Thousandth, and last, post.

This is the last post here at God Plays Dice. It happens to be the thousandth, but I didn't plan that.

I'm moving to Wordpress, and to gottwurfelt.wordpress.com. (The obvious subdomain was taken, by somebody that I don't want to send traffic to.)

I'm also hoping to update more frequently there. Wordpress seems to have better support for adding images to posts, definitely has better support for mathematical notation, has built-in analytics, and, let's face it, has a better image. So it's (perhaps past) time to move.

So update your bookmarks, your feed readers, or whatever you kids are using to follow blogs these days. I'll see you there.

Feed change

I just transferred the RSS feed on this blog to a Google account (Feedburner, the service I'd been using, has recently been integrated into Google). There should be no problems, but if there are let me know.

E-mail address change

I have a new e-mail address.

To figure it out, concatenate the first three letters of my first name, my entire last name, and "@gmail.com".

The intrepid reader can figure out my "academic" e-mail address. Once I get things set up those should redirect to the same place anyway. (I'm tired of checking multiple addresses.)

And I apologize for obfuscating the address like this, but it's a new address, and I'd like to keep the spammers at bay for at least a little while.

Happy New Year! (Do I have any readers in Japan, Korea, Australia, or anywhere else where it's 2009 already? And Kate, if you're reading this, I urge you to remember that you're on vacation and you should get off the Internet.)

Change of name

After long consideration, I have recently decided to change my name. I will henceforth be Michael Lugo. (My e-mail address remains the same for now.)

I hope to still bring you the same, well, whatever it is I've been bringing you for some time to come.

A nonreligious statement

Through my logs, I came across a forum where people have pointed to a post on this blog.

They then veer off into saying things about religion. I suspect this may be due to the title of this blog.

I just want to state that "God Plays Dice" has nothing to do with the Judeo-Christian-Islamic-etc. deity. It is a reference to the following quote of Einstein, in a letter to Max Born:

Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secrets of the Old One. I am at any rate convince that He does not play dice."

(I'm copying this out of Gino Segre's Faust in Copenhagen; it's originally from Einstein's letter to Born, December 4, 1926, which is reprinted in The Born-Einstein Letters.) The "Old One" to whom Einstein is referring here was, as far as we know, not what is usually meant by "God"; I suspect that this is why the translator (Irene Born) chose this translation, although I don't know what Einstein said in the original German. To be totally honest, I don't know if the original was even in German.

The purpose of the title is that I feel that probability is an important tool for understanding the world, which Einstein may have been a bit skeptical about, at least in the case of quantum mechanics. And there's something of a tradition in the titling of math blogs of taking sayings of well-known mathematicians and "replying" to them. (By "tradition" I mean The Unapologetic Mathematician also does it, in response to Hardy's A Mathematician's Apology.)

Also, for some reason I had thought it was Bohr, not Born, that he wrote this to. I suspect this is because I've heard more things about Bohr than Born, and they sound similar.

I suspect the people at the forum in question won't read this, though. But making this post makes me feel like I've replied to them.

edited, 5:56 pm: I was wondering if there were any blogs whose titles riff on the quote that "A mathematician is a device for turning coffee into theorems" (usually attributed to Erdos, but supposedly actually due to Renyi). I found Tales from an English Coffee Drinker. The quote from Goethe, "Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different", also would be good as a source for a blog title.

Loose ends

You may have noticed that posts have been less frequent than usual recently.

This is because first I was finishing up the semester. Then I spent this weekend recovering from the semester. The good news is that I am done taking classes for credit, forever! This is also somewhat terrifying, because the prospect of doing research full-time and writing a thesis is daunting -- but also exciting...

Anyway, not too long ago I wrote about the napkin ring problem in calculus, inspired by Keith Devlin's article; Devlin has given a calculus-free solution, basically that corresponding cross-sections are equal. I alluded to this in the post a couple weeks ago but didn't write out the details. In his May column, Devlin gives some reader remarks to Paul Lockhart's A Mathematician's Lament, which I wrote about back in March.

Also, here's an interview from Leonard Mlodinow, at Carl Bialik's The Numbers Guy -- my mother fairly reliably forwards me some of the The Numbers Guy columns, because she gets some sort of e-mail from the Wall Street Journal, and I don't have the heart to tell her that I'm a step ahead of her! I previously wrote about Mlodinow's probability quiz. Unfortunately, the cover of Mlodinow's book The Drunkard's Walk no longer seems to feature dice.

In case you need more things to procrastinate with...

The list of blogs that I read, over on the right sidebar, has been updated.

There's no real rhyme or reason to this list; I just took my Google Reader list, filtered out the blogs that aren't mathematical in any way, and stuck them in there. If you want more things to read, take a look there. Basically, these are the blogs I find interesting enough that I want the magic of RSS to let me know when they've been updated.

I promise I won't be offended if you go read them instead of me.

fostering mathematical conversation

Expect the frequency of posting here to drop off somewhat after tomorrow.

This is because Wednesday is the first day of classes here. I originally began this blog in part because I didn't have much else to do with my time during the summer; now I will have classes and teaching and (at least in theory) research that I'm working on.

I will be taking courses in algebraic topology (homotopy theory, etc.; I'm not particularly looking forward to this one, but it's required for my program); logic and computability (using Enderton's text, A Mathematical Introduction to Logic); and probability inequalities and machine learning. (This last one is probably the one that will inspire the most posts over the course of the semester, if I had to guess.) I'm also TAing a multivariate calculus course.

The reason I mention the text for the logic course is that Enderton has produced an Author's commentary for his text, about which he says:

The purpose of these comments is to explain, section by section, what I am trying to do in the book. My hope is that the commentary will add a helpful perspective for the reader.

