## How do I do a matrix in WordPress LaTeX?

I wanted to walk through the calculation that Atlas the Mental Giant did in that installment of Barnaby which I shared on Monday. I’ve been stymied, though. To have anything comprehensible, I need a matrix. (To be precise, I need the determinant of a matrix.) It needs to be typeset in a particular way.

In normal mathematics communications this is easy. We can use the LaTeX typesetting standard, and I would write something like this:

\left(U - TS\right)\left|\begin{tabular}{cc} -dT^2 & S \\ e^{\imath \pi} & \zeta(0) L \end{tabular} \right|

I haven’t checked that I have the syntax precisely right, but it’s something like that.

WordPress includes a bit of support for LaTeX expressions. Here I mean the standard free account that I have; I can write in some line like

\int_0^M \sum_{j=1}^{N} a_j x^j dx

and it will get displayed neat and clean as

$\int_0^M \sum_{j=1}^{N} a_j x^j dx$

Thing is, the standard installation only has a subset of LaTeX’s commands. This is fair enough. It’s ridiculous to bring the entire workshop out when all you need is one hammer. What I can’t find, though, is a description of what LaTeX tools are available to the standard default WordPress free-account user. My experiments in my own comments suggest that the tabular, and the table, structures aren’t supported. But I can’t find a reference that says what’s allowed and what isn’t. I might, after all, be making a silly error in syntax, over and over. When you make an error in WordPress LaTeX you get a sulky note that the formula does not parse. There’s no hint given to what went wrong, or where. You have to remove symbols until the error disappears, and then reverse-engineer what should have been there.

(And the new WordPress editor does not help either. There is not a single point in the new editor where I am fully sure what clicking the mouse will do, or why. Whether it’ll pop up a toolbar I don’t need, or open a new section I don’t want, or pop up a menu where items have moved around from the last time, or whether it’ll jump back to the start of my post and challenge me to remember what I was doing. I realize it is always popular to complain about a web site change, but usually the changes make at least one thing better than it used to be. I can’t find the thing this has made at all better.)

So I’m hoping to attract information. Does anyone have a list of what LaTeX commands WordPress can use? And how the set of what’s available differs between the original post and the comments on the post? And what, for a basic subscription, you can use to represent a matrix?

Incidentally, here’s how to make WordPress print a line of LaTeX larger. Put a &s=N just before the closing \$ of your symbol. That N can be 1, 2, 3, or 4. The bigger the N, the bigger the print. You can also put in 0 or negative numbers, if you want the expression to be smaller. I can’t imagine wanting that, but it’s out there.

## Great Stuff By David Hilbert That I’ll Never Finish Reading

And then this came across my Twitter feed (@Nebusj, for the record):

It is to Project Gutenberg’s edition of David Hilbert’s The Foundations Of Geometry. David Hilbert you may know as the guy who gave us 20th Century mathematics. He had help. But he worked hard on the axiomatizing of mathematics, getting rid of intuition and relying on nothing but logical deduction for all mathematical results. “Didn’t we do that already, like, with the Ancient Greeks and all?” you may ask. We aimed for that since the Ancient Greeks, yes, but it’s really hard to do. The Foundations Of Geometry is an example of Hilbert’s work of looking very critically at all of the things we assume, and all of the things that we need, and all of the things we need defined, and trying to get at it all.

Hilbert gave much of 20th Century Mathematics its shape with a list presented at the 1900 International Congress of Mathematicians in Paris. This formed a great list of important unsolved problems. Some of them have been solved since. Some are still unsolved. Some have been proven unsolvable. Each of these results is very interesting. This tells you something about how great his questions were; only a great question is interesting however it turns out.

The Project Gutenberg edition of The Foundations Of Geometry is, mercifully, not a stitched-together PDF version of an ancient library copy. It’s a PDF compiled by, if I’m reading the credits correctly, Joshua Hutchinson, Roger Frank, and David Starner. The text was copied into LaTeX, an incredibly powerful and standard mathematics-writing tool, and compiled into something that … looks a little bit like every mathematics paper and thesis you’ll read these days. It’s a bit odd for a 120-year-old text to look quite like that. But it does mean the formatting looks familiar, if you’re the sort of person who reads mathematics regularly.

