WHAT COLOUR WAS THE BEAR? 1990

It’s 1990, I am 42. You are bear hunting. Suddenly you see a bear stationary 50 metres due west of you. You walk 50 metres due north to get a better view, turn and fire due south and kill the bear. What colour was the bear?

White – it was a polar bear, you were standing at the North Pole where all directions are south. So here we see one of the peculiarities of spherical geometry – all directions were south – completely counter intuitive. This is a standard lateral thinking problem I was familiar with when I came across ‘E A Reeve’s Rugby Diagram’ 1929. In the heady days of the British Empire, on which ‘the sun never set’ the BBC World Service broadcast from a radio station in the centre of Britain at Rugby (which also broadcast the Greenwich Time Signal and communicated with ships anywhere in the World). If you were in say, Singapore, and wished to tune in you had to point you aerial ‘at’ Rugby, along a great circle. This is not a trivial problem. You can’t just draw a straight line on a Mercator map and measure the angle, great circles are curved on a Mercator. The  Reeves Rugby Diagram was a Mercator map with ‘contour’ lines joining places of equal bearing to Rugby; its retro-azimuths – you put a dot on the map where you were and then read off the correct bearing from the nearest contour.

At first glance it is a surprising map, with contours swirling all over the place in a completely non-obvious manner, apart from anything else there is a point 800 miles south of  New Zealand directly opposite Rugby where, as in the bear problem, all directions are Rugby.

This got me thinking, were there any other locations one needed to know the bearing of? Obviously Mecca, towards which Muslims pray, and on which all Mosques are aligned. On investigation I found that Muslims can buy a compass and accompanying booklet listing every significant city in the world with its bearing to Mecca, the Qibla to the Ka’ab in Makkah. But no one had apparently produced a map, a much more compact and easily used method. I decided to produce one.

It is just (!) a problem in spherical trigonometry, and is relatively straight forward for locations less than 90 degrees along the great circle, but as the formula entails anti-tan, which can be negative or positive over 90 degrees, and there is no obvious way of telling which, it is a bit of a pain to automate. I wrote a programme in BASIC on my PC which generated the bearing for any given Latitude and Longitude. Of course, I immediately got the bearing for London.

Architects have a number of Urban Myths of catastrophic mistakes others have made – the north point on a plan constructed as a raised flowerbed  at great expense by the contractor; the Australian bus station which the buses couldn’t turn in to because it had been constructed to Australian feet not Imperial; the tower block that was found to be on top of a tube line at the last moment and had to be turned through a right angle; the concrete prefabricated stair (x 50) that didn’t take into account the floor screed thickness; and the mosque incorrectly aligned because the architect has added not subtracted the magnetic variation.

The only  specially built mosque in London at that date was the Central Mosque in Regent’s Park, could it have been misaligned? It would make a good story if it was.

So I bought a hand bearing compass, and visited the Regent’s Park mosque. Fortuitously I found I could sight along all four sides, and so measured their bearings twice in either direction – a total of sixteen measurements. Then I went home and averaged them to get a final magnetic bearing, correctly applied the magnetic variation for the date, and compared it to my programme’s result.

Disappointingly it was exactly correct! Well done Frederick Gibberd in 1977!

I modified my programme so it calculated contours at 10 degree intervals, and laboriously plotted these as a layer on Google Earth – this was as counter intuitive as the Rugby Diagram. There was of course the anti-point to Mecca, which turned out to be Mururoa Atoll in the South Pacific, used for the French nuclear tests, and huge areas in South America and Indonesia where there was practically no variation in the bearing. To demonstrate  how deceptive a Mercator map can be, below is my map equivalent to the Rugby Diagram - the bearing of Mecca from Cape Horn is 90 degrees clockwise from north; barely believable but correct - stretch a string between them on a globe. Of course, like a number of my other inventions, this has been superseded by smartphone apps which tell you where to face instantly.

The direction of Mecca map is still interesting as a cartographical oddity and if anyone would like a Google Earth *.kml file so they can display it on their own PC they are available for a moderate charge!

Back