Portraits of Wildflowers

Perspectives on Nature Photography

A warmer nod to arithmetic

with 35 comments

Seventeen months ago today, in a post entitled “A warm nod to arithmetic,” I wrote the following:

I’m sure you noticed something curious in the last post: the equivalent (rounded to the nearest whole degree) of Thursday’s warm high temperature of 82°F was 28°C, a number consisting of the same two digits but in reverse order. Some of you must have rushed to Twitter and Facebook to tell all your friends, who must have been thrilled to hear it.

Ever alert math teachers would interrupt their classes with a question now: “Students, are there any other two-digit pairs of equivalent Fahrenheit ~ Celsius temperatures with reversed digits like that one?” What do you think, readers?

All of you who read that post were probably too overwhelmed with emotion by the equivalent pair of 82°F and 28°C to do any further looking, and no answer to my question was ever forthcoming (or ever forthcame, for that matter). As you’ve all been waiting with bated (not baited) breath and have long since turned blue, I’d better tell you the answer. Yes, there is another reversed-digits pair of Fahrenheit ~ Celsius temperatures that are equivalent (when rounded to the nearest whole degree): 61°F and 16°C. Now go give a shout-out and spread the news to everyone you know. Tell ’em Steve sent you.

You can also tell them that Steve sent you the photograph below so you wouldn’t feel bereft of a picture today. I hope arithmetic hasn’t made your head feel the way this Texas thistle head (Cirsium texanum) looks.

Texas Thistle Flower Head Decomposing 5161

© 2014 Steven Schwartzman

Written by Steve Schwartzman

August 10, 2014 at 5:57 AM

35 Responses

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  1. Arithmetic (the basic variety), although a toughie for me, does not make my head explode. Converting from F to C does however. So I just go to a web converter to do the thinking for me. Who wants to think for him or herself when the web can do it for you? While in school a few eons ago, I learned a formula for the conversion. Long forgotten along with a myriad other formerly useful items.
    I am sure that the next time one of my overseas friends says it is warm and 28 degrees C (for some reason Firefox/WP would not let me do alt+0176 today) I’ll remember that is 82 degrees F.

    Steve Gingold

    August 10, 2014 at 6:20 AM

    • You and Linda (below) mentioned the conversion formula, so here’s a link to it:


      Given any two pairs of equivalent temperatures, it’s possible to derive the formula. Still, having a few equivalent pairs in our normal range of temperatures memorized allows for a quick approximation of other nearby conversions.

      Another approach is to start with 0°C = 32°F, and for each advance of 10°C there’s an advance of 18°F:
      10°C = 50°F
      20°C = 68°F
      30°C = 86°F
      40°C = 104°F

      That also means that for each advance of 5°C there’s an advance of 9°F. So, if
      20°C = 68°F, then
      25°C = 77°F.

      Steve Schwartzman

      August 10, 2014 at 8:52 AM

      • Thanks. It does seem very familiar but the chances I will ever remember that are pretty slim. Maybe I should write it on my palm. I’ll make sure not to delete my conversion table.

        Steve Gingold

        August 10, 2014 at 1:17 PM

        • Actually, as long as you can put a smart phone or a computer mouse in your palm, you’ll have access to an online temperature conversion site whenever you need one.

          Steve Schwartzman

          August 10, 2014 at 2:00 PM

  2. Well, by golly gosh, I do believe it actually reached 16C or 61 F at my house today. That’s warm for this time of year. We rarely manage 28 or 82 at any time. And my head feels exactly like the Texas thistle but not because of arithmetic, but because of pollen problems.


    August 10, 2014 at 6:57 AM

    • If you rarely manage 28°C or 82°F at any time, I’m not sure you’d enjoy Texas. Yesterday afternoon it hit about 39°C here. Sorry to hear about your allergy-induced head that feels like this thistle head. Happy antihistamine to you.

      Steve Schwartzman

      August 10, 2014 at 8:55 AM

  3. Ha! Well, I’m glad that’s sorted out!

    ….running off to twitter to spread the word. 😉

    Alex Autin

    August 10, 2014 at 7:34 AM

  4. I’m just glad I wasn’t called upon to guess the number of thistle bits on that thistle head!

    Susan Scheid

    August 10, 2014 at 7:39 AM

  5. At one time, I might have said this post leaves me cold — but no more! I do remember the 0C – 32F equivalence, but the conversion formula? Gone. It’s time for a refresher course.

    As for that thistle, I’ve been thinking a good bit about my very early language skills. There were words I had trouble with, and this was one. “THI-thel” was my preferred pronunciation.


    August 10, 2014 at 7:57 AM

    • 🙂 When young, I had a thevere lithp. Although I overcame it, I can thtill lithp on demand. Not exactly a thkill with much value, but I am quite good at it. 🙂

      Steve Gingold

      August 10, 2014 at 8:10 AM

    • I put a link to the formula in my reply to Steve Gingold’s first comment.

