Antipodean Syzygies

[You might have thought that I would come back from Down Under with something of actual human interest to blog about.  You would be wrong  … well, at least for now. – JPS]

As an accomplished master of the obvious, let me point out that we live on a the surface of a sphere.  However, for most practical purposes we might as well live on a big flat world with a rectilinear North-South/East-West grid (and a big mongo Greenland to boot – you know, so we have more ice to raise the sea level with ….)  Very long distance travel is an exception, and especially so when it takes you close to the antipodes of your usual haunts. I just returned from Perth in Western Australia, which is the closest antipodal city to the Eastern U.S. *(I also got down even further south to the fabulous Augusta/Cape Leeuwin area at the extreme SW of Australia, which is even closer to being the anti-NE U.S.) It got me thinking about some of the interesting and somewhat counter-intuitive aspects of antipodes.  [Quick question (verbal and visual answers down below somewhere ) – If you go northwest from your current position, which way does your antipode go?  (assuming you are not at one of the poles.) ]

Note that Australia and New Zealand are often referred to in general as The Antipodes given their position relative to England, although in actuality Counterpane-Australia fits nicely into the North Atlantic between the US and Spain, while New Zealand is mostly over Spain. (The actual Antipodes Islands – windblown specks of penguin and seabird habitat southeast of New Zealand – come in right about at the Channel Islands.)

Between you and your antipode there lies an equally short route in every direction, i.e. from your antipode all directions lead home. And these paths cover every inch of the earth’s surface. In fact, they all follow Great Circles  (so they also encompass every “shortest path” from where you are to every point on Earth. ) The easiest way I find to think about this, is to imagine that you are at one of the Poles, so the other Pole is the antipode, and the paths are then all of the meridians of longitude. This is essentially then the same observation as that you can only go one direction (south) from the North Pole and vice versa. (Since many of the paths go over Antarctica, this got me thinking whether there are any scheduled air flights that pass over Antarctica  – other than ones actually going there. Discussing this with my Aussie mates, the best we came up with was Sydney/ Santiago – which does “bend” south quite a distance, but does not seem to get over the Antarctic landmass. Auckland to Capetown or Perth to Santiago looks like they would do it , but it seems that there are no direct flights   – see this Great Circle mapping page)

Answer to quick question above. If you go northwest the antipode goes southwest. Not too hard – North-South and East-West are quite different concepts when you get to the global scale, (for instance there is no preferred “East Pole” – sorry Pooh**) but if you are like me, it is not obvious and takes a bit of mental  visualization.

But even more intriguing to me is how in my actual visual imaging of this moving of antipodes,  (not just the assignment of directional names “east”, “north” etc.), I find that I chase my antipode in the east-west dimension, while I seem to move opposite to it in the north-south one. After a bit, I can turn  the north-south movement into a “chase”, basically by following my line of longitude up and over the pole and around to the antipode – I chase it along this particular great circle. However, it is much more difficult to turn the east-west into any kind of “oppositional” movement. 

At first blush I thought this came back to  North-South being a very different animal from East-West. When you go north-south you are following a great circle, when you go east-west you are not. (Wait a minute,  didn’t I say up above that every direction gets you to your antipode along a great circle? Yes it does. But the “east-west” great circle that gets you to your antipode is the one that is tangent to your line of latitude, it then “bends away” to the south if you are in the Northern Hemisphere at at a “rate” dependent on your latitude.) But it turns out that the problem is (mostly) in my (and I suspect others) default representation of the world.  If I need to actually take into account the “roundness” of the world, my first representation is as a cylinder – just take that flat rectilinear map and glue it together along the date line.  [And in fact,  in the map-filled bedroom of my youth I had a cylindrical wastebasket with a map of the world on it.] In such a representation  north-south great circles get broken into two parts which go “opposite” of one another.  [Note that general utility of the “cylindrical” representation is greatly helped by the relative lack of the need to identify locations in the Polar regions. You might view this as happy chance,  good timing with respect to our evolution of intelligence and the current climate,   or even make the argument that the polar regions (areas near the axis of rotation) of planets are most likely to be of diminished interest  to newly emerged intelligent species (or even most species … as opposed to say the representation of most use to an Arctic Tern.)  Elucidation and criticism of this argument left as an exercise to the reader.]

* Perth is actually just about directly opposite of Bermuda.  Nice addition to the “sun never sets on the British Empire” pairs, which also includes Auckland- Gibraltar.  Oh and “the Pacific Ocean is really, really, really big”  winner goes to the parts of the Peruvian and Vietnam coastlines that match up. That’s right it is as far around between them as is crossing SE Asia, Indian Ocean/Indian sub-continent, Africa, South Atlantic and South America combined. See the nice map below or at the Wikipedia article on Antipodes.

** re: East Pole. I am talking about the real Winnie-the-Pooh, not the corporate IP terrorism fraud that Disney rolls out daily in the various Rat Parades around the world.

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3 responses to “Antipodean Syzygies

  1. (no preview? he steps gingerly off the platform, onto the thin wobbly wire. how will his ellipses render? …)

    Words aren’t the best tool for imagining and rendering 3D mapping problems. My thought process got as far as “the antipode must not move northwest because that’s the only answer I can imagine”.

    Jumping down to the answer and reverse engineering: the east/west-ness of the antipode tracks directly. Moving north in the Northern Hemisphere is a movement towards the pole, a movement that forces the antipode to move towards its pole; south. Don’t know how general this abstraction, it works here.

    Further antipodean computation weirdness. When using numeric coordinates to express and calculate our immediate polar opposite it is the E-W that is tricky. Lincoln NE ( 40.82N – 96.71W) is opposite the middle of the Indian Ocean (40.82S – 83.29E). This time it is N-S I can do in my head.

  2. Yes, the “no preview” is a real drag. I started this just as a test when looking at alternatives for the WAAGNFNP site . It has some nicer features than Blogger, but the no preview is a real drag, so do not know if I will keep it going here.

    Words aren’t the best tool for imagining and rendering 3D mapping problems.

    Yes, man obviously wasn’t “meant” to live on a sphere…

  3. Hi JP-
    I’m too tired to write/think of anything more than “Welcome Back”, so I’ll just say that.

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