Portraits of Wildflowers

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Archive for April 12th, 2021

A visit to Bastrop

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On March 26th we visited Bastrop State Park for the first time since last fall. Almost 10 years ago a disastrous fire destroyed the majority of trees in the park, and the landscape is still full of burned dead trunks, both standing and fallen. The charred pine trunk in the photograph above was on the ground. I don’t know why the resin in the upper part of the picture picked up so much blue.

In contrast to that log, take this opening flower of plains wild indigo, Baptisia bracteata var. leucophaea, a species that makes its debut here today.

If you’re wondering what a full inflorescence looks like, the last picture will show you,
complete with the kind of insect that I assume was eating the flowers.

Four posts back I noted that it’s common to hear politicians and activists bandy about the phrase “common sense.” I said that’s a loaded and misleading term because some or even many things that a majority of people believe to be common sense are easily shown to be untrue. In that post and the next and the next and yesterday’s I gave examples of “common sense” leading to incorrect conclusions. Here’s another example.

Every person has a birthday. A year consists of 365 days—or 366 if you want to count February 29, which occurs only about a fourth as often as other days, thanks to leap year—so there are 365 or 366 possible birthdays. You’re naturally curious, and you get to wondering about groups of people, and how likely or unlikely it is that at least two people in a group have the same birthday (the day, not the year). In particular, you get to wondering how large a group of randomly chosen people it would take for there to be a 50-50 chance, i.e. 50%, that at least two people in the group share a birthday.

Many folks would answer that “common sense” tells them they’d need a group half as big as 366, namely 183 people, for there to be a 50-50 chance of a matching birthday. The truth is that with a group of only 23 randomly chosen people in it there’s about a 50% chance two or more people in the group will have matching birthdays. (I won’t go into the math, though it’s not difficult). By contrast, in a group of 183 people there’s a virtual certainty of at least one matching birthday.

You could also turn things around and ask how likely it is that in a group of 23 people there’ll be at least one pair of matching birthdays. Many folks might pull out a calculator, find out that 23 is about 6% of 365, and conclude by “common sense” that there’d be only a 6% chance of a pair of matching birthdays. You’ve already heard that in fact there’s about a 50% chance.

Here’s a way to confirm this without trying to rely on “common sense.” Stand on a busy street and ask people passing by what their birthday is. Mark the dates on a yearly calendar to keep track of them and see if there’s a match. If necessary, keep going until you’ve asked 23 people and still haven’t found a match. Then repeat the experiment a bunch of times. With enough repetitions, you should find that about half of the time you’ll get a matching birthday pair.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 12, 2021 at 4:22 AM

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