Data analysis involves a lot of technicalities, but also sometimes accounting for human error. If data have been manually keyed in, typos are inevitable. Checking numerical values for outliers can find some of these mistakes; but what should we look for?

In a computer game you can have numerical variables that span any range, that are even non-linear, and otherwise very complex. But in a tabletop game, the players have to do the math themselves (or consult tables) and must track everything too. Tracking if variable states is especially tough with mi...

Computer generated terrain usually begins with a base of random noise, or perhaps a fractal. These look nice in small sections, but are unconvincing for a continent: noise has none of the major features it should, like mountain ranges, and fractals are nothing but feature -- they're too regular. Here's a method for generating continent-level trerrain using distortion fields.

To many, the most perfect shape is the circle -- emblematic of unity -- or the square -- for combining with itself in a tile. But in the city Pherasa, the people have long held the spiral above all other forms. For them it is the basis of all aesthetics, and used in architecture, art, religion and war.

We all know that statistics can lie and confuse. We can easily confuse ourselves, in fact -- if we don't think very carefully about what a statistic is measuring, and what we want to know. A subtle mismatch between these can cause "bugs" in our calculations and our thinking. Here is one interesting sort of statistical bug, based on very simple math.

If a bank is creating new paper notes, what sizes should it issue to make transactions easiest for the public? This is one example of an type of problem I've become interested in. It is basically about how to divide a scale into discrete intervals, under various constraints. It seems very abstract, but it actually has a lot to do with real-world design and engineering.

Graphs and charts often mislead by obscuring the unreliability of their source data. But even if a graph-maker wants to do better, it can be hard to present such information intelligibly, without long or technical sidebars. Here is one approach for visually displaying both the primary data, and their reliability, in one graph.

The fighters launch from their carrier! They jink and turn -- shooting bogeys down as they go. Finally, they approach the enemy capitol ships. They fly close, fire torpedoes -- and escape, leaving behind billowing fire. Wait. Is this World War II or a space opera confection?

In this article, we'll consider how the size of ships affects how they can fight -- and come to some surprising conclusions.

Imagine you're given the task of evaluating the abilities of the individuals in a group -- perhaps in sharp-shooting -- and award ratings like A or F. You might plan a series of challenges of increasing difficulty. What should you do if these turn out to be much harder than you planned -- so that while you expected a mean success rate of 60%, it was actually 20%? An obvious solution is to multiply all scores by 3 to bring up the average. But it turns out that this (and any other linear correction) penalizes the weaker performers. Better alternatives exst.

In my previous article on the geometry of empires, I considered two essential strategies for organizing the defense of a territory. In one, troops were positioned along the border, ready to intercept enemies but spread thin. In the other, a single, centrally-located force was powerful but slow to respond. These are extreme approaches, though, lying at the ends of a spectrum filled with intermediate strategies.