Portraits of Wildflowers

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Texas flax

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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

Written by Steve Schwartzman

April 16, 2021 at 4:36 AM

Oh that phlox

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Here’s another flowerful view from our April 2nd jaunt down south. In particular, it’s from the cemetery in Stockdale. Unlike the long exposures you saw a few posts back, this time I used a shutter speed of 1/640 of a second to freeze the wildflowers that the breeze was whipping into motion.

And while we’re looking at bright magenta phlox, let me back up to our March 19th drive down to Gonzales, where I photographed some old plainsman buds (Hymenopappus sp.) with a foxy phloxy mask-like wraith behind them.

* * * * * * * *

A theme I’ve been pursuing here for a week now is that it’s common to hear politicians and activists bandy about the phrase “common sense,” which is 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.

One of the greatest fields of abuse is popular psychology, where many notions are passed off as “common sense” that the evidence shows aren’t true. I’d like to refer you to a wonderful book about that: 50 Great Myths of Popular Psychology, by Lilienfeld, Lynn, Ruscio, and Beyerstein. Here’s an example of one myth as described on Amazon’s page about the book:

Low Self-Esteem is a Major Cause of Psychological Problems.

Many popular psychologists have long maintained that low self-esteem is a prime culprit in generating unhealthy behaviors, including violence, depression, anxiety, and alcoholism. The self-esteem movement has found its way into mainstream educational practices. Some athletic leagues award trophies to all schoolchildren to avoid making losing competitors feel inferior (Sommers & Satel, 2005). Moreover, the Internet is chock full of educational products intended to boost children’s self-esteem.

But there’s a fly in the ointment: Research shows that low self esteem isn’t strongly associated with poor mental health. In a painstakingly – and probably painful! – review, Roy Baumeister and his colleagues (2003) canvassed over 15,000 studies linking self-esteem to just about every conceivable psychological variable. They found that self-esteem is minimally related to interpersonal success, and not consistently related to alcohol or drug abuse. Perhaps most surprising of all, they found that “low self-esteem is neither necessary nor sufficient for depression” (Baumeister et al., 2003, p. 6).

Because activists and ideologues have captured the American educational system, schools here now spend inordinate amounts of time promoting self-esteem. Because a school day has a finite number of hours in it, the more time teachers devote to self-esteem, the less time they have for actual knowledge. The result is that many students are handed diplomas even when they know practically nothing about history, geography, arithmetic, government, science, and logic. But they ooze self-esteem.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 15, 2021 at 4:48 AM

Textures of different kinds

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At the Doeskin Ranch in Burnet County on March 24th I focused on textures of different kinds. The photograph above reveals a prickly pear cactus pad from which all the outer covering and inner cells and water had passed away, leaving only the sturdy structure that once supported them. In contrast, the picture below shows a rounded, colorful patch of lichens on a boulder.

For those interested in the art and craft of photography, I’ll add that the first photograph exemplifies point 4, and the second one point 15, in About My Techniques.

* * * * * * * * * *

A theme I’ve been pursuing here for a week now is that it’s common to hear politicians and activists bandy about the phrase “common sense,” which is 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 a simple example from the everyday world of buying and selling. Suppose an item in a store goes up 50% in price and later comes down 50% in price. A lot of people would say it’s “common sense” that the rise in price and then the fall in price by the same percent would bring the item back to its original price; in this case the +50% and the –50% would cancel each other out.

Alas, that bit of “common sense” isn’t true. To see that it’s not, let’s give the item in question a specific price, say $40. After that price goes up by half (+50%), it’s $60. After the $60 price gets reduced by half (–50%), it drops to $30. The new price is less than the original $40 price, not equal to it.

Now let’s go a step further. In the real world, switching the order of two actions usually leads to different results. For example, mixing the ingredients for a cake and then baking them will give a very different cake than the one you’d get by baking the ingredients first and then mixing them. Waiting for an empty swimming pool to fill up and then diving head-first into it is recreational; diving head-first into an empty swimming pool and then waiting for it to fill up could well be fatal.

