Texas flax

From April 9th along FM 1431 north of Marble Falls comes a colony of what I take to be Linum hudsonioides, known as Hudson flax or Texas flax, that turned the land yellow. Below is a closer look that includes some flowering and budding globes of antelope horns milkweed, Asclepias asperula.

The third picture offers an even closer view so you get a better sense of what these flax flowers are like. The yellow flowers without red centers are a kind of bladderpod (Physaria sp., formerly Lesquerella).

A theme I’ve been pursuing for over a week now is that it’s common to hear politicians and activists bandy about the phrase “common sense,” which I find to be a loaded and misleading term because some or even many things that a majority of people believe to be common sense can be shown not to be true.

Here’s an example from geography. Suppose you have access to a list of all the rivers (including streams, creeks, etc.), in the United States, along with the length of each one (rounded to the nearest whole mile). For example, that list would include:

The Missouri River (various states): 2341 miles.
The Rio Grande (various states): 1759 miles.
The Ohio River (various states): 979 miles.
The Yellowstone River (mostly Wyoming): 678 miles.
The Cache River (Missouri): 213 miles.
The San Marcos River (Texas): 75 miles.
The Scott River (California): 60 miles.
The East Mancos River (Colorado): 12 miles
The Chelan River (Washington): 4 miles.
The Kisco River (New York): 3 miles.

There’d be thousands of rivers in the full list. The number for the length of each river has a first—and in some cases only—digit. Now here’s the question: of all those thousands of lengths, what portion (or fraction or percent) of them have 1 as their first digit? “Common sense” would lead many people to think as follows: “Rivers are natural phenomena, free from any human bias. They come in all sorts of lengths, from very short to very long, so it seems the length of a river is as likely to begin with any digit as with any other. There are 9 possible first digits (0 can’t be a first digit for a length), so on average 1/9 of the lengths, or about 11%, would have 1 as their first digit. The same would be true for each of the other possible first digits.”

Alas, rivers don’t have that sort of “common sense.” Dumb aqueous brutes that they are, they keep on going with the flow in their own stubborn way. If you could see the list of all the river lengths, you’d find that about 30% of them begin with a 1, nearly 18% with a 2, and so on down the line in decreasing fashion, with not even 5% of the lengths beginning with a 9.

Ah, you say, maybe that’s because Americans are recalcitrant and cling to antiquated measures of length like inches, feet, yards, and miles. Surely there’d be “equity” (oh, that horrid word, which means forced sameness of outcomes for groups) if we did our measuring in civilized kilometers rather than hillbilly miles. It turns out that if you converted miles to kilometers, most individual river lengths would end up having a different first digit than before, yet amazingly the first digits as a group would still follow the same distribution, from 1 as the most common down to 9 as the least common!

This phenomenon, which holds for many things other than lengths of rivers, has come to be known as Benford’s Law. You’re welcome to read more about it. (And we should add that Benford’s Law follows Stigler’s Law, which “holds that scientific laws and discoveries are never given the names of their actual discover.”)

© 2021 Steven Schwartzman