(There are a couple lines that read weird to me, but I can’t judge whether that owes to a typo in the preparation of the document or just that the translation from Hilbert’s original German to English produced odd effects. I’m thinking here of Axiom I, 2, shown on page 2, which I understand but feel weird about. Roll with it.)

## What I Learned Doing The End 2016 Mathematics A To Z

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

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

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

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

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

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

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

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

## Reading the Comics, April 15, 2016: Remarkably, No Income Tax Comics Edition

I’m as startled as you are. While a couple comic strips mentioned United States Income Tax Day, they didn’t do so in a way that seemed on-point enough for this Reading The Comics post. Of course, United States Income Tax Day happens to be the 18th this year. I haven’t seen Sunday’s comics yet.

David L Hoyt and Jeff Knurek’s Jumble for the 11th of April one again uses arithmetic puns for its business. Also, if some science fiction writer doesn’t take hold of “Gribth” as a name for something they’re missing a fine syllable. “Tahew” is no slouch in the made-up word leagues either.

Ryan North’s Dinosaur Comics for the 12th of April obviously originally ran sometime in mid-March. I have similarly ambiguous feelings about the value of Pi Day. I suppose it’s nice for people to think of “fun” and “mathematics” close together. Utahraptor’s distinction between “Pi Day” of March 14 and “Approximate Pi Day” of the 22nd of July s a curious one, though. It’s not as though 3.14 is any more exactly π than 22/7 is. I suppose you can argue that at some moment on 3/14 between 1:59:26 and 1:59:27 there’s some moment, 1:59:26.5358979 et cetera going on forever. But that assumes that time is a continuous thing, and it’s not like you’ll ever know what that moment is. By the time you might recognize it, it’s passed. They are all Approximate Pi Days; we just have to decide what the approximation is.

Bill Schorr’s The Grizzwells for the 12th is a silly-homework problem question. I know the point is to joke about how Fauna misunderstands a word. But if we pretend the assignment is for real, what might its point be? To show that students know the parts of a right triangle? I guess that’s all right, but it doesn’t seem like much of an assignment. I don’t blame her for getting snarky in the face of that.

Rick Kirkman and Jerry Scott’s Baby Blues for the 13th is a gag about picking random numbers for arithmetic homework. The approach is doomed, surely, although it’s probably not completely doomed. I’m not sure Hammie’s age, but if his homework is about adding and subtracting numbers he probably mostly gets problems that give results between zero and twenty, and almost always less than a hundred. He might hit some by luck.

I’ve mentioned some how people are awful at picking “random” numbers in their heads. Zoe shows off one of the ways people are bad at it. People asked to name numbers “randomly” pick odd numbers more than even numbers. Somehow they just feel random. I doubt Kirkman and Scott were thinking of that; among other things, five numbers is a very small sample. Four odds out of five isn’t peculiar, not yet. They were probably just trying to pick numbers that sounded funny while fitting the space available. I’m a bit surprised 37 didn’t make the list.

Mark Anderson’s Andertoons for the 13th is Mark Anderson’s Andertoons entry for this essay. I like the teacher’s answer, though.

Patrick Roberts’s Todd the Dinosaur for the 14th just uses arithmetic as the most economic way to fit several problems on-screen at once. They’ve got a compactness that sentence-diagramming just can’t match.

Greg Cravens’s The Buckets for the 15th amuses me with its use of coin-tossing as a way of making choices. I’m also amused the coin might be wrong only about half the time.

