Occasional reflections on Life, the World, and Mathematics

The unexpected autocracy


One of my favourite logic paradoxes (does everyone have favourite logic paradoxes?) goes by the name of The Unexpected Hanging. There are numerous versions, but a standard story is: A man has been condemned to death for some crime. The judge tells him, “Today is Monday. You are to be hanged at noon some day in the next week, but you will not know until the morning of the day of the hanging which day it will be.” The man then reasons, it can’t be Sunday, because if I haven’t been hanged by Saturday noon, I’ll know it must be Sunday, which would contradict the judge’s order. Since it can’t be Sunday, if we get to Friday afternoon, I’ll know it must be Saturday. Again a contradiction. So it can’t be Saturday. Working backward in this way, he is confident that he cannot be hanged at all. But then Thursday dawns, and he is hanged, and he never anticipated it.

I was thinking about this, particularly in the light of this comment by Josh Marshall:

One thing we can say in Donald Trump’s favor, there was no bait and switch. They told us they would do all of this and more.

It’s true, and I’m not surprised. And yet… Trump did say he would ban Muslims. He would build a wall. He would ban abortion. He would revoke the Affordable Care Act. And yet, at the same time, he was saying over and over again, I’m going to be unpredictable. I won’t say what I’m really going to do. More than that, his whole demeanor suggested that you couldn’t believe the specifics of what he was saying. So, in the end, he does exactly what he said he would do, and it actually is somewhat surprising.

As much as continuing the Nazi analogy is embarrassing, this is very much like how many people, inside and outside of Germany, responded to Hitler. After the fact people could say, “He wrote exactly what he planned to do in Mein Kampf.” It’s true. But Mein Kampf is a crazy book, and Hitler played the screaming madman in public so well that people who were familiar with him thought all that stuff was just for the rubes, while sophisticated people could set themselves to figuring out what Hitler really wanted.

It’s the classic con game: He let people think they were in on the con, that other people were being fooled.

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