Month: June 2022

The FDA has ordered Juul to take its vaping devices off the market due to "insufficient and conflicting data" about the safety of its e-liquid pods. This has prompted another round of arguing about whether or not vaping is, on net, a public safety improvement, especially among teens. But I think the data is in on this:

Most teen vaping (roughly 80%) is nicotine vaping, and it's obviously bad to get kids hooked on nicotine. On the other hand, vaping is better than cigarette smoking, so if more vaping leads to lower cigarette use then it might be a net positive.

But as the chart shows, that's not the case. Teen cigarette smoking has been declining steadily for the past couple of decades and doesn't appear to be influenced even a tiny bit by vaping. This means that vaping has gotten more teens hooked on nicotine with no corresponding drop anywhere else to make up for it.

This doesn't mean you have to support a ban on vaping, or even a ban on non-prescription nicotine vaping. But as you think about it, this is the factual background to consider.

I got aimlessly directed to the latest Fox News poll this morning, and as I was browsing through it I came across its results for the generic congressional ballot ("Would you vote for the R or D candidate in your district?"). Here it is:

For some reason I was under the impression that Democrats were way underwater right now, but the difference is actually only three points. FiveThirtyEight has it at two points.

Obviously that's hardly good news for Democrats, who need to be well ahead to retain their majority, but it doesn't quite sound like a disaster either. And who knows? Maybe Dems can get their act together and improve on this. It's not the craziest idea in the world.¹

¹Close, though.

This is sunrise on the Seine, somewhere near Les Andelys. For some reason—probably jet lag, I suppose—I was up every morning during our Seine cruise and spent my time on the sun deck taking pictures and watching the crew. There were never more than one or two other passengers there. Just not an early-rising bunch, I guess.

Today is ATUS day, the day when the BLS releases the latest numbers from the American Time Use Survey. I was looking forward to comparing 2021 with 2020, but I forgot that ATUS had been suspended in 2020 due to COVID.

Still, we have charts. Here's one for the percentage of people who worked at home in 2021:

According to the BLS, this compares to 24% who worked at home in 2019. Unfortunately, this particular statistic doesn't appear to be available in their database tool, so I can't get a time series for it. However, you'll be unsurprised to learn that working at home is primarily an elite activity:

And here are a couple of old favorites. First, the amount of time spent in various activities for men and women:

Second, the number of men and women engaged in household work:

As usual, when you add up hours worked outside the home and hours engaged in housework (childcare, cleaning, food prep, etc.) they come out nearly the same for men and women. I put it at 6.82 hours per day for men and 6.93 hours for women in 2021, but if I chose a slightly different set of activities the numbers would change.

(These are averages for working-age people. It doesn't include retirees, but it does include people who don't work or who work part-time. This is why the numbers seem low: Men worked an average of 5.23 hours per day and women worked an average of 3.83 hours.)

I might have more later if I dig up anything that seems especially interesting.

In the New York Times today, Jessica Grose interviews Linda Villarosa about the maternal mortality rate. It's worth a read, but first I'd like to reacquaint you with the basic statistics. First, here are the latest US maternal mortality rates by race:

And here's the US maternal mortality rate over time:

Everything here is nuts. The Black maternal mortality rate is nearly 3x higher than the white rate. And the maternal mortality rate for everyone has nearly tripled since the late '90s. Meanwhile, in Europe, the maternal mortality rate has been steadily dropping and is now about one-third the US rate.

The big kicker is this: No one knows anything. No one knows why the rate has been skyrocketing. No one knows why the Black rate is so much higher than the white rate—while the Hispanic rate is a bit lower. In fact, we don't even have good data for the period from 2005-2018, so you'll see lots of different estimates for those years. (However, the big spike over the past three years comes direct from the CDC, which finally released new data a couple of years ago. It was the first in over a decade.)

And we're still in the dark about why Black women suffer such an astonishingly high rate of maternal mortality. As I said three years ago:

Poverty, education level, drinking, smoking, and genetic causes don’t seem to explain the black-white difference in maternal mortality. The timing of prenatal care doesn’t explain it. Medically, the cause of the difference appears to be related to the circulatory system, which is sensitive to stress. This makes the toxic stress hypothesis intuitively appealing, but it has little rigorous evidence supporting it. There’s some modest evidence that wider use of doulas could reduce both infant and maternal mortality, but no evidence that it would reduce the black-white gap.

