Textures of different kinds

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.

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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