A favourite of our kids is to play opposites day. It usually starts with something simple like where we say “No, they can’t have chocolate for breakfast,” and they then announce that it’s opposites day so that means they can have chocolate for breakfast. Then I say, but if it’s opposites day then that means you just said it’s not opposites day. Then they say, if it’s not opposites day then what they said is true so it is opposites day. After a while we end up being late for school.

This is a version of the liar paradox, also known as the Epimenides paradox after a chap from Crete who is supposed to have announced that all Cretans are liars. There are a bunch of versions of the paradox including the simpler one: this sentence is a lie.

Some other paradoxes: Jevon’s paradox, the coastline paradox, the Abilene paradox.

The liar paradox

The paradox of how groups of people are able to take actions that no one in the group actually thinks is a good idea. Though individually we each may think that an idea is a bad one, we may go along with the group decision thinking that it’s just us that disagree when, in fact, no one thinks it’s a good idea.

Coined by Jerry Harvey, a management professor, who illustrated the phenomenon with a fictional story of a family who end up on a rubbish day out to Abilene that no one wanted to do.

On a hot afternoon visiting in Coleman, Texas, the family is comfortably playing dominoes on a porch, until the father-in-law suggests that they take a trip to Abilene (53 miles north) for dinner. The wife says, “Sounds like a great idea.” The husband, despite having reservations because the drive is long and hot, thinks that his preferences must be out-of-step with the group and says, “Sounds good to me. I just hope your mother wants to go.” The mother-in-law then says, “Of course I want to go. I haven’t been to Abilene in a long time.”

The drive is hot, dusty, and long. When they arrive at the cafeteria, the food is as bad as the drive. They arrive back home four hours later, exhausted.

One of them dishonestly says, “It was a great trip, wasn’t it?” The mother-in-law says that, actually, she would rather have stayed home, but went along since the other three were so enthusiastic. The husband says, “I wasn’t delighted to be doing what we were doing. I only went to satisfy the rest of you.” The wife says, “I just went along to keep you happy. I would have had to be crazy to want to go out in the heat like that.” The father-in-law then says that he only suggested it because he thought the others might be bored.

The group sits back, perplexed that they together decided to take a trip which none of them wanted. They each would have preferred to sit comfortably, but did not admit to it when they still had time to enjoy the afternoon.

More paradoxes: The coastline paradox, Jevon’s paradox

Harvey, J. B. (1974). “The Abilene paradox: the management of agreement”. Organizational Dynamics. 3: 63–80. Excerpt as quoted from Wikipedia :) 

This is not to diss Abilene. I’m sure it’s a neat place.

The Abilene paradox

This is the fascinating observation that it’s not straightforward to say how long a coastline is. If you were to measure the coastline of a country by using a ruler on a globe, you would come out with a vastly different number than if you were to pace around the edge. The closer you look, the more wiggles and squiggliness you come across and instead of converging on a more accurate length, the coastline just keeps getting longer. The smaller your ruler, the longer it gets.

This was originally spotted, incredibly, in the 1950s, by an Englishman, Lewis Richardson, when trying to check a theory he had that the likelihood of war between countries depended on the length of their shared borders. Remarkably, he found that the quoted lengths of borders varied significantly. While measuring on maps at different scales he saw that the smaller scale map he used, or the smaller the width of his calipers he was measuring with, the length systematically increased. When looking at coastlines, instead of borders, some countries had wigglier coasts and so the length increased at a faster rate with the scale — for instance, Norway’s coastline, with it’s crinkly fjords, increases faster than Britain’s, which in turn increases faster than South Africa’s, as he zoomed in. The rate of this increase later became known as its fractal dimension.

Long after Richardson’s research, Benoit Mandelbrot published a paper How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension that discussed how the wiggliness of something like a coastline at one scale can be repeated at smaller and smaller scales. The work led to the later term fractals. Many other things exhibit fractal-like behaviour such as river networks, borders, brains, frequencies, lightning or even the stock market.

More mindbending mapping, and the difference between Great Britain, the UK and the British Isles.

There’s a super section on this in Scale, by Geoffrey West.

The coastline paradox

Word on the street is that back in 1865 a chap called William Stanley Jevons noted that while there had been a number of improvements in coal efficiency in steam engines and the like, instead of reducing consumption the effect was to increase consumption instead.

While it’s not a surefire outcome, there are plenty of parallels like more efficient batteries leading to more overall battery use, washing machines leading to doing more washes rather than less time spent washing, or the ability to recycle some plastics leading to more overall plastic consumption.

Also see, the fifth fuel: energy efficiency, and save some landfill.

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