With those examples in mind, it seems “common sense” that if we go back to our example of prices and reverse the order of the two equal-percent changes, we might well get a different result. Specifically, what will happen if this time we first apply a 50% decrease to a price and then a 50% increase? Last time the final price ended up lower than where it started. By reversing the order of the changes, might the price now end up higher than where it started? As I used to say to my students: when in doubt, try it out. Beginning once again with a price of $40, if we reduce it by half (–50%) the new price is $20. If we now increase that $20 price by half (+50%) the final price is $30. The result comes out exactly the same as before: the original $40 price will still end up getting reduced to $30. Unlike many things in the real world, in this situation reversing the order of our actions makes no difference.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 14, 2021 at 4:28 AM

Non-blue bluebonnets

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Above, from our first 2021 visit to the Lady Bird Johnson Wildflower Center on March 25th comes a bluebonnet displaying a purple as richly saturated as I think I’ve ever seen in Lupinus texensis. No extra charge for the tiny green nymph of a katydid or grasshopper. And below are two white bluebonnets scattered in the large colony we saw in Dubina on March 29th.

A theme I’ve been pursuing here for some days now is that it’s common to hear politicians and activists bandy about the phrase “common sense,” which is 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.

Take taxes. Many say it’s only “common sense” that if a jurisdiction raises a tax rate it will bring in more revenue. The truth is that sometimes it will and sometimes it won’t. For example, if a tax rate goes from 10% to 11%, the increase is small enough that the higher rate won’t be enough to cause people to take an easier job with a lower salary to avoid the higher tax, so revenue will increase. On the other hand, if a tax rate goes from 10% to 50%, a lot of people will lower their earning and spending because the higher rate is just too burdensome, and as a result the government may well end up taking in less than before. And, to take an easy-to-understand extreme, if a government imposed a 90% tax on earnings, many people would stop working altogether, go on welfare, and the government would have no income of theirs to tax. There’s a good example of that kind of work avoidance in the current pandemic: the American government has given out such high supplemental unemployment benefits during the pandemic that some people find they make more money by not working than by going to a job. As a result, some owners of small business have been having a hard time finding workers.

Another consideration is that if one jurisdiction raises its tax rates to be significantly higher than the rates in other jurisdictions, people and companies have an incentive to go elsewhere. That’s happening now as people and companies from high-tax states like New York and California move to lower-tax states like Florida and Texas, so New York and California will lose all the money they used to get by taxing those people and companies. If federal corporate tax rates are raised to the point that they’re significantly higher than corporate tax rates in other countries, some companies will relocate a portion or even all of their operations to foreign countries with lower tax rates, and the United States will lose the revenue it used to get. As a historical example, in Britain by the end of the 1960s the upper tax rates were so high that the Rolling Stones moved to the south of France and John Lennon moved to the United States.

In the opposite direction, sometimes lowering tax rates ends up bringing in more revenue by encouraging people to spend more now that they have more. Lowering corporate tax rates can induce American companies to repatriate earnings they’ve kept in foreign countries to avoid excessively high tax rates at home.

In short, it’s not always true that raising tax rates brings in more revenue. The sweet spot depends on many factors, and finding it seems more magic than science.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 13, 2021 at 4:46 AM

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

Not done with bluebonnet colonies yet

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On April 9th we visited a new place, Turkey Bend Recreation Area in western Travis County. The bluebonnets were still thriving there, despite some unsightly trampled spots where people had obviously plunked themselves or more likely their kids down for pictures among the best-known Texas wildflowers.

In the upper part of the second picture you see Lake Travis, which was created in the 1930s by damming the Colorado River. Given central Texas’s propensity for both droughts and tremendous downpours that cause flash flooding, the water level in Lake Travis has fluctuated a lot. In some years the land on which these bluebonnets are now flowering was under water.

* * * * * * * * *

Three 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 yesterday’s I gave examples of “common sense” leading to incorrect conclusions. Here’s another, this time from baseball.

Let’s compare two players on a baseball team, Casey and Roger. When the team finished the first half of the season, Casey’s batting average was a whopping .387 (meaning he got a hit 38.7% of the times he was officially at bat). Roger’s batting average during the same period was almost as good at .375.

During the second half of the season (in its own right, not cumulatively from the beginning of the year), both players declined. In that second half of the season Casey batted .246 and Roger batted only .216.

Summarizing: in the first half of the season Casey out-hit Roger, and again in the second half of the season Casey out-hit Roger. Who had the better batting average for the season as a whole?

Almost everyone will say that because Casey outperformed Roger in the first half and also outperformed him in the second half, there’s no doubt that Casey ended up with the higher batting average of the two for the season as a whole.