John Deering’s Strange Brew for the 15th is a visual puzzle. It’s intending to make use of a board full of mathematical symbols to represent deep thought. But the symbols aren’t quite mathematics. They look much more like LaTeX, a typesetting code used to express mathematics in print. Some of the symbols are obscured, so I can’t say exactly what’s meant. But it should be something like this:

$F = \{F_{x} \in F_{c}: (is ... (1) ) \cap (minPixels < \|s\| < maxPixels ) \\ \partial{P} \\ (is_{connected}| > |s| - \epsilon) \}$

At the risk of disappointing, this appears to me gibberish. The appearance of words like ‘minPixels’ and ‘maxPixels’ suggest a bit of computer code. So does having a subscript that’s the full word “connected”. I wonder where Deering drew this example from.

## How To Build Infinite Numbers

I had missed it, as mentioned in the above tweet. The link is to a page on the Form And Formalism blog, reprinting a translation of one of Georg Cantor’s papers in which he founded the modern understanding of sets, of infinite sets, and of infinitely large numbers. Although it gets into pretty heady topics, it doesn’t actually require a mathematical background, at least as I look at it; it just requires a willingness to follow long chains of reasoning, which I admit is much harder than algebra.

Cantor — whom I’d talked a bit about in a recent Reading The Comics post — was deeply concerned and intrigued by infinity. His paper enters into that curious space where mathematics, philosophy, and even theology blend together, since it’s difficult to talk about the infinite without people thinking of God. I admit the philosophical side of the discussion is difficult for me to follow, and the theological side harder yet, but a philosopher or theologian would probably have symmetric complaints.

The translation is provided as scans of a typewritten document, so you can see what it was like trying to include mathematical symbols in non-typeset text in the days before LaTeX (which is great at it, but requires annoying amounts of setup) or HTML (which is mediocre at it, but requires less setup) or Word (I don’t use Word) were available. Somehow, folks managed to live through times like that, but it wasn’t pretty.

## Some Facts For The Day

I’d just wanted to note the creation of another fact-of-the-day Twitter feed from the indefatigable John D Cook. This one is dubbed Unit Facts, and it’s aiming at providing information about where various units of measure come from. The first few days have begun with, naturally enough, the base units of the Metric System (can you name all seven?), and has stretched out already to things like what a knot is, how picas and inches are related, and what are ems and fortnights besides useful to know for crossword puzzles, or how something might be measured, as in the marshmallow tweet above.

Cook offers a number of interesting fact-of-the-day style feeds, which I believe are all linked to one another through their “Following” pages. These include algebra, topology, probability, and analysis facts of the day, as well as Unix tool tips, RegExp and TeX/LaTeX trivia, symbols (including a lot of Unicode and HTML entities), and the like. If you’re of the sort to get interested in neatly delivered bits of science- and math- and computer-related trivia, well, good luck with your imminent archive-binge.

## ASCII-Art Math

I had forgotten the challenges of doing more than the most basic mathematics expressions in ASCII art, and had completely forgotten there were tools that tried to make it a bit easier. Enteropia here’s put forth a script which ought to make it a bit easier to go from LaTeX into an ASCII representation, and I have the feeling I’m going to want to find this again later on, so I’d best make some kind of link I can locate when I do.

Many of computer algebra systems date back to the times when GUI machines were rare and expensive, if were present at all. Thus command line was a standard interface. Unfortunately text terminal doesn’t fit very well for displaying mathematical expressions which demand for rich typesetting. To represent math formulas CAS’s resorted to some kind of ASCII art:

 inf 1 ==== / n n \ [ x log (x) > I ---------- dx / ] gamma(n x) ==== / n = 0…

That’s the output of Maxima. Some of the systems went further and don’t restrict themselves to plain ASCII. Axiom can produce such a nice output:

                         2
x   - %A  ┌──┐
┌┐  %e     \│%A
│   ──────────── d%A
└┘    tan(%A) + 2


Even now most CAS’s retain command line interface, for example Mathematica 8’s terminal session:

In[14]:= Pi*(a+b^2/(Exp[12]+3/2 ">2)) 2 b Out[14]= (a + -------) Pi 3 12 - + E…

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