Portraits of Wildflowers

Perspectives on Nature Photography

Winecup flower center

with 26 comments

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

26 Responses

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  1. If you apply “horse sense,” it averages out to 8 MPH, traveling at a trot. And then “street smarts” comes into it, if you fall off the horse, ouch that smarts! But then you’re well grounded.

    Robert Parker

    April 8, 2021 at 7:22 AM

    • Some might say you’re falling all over yourself to show off your good grounding in wordplay. I’ll show off my grounding in etymology by pointing out that the smart that means ‘intelligent’ is in fact the same word as the smart that means ‘to cause a stinging feeling.’ It’s the same kind of metaphor that has us describing an intelligent person as someone who has a keen or sharp mind.

      Steve Schwartzman

      April 8, 2021 at 7:59 AM

  2. “Common sense” is sure an American expression I don’t find an equivalent to back where I come from. To me it’s an obscure and often misleading term.

    Alessandra Chaves

    April 8, 2021 at 8:14 AM

    • Politicians use “common sense” to label every proposed law that they’re for—and therefore to imply that their opponents don’t have any sense. You’re correct that when politicians use the term you can ignore it.

      As for your country, I found this:

      Steve Schwartzman

      April 8, 2021 at 10:30 AM

      • I think I did not express myself very precisely, which is not surprising. To elaborate and to be clear, I meant to say that the term “senso comum” is not used, where I come from, in the same manner that it’s used here. It is also not spoken with the same frequency. For example, when my husband says to the kids “use some common sense”, he is implying that the kids are being idiots, refusing to use straightforward reasoning or something like that 😉 Conversely, where I grew up, Rio de Janeiro, this expression would make no sense whatsoever. We will use the term very sparingly and usually within a sentence that translates like that “contrary to common sense…the way you calculate average speed is… ” I hope this was more clear.

        Alessandra Chaves

        April 8, 2021 at 11:13 AM

  3. Those miscalculations under the guise of common sense are too often used and remind me of a book I once read: How to lie with statistics.

    Peter Klopp

    April 8, 2021 at 8:34 AM

  4. […] 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 […]

  5. It took me forever to find your gnome or ogre, but I finally did. All of the winecup species are so pollen rich; I like the way your photo picks up both the color and the scattering of pollen grains.

    I stuck with you through the example of “common sense,” and was pleased that I understood it. I started thinking about related matters, and realized that one reason I can’t depend on “distance and driving time” calculators is that the built-in assumptions of such sites have little to do with the way I travel. From Kemah to Kerrville is a minimum of six hours for me, but most sites put it at four hours (give or take). The difference, of course, is that I-10 is part of their calculation, and stopping to photograph wildflowers isn’t. I’ve done Kemah to Kerrville in nine hours, and though that’s not exactly “making good time,” it’s always a great time.


    April 9, 2021 at 11:16 PM

    • From Kemah to Kerrville (isn’t there a song with that name?) is slightly under 300 miles, according to Google Maps. For you to take nine hours doing it is more than we spent on our circuit of similar length down to near San Antonio eight days ago. Yesterday was our turn to outslowpoke you: we spent eight hours on a circuit of some 220 miles. Part of that was the eastern side of the Willow City Loop. Whether bluebonnets were better on the other half of the loop I don’t know, but they were nothing to go out of your way for on the side we saw. If it’s white prickly poppies you’re after, however, we saw scads of them. Bluebonnets worth photographing for their density and expanse did come our way near the end of the trip, about 20 miles southeast of Marble Falls, at a place we’d never previously visited called Turkey Bend Recreation Area on Lake Travis.

      Steve Schwartzman

      April 10, 2021 at 5:33 AM

      • I wonder if you’re remembering “From Boulder to Birmingham.” Emmylou Harris wrote it with Bill Danoff after the death of Gram Parsons. Uncounted people have clung to it to help them get through a grief. I sure did.


        April 10, 2021 at 7:23 AM

        • Perhaps you’re right. Or it may have been that I felt there should be a song with that alliterative name.

          Steve Schwartzman

          April 10, 2021 at 7:40 AM

  6. […] 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 […]

  7. […] 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 […]

  8. […] 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” […]

  9. And that is an above average explanation.

    Steve Gingold

    April 15, 2021 at 3:57 AM

    • Your comment suddenly made me realize there’s no exact rhyme for average in English.

      Steve Schwartzman

      April 15, 2021 at 5:17 AM

      • How about the exchange rate for Canadian versus US dollars?

        Steve Gingold

        April 15, 2021 at 5:23 AM

        • Yeah, especially now that money has to get vaccinated before being allowed across the border.

          Steve Schwartzman

          April 15, 2021 at 5:37 AM

          • Not sure if we communicated so I should have mentioned that word…cadvantage.

            Steve Gingold

            April 15, 2021 at 6:05 AM

            • Ah, that makes sense of it. I hadn’t heard that term. The nominal advantage Americans get when converting to Canadian currency may be at least partly offset by higher-denominated prices in Canada. And I remember my surprise years ago when I bought some stamps at a Canadian post office to mail postcards home and discovered that I had to pay a sales tax on the price of the stamps.

              Steve Schwartzman

              April 15, 2021 at 6:11 AM

              • Actually a better rhyme would be leverage. Don’t give anyone here the idea that somewhere charges sales tax for stamps.

                Steve Gingold

                April 15, 2021 at 4:26 PM

                • We certainly don’t want to give politicians leverage to find more things to tax.

                  Steve Schwartzman

                  April 15, 2021 at 6:41 PM

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