But it’s time once again for me to say hold your horses, not so fast. In fact it’s easy to show how Roger could still have ended up with the better batting average, despite trailing in each individual half of the season. Here are three charts that do the trick (I’m sorry WordPress doesn’t seem to let me control the formatting the way I’d like).

First Half of the Season
– – – –At-batsHitsAverage = Hits ÷ At bats
Casey3112 12 ÷ 31 = .387
Roger15257 57 ÷ 152 = .375

Second Half of the Season
– – – –At-batsHitsAverage = Hits ÷ At bats
Casey6115 15 ÷ 61 = .246
Roger5111 11 ÷ 51 = .216

Season as a Whole
– – – –Total At-batsTotal HitsAverage = Total Hits ÷ Total At bats
Casey31 + 61 = 9212 + 15 =27 27 ÷ 92 = .293
Roger152 + 51 = 20357 + 11 = 68 68 ÷ 203 = .334

So you see Roger did significantly better than Casey for the season as a whole even though Roger had a lower average in each individual half! This is an example of the very interesting phenomenon known as Simpson’s Paradox. What throws people’s “common sense” off here is that Roger had a lot more at-bats than Casey, especially in the first half of the season, when Roger was batting extremely well. You could say that the players were weighted differently. This is akin to the example a few posts back about average rates of speed while driving, where more time was spent at a slow speed than at a fast one. This baseball example is another one that shows you can’t average averages.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 11, 2021 at 4:45 AM

Go with the blow

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The blowing of the wind, that is, which I had to deal with on April 2nd at the cemetery in Stockdale, about a hundred miles south of home. First I took a bunch of wildflower pictures at high shutter speeds to try and stop the motion. Then I relented—literally—and switched to slow shutter speeds, knowing that the blowing would bring blurring. I’ll anticipate some comments and say that the resulting photographs suggest Impressionist paintings.

I took the top picture at 1/8 of a second and the bottom one at 1/15th of a second. The magenta/hot pink flowers are a Phlox species; the red-orange ones Indian paintbrush, Castilleja indivisa; the blue sandyland bluebonnets, Lupinus subcarnosus; the yellow Nueces coreopsis, Coreopsis nuecensis; the white are white prickly poppies, Argemone albiflora.

* * * * * * * * *

Two 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 yesterday’s I gave examples of “common sense” leading to incorrect conclusions. Here’s another.

Suppose you live in an old house with a carport. Because of the topography, whenever you get a heavy enough rain, water flows onto your carport and collects there, taking hours and hours to eventually drain away. It’s a nuisance, but you put up with it because having an engineering company fix the problem would cost thousands of dollars. One night you get home from a long trip and are so exhausted you go to bed and quickly fall into a sound sleep. It’s such a deep sleep that nothing disturbs you, and you wake up the next morning feeling refreshed. A little later you open your side door and see water a couple of inches deep on your carport. What happened?

“Common sense” would lead many if not most people to say it must have rained hard during the night and that’s why the carport got flooded. You must have been sleeping so soundly that the rain didn’t wake you up.

Anyone who concludes that it must have rained is committing an error of logic. Just because event A (in this case a hard rain) always leads to event B (in this case a flooded carport), you can’t “reason” backwards and assume from the occurrence of event B that event A must have occurred. It just so happens that our previous house in Austin did suffer from a flooded carport after sustained downpours, and one morning I did open the side door and see water flowing through the carport—and yet it hadn’t rained. Instead, we’d had a sustained freeze, and a poorly insulated pipe leading from the house out to the washing machine at the back of the carport had burst. You can think of other explanations. Maybe the next-door neighbor’s sprinkler system had gone awry. Maybe a large water tanker truck had gotten into an accident nearby and the tank had split open. Maybe a water main in the street out front had ruptured. Maybe a dam had collapsed and flooded the whole neighborhood.

You get the point: just because something is plausible or even likely doesn’t mean it’s true. The world could be saved so much misery if only people investigated situations rather than jumping to conclusions—and worse, acting on hasty and unwarranted assumptions.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 10, 2021 at 4:38 AM

Nueces coreopsis alone and in combination

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On March 29th in Colorado County I photographed mixed colonies of Nueces coreopsis (Coreopsis nuecensis) and sandyland bluebonnets (Lupinus subcarnosus). I also got on the ground and aimed upward so I could get a different blue overhead and use it to isolate one of the Nueces coreopsis flower heads.

