a programming blog

Method of Differences Add'l Applications

In my post on the Method of Differences, I focused on using the technique to generate mathematical tables. As some readers noted, there are additional and interesting modern applications of the technique. This post will discuss two of them: sequences to functions, a method of analyzing sequences, and strength reduction, a compiler optimization technique.


Method of Differences

The “Method of Differences” is a mathematical technique for reducing the computation of polynomials to repeated addition. Once the system is setup, relatively unskilled human computers can populate dense mathematical tables. This is the “difference” in the Charles Babbage’s Difference Engine which aimed to automate the creation and printing of these tables.


Konrad Zuse's Early Computers (Review)

Although historians are usually pushed to decide questions of “who was first,” the question of impact is more interesting. Konrad Zuse has a claim to the first computer, the first high-level computer language, and the first European commercial computer sale, but his relative isolation working in Germany in the 30s and 40s limited his visibility and impact. It wasn’t until the 1970s for his innovations to become more widely known. Raúl Rojas has long contributed to the historical appreciation of Zuse and the remarkable modern nature of his machines. This volume collects and makes available in English many of his previous articles on the subject.


Monsters, Aliens, and Holes in the Ground (Review)

For those interested in the history of tabletop roleplaying game design, Monsters, Aliens, and Holes in Ground is an excellent, near encyclopedic treatment. The author, Stu Horvath, documents major and minor game systems, how they innovated or were influenced by other game systems, and how the systems expanded with settings and adventures.


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