Monday, April 23, 2007


XKCD is by far the nerdiest web comic that I've run across. So really, I shouldn't be surprised when I identify with it so strongly, like I did today. Fortunately, the comic is still usually nerdier than me. (Although I might have to try that sometime...)


Matt said...

I hate to admit it, but I do that sometimes when I'm bored. I am such a huge dork.

Alan Rosenwinkel said...

maybe dave will share his econometric theory of escalators with us ....

dave hiller said...

Yeah based on the title I really thought it was going to be the explanation for why people stand still on escalators. I guess the cartoon's good too.

dave hiller said...

Here's the link for the article on why people stand still on escalators (but not on stairs).

The interesting thing about it, to me, is that this analysis (and you can even do a little math) makes predictions beyond the initial statement - for instance if someone does walk up an escalator, it's a good bet that they jog up stairs.

Alan Rosenwinkel said...

The article Dave linked to is really interesting. I love it! That being said, I think it's wrong, partly.

"getting one foot closer to where you're going" is the wrong way to measure benefit. Who cares how close you are to where you're going? What matters is how long it takes to get there. Benefits should be measured in time, not distance. And a step on the stairs saves you more time than a step on the escalator because—well, because if you stand still on the stairs, you'll never get anywhere. So walking on the stairs makes sense even when walking on the escalator doesn't.

I disagree. You don't measure benefit in distance or time. All of us know that meters and seconds aren't measures of benefit. You ultimately measure benefit in happiness or joy or whatever you live your life for. Then you measure the benefit of saving time, or of moving a distance.

The problem with the above analysis is that the benefit here is not gained until you actually reach the destination, unless someone is giving you a hot dog for every step to take. The problem should not be thought of as benefit-per-step problem but as total-benefit vs total-cost. If the benefit of getting where you're going is greater than the total cost of walking up the steps, then you'll walk. If there is something else you can do that will get you a greater net benefit (like running up the steps or blowing of the top-of-the-steps dentist and going to get a cheesesteak) then you'll do that instead. Same goes with the escalator. If the benefit of getting to your destination sooner warrants running up the steps, then you'll run. If the benefit of getting to your destination faster is greater than the cost of walking up the escalator, then you'll walk up it. Like Dave says, this means that if you're walking up the escalator, chances are good that you'll jog up the steps, but not necessarily. Note that it takes less steps to walk up the escalator than to walk up the steps, and thus a lower total cost to walking the escalator than walking the steps. This means that's it's possible, say in the case of getting to a shop before closing time, that one would walk up the escalator to make it JUST in time, but not walk up the steps at all because the benefit of getting there isn't worth the added cost of walking the steps vs walking the escalator.

All this is true even though a single step on the stairs and escalator get you the same distance closer to your destination and take the same amount of time.

dave hiller said...

I think you're a bit missing the point, Alan. It's true that there are concerns other than "how quickly can I get to my destination" that go into a person's calculation. However, I think it's a pretty good approximation in many cases, this model makes useful predictions, and it is sufficient to account for the observed result.

Perhaps you would better like it if the decision were phrased "at what speed am I going to propel myself along this route?" For every mph you increase your speed, you save more time on stairs than you do on an escalator (the math for this is fairly straightforward). The increased energy expenditure is also greater on the stairs, but not by the same amount. Therefore, if your benefit is time saved, and your cost is energy expended, you will have some point on the stairs where the marginal benefit of an increase in speed is equal to the marginal cost - that is the speed you walk up the stairs. The prediction made by this analysis (which I think largely holds true) is that since for the same person the value of a unit of time saved and the value of a unit of energy expended are the same, the point at which the marginal benefit equals the marginal cost will be a slower speed on the escalator (and in fact the faster the escalator moves, the slower the same person will walk).

Of course, in a given situation you may include things other than time or energy. Maybe someone is chasing you.

Alan Rosenwinkel said...

Perhaps you would better like it if the decision were phrased "at what speed am I going to propel myself along this route?"

Yes, I would have been happier had that been the initial question. The author also probably wouldn't have gotten himself all confused had he framed it to himself that way to begin with. The initial question was "why do people walk up stairs and not up the escalator". The subtle difference between the two questions implies intuitive understanding of the problem which the author clearly did not intially have. In effect, knowing to frame the question in that manner was his problem.

My issue then is more about how he got to his solution than the solution itself. He should have started with the total benefit vs total cost analysis. It is simple and completely general, with no implicit assumptions and thus required little intuition. It can then be reduced to the author's model given appropriate assumptions (much like integral vs differential formulations in mathematics) Let's face it, had this guy had true mathematical intuition, he'd probably have been a real scientist rather than an economist :-) Here he made an implicit assumption that the benefit of moving a given distance is independent of other variables in the problem, which it isn't. In retrospect, the model he has described is simple, but the intuition which leads to it is not. I think he would have been better of starting with a broader (and more intuitive) analysis, even though he would have reached the same result.

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