I’m reading a charming “slow travel” memoir by Dan Kieran, and came across this passage (reflections during a period that he and two friends took a milk float across southern England) about the paradox of measuring the coast of the island, and pointing the way (although Kieran doesn’t mention it) to fractals.
At the time I was going slightly mad, but when I got home a friend pointed me towards the paper called ‘How long is the coast of Britain?’, published in 1967 by a mathematician named Benoît Mandelbrot. It suggests that the depth of your journey–in terms of how closely you perceive it–really does increase its length in mathematical terms. The answer to the question posed by the paper is that there is no answer. It’s a paradox because the length of a coastline depends entirely on the way you measure it. It comes down to context, and the context in which you perceive something is a function of the brain.
To explain the coastline paradox you first have to accept that there is a definitive geological coastline of Britain, which would depend on high or low tide and all manner of other variables. Assuming you’re prepared to accept this, you then have to imagine measuring this coastline with a three-foot ruler. You would, eventually, come up with the coastline’s length. But what if you then repeated the experiment with a one-foot ruler? The smaller ruler would give you a greater distance because you would be able to get into lots of nooks and crannies that the three-foot one would have to stretch across.
Now you’re probably thinking, ‘Well, fine, but if you went down to a one-inch ruler you get an even greater distance. At least that would be accurate though, because you can’t get smaller than a one-inch ruler.’ The problem is, of course, that you can. You can shorten the ruler over and over again, going deeper and deeper, getting smaller and smaller, and the length of the coastline will increase each time. So there really is no definitive answer to the question. It’s a rather disconcerting thought, isn’t it? We all work on the assumption that the real world is defined according to measurable things, but once you begin to focus on it, the act of measurement itself becomes fraught with uncertainty.
Took a short trip to Europe last month and going to make you sit through some of the slides. Pull up a chair.
A bit of blue in Bruges, where the picturesque medieval old center—mostly shades of dignified red, orange and black—was almost overwhelmingly scenic. Loved this bit of blue.
The town’s symbol, a rather dashing bear, in his niche on the Burghers’ Lodge.
Bruges’ version of a (former) storefront church.
The alley ways (through which Colin Farrell wanders in the dude flick “In Bruges”–sample dialogue: Ken: [preparing to climb the bell tower]: Coming up? Ray: What’s up there? Ken: The view. Ray: The view of what? The view of down here? I can see that from down here. Ken: Ray, you are about the worst tourist in the whole world. Ray: Ken, I grew up in Dublin. I love Dublin. If I grew up on a farm, and was retarded, Bruges might impress me but I didn’t, so it doesn’t.
Fake “vintaged” photo that I took–given that Bruges has had a century of being sold as a ‘vintage’ tourist spot, seemed appropriate to Photoshop it, the whole city is sort of Photoshopped.
Some 20,000 people manage to live in the old center, although the rest of the city extends to the North Sea and houses the remaining 80,000 inhabitants.
Windmills ring the old city wall.
A few days later, we were off to Antwerp, which was my favorite destination on the trip, a working city and a historic one on top of each other. The vault of the train station.
You have to love a city where the most spectacular building is a transit center, not a church. The Antwerp one is really a children’s book dream of train-station-ness. (And Belgian Rail was pretty eye-opening for this monthly Amtrak user.)
Another view of the Antwerp Train Station.
The child angel with lighting bolts–not sure if this is commerce or religion, but loved it.
The highlight of the trip for me was a tour of the Museum Plantin-Moretus, the 300+ year history of printing by one of the publishing houses that brought you the Renaissance.
The press room, as it was for a century and a half at least.
Last day in Amsterdam, took a great walking tour about the economic history of the city.
Not sure how the economics work, but not one city in Belgium or Holland lacked for bookstores. We saw them all over.
And to end, a reminder of the North Sea, which stands at the edge of all this busy industry and beauty, awaiting its moment. Here it is encountered at Katwijk on a suitably cold, wet day.