Monthly Archive for December, 2018

Walls Versus Walls

The President of the United States tweets that his proposed border wall is essentially “the same thing” as a wall built around the Obamas’ house (or presumably anyone else’s house) to keep away intruders.

No, you idiot. There is absolutely no relevant similarity between a wall somebody builds around his own house and a wall that you build between other people’s houses. The effect of a wall around my house, if I had one (and if I controlled the gates), would be to increase my control over who enters my living room. The effect of a border wall would be to decrease my control over who enters my living room.

That doesn’t prove that the border wall is a bad idea. But if the President believes there are good arguments for his pet project, why does he resort to ridiculous analogies that have absolutely zero chance of being taken seriously by anybody on either side of the issue? I’m pretty sure Rex Tillerson had this right.

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Escalators (The Geeky Version)

I hadn’t expected this escalator business (and see also here) to go on so long, but there have been a lot of smart comments, and a lot of smart disagreements, and a lot of smart changing and re-changing of minds, some of it the unavoidable consequence of the fact that we might all be using language a little differently.

So here is the geeky (i.e. precise!) version of what I want to say.

I. Your journey consists of some time on the stairs and some time on the escalator. You rest for a total of one minute, which you can take on the stairs or on the escalator (or split it if you like).

II. Define some constants:

W = your walking speed

V = the escalator speed

L = the distance from your starting point to your destination

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Escalating Matters

There were a lot of great comments on my recent post about escalators, but none better than Bennett Haselton’s, which is so good I want to highlight here in a separate post.

I’m going to strip his argument down to make it even simpler, but this is all Bennett’s idea:

A New Puzzle: You’re boarding an escalator precisely at noon. You know that on a normal day, if you walk the entire way, the ride takes exactly ten minutes. But you also know that this is not a normal day, because the escalator is scheduled to be stopped for maintenance beginning at 12:05, and will at that point turn into the equivalent of a stairway. You’re planning to take a one-minute rest from walking at some point along your journey. Should you rest before 12:05, when the escalator is moving, or after 12:05, when the escalator is stopped?

Answer One:Of course you should rest while the escalator is moving, because that way, at least you make some progress while you rest.

Answer One, Reworded: Of course you shouldn’t rest while the escalator is stopped, because then you’ll spend an entire minute not getting anywhere.

Here’s the thing about Answer One: It’s completely wrong. It doesn’t make a bit of difference whether you rest from 12:00 to 12:01 or from 12:05 to 12:06 or for any other minute in between. If you don’t believe me, try an example: Suppose the escalator travels, oh, say, 20 yards per minute and your walking speed is 10 yards per minute. Then if you rest from 12:00 to 12:01, with the elevator moving, you’ll have traveled 160 yards by 12:07, and will continue to gain ten yards per minute after that. If instead you rest from 12:05 to 12:06 with the escalator stopped, you’ll have traveled exactly the same 160 yards by 12:07, and will continue to gain exactly the same ten yards per minute after that.

The Old Puzzle: You’re going to travel on a 100 yard staircase followed by a 100 yard escalator. You’re planning to take a one minute rest somewhere along the way. Should you take it on the stairs or on the escalator?

Answer One: You should rest on the escalator, because at least that way you make some progress while you rest. Or to put this another way, you shouldn’t rest on the stairs because then you’ll spend an entire minute not getting anywhere.

This time Answer One gives the right conclusion. But the reasoning can’t be right, because it’s the exact same reasoning that we applied to the New Puzzle, whereupon that reasoning led us totally astray.

Bennett’s lovely example illustrates as starkly as possible why we must reject Answer One even though it sometimes yields the right conclusion. The reason is that it also sometimes leads to the wrong conclusion. I’ve been trying to argue in the abstract that the logic of Answer One makes no sense; Bennett has done us the awesome service of pointing to a concrete example where that logic leads you inarguably astray.

It also illustrates my other main point: The real reason to rest on the escalator in the Old Puzzle is that resting on the escalator buys you more time on the escalator. Bennett has removed that advantage by giving you exactly five minutes on the escalator regardless of where you rest. In other words, when you cook up an example (like Bennett’s) in which resting on the escalator doesn’t buy you more time on the escalator, the argument for resting on the escalator vanishes in a puff of smoke.

This, incidentally, is related to a cryptic comment of my own on that earlier post, where I replied to an inquiry from Bob Murphy about my observation in an old Slate column that the fundamental confusion arises from measuring benefits in distance instead of time. (I claim that this is, in a sense that might not be entirely obvious, an equivalent description of the problem with Answer One.) In the Old Puzzle, you’re on the escalator for a fixed distance; in Bennett’s New Puzzle, you’re on the escalator for a fixed time. That illustrates exactly the distinction I had in mind, and if I find the time, I’ll write out the details sometime soon.

Ups and Downs

escalator_photo_2

There are two kinds of people in this world: The first kind wonders why people stand still on escalators but not on stairs. The second kind wonders what’s wrong with the first kind. After all, if you stand still on the stairs you never get anywhere.

But people of the first kind are not usually dumb. I could give you a long list of top-rate economists and mathematicians who have been stumped by this puzzle. But I could also give you a long list of equally smart people who have been stumped by why anybody thinks it’s a puzzle in the first place. It’s come up again several times recently, because I included it in Can You Outsmart an Economist? and because I talked about it on my podcast with Bob Murphy, which generated a small flurry of email from listeners. So let me try once again to explain what’s going on here.

Let’s divide this into two parts: First, what’s the right way to think about this problem? Second, why is it a problem in the first place?

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Hypothetical Questions

Suppose, for the sake of argument, that the following three things are true:

  1. You believe, to the depths of your soul, that the future freedom, safety and prosperity of your 300 million countrymen depends critically on a construction project that would cost roughly 5 billion dollars, but that nobody else seems willing to fund.
  2. The welfare of your countrymen is one of your highest priorities. Sometimes you express this priority by calling yourself a “nationalist”.
  3. Your personal net worth is in the vicinity of 10 billion dollars.

Now my questions:

  1. Continuing to assume that all of these three things are true, what action do you take?
  2. If I observe you failing to take that action, can I reasonably infer that not all of these three things are true after all?

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This is not a blog post

From the Twitter feed of my brilliant friend (and Usenet legend) Tim Pierce:

timp

CAPTCHA: Click on all the squares that are not a pipe.

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Wednesday Mystery

This is a true story. The names have been changed and some personal details have been blurred by request.

In the American heartland, there lives a university professor named Fletcher. Like most university professors, Fletcher has collaborated with colleagues from around the world, including my friend Zenobia, who teaches at a college in New England. Their collaboration is relatively recent and has not yet resulted in any publications, though some of their joint work has been posted on the web.

Recently, Zenobia has started to receive (by snail mail) a number of magazines — the sort you might find in dentists’ office, like People and Working Mother — addressed to Fletcher, but at Zenobia’s home address. Fletcher purports to know nothing of how this came about, and Zenobia believes him. Moreover, a number of Fletcher’s other friends, collaborators, acquaintances and relatives have also begun to receive the same sorts of magazines with Fletcher’s name, but their own addresses, on the mailing labels.

The magazine publishers, when queried, have refused to divulge any information about who is paying for these subscriptions.

Zenobia notes that the only possible direct connection between Fletcher’s name and her own home address is that once, on the occasion of the birth of Fletcher’s first child, she used her Amazon account to send him a baby gift. However, there appears to be no similar connection between Fletcher and any of the others who are receiving magazines addressed to him.

This leaves us with two mysteries:

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