Magnifying glasses operate on a pretty simple concept: when an object is within the focal length of a convex lens, a magnified ‘virtual’ image is produced, as demonstrated by simple ray optics:

… with just the slight problem that the magnified image is always further away. An object at the focal point produces an image that is literally infinitely big – but it’s also at an infinite distance. And that really doesn’t help; the moon is quite sizeable itself, but that won’t show you the dust on its surface.

Still, magnifying glasses certainly seem to have an effect – but …

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.

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 …

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 …

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 …