Portraits of Wildflowers

Perspectives on Nature Photography

Low wild petunia

with 46 comments

From Vaught Ranch Road on June 13th come two views of a native wildflower
I’d never photographed before: Ruellia humilis, known as low wild petunia.

Here’s an unrelated little mathematical diversion: the four numbers 1, 1.2, 2, and 3 have the interesting property that whether you add all of them or multiply all of them you get the same result (in this case 7.2). Are they the only foursome like that? Hardly. For example, whether you add -2, -1, 0, and 3 or multiply -2, -1, 0, and 3, you get the same result (in this case 0). Would you believe that infinitely many sets of four numbers exist that also have the property that adding the four numbers gives the same result as multiplying them? That turns out to be the truth of the matter. Are you surprised?

The second example suggests a template for generating as many more sets of numbers as you like that have the desired property. Let the first of the four numbers be 0. Now pick any two different negative numbers you like (say for example –4 and –6). Finally, add the two negative numbers and make the sum positive (in this case 10). You’ll now have four numbers with the desired property (–4, –6, 0, 10). This works because 0 times any other number is 0, and you’ve rigged the addition in such a way that the positive number cancels out the two negative numbers. In fact you can extend the pattern to as many numbers as you like. For instance, here are six numbers such that adding them gives the same result as multiplying them: 0, -3, -7, -10, -15, 35.

As a quotation for today, let me quote myself: Zero may be nothing, but not for nothing is zero special.

© 2020 Steven Schwartzman

Written by Steve Schwartzman

August 4, 2020 at 4:37 AM

46 Responses

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  1. Low? Seems like a cheerful little flower. Zero!

    Steve Gingold

    August 4, 2020 at 5:04 AM

    • Low compared to other Ruellia species.

      My experience with “Zero is my hero” was zero till now, so I’m glad you linked to it.

      Steve Schwartzman

      August 4, 2020 at 7:07 AM

      • Although aimed at school aged children, I used to enjoy Schoolhouse Rock while working Saturdays at a furniture store many years ago. It sure beat watching Haystacks Calhoun and Andre the Giant make believe they were wrestling which was usually the TV fare on that day at work.

        Steve Gingold

        August 4, 2020 at 3:56 PM

  2. “Nothin’ from nothin’ leaves nothin’/You gotta have somethin’ if you wanna be with me…”
    That profound thought comes via Billy Preston, in a song with no negatives, I positively love it.

    Robert Parker

    August 4, 2020 at 6:46 AM

    • You’ve really signed off on that song. I see that in the previous year, 1973, Bill Preston also reached #1 with the song “Will It Go Round in Circles?”, which takes us into geometry.

      Steve Schwartzman

      August 4, 2020 at 7:11 AM

      • That’s a great tune, too. I’ve read that he was sometimes called “The 5th Beatle,” but definitely not a 3rd or 5th wheel. He toured with the Rolling Stones, too, and played keyboard on George Harrison’s song “Circles,” so lots of geometry goin’ on.

        Robert Parker

        August 4, 2020 at 8:24 AM

        • I first heard about him as the 5th Beatle, when he appeared with them in the 1970 film “let It Be.”

          Steve Schwartzman

          August 4, 2020 at 10:31 AM

  3. Thank you, Steve, for the portraits of the wild petunia and the wonderful mathematical diversion! It is easy to create groups of four numbers for this property with a zero. But are there any more such groups without the negative numbers like in your first example?

    Peter Klopp

    August 4, 2020 at 8:30 AM

    • Sure, a zillion of them. Here’s another foursome: 1/2, 1/3, 7/6, -72/29. And here’s another: -0.2, -2, 1, 2.
      You want to solve the equation w + x + y + z = wxyz. Just plug in whatever you like for w, x, and y, then solve for z.

      Steve Schwartzman

      August 4, 2020 at 12:00 PM

      • Thanks for the solution, Steve! Who said that math isn’t any fun to play with?!

        Peter Klopp

        August 5, 2020 at 12:37 AM

        • Well, the truth is that most of the people who come here because of their interest in nature don’t find math fun to play with. That’s why I only occasionally bring in math, and even when I do I keep things simple.