In addition being a place for helpful material, this website gives me the chance to post additional material. Users of the book might have varying views on this role of the website.

I welcome suggestions for how the commentary can be made more useful.

This is the sort of thing that I was talking about, to some extent, in this post about "companions to books". I gave there as an example of a companion to a textbook Bergman's A Companion To Lang's Algebra, wich were written by a professor to supplement the textbook for the course he was teaching; this is different in that it's written by the author.

From what I can gather, Enderton's book is one of the standard textbooks for an introductory logic course; presumably the many people who have taught courses based on this book have had similar sets of thoughts (although perhaps less extensive, as teaching a course takes less time than writing a book) and it would be nice to see all of those in some central place.

I said in my previous post that with this sort of companion I did not mean something like Wikipedia, because the original text would be inviolable. But in one sense I do mean something like Wikipedia -- no particular contributor's contribution would be all that valuable but they'd add up to something. The question, though, is who would use that something. The student wouldn't read it, because students are by nature lazy. Would professors teaching the courses care enough to read such a work? And more importantly, would they contribute to it?

I'd also like to point out something that cwitty mentioned in a comment here, namely the apparently dead project called "Fermat's Last Margin". Shae Erisson wrote in 2004:

The idea behind Fermat's Last Margin is...
I write a lot margin notes in books that I own, and research papers that I print out. To me, a research paper is an unfinished discussion. I like to argue, exclaim, deride, doodle, and generally get completely comfortable with academic publications that I read.
There is a downside. Andrew Bromage once made some questioning comments about a Comonads paper on the #haskell irc channel. Six months later, someone else made the same questioning comments. I realized that we can't share our margin notes! Who knows what brilliant ideas we've missed because we had one half, and someone else had the other half? Fermat's Last Margin is my answer.
The names comes from the story of Fermat's Last Theorem. The story is that Fermat wrote in the margin of a book that he had thought of a novel proof for this theorem, but the margin was too small, the proof would not fit. If Fermat had this margin I am making, it would be the last margin he would ever need.

Unfortunately that doesn't seem to have quite gotten off the ground. The point, though, is that there don't seem to be channels for communicating results on a level smaller than the research paper or the conference presentation, which causes unnecessary duplication of effort. Imagine if you couldn't share a body of mathematical ideas until you had enough of them to fill up a semester-long course or a book; chances are math never would have gotten off the ground if that were the case. Sure, there are ways for people to share ideas that aren't enough for a paper or a talk (for example, just talking to each other), but I don't think more of them would hurt, and I think the mathematical community ought to explore how to foster those sorts of interaction using the Web 2.0 paradigm. (I was trying to avoid using the words "Web 2.0" but they're a convenient shorthand for what I want to say.)

non-nonstandard calculus, and the Carnival

Matt at The Everything Seminar talks about his experiences in teaching "non-nonstandard calculus". Formally, this is calculus done over the ring R[dx]/((dx)²=0); informally, this is calculus where dx is treated as a number whose square is zero. He writes:

By treating infinitesimals on the same footing as finite numbers, the approximation schemes of calculus become more intuitive. I think every mathematician has discovered this on their own, in their own private language. Why not make the language commensurable with the computations that we do?

I agree with this -- the reason we do whatever computations we do in a certain way is often because it's the easiest way we know. Why make the students suffer more than we have to?

As people have pointed out in the comments to Matt's post, this approach seems to have nothing to say about integration. But does the usual approach to teaching differentiation have anything to say about integration?

In general, it seems to me that mathematics and mathematics education are more separated from each other than they need to be. Obviously, some differences are necessary -- but why erect an artificial wall? (I feel this somewhat keenly because I am at the moment in my life -- two years into grad school -- where I am expected to jump over this wall.) John Armstrong has written about the Carnival of Mathematics and how it is becoming split between people who do lower-level mathematics and people who do higher mathematics, with the lower-level people winning. But it strikes me that they're claiming that the difference is one of kind, not one of degree. There should be a smooth continuum from 1+1=2 to, say, the Riemann hypothesis -- everything currently taught to students was research once -- but there isn't. It seems, though, that the Carnival of Mathematics welcomed submissions at all levels and it just turned out that there are more people writing at the lower levels.

This blog goes back and forth between levels quite often, so you'd expect me to think this. And that's intentional. One of my goals here is to make the point that mathematics -- well, at least some parts of it -- is not all that divorced from everyday experience.

(Oh, and by the way, yes I changed the layout. People have said for a while they didn't like it; the Adsense ads were making me only a pittance; and the old layout was orange and blue which are the Mets' colors.)

Ten thousand

The ten thousandth page load on this blog came today, at 5:31:47 AM (US Eastern Daylight Time, UTC-4), from someone located in or near Ithaca, New York, using Time Warner Cable's RoadRunner internet service; they viewed my post on the high school prom theorem (the article from the New York Times that inspired this, in which medians and means were confused, has been mentioned in quite a few blogs).

They came from this post at The Volokh Conspiracy; I'm not mentioned in the post, but John Armstrong provides a link to me in the comments.

They were using Firefox 2.0.0, wich is the browser used by slightly more than half of my readers. (Generally the statistics hover around 60% Firefox, 20% IE, 10% Safari, and 10% random other browsers, which is much different from the Internet as a whole.)

Ten thousand isn't a huge number, but it's enough to make me realize that people actually are willing to hear what I want to say, and I appreciate that. Thanks for reading.

A note from the management

I recently switched this blog from a full-text feed to a feed which shows just the beginning of each post. The reason I did this was in order to encourage more people to come to the actual site, which I am hoping will encourage more comments and discussion. I'm open to going back to the old format, though. If you have any thoughts on this matter please let me know.

edited, 6:02 pm: I've gone back to the full-text feed.