In the last post I noted that it’s common to hear politicians and activists bandy about the phrase “common sense.” I said it’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. The first example came from arithmetic, and now here’s one from chemistry.

Suppose that you have an empty one-quart clear glass container with markings on the sides so you can tell how much liquid is in the container. Now pour a measuring cup’s worth of water and then a measuring cup’s worth of alcohol into the container. How much liquid will you have in the container? “Common sense” will tell most people that 1 cup plus 1 cup equals 2 cups, but that’s not correct here. Water molecules and alcohol molecules interpenetrate somewhat, so the volume in the container will fall short of the 2-cup mark on the glass container. You’re welcome to watch a couple of cheerful kids perform the experiment.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 9, 2021 at 4:39 AM

Winecup flower center

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In this closeup of a winecup (Callirhoe sp.) at the Lady Bird Johnson Wildflower Center on March 25th the shadow struck me as appropriate for the profile of a gnome or ogre or some such creature.

* * * * * * *

It’s common to hear politicians and activists bandy about the phrase “common sense.” 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. Over the next week I’ll give some examples, starting now.

Suppose you live in City A. One morning you get on an Interstate highway, drive to a place in City B, and with light traffic you end up averaging 70 mph for the trip. Three days later you return along the same route, but this time traffic is heavy, and in addition rain pours down for much of the time. As a result, you end up averaging a pitiful 30 mph for your return trip from City B to City A. Now here’s my question: what was your average speed for the round trip? Most people who are given these facts and asked that question will say the average speed for the round trip was 50 mph, which they got by averaging 70 and 30: 70 + 30 = 100, and 100 ÷ 2 = 50. It’s common sense, right?

So simple, so easy—and so wrong! People who come up with an answer of 50 mph don’t understand what an average is. An average is the total of one kind of thing divided by the total of another kind of thing. The very label “miles per hour” tells you what to do: take the total mileage traveled on the round trip and divide by the total number of hours spent doing it.

Let’s suppose City A and City B are 210 miles apart. Driving that 210 miles on the way from A to B at an average of 70 mph took you 3 hours. Returning another 210 miles from B to A at an average 30 mph hour took you a whopping 7 hours. The total distance you drove was 210 miles out plus 210 miles back, or 420 miles. The total time you spent was 3 hours out plus 7 hours back, for a total of 10 hours. As a result, 420 miles ÷ 10 hours gives an average speed of 42 miles per hour for the round trip.

Now, most people’s “common sense” would probably have them objecting: Wait a minute, not so fast (which is a convenient play on words in an example about speeds). These people would assume the average speed depends on how far apart City A and City B are. Well, in fact it makes no difference at all how far apart City A and City B are. Pick any distance you like, do the same kinds of calculations I did (which may mean you’ll need to pull out a calculator because the numbers probably won’t come out so pretty), and you’ll still end up with an average of 42 mph for the round trip.

The reason the true round-trip average speed ends up below the “common sense” but wrong average of 50 mph is that you spent more time driving at a slow speed of 30 mph than at a fast speed of 70 mph, and that pulls the average speed down. In summary, the truth is that despite “common sense” you can’t generally average averages.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 8, 2021 at 4:43 AM

Return to the Floresville Cemetery

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Across a swathe of territory below San Antonio, the spring of 2019 proved a fabulous season for wildflowers; someone told us he’d heard it was the best in 10 years. One place that provided many pictures then was the city cemetery in the aptly named Floresville (flores means flowers in Spanish), a town it takes about two hours to drive to from our home in Austin. On April 2nd of this year, now feeling somewhat freed from the isolation of 2020, we headed back to that cemetery in hopes of finding it as bloomful as in 2019.

While the flowers growing among the graves weren’t as numerous as two years ago, a field along the northeast edge of the cemetery offered wildflowers at least as abundant as they’d been two years earlier. The red-orange ones are Indian paintbrushes, Castilleja indivisa. I take the white ones to be Aphanostephus skirrhobasis, known as lazy daisies or doze-daisies because they generally don’t open up till midday.

And here’s a thought for today: “People shouldn’t expect the cavalry to come to save them. The cavalry is you.” — Douglas Murray, 2021. That’s reminiscent of the venerable saying “God helps those who help themselves,” which many people incorrectly think is in the Bible. It’s actually from Algernon Sydney’s Discourses Concerning Government, published in 1698.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

April 7, 2021 at 4:35 AM

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