Complex Derivative Field

There is a direct analogy relating the real and imaginary components of the complex derivative to divergence and curl (respectively) of a 2D vector field. Let be a complex-differentiable complex function and be the corresponding 2D vector field: Complex Number Surface Vector Field     (note) So         (note) Here curl is […]

There is a class of multivariate functions that have some kind of “univariate character” except that they “combine effects”. A+B is king of them. Some of his subordinates are: These expressions are all commonly used. Number 3 is so common that it has it’s own shorthand: . Let’s define a family of operators where  is […]

Multilinear Interpolation

There is a neat visualization of linear interpolation that generalizes to higher-dimensional spaces, including bilinear (2D) interpolation, trilinear (3D) interpolation and general multilinear interpolation. At all levels it is much easier to remember the visualization than the formulas directly. Let’s start with the simplest case… Linear Interpolation Linear interpolation is a weighted average of 2 […]

Information Theory Plots

When considering a matter in the light of both probability- and information theory, it sometimes becomes tiresome to switch between the two perspectives. Here is a little assistant for the mental juggling. (PDF)

Funny Tax Laws

Humour is not the first thing that comes to mind when you think of accountants and lawyers, but somehow, a joke has slipped into the South African Tax Code. It concerns depreciating assets, but before you can depreciate… ahem… appreciate the joke, you need a little accounting background. In the world of accounting, assets depreciate […]