Economist Steven Landsburg writes about economics, math, paradoxes, probability and law, with occasional posts testing AI.
HN commenters cite his eulogy for Grothendieck, his GPT-4 economics exam post and its comments, and a thought experiment; one questions his views on jurors.
From: http://www.thebigquestions.com/2020/04/15/goofus-gallant-and-the-law/
>You have three pieces of meat, two kosher, one not. You lose track of which is which. Can you eat them? Answer, according to (my memory of Sternberg’s account of) the Talmud: Each individual piece of meat has a 2/3 chance of being kosher. So if you choose one of them and ask “Is this kosher?”, a “yes” answer gives you a 2/3 chance to be right and a “no” answer gives you only a 1/3 chance to be right. A 2/3 chance is better than a 1/3 chance, so you should say yes. Repeat three times and you’re allowed to eat all of the meat.
>There is much that is troubling here, because that strategy actually gives you a 100% chance of eating a non-kosher piece of meat, so it matters whether you inquire about each piece separately or whether you inquire about all three as a group. I’m not sure what principle the Talmud invokes to settle that issue. But that’s not the point that concerns us here. The point here is that we’re instructed to focus strictly on probabilities, without regard to any measure of how bad it would be to be wrong in either direction.
>You’re traveling to town with a left pocket full of coins designated for charity and a right pocket full of coins designated for your personal expenses. (In certain circumstances, you’re required to designate these coins in advance, and cannot substitute a coin from one pocket for a coin from the other, even if they’re otherwise identical.) You fall off your…
If anyone's curious about the actual math Grothendieck was doing but is (like me) a layman when it comes to mathematics, there's a useful summary of one of his major areas of work in parts II and III of this blog post [0].
The essence, I believe, is
>Bottom line: To study the Weil conjectures, you have to think very hard about the subtle properties of curves, surfaces and higher-dimensional objects. When you do this, you find yourself mentally “moving around” the curve, trying to hop from point to point. And — in a sense that I cannot hope to make precise here — you sometimes find that your mental exploration is hampered by the fact that there somehow aren’t enough points to hop to.
>So life would be easier if these curves (and other objects) had more points. A normal person might say “Well, life’s not always easy. We’ll just have to get by somehow with the points we’ve got”. But Grothendieck lived by the conviction that everything is easy if you look at it right — which means there have got to be enough points. And if we think there aren’t, it must be because we haven’t yet figured out what a point is.
I don't think I'm closer to understanding what it is he was working on after reading it, at least not in a meaningful sense, but it is fascinating to me to read about.
[0] http://www.thebigquestions.com/2014/11/17/the-generalist/
I actually did find the "nightmare dilemmas" on the site more interesting.
http://www.thebigquestions.com/2012/03/22/another-nightmare/
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Today’s Dilemma
In front of you are two childless married couples. For some reason, it’s imperative that you kill two of the four people. Your choices are:
A. Kill one randomly chosen member from each couple.
B. Kill both members of a randomly chosen couple.
All four people agree that if they die, they want to be well remembered. Therefore all four ask you, please, to choose A so that anyone who dies will be remembered by a loving spouse.
If you care about the four people in front of you, what should you do?
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Argument 1. For goodness’s sake, they’ve told you what to do. If you care about them, of course you should respect their wishes. Choose A.
Argument 2.Once the killings are over, Option A leaves two grieving spouses, whereas Option B leaves one relieved couple. Surely two dead plus two happy is better than two dead plus two sad. Choose B.
Which argument do you buy? And what’s wrong with the other one?
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On the other hand, a consumption tax taxes people proportionally to the benefits they receive from society. It might be less progressive w.r.t. income than our current system, but it is arguably more fair.
It's also hardly clear that the tax burden is even felt by the rich. Consider an investor with millions in investments who only consumes $50k/year. He would like to invest in his new venture, a medical search engine. But because of the taxation, he has less money for this investment. Think: who is forced to consume less as a result of taxation? The rich man continues to consume $50k/year. Instead, goods and services have been redistributed from the medical search engine to government uses.
The real question about taxing investors: do we believe the government will spend the money better than Fred Wilson would?
See also: http://www.thebigquestions.com/2011/04/18/the-man-who-cant-be-taxed/
... interesting author ( http://en.wikipedia.org/wiki/Steven_Landsburg#Popular_writings )
> Landsburg also addressed legal issues: in a Slate column from 2003, he proposed punishing jurors when a jury's decision is later "proven" to be wrong, such as when an acquitted defendant later admits to committing the crime. If a jury's judgement is later "proven" to be right, Landsburg suggested the jurors should be financially rewarded.[4]
> http://www.thebigquestions.com/2012/03/02/rush-to-judgment/
> To his far greater credit, he did so with a spot-on analogy: If I can reasonably be required to pay for someone else’s sex life (absent any argument about externalities or other market failures), then I can reasonably demand to share in the benefits.
http://www.thebigquestions.com/2014/04/21/high-frequency-rentseeking/
This seems pretty convincing to me. The argument is that, based on the amount that firms are willing to spend on fiberoptic cables to perform hft, they put an extremely high value on hft. On the other hand, reasonable back-of-the-envelope calculations show that the social benefit of making the trade slightly faster are much less than the private cost. This indicates that almost all of the private benefit from hft comes from value accruing to the hft firm at the expense of other hft firms. We therefore expect to see overinvestment in hft.
What about this do you find objectionable?