 2013


As promised, I’ve got a fresh round of mathematics-themed comic strips to discuss, something that’s rather fun to do because it offers such an easy answer to the question of what to write about today. Once you have the subject and a deadline the rest of the writing isn’t so very hard. So here’s some comics with all the humor safely buried in exposition:

Allison Barrows’s PreTeena (September 24, Rerun) brings the characters to “Performance Camp” and a pun on one of the basic tools of trigonometry. The pun’s routine enough, but I’m delighted to see that Barrows threw in a (correct) polynomial expression for the sine of an angle, since that’s the sort of detail that doesn’t really have to be included for the joke to read cleanly but which shows that Barrows made the effort to get it right.

Polynomial expansions — here, a Taylor series — are great tools to have, because, generally, polynomials are nice and well-behaved things. They’re easy to compute, they’re easy to analyze, they’re pretty much easy to do whatever you might want to do. Being able to shift a complicated or realistic function into a polynomial, even a polynomial with infinitely many terms, is often a big step towards making a complicated problem easy.

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September 2013’s Statistics


And as it’s the start of the month I have a fresh round of reviewing the statistics for readership around here. I have seen a nice increase in both views — from 367 to about 466 total views — and in visitors — from 175 to 236 — which maybe reflects the resumption of the school year (in the United States, anyway) and some more reliable posting (of original articles and of links to other people’s) on my part. (Maybe. If I’m reading this rightly I actually only posted nine new things in September, which is the same as in August. I’m surprised that WordPress’s statistics page doesn’t seem to report how many new articles there were in the month, though.) My contrarian nature forces me to note this means my views-per-reader ratio has dropped to 1.97, down from 2.10. I suppose as long as the views-per-reader statistic stays above 1.00 I’m not doing too badly.

The most popular articles the past month were:

  1. From ElKement: Space Balls, Baywatch, and the Geekiness of Classical Mechanics, which is really just pointing and slightly setting up ElKement’s start to a series on quantum field theory which you can too understand;
  2. How Many Trapezoids I Can Draw, which is a persistent favorite and makes me suspect that I’ve hit on something that teachers ask students about. If I could think of a couple other nice little how-many-of-these-things problems there are I’d post them gladly, although that might screw up some people’s homework assignments;
  3. Reading the Comics, September 11, 2012, which is another persistent favorite and I can’t imagine that it’s entirely about the date (although the similar Reading the Comics entry for September 11 of 2013 just missed being one of the top articles this month so perhaps the subject lines are just that effective a bit of click-baiting);
  4. What Is Calculus I Like?, about my own realization that I never took a Calculus I course in the conditions that most people who take it do. I’d like more answers to the question of what experiences in intro-to-calculus courses are like, since I’m assuming that I will someday teach it again and while I think I can empathize with students, I would surely do better at understanding what they don’t understand if I knew better what people in similar courses went through;
  5. Some Difficult Math Problems That You Understand, which is again pointing to another blog — here, Maths In A Minute — with a couple of mathematics problems that pretty much anyone can understand on their first reading. The problems are hard ones, each of which has challenged the mathematical community for generations, so you aren’t going to solve them; but, thinking about them and trying to solve them is probably a great exercise and likely to lead you to discovering something you didn’t know.

I got the greatest number of readers from the United States again (271), with Canada (31) once more in second place. The United Kingdom’s climbed back into the top three (21), while August’s number-three, Denmark, dropped out of the top ten and behind both Singapore and the Philippines. I got a mass of single-reader countries this time, too: Azerbaijan, Bangladesh, Belgium, Cambodia, the Czech Republic, Indonesia, Israel, Italy, Mexico, Norway, Poland, Qatar, Spain, Sri Lanka, Switzerland, and Thailand. Bangladesh and Sri Lanka are repeats from last month, but my Estonian readership seems to have fled entirely. At least India and New Zealand still like me.

