So here's a fun little story that I came across while prepping my models syllabus for the fall. It's a story about humility, most of all, but it's also a story about cats. And fighter planes. 1/

Cats, as everyone knows, have an uncanny ability to land on their feet when they fall, thanks to their sense of balance and their flexibility. That ability is known as a "righting reflex." 2/

In 1987, in fact, a couple of vets in New York City discovered that cats that fall more than seven stories (!) and are brought in to the vet are actually *more* likely to survive than cats that fall from lesser heights. 3/

They referred to the injuries sustained in such falls by the catchy name of "high-rise syndrome." It got a lot of attention. Jared Diamond wrote about it the following year in Nature and included this jawdropping graph. 4/

(The graph is a little less impressive when you count the number of cases, especially of cases of falls from higher stories. But still.) 5/

Diamond goes into great detail to explain this phenomenon. He discusses the properties of falling bodies and how they relate to impact, the vestibular systems of cats, the terminal velocity of cats, and their ability to dissipate the force of impact via soft tissues. 6/

It's got all the elements of a fascinating scientific story, including cats. There's only one problem: There's a very compelling alternative explanation that wasn't taken into account. 7/

This is where the fighter planes come in. 8/

Let's go back to World War II, when the U.S. military is trying to figure out how to keep its bombers from getting shot down. What they have to go on, mostly, are data showing where their bombers are being hit by enemy fire. 9/

Those data look something like this clever reconstruction (by McGeddon - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=53081927). As you can see, the bullet holes show up in discrete clusters. 10/

The recommendation of the military was to add armor to the points that were getting shot the most. Seems logical, right?

Fortunately, they ran this conclusion past a group of statisticians at Columbia that included the legendary Abraham Wald. 11/

Wald pointed out something that they'd missed: They only had data for bombers that hadn't been shot down. If bombers returned with bullet holes in the wings, it was proof that they could survive bullet holes in the wings. 12/

So he recommended adding armor to the places that, on returning bombers, did NOT have lots of bullet holes, arguing that those places were more important for the bomber's survival.

He was right. 13/

This bias came to be known as "survivorship bias." It happens when the set of cases that survive some selection process are unrepresentative of the larger set of cases. And as the case of the bombers showed, ignoring it can lead to exactly the wrong conclusion. 14/

Which brings us back to the cats. Recall that I wrote that "cats that fall more than seven stories *and are brought in to the vet*" are more likely to survive. The second part of that phrase is awfully important, for the same reason that Wald's bombers are important. 15/

To put it delicately, not all cats that fall from a height of more than seven stories make it to the vet. 16/

The ones that do—from staggering heights, sometimes—often bounced off of an awning or landed in a tree or did something other than plow straight into concrete at feline terminal velocity. It's perhaps a bit less surprising that they sustain fewer injuries. 17/

No lesser authority than Cecil Adams, of the legendary Straight Dope, pointed this out in a column in 1996. https://www.straightdope.com/columns/read/1143/do-cats-always-land-unharmed-on-their-feet-no-matter-how-far-they-fall/ 18/

Why is this a parable about humility? Well, this was a terrific story. It incorporated people's observational impressions of cats, and it told them something amazing that they could tell their friends. Diamond even gave a learned account of why it might make sense. 19/

But Mother Nature had some cards up her sleeve. As she often does. So even if someone gives you an explanation for something that makes a ton of intuitive sense and is backed by peer-reviewed findings (or really compelling YouTube videos), it makes sense... 20/

...to retain a modicum of humility, and to take into account the possibility that the explanation might be wrong. Hedge your bets, and retain at least a little bit of uncertainty about everything. No matter how smart you are, Nature doesn't yield her secrets easily. fin/

(P.S. Substitute “bomber” for “fighter plane” above—I misremembered, updated, and then failed to correct earlier tweets. More than a little ironic in a thread about fallibility and humility....)