The Empire of Mathmech Diameter is a massive, pleasant nation, renowned for its irreverence towards religion. The hard-working population of 2.461 billion Mathmech Diameterians have some civil rights, but not too many, enjoy the freedom to spend their money however they like, to a point, and take part in free and open elections, although not too often.

The relatively small government juggles the competing demands of Defense, Healthcare, and Law & Order. The average income tax rate is 16.5%.

The Mathmech Diameterian economy, worth 114 trillion Duckcoins a year, is fairly diversified and led by the Gambling industry, with major contributions from Beef-Based Agriculture, Tourism, and Retail. State-owned companies are reasonably common. Average income is 46,666 Duckcoins, and evenly distributed, with the richest citizens earning only 3.1 times as much as the poorest.

Citizens seem fixated on 105m x 45m rectangles, a large concrete wall is being built around the country's borders, autocrats are persona non grata, and disadvantaged neighbourhoods have become no-go areas after sundown. Crime is relatively low, thanks to a capable police force and progressive social policies in education and welfare. Mathmech Diameter's national animal is the Duck.

Mathmech Diameter is ranked 248,944^th in the world and 4^th in US Preppers for Most Scientifically Advanced, scoring 26.46 on the Kurzweil Singularity Index.