          Steve Schwartzman

          August 5, 2020 at 6:15 AM

  4. The wild petunia is beautiful. I especially like that second image!


    August 4, 2020 at 9:28 AM

  5. It’s a lovely wildflower, and I really like all the texture in the second image. I’ve always thought Math and Music are the only perfect things in our world.


    August 4, 2020 at 11:06 AM

  6. I hate math, but love that flower. And your photos.


    August 4, 2020 at 1:30 PM

  7. The mathematics of the infinite is something that has fascinated me since high school, though I am quite certain that most of it goes over my head…..

    Here’s my quote for the day: “Some infinities are smaller than others.”

    Johnny Crabcakes

    August 4, 2020 at 2:19 PM

    • The existence of a hierarchy of infinities came as quite a surprise to mathematicians in the late 1800s. It’s still surprising.

      Steve Schwartzman

      August 4, 2020 at 2:24 PM

  8. It is a pretty flower, isn’t it? Coincidentally I saw some yesterday at a forest preserve I haven’t walked in before.


    August 4, 2020 at 5:15 PM

  9. Not for nothing, spoken like a true New Yorker.

    Michael Scandling

    August 4, 2020 at 9:06 PM

  10. I haven’t seen any Ruellia humilis for about 8 years, when doing field trips with NPSOT at the River Ranch property, which is supposed to open in the near future (don’t know for sure) as a Williamson County Park. The one I photographed back then was white, though. I assume that the color variations are typical to many plants. Especially like the second photo, taken from the “unusual”(but not for SS) angle from below.
    The little math puzzle is interesting and fun, and “nothing” to be dismissed – promoting affect for learning is important.


    August 5, 2020 at 11:43 AM

    • I don’t know how I missed this species before. Maybe I did see some without realizing it wasn’t the common Ruellia nudiflora. In contrast, I have noticed that purple flowers often generate white variants (bluebells and bluebonnets, for example). I’m happy you enjoyed the math. Affect can produce a good effect.

      Steve Schwartzman

      August 5, 2020 at 3:33 PM

  11. I love the second photo. The texture almost like powder. And the math play is great.


    August 5, 2020 at 8:56 PM

    • Hooray for one more person who appreciates the math play. I agree that the underside of the flower has a powdery look to it.

      Steve Schwartzman

      August 5, 2020 at 10:11 PM

      • I’ve begun relearning algebra to help my aging brain. Now that it’s not high school math, it’s very engaging. So it was great to read your math play.


        August 6, 2020 at 9:26 AM

        • I’ve sometimes thought that when kids finish junior high school, they should be sent out into the real world to work for a few years. Then bring them back to continue with high school, and they might appreciate it a lot more.

          Steve Schwartzman

          August 6, 2020 at 11:35 AM

  12. I just spent entirely too much time trying to find the symbol that corresponds to the design in the middle of the flower: the straight line with the curved line intersecting it. I’ve been through math, physics, astronomy, and the Greek alphabet, and can’t find it, but it jumped out at me as soon as I saw the flower. It’s familiar, but remains a mystery. Maybe I need to turn it upside down and try again.

    What’s not mysterious at all is the appeal of that second view: so detailed. I like the gray tones, particularly. I suspect all those little hairs contribute to the effect. As much as I enjoy bold, bright colors, the subtlety of this one’s appealing. It looks nice in a garden, too, as one of my readers who lives in Illinois has shown..


    August 6, 2020 at 8:23 AM

    • Upside down sounds like a good approach: https://en.wikipedia.org/wiki/Psi_(Greek)#

      After Melissa commented about having seen one of these wild petunias the previous day, I checked and learned that this species grows in many parts of the country, which I hadn’t known. As for all the details on the underside of the flower, I wonder whether a zoomed-in look could pass for an aerial view of some dry terrain.

      Steve Schwartzman

      August 6, 2020 at 11:02 AM

  13. I’m not a lover of the decorative petunia, but this one certainly takes my eye!


    August 7, 2020 at 12:13 AM

    • “What’s in a name?” asked the bard. The popular cultivated petunias belong to the nightshade botanical family, while the so-called wild petunias of the genus Ruellia are in the acanthus family. As a result, none of your non-fondness for the former need carry over to the latter, and you’re free to have your eye taken.

      Steve Schwartzman

      August 7, 2020 at 7:06 AM

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