Low income is weakly associated with higher maternal mortality rates, but it explains very little. The allostatic stress theory is appealing but probably wrong. And racism doesn't seem to play much of a role either.

It's the damnedest thing. The US rate of maternal mortality is crazy in multiple ways, and no one can produce a credible explanation. Every avenue of study turns up almost totally empty. I've rarely seen anything like it.

This is a Louisiana egret resting in a bed of daisies that match his beak. Apparently this egret has an excellent color sense.

Over at Vox, Rachel Cohen asks:

Should you keep abortion pills at home, just in case?

With Roe on the brink, more experts are talking about advance provision of mifepristone and misoprostol.

Medication abortion, or taking a combination of the drugs mifepristone and misoprostol, is an increasingly common method for ending pregnancies in the United States....With more in-person clinics shuttering and a Supreme Court that’s threatening to overturn Roe v. Wade, a small but growing number of reproductive experts have been encouraging discussion of an idea called “advance provision” — or, more colloquially, stocking up on abortion pills in case one needs them later.

Cohen spends 1,500 words to fully answer the question in her headline, but I'll use just one: Yes. They're safe, they have a long shelf life, we have years of experience with them, and bad side effects are minimal. And the cost is low: $30-60 or so depending on where you buy them and what your insurance pays for.

As with any drug, there are precautions. WebMD has a good writeup here. Or talk to your doctor.

Generally speaking, though, I can't see any reason not to have abortion pills handy if you have any risk of having an unwanted pregnancy. If you live in California and there's a good clinic around when it happens, fine. You wasted a few bucks on some pills. If you live in Texas, it might be your only choice. So just do it. What's the argument against it?

In a review of Talent, Edward Nevraumont says:

Everywhere I have worked, the organization’s hiring processes were tilted in favor of experience over intelligence. Interviews include behavioral questions or assessments of specific skills. Rarely is anyone on the hiring loop running problem-solving sessions that require the candidate to demonstrate how they might deal with the real-world challenges they will encounter in the workplace.

That's been my experience too. And for a great many jobs it's fine. The problem is that it often goes way too far.

In sales, specifically, hiring managers not only want someone with a good track record, but a good track record within their highly specific niche of the market. This is a mistake. Just pick the best sales person! A lot of people are surprised by how quickly a new hire with smarts can get up to speed with an unfamiliar product and an unfamiliar set of clients (resellers, distributors, large customers, etc.).

I recall one especially frustrating experience trying to hire a VP of marketing to replace me. One candidate struck me as exceptionally smart, qualified, and with excellent savvy. But she didn't work in our industry. She worked in the software industry, but not our little piece of it.

I didn't think that mattered. She obviously knew the basics of selling business software, and our particular type was hardly so esoteric that it would take years to learn. Anyone talented could pick up the basics in a few months and be 90% up to speed within half a year. In the meantime, the entire rest of the company would be around to keep things on track.

But I lost that battle. My peers just couldn't stomach the thought of hiring someone whose experience was so far afield. I'm still pretty sure it was a mistake. Relevant experience is obviously important, but don't insist on it being hyper-relevant.

POSTSCRIPT: Then again, maybe they didn't like her for some reason they didn't want to admit. Maybe they didn't like the idea of a woman VP. Maybe they didn't like the color of dress she wore. Who knows?

Or maybe she wasn't as smart and qualified as I thought. Perhaps they saved me from making a bad mistake.

Bob Somerby wants to know if the logician/mathematician Kurt Gödel is a genius or a charlatan. The answer is "genius," but it's hard for non-mathematicians to understand his seminal theorem or why it matters. Bob is relying on Rebecca Goldstein's biography of Gödel, and this is a mistake since it's a biography, not a mathematical treatise.

But it's dex night, so I'll take a crack at it. Fair warning: you really need to have at least a little bit of background in math to understand this. There's just no way around it. However, you don't need much as long as you're willing to tolerate a bit of mathematical symbology. Here goes.

