Dual numbers

https://ericlippert.com/2019/01/07/dual-numbers-part-1/ [ericlippert.com]

2019-01-17 23:23

I’ve recently been looking into a fascinating corner of mathematics that at first glance appears a little bit silly, but actually has far-reaching applications, from physics to numerical methods to machine learning. I thought I’d share what I’ve learned over the next few episodes.

I assume you recall what a complex number is, but perhaps not all of the details. A complex number is usually introduced as a pair of real numbers (a, b), where a is called the “real part” and b is called the “imaginary part”.

A brief aside: it has always bugged me that these labels are unnecessarily value-laden. There is no particular “reality” that is associated with the real part; it is every bit as “imaginary” as the imaginary part. They might as well be called the “rezrov part” and the “gnusto part”, but we’re stuck with “real” and “imaginary”. Moving on.