Category — mathematics

To me, an intermediate and somewhat casual Mathematica user, the news that Mathematica 7 had been released was a surprise. Surprising to me because Mathematica usually goes much longer between major-digit releases; I would have anticipated this to be Version 6.1. For fun, I’ve plotted the history of Mathematica versions¹ :

Release dates of versions of Mathematica

Mathematica 6 was a substantial upgrade: the graphics system was completely overhauled, the curated data, that I’ve used as the basis for some posts here, was added, and the ability for dynamic interactivity was added with Manipulate and Dynamic. 

I am not, of course, a major Mathematica user. In fact, although I’m a physicist, I haven’t made tremendously much use of Mathematica for my professional work. This is partly because I tend to deal with relatively small data sets, for which a GUI-based data analysis tool is usually easier to work with than the command-line Mathematica. And I’d consider myself an advanced user of Pro Fit, the data analysis tool that’s made all the graphs for all the work I’ve done since about 1998.

In fact, my Mathematica license is my own personal one. As a graduate student, I bought the Student version of Mathematica, which they allow you to upgrade to a full professional license for only a few hundred dollars, compared to the $2500 list price of a new professional license.

Wolfram really wants its users to buy Premier Service, a several hundred dollars per year service which entitles you to all upgrades, major and minor. If you don’t buy premier service, then you need to pay for all upgrades, even the N.M.X to N.M.X+1 minor bug-fixing upgrades. And without premier service, you’re not even supposed to install Mathematica on more than one computer. Draconian and greedy, if you ask me, but they can do that, because they’re Wolfram. And for tech-heavy firms that make heavy use of Mathematica and get millions of dollars worth of value from whatever they compute in Mathematica, it makes sense. But it makes it very difficult to be a casual user.

And even though your existing copy can do everything it could the day you bought it, once the difference between your copy and the current release gets large enough, there is no longer an upgrade path. I think this is one of the motivations to release this as version 7 and not 6.1: I don’t recall the precise figure, but Wolfram generally offers an upgrade path only for jumps smaller than 1.5. If this is still the case,² what this does is cut off anyone who hadn’t upgraded to version 6. Update: enough with the conspiracy theories! Wolfram clears up the upgrade policy in the comments.

In my case, with Version 6.0.1, I have a choice of paying $750, and getting a year of Premier Service, or paying $500 for just version 7.0.0 with no service. Out of my own pocket, ouch! But what makes it really enticing, for me, is that Mathematica now reads SHP files. These are the Geographic Information System data files, promulgated by ESRI, in which vector-valued geographic data is commonly exchanged. In particular, the DC Office of Planning makes an amazingly large collection of DC GIS data available in SHP format. The possibility for quantitative analysis of DC mapping data is very tantalizing.

Of course, Wolfram wouldn’t release a major number upgrade without hundreds of other new features. As of yet, there isn’t much substantial written about version 7. I did find some notes from a beta-tester and from a college math teacher. I’ll probably buy it, even though it would mean delaying other expensive toys that I want.

1. most of the dates come from the Wolfram News Archive, some from the Mathematica scrapbook pages [↩]
2. I’ve asked Wolfram, but haven’t received a reply. [↩]

The recent issue of the alumni magazine from my undergraduate alma mater, The University of Chicago, includes a profile of mathematician Paul Sally, who taught the Honors Analysis in Rⁿ sequence I took in my second year. 

Despite the rigorously intellectual image of itself that the University promotes, the alumni magazine is usually as circumspect as an in-flight magazine. Of course the primary purpose of the magazine is to cultivate us as donors, so on-campus controversy, intellectual or otherwise, gets scant attention. The article on Sally certainly follows the magazine’s formula of uncritical boosterism, but I still found it a delight to read: it took me back to what was probably the most intellectually fulfilling experience of my academic career, a time when all the promotional slogans about the life of the mind were very real for me.

Although my enthusiasm for working in a lab led me to choose physics over mathematics, I still have a fondness for pure mathematics. I retain a handful of habits  that are more a part of math culture than physics culture.¹ Sally’s course kept me on the fence between the two disciplines.

Sally delivered his classes entirely without notes, and the course rarely made reference to the assigned book (a cheap Dover reprint and a small volume from Spivak). He led a “discussion session,” Tuesday evenings from 6:30 until 8 or 9, stretching the amount of class time. He told us he expected at least 25 hours per week from us, at one point advising us to make posters which read “Mathematics… is a full time job.” It was mathematics by immersion.

Not every teacher can pull this off so successfully: it’s easy enough to assign lots and lots of work, but the combination of a heavy workload and an uninspiring instructor usually results in lots of incomplete assignments. 

Sally once remarked that, as you continue in mathematics, you get to a point where hard work is not only necessary, but also sufficient, to prove theorems and make progress. He was getting us to develop the sort of attitude and work ethic to reach that point.

There are many things I learned in college that I’ve now forgotten, many problems I can no longer solve. I don’t know how much review it would take for me to be able to solve the problems from Honors Analysis again, but, 15 years on, I feel I still have a well-developed understanding of the structure of the real numbers. 

Here’s another article about Sally, for winning a teaching award.

1. In particular, I can’t stand the common-in-physics habit of using the word “finite” when what is really meant is “non-zero” or “infinitesimal.” [↩]