A recent xkcd comic had me thinking about the possibility of listing every possible chess move, rather than enumerating only the moves available from a given position.

Chess moves are typically notated as a piece type and the square it moves to. There are 6 types of pieces and 64 squares to move to, so the easiest starting point is $6\times 64=384$ moves. But there are a few layers of complexity on top of this.

A friend and I recently managed to finish a playthrough of Divinity: Original Sin 2 as a lone-wolf lizard-wizard drudanae-doping duo. He was a rogueish polymorph with the horribly-underleveled vulture armour, and I was an elementalist conjurer with the delightful devourer armour.

Lizards are obviously the most meta choice because they can dig without a shovel. Undead lizards are even more optimal because they can dig without a shovel and pick locks without lockpicks, but lacking lungs lamentably leaves little leeway to definitively dream on drudanae, which is unambiguously a fate exceeding death and proceeding all the way into undeath …

Ever seen a diagram of the geomagnetic field that looks something like this?

While I might technically be exaggerating, every deficiency of this diagram is something I have legitimately seen on the world wide web. In summary:

1. Field lines converge at poles

2. Those poles are the geographic poles

3. Field emanates from pole marked ‘S’ and converges at ‘N’

4. Field is parallel …

Paths of constant bearing (known as ‘loxodromes’ or ‘rhumb lines’) are often mentioned in the context of the Mercator projection, as they are always straight lines on the map. It’s often emphasised that this is not the shortest route between two locations, but something I feel is glossed over is the direct consequence that these paths are not straight on a sphere, even though the bearing is consistent. In general, following a steady course on a compass requires turning slightly along the entire journey. Perhaps the most obvious indication of this is to imagine travelling due east when only …

There was an online discussion regarding ‘magic numbers’ in software – numeric constants serving an important role with no description or justification for their value – and one static analysis tool’s assertion that the only numeric constants permissible in statements are -1, 0, and 1. Although the significance of undocumented numbers in written software is often not readily apparent, sometimes the function of a number really is nothing beyond its literal value, and this sort of overzealous rule is guaranteed to complain about expressions whose intent actually is readily apparent – but none of that actually matters because someone soon ported the …

It’s a simple fact of life that everyone loves the azimuthal equidistant projection, which shows the world at the correct distance and direction from its central point, even those who have never seen the term in their life.

For example, when centred on Sydney:

One particular point of interest is that Cuba is shown east of Sydney, despite being in opposite hemispheres. And while this is literally true…

It doesn’t do much to affirm ill-conceived views of the world perpetuated by cylindrical and pseudocylindrical maps. Wouldn’t it be nice to use terrible metrics for ‘distance’ and ‘direction …

Last year I said, “Last year was nice and all, but […] if part of the goal is to practise then next time I should do something more in line with my typical approach.” The same held true this year, so this time I went for full colour and abandoned any remaining semblance of ‘Inktober’ beyond lifting the prompts. Except I didn’t really have time for daily drawings and haven’t generally enjoyed the experience of finding something for prompts that don’t inspire, so this time I decided from the outset that if I didn’t have time or …

Everyone loves the azimuthal equidistant projection; some just don’t yet realise it. For that latter camp, a quick refresher: azimuthal equidistant maps show all courses from the centre point at the appropriate angle and with correct scale – a ray from the centre to any point shows the initial bearing and length of the direct route to that point. The azimuthal equidistant projection, which unfortunately lacks a more concise name (‘Postel’?), is quite popular with some rather diverse groups, including the contemporary ‘zero-Gaussian-curvature Earth’[1] crowd. Perhaps more perplexing than this movement’s modern resurgence, is their insistance on the …

One of the labours of Hercules was surely to find a map of Earth’s magnetic field.

There’s no shortage of crude diagrams of bar magnets superimposed over cartoon globes, and plentiful plots of isogonic lines to be procured from multiple perspectives; yet for accurate depictions of the simple lines of magnetism over Earth’s surface, the offerings seem sorely slack. So just imagine how hard that would have been two thousand years before the internet.

The most common chart I see that has an actual connection to reality, is a map of isogonic lines – contours of equal magnetic …