## Archive for **November 24th, 2021**

## After Lost Maples

You’ve heard that on November 10th we spent a couple of hours at Lost Maples, disappointed that the fall foliage this year fell far short of what we’d seen there in 2014. Our route home took us along TX 39 by the Guadalupe River, which also proved not as fall-ful as in 2014. Finally, coming northeast from Kerrville along TX 16, Eve spotted something off to the side that I as the driver with my eyes glued to the road in front of me had missed: three strands of brightly reddened Virginia creeper vines *(Parthenocissus quinquefolia)* climbing diagonal branches of a live oak tree. I made a U-turn and went back to do my photographic thing. Later I thought about wordplayfully labeling the view “Red-olent of fall.”

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UPDATE. After yesterday’s commentary appeared, I was made aware of a Newsweek opinion piece entitled “I’m a Black Ex-Felon. I’m Glad Kyle Rittenhouse Is Free.”

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It’s not unusual on intelligence tests to see a question like this: What’s the next number in the sequence 2, 4, 6, …? All such questions are inherently invalid because they incorrectly assume there’s only one right next number or even one “most likely” next number. A better question would be: Give a possible next number in the sequence *and a reason to justify it*. For instance, if you say the next number is 8, a reason would be that you’re continuing with the consecutive even integers. If you say the next number is 9, you could be following the rule that each new number has to be larger than the one before it. If you say the next number is 6, you could be following the rule that each new number has to be at least as large as the one before it. If you say the next number is 1, a reason could be that every number in the sequence has to be a positive integer. If you say the next number is 50, a reason could be that the English-language word for every number in the sequence has to begin with a consonant. If you say the next number is 7, you could be alternating between numerals that have a curve in them and numerals that are written entirely with straight strokes.

One* lesson to take from this is that many possible explanations exist for an occurrence. If it’s important to know how or why something happened—as for example in a legal trial—then we have to investigate and try to find the actual explanation for the occurrence. Jumping to a conclusion without enough evidence can and does lead to mistakes and to injustices.

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* I started to write “*The* lesson to take from this” but I realized I’d be making the very mistake I’m cautioning against because more than one lesson could be drawn from this discussion. One obvious point is the one I suggested at the outset: people who design tests should stop asking what the next number in a sequence is. Another lesson I could go on to elaborate—and used to when I taught high school math but will spare you the details of here—is that if you tell me what you want the fourth number to be, within a few minutes I can come up with an algebraic formula such that when you put 1 into the formula it produces the value 2; when you put 2 into the formula it produces the value 4; when you put 3 into the formula it produces the value 6; and when you put 4 into the formula it produces the value you wanted for the fourth number. In fact I can come up with as many formulas as I like that will produce the same four values—a reality that reconfirms the important idea that there can be more than one explanation for something.

© 2021 Steven Schwartzman