1. Mathematical symbols

Although most of us don't think of it this way, mathematics is actually a formal logical system of symbol manipulation.¹ For this to work, it must be possible to express all mathematical statements in a formal symbolic language. And it is! Take this statement, for example:

For every number there is a number that's one higher

In mathematical symbology it looks like this:

∀ x ∃ x + 1

(For all numbers x there exists x + 1)

There is a symbol for anything you can say in the language of mathematics. If you're interested, a complete list is here—though there are some complicated nuances for certain kinds of expressions. Basically, though, there's a symbol for everything, although non-mathematicians are unfamiliar with most of them.

2. Gödel numbering

Gödel's initial insight was that you could assign a unique number to every symbol. Here's a sample:

After a bit of rewriting to mathematical standards, our statement from above looks like this:

In essence, Gödel numbering is simple. In line 3 we replace every symbol with its Gödel number. In line 4, we take a series of prime numbers starting with two, and raise each one to its Gödel number. The first prime is 2, so we calculate 2⁹. The next prime is 3, so we calculate 3¹¹. Etc.

In the final line we multiply all these numbers together to get the Gödel number for the entire statement. It's a big number, and for more complicated statements the number becomes astronomical. But who cares? We don't actually have to calculate this number, we just have to know that it exists and that it's unique. Which it is. That final number represents our statement, only our statement, and there's no other number that also represents our statement. This number is our statement.

3. Gödel's proof

So far, what Gödel has done is inventive and easy to understand. What comes next is world historically insightful and more or less impossible to understand for non-mathematical laymen. But let's go ahead with a simplified version.

Every mathematical system—arithmetic, geometry, set theory, etc.—consists of (1) a set of symbols, (2) a set of rules for constructing statements that are valid expressions (i.e., strings of symbols) but which may be either true or false, (3) a set of rules for manipulating symbols, and finally, (4) a set of axioms to start with. This is called an "axiomatic system," and it's the foundation of nearly all modern mathematics.

A formal proof of a theorem starts with axioms (in symbolic form) and then moves in small steps using valid statements that are created using the rules of manipulation. When this series of statements finally reaches the theorem itself, the theorem is said to be proven.

Any respectable system of mathematics must fulfill two requirements: it must be complete and it must be internally consistent. "Complete" means that every true theorem can be proven. "Consistent" means that it's not possible to prove both a theorem and its opposite. But how do you prove that a mathematical system is both complete and consistent?

It's not easy! David Hilbert, the namesake of one of my cats, famously created an axiomatic system of geometry in 1899, and in 1910 the philosopher/logician Bertrand Russell and his coauthor Alfred North Whitehead produced a massive three-volume work called Principia Mathematica, which attempted to completely systematize arithmetic and set theory and make them both complete and free of contradictions. Along the way, Russell and Whitehead created a remarkably comprehensive system of notation that allowed all statements of arithmetic to be written in a standard manner. It is one of the most famous treatises on logic and mathematics ever written.

But was it correct? In the same way that individual symbols and statements can be reduced to Gödel numbers, an entire proof can also be given a unique Gödel number. Gödel's genius was in realizing that certain properties of these numbers could tell us things. In particular, they could be used to decide whether a system of mathematics was complete and consistent.

And it turns out that no interesting system of mathematics is both. In 1931 Gödel published a famous paper which showed, using Gödel numbers, that assertions about mathematics (for example, "the series of statements with Gödel number x is a proof of the formula with Gödel number y") could be reduced to ordinary statements within mathematics ("x is related to y"—though in a complicated way that we will skip over lightly). This in turn allowed Gödel to demonstrate that in any system of mathematics complex enough to be useful—such as ordinary arithmetic—you can construct at least one statement about arithmetic that (1) can be transformed into a normal statement within arithmetic, (2) can be proven, but (3) only if its opposite can also be proven. That's impossible in any consistent system, which means the statement is unprovable in an allegedly consistent system like arithmetic. But Gödel did more: he showed that even though this statement couldn't be proven, it was clearly true. This means that arithmetic is incomplete: it contains true statements that can't be proven.

