Monthly Archive for April, 2020

Are Old Lives Worth Less?

Published
by
Steve Landsburg
on April 20, 2020
in Current Events, Economics and Policy
. 57 Comments

For cost-benefit analysis, the usual ballpark figure for the value of a life is about $10,000,000. But I keep hearing it suggested that when it comes to fighting a disease like Covid-19, which mostly kills the elderly, this value is too high. In other words, an old life is worth less than a young life.

I don’t see it.

People seem to have the intuition that ten years of remaining life are more precious than one year of remaining life. That’s fine, but here’s a counter-intuition: An additional dollar is more precious when you can spend it at the rate of a dime a year for ten years than when you’ve got to spend it all at once — for example, if your time is running out. (This is because of diminishing marginal utility of consumption within any given year). So being old means that both your life and your dollars have become less precious. Because we measure the value of life in terms of dollars, what matters is the ratio between preciousness-of-life and preciousness-of-dollars (or more precisely preciousness-of-dollars at the margin). If getting old means that the numerator and the denominator both shrink, it’s not so clear which way the ratio moves.

Instead of fighting over intuitions, let us calculate:

I. Value of Life for the Young

Suppose you’re a young person with 2 years to live and 2N dollars in the bank, which you plan to consume evenly over your lifetime, that is at the rate of $N per year. I’ll write your utility as

U(N,N)

Suppose also that you’re willing to forgo approximately pX dollars to avoid a small probability p of immediate death. Then (by definition!) X is the value of your life. (The reasons why this is the right definition are well known and have been discussed on this blog before. I won’t review them here.) This means that

(1-p)U(N,N) = U(N – (pX/2), N – (pX/2))

= U(N,N) – (pX/2)U1(N,N) – (pX/2)U2(N,N)

(where the last equal sign should be read as “approximately equal” and the Ui are partial derivatives).

Because you’ve optimized, U2(N,N) = U1(N,N), so we can write

X = U(N,N)/U1(N,N)

Continue reading ‘Are Old Lives Worth Less?’

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Aftermath

Published
by
Steve Landsburg
on April 18, 2020
in Puzzles
. 2 Comments

The victors in last week’s crossword challenge were:

First place, with a score of 276/276: A tie between Dan Williams and Richard Kennaway.

Second place, but heartbreakingly close, with a score of 274/276: Another tie, between Tim Goodwyn and the team of Dan Grayson & Carol Livingstone

Third place: Paul Epps

Fourth Place: Eric Dinsdale

Fifth Place: A tie between Paul Grayson and Biopolitical

Thanks to all of the above and all the rest who participated.

Some notes:

1) There are 276 white boxes in the puzzle. I scored one point per box. Other scoring systems are possible, such as one point per word.

2) I am open to the possibility that some of the answers marked wrong are just as good as the answers counted as right. I’ll try to give this some thought.

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Goofus, Gallant and the Law

Published
by
Steve Landsburg
on April 15, 2020
in Law and Rationality
. 17 Comments

I.

Why do some people sign up to have their brains frozen for possible future resurrection, while others don’t? You might think it’s because the first group has more faith in future technology, but Scott Alexander has survey data to suggest otherwise. Active members of the forum lesswrong.com, many of whom had pre-paid for brain freezing, thought there was about a 12% chance it would work. Among members of a control group with no interest in the subject, the estimate was about 15%.

In a long and characteristically thoughtful blog post, Alexander concludes that:

Making decisions is about more than just having certain beliefs. It’s also about how you act on them.

and

The control group said “15%? That’s less than 50%, which means cryonics probably won’t work, which means I shouldn’t sign up for it.” The frequent user group said “A 12% chance of eternal life for the cost of a freezer? Sounds like a good deal!”

Goofus (says Alexander) treats new ideas as false until somebody provides incontrovertible evidence that they’re true. Gallant does cost-benefit analysis and reasons under uncertainty.

So a few weeks ago when we all thought that the chance of a global pandemic was, oh, about 10%, Goofus said “10%? That’s small. We don’t have to worry about it.”, while Gallant would have done a cost-benefit analysis and found that putting some tough measures into place, like quarantine and social distancing, would be worthwhile if they had a 10 or 20 percent chance of averting catastrophe.

Continue reading ‘Goofus, Gallant and the Law’

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Current Events

Published
by
Steve Landsburg
on April 12, 2020
in Current Events, Heroes and Math
. 11 Comments

conway.small The poster to the left hangs on the wall of my office. Can you figure out the pattern to the sequence? Now can you estimate the size of the nth entry?

John Horton Conway died yesterday, a victim of Covid-19. His unique mathematical style combined brilliance and playfulness in equal measure. I came across his “soldier problem” at an impressionable age, and was astonished by the beauty of the solution. You’ve got an infinite sheet of graph paper, with one horizontal grid line marked as the boundary between friendly and enemy territory. You can place as many soldiers as you like in friendly territory, at most one to a square. Now you can start jumping your soldiers over each other — a soldier jumps horizontally or vertically, over an adjacent soldier (who is then removed from the board) into an empty square. The goal is to advance at least one soldier to the fifth row of enemy territory. Conway’s proof that it can’t be done struck me then as utterly beautiful, utterly unexpected, and a compelling reason to learn more about this mathematics business.

He invented the Game of Life. He invented the system of surreal numbers, a vast generalization of the usual real numbers, designed for the purpose of assigning values to positions in games but adopted by mathematicians for purposes well beyond its original design. (Don Knuth’s book on the subject is a classic, and easy reading). His Monstrous Moonshine conjecture is the reason I own a t-shirt that says:

which I am prepared to argue is the most remarkable equation in all of mathematics. He was the first person to prove that every natural number is the sum of 37 fifth-powers. More than a century after mathematicians first gave a complete classification of two-dimensional surfaces, Conway (together with George K. Francis) found a much better proof. He worked in geometry, analysis, algebra, number theory and physics. And reportedly, he could solve a Rubik’s Cube behind his back, after inspecting it for a few seconds.

Gone now, along with John Prine — another icon of my youth — and too many others. I got the word about Conway just as I was about to go to bed, and am typing this in a state of exhaustion. If I were more awake, it would be more coherent, but it will have to do.

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Animation

Published
by
Steve Landsburg
on April 8, 2020
in Uncategorized
. 9 Comments

You should watch this:

Click here for full-size version.

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Wednesday Puzzle

Published
by
Steve Landsburg
on April 8, 2020
in Puzzles
. 15 Comments

Feeling isolated? Perhaps a crossword puzzle will help.

Click on the image to do the crossword puzzle on line, or click here for a printable pdf.

If you do the puzzle on line, you can click the “submit” button to bring up a form where you can enter your name and submit your solution. I will find a suitable way to honor the best submissions.

Meanwhile, please do not post spoilers!!!.

Update: Thanks to biopolitical, who pointed out that there was a problem with the clue for 24A. That clue is fixed now.

Thanks also to my Mom, who informed me that the pdf wasn’t printing properly. That’s fixed now too.

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