## Tuesday, 29 September 2015

### #16

Geography – GCSE level.

The concept of a spherical earth dates back as least as far as the 6th century BCE, and is commonly attributed to Pythagoras. Ptolemy’s world map of 150CE, despite a mistaken measure of the earth’s circumference, is clearly based on a sphere with lines of longitude and latitude to record its coordinates, and contrary to popular belief, even in the dark ages hardly anyone thought that the earth was flat.

However, maps are often more useful than globes – they fold for convenient transport, they can be laid out flat for simple perusal, and they can be easily made at a vast range of different scales. Take a large scale globe with you on your travels and instead of a conquistador, the natives might think you were a pilates instructor.

But the problem of map projection – portraying a sphere’s surface on a plane – has existed for as long as the knowledge that one can’t sail off the edge of the world, and in the early 19th Century, Gauss’s Theorema Egregium proved once and for all that a sphere’s surface couldn’t be represented on a plane without distortion. Which brings us to this attempt to fit an oblate spheroid peg into a two-dimensional hole...

The teacher has made a good choice of map projection by avoiding the infamously distorting Mercator projection, which was deprecated with all other cylindrical projections in a 1989 resolution by seven North American geographical groups. The Mercator projection maps the sphere on to a rectangle, and the teacher here is clearly using a pseudocylindrical projection, using only the central meridian as a straight line. From the shape of the oval that she has drawn around her continents it looks like she is using a Mollweide or Tobler hyperelliptical projection – a good compromise between not distorting shapes and preserving area measure.

The Mercator projection, albeit useful for mariners with its ability to represent lines of constant course as straight segments that conserve the angles with the meridians, infamously makes Greenland larger than Australia. At least the teacher has avoided that error, albeit by not putting either Greenland or Australia on her map. Any map larger in scale than 1:1 must omit some detail, and the best maps are masterpieces of simplicity and clarity (consider Harry Beck's iconic London Underground diagram to realise that what is left out is as important as what is put in), but leaving out entire continents really cannot be excused. Although this photograph is undated, Australia was definitely discovered before the whiteboard was invented. Or indeed photography.

The Mercator projection is also criticised for being Euro-centric, for example showing Finland as extending further from north to south than the vast Indian subcontinent. Again, the teacher has avoided that politically incorrect error, but by not putting either Finland or India on her map. In fact, it would be easier to list what is on her map: the Americas (although Ferdinand de Lesseps would have a hard time building the Panama Canal across this Central American isthmus that is barely narrower than Brazil), Africa, and a blob that by a process of elimination must represent all the intricate islands and peninsulas of Europe. Russia extends east into Asia, but the age of discovery ends here, without so much as a “Here be kangaroos”.

Even with a globe in front of her to copy from Ptolemy’s map looks better than this, and he didn’t have the advantage of having a whiteboard to rub out any mistakes.

3/10 A good start, but over-simplified and incomplete to the point of being useless.