We don’t see what we don’t consider
As was fitting on 25th December in the West, our breakfast discussion was largely focused on the various traditions that have grown up around the late-Victorian approach to celebrating this date. My brother innocently asked, “How many gifts did the lady receive in total?”
For those of you unfamiliar with English nonsense, this question refers to a song composed in 1909 by the composer Frederic Austin about a man attempting to curry favor with a woman by sending her gifts across the Twelve Days of Christmas, the twelve days derived from Christian mythology regarding the elapsed time between the birth of the Jesus god and the eventual arrival of the magi bearing gifts.
On the first day the suitor presents a partridge in a pear tree, on the second day the suitor delivers two turtle doves and a partridge in a pear tree, and so on until twelve days have elapsed and the pile of gifts has grown.
To solve this puzzle we need only construct a simple matrix:
Summing the column #GiftsTotal we arrive at 364 gifts.
Problem solved, or so it would seem, and a quick Google search confirms that this is indeed the consensus number.
The more astute, however, among whom I must count my brother, may notice that we’ve neglected to account for the Pear Tree, one of which accompanies each Partridge. The correct total number of gifts therefore is in fact 364+12 = 376.
My brother is now attempting to create a social media movement centered around the hashtag #PearTreesMatterToo
Moving away from the winter festival we come to a classic brain-teaser: Two cyclists are 120 kilometers apart and they are facing each other. They will travel at a constant 40 kilometers per hour. A fly is trapped in a flightpath that can only move between the front wheel of bicycle A to the front wheel of bicycle B and vice-versa. The fly’s fate therefore is to be crushed between the two wheels when the bicycles have closed the distance between one another. So how long does the fly have to live?
We can solve this problem by using a series approach (e.g. after 10 minutes each bicycle will have moved X kilometers, thus reducing the total distance by 120–2X, in the next ten minutes the distance will be reduced by (120–2X)-2X, and so on.
Or we could simply note that if we divide 120 by 80 (the combined speed of both bicycles) we get 1.5 which equates to 90 minutes, and therefore the fly’s brief thought-experiment life will come to a squishy end in precisely one-and-a-half hours.
Our third and final example of a similar type of problem is the classic question posed as follows: The circumference of the Earth at the equator is 40,075 kilometers (24,901 miles or 216,621 stadia for those attached to old-time Neolithic measurements). If there are two trains pointing in opposite directions on a single track and each train can travel at 100 kilometers per hour, how long will it be before the trains collide?
Before we jump into solving the problem we can simply note (as very few people do, apparently) that it all depends on the starting position of the two trains. In all cases the solution will be a function of distance divided by twice the given velocity. But if they are face-to-face and a mere meter apart, the time required to close the gap will be much less than if they begin their journeys back-to-back.
What these very silly examples serve to point out is that our level of abstraction determines how we view a particular problem. So it can be worth taking a moment to step back, try to consider the entire question, and only then look for suitable methods to address it. It’s too common for us to assume that because we have a hammer, the solution to every problem is to whack it on the head.
Einstein is supposed to have said, “The definition of insanity is doing the same thing over and over again and expecting a different result.”
Most public policy is, by this definition, insane. We need only think of practically every aspect of US policy, for example: the “war on drugs,” the “gun control” debate, the utterly dysfunctional health care system, the education system, and every theocratic piece of nonsense since the Puritans arrived to poison society. All are classic examples of us resolutely ignoring real-world outcomes in favor of continuing to do stupid things in the belief that even if they haven’t worked in the past and aren’t working now we need to continue in the hope that magically they will work at some point in the future because, well, we’re so heavily invested in them.
But as the adage goes, “If you find yourself in a hole then stop digging.”
Perhaps it’s time, when the time comes for us to make our New Year’s resolutions, that we all consider including this one among the bundle of remorse-driven promises we make to ourselves. Because when we look around at the world it’s absolutely clear:
We need to stop digging.