Not so long ago I realised that I might not be a northerner any more (statistically speaking). I have a bit of an accent, I have my dinner at lunchtime and my tea at suppertime, so this came as a bit of a wake-up call! I’ve lived in Cambridge since undergraduate days: it’s the place I’ve spent most time living, and round about now I’m passing the point at which it’s been my home for 50% of my life (so far!). It’s certainly my geographic modal home.
What about mean? My mean geographic location should be somewhere in the Midlands, right? I like to picture a ghost “me”, following me since my birth in Liverpool, wandering out over the Atlantic while I lived in Portland for a year or so, then turning back towards England and heading towards the South East. Maybe somewhere near Loughborough there could be a little virtual me, slowly ambling in the direction of Cambridge.
So I’d like to calculate my geographic mean location. What does “mean” mean, in this context? Let’s say I can ignore the “noise” caused by my daily travels, and only have to consider places where I’ve lived for more than 6 months. I can get latitude and longitude from the internet. I can’t simply sum the latitudes and longitudes and calculate a weighted average though. I want this to be mathematically correct; that method is demonstrably wrong. A person who spent their life in the Pacific Islands, straddling the international date line (sometimes +180°, sometimes -180°) might end up with an average longitude close to zero. Latitude/longitude is an inappropriate coordinate system for (easily) calculating geographic mean.
The co-ordinates problem is easier to think about using vectors and spherical geometry. I can convert a lat/lng pair into a 3-dimensional vector (x,y,z). My geographic mean is then the weighted average of the vectors representing my life, and it’s possible to convert back to latitude and longitude to find it on a map.
I ran the numbers, including the fact that I’ve lived in Portland, Oregon for a year, and Dunedin, New Zealand for about 6 months. Plotted out “virtual me” and found him near Wennington in northern Lancashire. North of where I was born. Huh? I was sure this was a mistake. It was only when I “zeroed out” my overseas adjournments that the mean location ended up where I’d expect, in the Midlands. What was going on?
Turns out… the shortest great-circle path from Cambridge to Dunedin (the furthest city in the world from London, and home to most southerly planetarium in the world), begins on a bearing of 048° (from geographic North). Yes, that’s correct: to get to the extreme south, start by going Northeast. Similarly, the bearing to get to Portland, approximately 7° of latitude further south than Cambridge, is 321 - northwest.
I’ve tried to illustrate why this is in the video below. Red lines show shortest distance from Cambridge to Dunedin, and to Portland. The Cambridge-Dunedin line goes over the “shoulder” of the North pole: it’d be ever so slightly further the other way round, across South America and Antarctica.
So - it seems that, if I can use my geographic mean as a measure, I’m still a northerner - and all because I lived in the far south for a short spell.
If you’d like to calculate your own geographic mean, here’s my spreadsheet with workings in.