Finally, in his coup de grâce, Gödel showed that the statement "arithmetic is consistent" is unprovable within the system of arithmetic itself. In all this he used the notation created in Principia Mathematica, which had been explicitly designed to create a system of arithmetic and formal logic that was complete and internally consistent. The result was a proof that Russell and Whitehead were wrong. No system of mathematics is both complete and consistent.

That was a kick in the gut.

4. But what does it all mean?

In day-to-day use, Gödel's theorem plays no role. In fact, a few years after it was published a fellow German mathematician proved that for all practical purposes the system of arithmetic we use (based on the Peano postulates, a set of five axioms for the natural numbers created by Giuseppe Peano in 1889) is indeed consistent. Workaday math is in fine shape, and most working mathematicians go through life never knowing anything about Gödel, who is of interest mostly to abstract logicians.

But on an abstract level Gödel's theorem was both a bombshell and a source of dismay. What's more, it does come into play sometimes in fairly ordinary mathematics.² For example, transfinite math defines various types of infinity, and the two smallest types of infinity correspond to the set of integers (represented as ℵ₀, or "aleph nought," because mathematicians like to fuck with us) and to the set of real numbers (represented as C, because mathematicians like to fuck with us). But is there any infinity between those two? In 1966 Paul Cohen won a Field Medal for using Gödel's theorem to show that this was impossible to prove one way or another.

(This is called the Continuum Hypothesis, first proposed by Georg Cantor, the inventor of transfinite mathematics. He believed there was no infinity between ℵ₀ and C, and this was #1 on David Hilbert's famous list of 23 unsolved problems that he presented to the mathematical community in 1900. As of today, eight of these problems have been fully proven; three are still unproven; ten are partially proven; and two have been tossed out for being too vague.)

Long story short, Gödel's theorem is both enormously important but also of little use in real life. This is the way of things.

5. Further Reading

If you really want to understand what Gödel did, the indispensable book is Gödel's Proof, by Ernest Nagel and James Newman. It was published the year I was born and is still in print. It does require a modest love of math, but it's only a hundred pages long and is written unusually clearly. Another possible text is Douglas Hofstadter's Gödel, Escher, Bach, which is massively long but also very entertaining. It's not everyone's cup of tea, but it does demonstrate how Gödel's theorem works, and it gets there in very tiny, non-mathematical steps.

¹Actually there isn't one formal system of mathematics, there are many. There's one for geometry, one for set theory, one for arithmetic, etc.

²I am, obviously, using "fairly ordinary" in a very specific sense.

Tyler Cowen directs us to Roland Fryer, writing today about the pay gap for Black workers:

For decades, social scientists have shown that raw gaps in employment outcomes [...] misstate the amount of actual bias in an organization.

....One of the most important developments in the study of racial inequality has been the quantification of the importance of pre-market skills in explaining differences in labor market outcomes between Black and white workers. In 2010, using nationally representative data on thousands of individuals in their 40s, I estimated that Black men earn 39.4% less than white men and Black women earn 13.1% less than white women. Yet, accounting for one variable—educational achievement in their teenage years—reduced that difference to 10.9% (a 72% reduction) for men and revealed that Black women earn 12.7 percent more than white women, on average.

This sounds exactly right. I've taken a look at this several times and found that Black students typically graduate from high school with test scores that place them (on average) at about a 9th or 10th grade reading level compared to 12th grade for white students. When you then compare various life outcomes, including income, of Black workers vs. white workers with 9th grade reading scores, they're nearly equal.

Not completely equal, as Fryer says. There's still a gap left, and the evidence suggests it's probably due to racial discrimination.

I've never been able to reliably get information disaggregated by gender, but what little evidence I've seen suggests that racial discrimination hits Black men harder than Black women. Fryer confirms this in a big way, and the difference remains about the same even after you account for high school education.

Education, as always, is key. If we really want to be anti-racist, improving the education of Black children is something we have to be dedicated to. It's hard, it's expensive, and white people largely hate it. What's more, we've tried and tried for years with little success. But we still have to do it.