Occasional reflections on Life, the World, and Mathematics

Posts tagged ‘paradox’

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. (more…)

Paradoxical times

I remember in my childhood, maybe when I was ten or so, talking with my brother about the weird counterfactual possibility that someone could be elected president without winning a majority of votes. Of course, we imagined the most extreme possibility, a candidate winning by one vote in a minimum collection of states, and getting not a single vote in the rest, so that he could attain the presidency with (we worked out) only about one quarter of the votes.

This was discussed in the same kinds of spooky tones that we used to discuss uncanny notions like that someone could be his own grandfather or God could make a stone so heavy that he couldn’t lift it. When grownups on television tried to defend the Electoral College it was generally in terms of turning small vote majorities into decisive Electoral College majorities, thus enhancing the popular credibility of the vote. Now we’ve gotten used to the Electoral College being used to entrench Republican government against Democratic majorities. Given that it was originally designed to enhance the power of slave states, we can say it’s working as planned.

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