Reading the Comics, August 18, 2013


I’m sorry to have fallen silent so long; I was away from home and thought I’d be able to put up a couple of short pieces along the way, and turned out to be rather busy doing other things instead. It’s given me at least one nice problem with dramatic photographs to use in a near-future entry, though, so not all is lost (although I’m trying to think of a way to re-do the work in it that doesn’t involve quite so much algebra; I’m afraid of losing my readers and worse of making a hash of the LaTeX involved). Meanwhile, it’s been surprisingly close to a month since the last summary of comic strips with mathematical themes — I imagine the cartoonists are taking a break on Students In Classroom setups what with it being summer vacation across so much of the United States — so let me return to that.

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Professor Ludwig von Drake Explains Numerical Mathematics


The reruns of Donald Duck comics which appear at creators.com recently offered the above daily strip, featuring Ludwig von Drake and one of those computers of the kind movies and TV shows and comic strips had before anybody had computers of their own and, of course, the classic IBM motto that maybe they still have but I never hear anyone talking about it except as something from the distant and musty past. (Unfortunately, creators.com doesn’t note the date a strip originally ran, so all I can say is the strip first ran sometime after September of 1961 and before whenever Disney stopped having original daily strips drawn; I haven’t been able to find any hint of when that was other than not earlier than 1969 when cartoonist Al Taliaferro retired from it.)

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My July 2013 Statistics


As I’ve started keeping track of my blog statistics here where it’s all public information, let me continue.

WordPress says that in July 2013 I had 341 pages read, which is down rather catastrophically from the June score of 713. The number of distinct visitors also dropped, though less alarmingly, from 246 down to 156; this also implies the number of pages each visitor viewed dropped from 2.90 down to 2.19. That’s still the second-highest number of pages-per-visitor that I’ve had recorded since WordPress started sharing that information with me, so, I’m going to suppose that the combination of school letting out (so fewer people are looking for help about trapezoids) and my relatively fewer posts this month hit me. There are presently 215 people following the blog, if my Twitter followers are counted among them. They hear about new posts, anyway.

My most popular posts over the past 30 days have been:

  1. John Dee, the ‘Mathematicall Praeface’ and the English School of Mathematics, which is primarily a pointer to the excellent mathematics history blog The Renaissance Mathematicus, and about the really quite fascinating Doctor John Dee, advisor to England’s Queen Elizabeth I.
  2. Counting From 52 To 11,108, some further work from Professor Inder J Taneja on a lovely bit of recreational mathematics. (Professor Taneja even pops in for the comments.)
  3. Geometry The Old-Fashioned Way, pointing to a fun little web page in which you can work out geometric constructions using straightedge and compass live and direct on the web.
  4. Reading the Comics, July 5, 2013, and finally; I was wondering if people actually still liked these posts.
  5. On Exact And Inexact Differentials, another “reblog” style pointer, this time to Carnot Cycle, a thermodynamics-oriented blog.
  6. And The $64 Question Was, in which I learned something about a classic game show and started to think about how it might be used educationally.

My all-time most popular post remains How Many Trapezoids I Can Draw, because I think there are people out there who worry about how many different kinds of trapezoids there are. I hope I can bring a little peace to their minds. (I make the answer out at six.)

The countries sending me the most viewers the past month have been the United States (165), then Denmark (32), Australia (24), India (18), and the United Kingdom and Brazil (12 each). Sorry, Canada (11). Sending me a single viewer each were Estonia, Slovenia, South Africa, the Netherlands, Argentina, Pakistan, Angola, France, and Switzerland. Argentina and Slovenia did the same for me last month too.

Reading the Comics, July 22, 2013


This is a shorter than usual entry for my roundup of comic strips mentioning mathematical topics, because I anticipate being a bit too busy to present this later in the week.

Ruben Boiling’s Tom the Dancing Bug (July 12) features one of his irresistible (to me) “Super-Fun-Pak Comix”, among them, A Voice From Another Dimension, which is a neat bit of Flatland-inspired fun between points in space. Edwin Abbot Abbot’s Flatland is one of those rare advanced-mathematical concepts that got firmly lodged into the pop culture, probably because it is a supremely accessible introduction to the concept of multidimensional space. People love learning about things which go against their everyday intuition, and the book (eventually) made the new notions of general relativity feel like they could be understood by anyone.

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