Month: July 2008

Distributions in Mathematica and R/S-PLUS

Posted on by John

I posted some notes this evening on working with probability distributions in Mathematica and R/S-PLUS.

I much prefer Mathematica’s syntax. The first time I had to read some R code I ran across a statement something like runif(1, 3, 4). I thought it was some sort of conditional execution statement: run something if some condition holds. No, the code generates a random value uniformly from the interval (3, 4). The corresponding Mathematica syntax is Random[ UniformDistribution[3,4] ].

Another example. The statement pnorm(x, m, s) in R corresponds to PDF[ NormalDistribution[m, s], x ] in Mathematica. Both evaluate the PDF of a normal random variable with mean m and standard deviation s at the point x.

It’s a matter of taste. Some people prefer terse notation, especially for things they use frequently. I’d rather type more and remember less.

Languages that are easy to pick back up

Posted on by John

Some programming languages are much easier to come back to than others. In my previous post I mentioned that Mathematica is easy to come back to, put Perl is not.

I found it easy to come back LaTeX after not using it for a while. It has a few quirks, but it’s basically consistent. The LaTeX commands for Greek letters are their names, lower case names for lower case letters, upper case names for upper case letters. The command for a mathematical symbol is usually the name a mathematician would give the symbol. Modes always begin with begin and end with end.

Python also has a consistent syntax that make it easier to come back to the language after a break. Someone has said that Python is similar to Perl, except that the word “except” does not appear nearly so often in the Python documentation.

It’s more important that a language be internally consistent than conventional. Each of the languages I mentioned have their peculiarities. Mathematica uses square brackets for function argument arguments. LaTeX uses percent signs for comments. Python uses indention to denote blocks. Each of these take a little getting used to, but each makes sense in its own context.

A special case of consistency is using full names for keywords. Mathematica always spells out words in full. For example, the gamma distribution object is named GammaDistribution. I don’t mind a little extra typing. I’d rather optimize for recall and readability than minimize keystrokes since I spend more time recalling and reading than typing. (One flaw in LaTeX is that it occasionally uses unnecessary abbreviations. For example, \infty for infinity. The corresponding Mathematica keyword is Infinity.)

Mathematica turns 20

Posted on by John

Mathematica was first released June 23, 1988. I started using Mathematica not long after it came out and used it for a few years. Then for several years after that I didn’t touch it. When I began using Mathematica again several years after that, I was afraid that like Rip Van Winkle, I’d find many things had changed while I was gone. Instead, I was pleasantly surprised how easy it was to start using it again.

Mathematica syntax is simple, consistent, and predictable. They got this right twenty years ago and stuck to it. They’ve managed to grow over the years without alienating users, even those of us who take a long hiatus from using the product. I’ve used Mathematica more or less regularly over the last few years, but I’ll still go for weeks at a time without using it. It’s easy to pick up every time I return to it. (The opposite of my experience with Perl.)