      You’re probably aware that the two th sounds in English (one voiceless, as in thin, the other voiced, as in this) are hard or even impossible for most foreigners to pronounce. Foreigners often substitute s or t for the first, and z or d for the second. Your childhood problem went the other way.

      Steve Schwartzman

      August 10, 2014 at 9:11 AM

      • Another childhood problem is about to go away. I just spent an hour on the phone with a friend who’s home-schooling her kids. She referred me to Khan Academy: free, self-directed, and apparently pretty well-respected. If I’m going to be roaming at 3 a.m. thinking about math, I might as well be doing something like this. Better late than never, no?


        August 10, 2014 at 8:57 PM

        • I’ve known a parent who home-schooled her kids and someone else who was herself home-schooled. The latter ended up having to go to Austin Community College to learn elementary algebra, and I’ve worried that the children of the former haven’t gotten a decent math education. As you indicated, the free videos provided by the Khan Academy can help a lot with home-schooling, but I still worry that there might not be anyone around to interpret puzzling things in those videos or to elucidate the fine points. Adults may be motivated enough to pursue learning on their own (even at 3 AM), but I know there are plenty of kids who aren’t motivated enough to learn well on their own. On a related note, and even if it’s self-serving, I’ve lamented the sidelining of teachers into “facilitators.”

          Steve Schwartzman

          August 10, 2014 at 9:29 PM

          • There are a lot of people who lament the rise of the “facilitator.” I’ve had a few extraordinary teachers, and I’ve nearly been facilitated into the ground. I’ll take the teacher, every time.

            I’ll grant your point about home schooling, and the gaps that can exist. But I’m the other side of that coin. I went through a terrific school system, took every required math class through junior and senior high — and college — and still need remedial work. Now, I think I have a good tool to work with. I took my “placement exam” last night, landed on the “arithmetic” level, and spent some time seeing how the program works. So far, I’ve had no need for the videos, but I’ve done a lot of problem-solving, and it’s been fun. It’s going to be even more fun to see how far I can go with it. I’ve already mastered 36% of the arithmetic level. 🙂


            August 11, 2014 at 9:45 PM

            • Then here’s to those fellow lamenters, and may mere facilitators be grounded far and near.

              Given what you say about having worked through 36% of the arithmetic level already without needing any of the videos, it sounds as if the knowledge was in your head already (which accords with what you said about having taken all required math courses through college) but merely needed a refresher to come to consciousness again after decades of having lain fallow.

              Steve Schwartzman

              August 12, 2014 at 6:44 AM

  6. Arithmetic – a great way to start the morning, Steve. And by the way, that’s exactly what my hair looked like this morning!


    August 10, 2014 at 8:45 AM

    • Yay for arithmetic, Lynn. On the other matter, uh oh: let’s hope it’s hair today, gone tomorrow (the unruliness, that is, not the hair itself).

      Steve Schwartzman

      August 10, 2014 at 9:15 AM

  7. I spent just a few short minutes trying to one-up you with similar sorts of reversals using the Kelvin scale … didn’t pan out. D

    Pairodox Farm

    August 10, 2014 at 5:38 PM

    • Even within the Celsius ~ Fahrenheit world I’ve wondered if there are any three-digit equivalent reversals, but I never took the time to investigate.

      Steve Schwartzman

      August 10, 2014 at 9:09 PM

  8. I’ve always liked the relationship that -40˚F = -40˚C.

    Jim in IA

    August 10, 2014 at 6:48 PM

    • If you plot any function and its inverse, the two curves are symmetric with respect to the line y = x (assuming we use those conventional letters). In the Fahrenheit ~ Celsius function and its inverse, both are functions that graph as lines with different slopes, and therefore those lines must intersect somewhere along the line of symmetry y = x. As you noted, that point of intersection occurs where y = x = –40.

      As a riddle you can ask people which temperature is colder, –40°F or –40°C?

      Steve Schwartzman

      August 10, 2014 at 9:17 PM

  9. I’m afraid I’ll forgo the maths and just focus on this magnificent thistle head. Lovely to view it inside a circle, against the black background.

    Mary Mageau

    August 11, 2014 at 5:06 AM

    • Once in a while, Mary, with subjects that by their shape lend themselves to it, I set a picture off in an ellipse with black around it. I’m glad you like the effect.

      Steve Schwartzman

      August 11, 2014 at 7:06 AM

  10. Steve, I have always so admired your fertile and active intellect. A mathematician, a linguist, a photographer, a botanist…so many interests and talents. Bless you for sharing them! Love to Eve. Hope to run into both of you soon.

    Diane Sherrill

    August 11, 2014 at 2:16 PM

    • Nice to hear from you, Diane. It’s true that I’ve ventured into various fields, some more deeply than others. I’ll always be much more of a photographer than a botanist, I’m afraid, but I keep learning. In any case, I expect we’ll run into each other at some event or field trip before too long, as has happened before. Happy autumn in advance.

      Steve Schwartzman

      August 11, 2014 at 2:35 PM

  11. 🙂


    August 12, 2014 at 7:14 PM

  12. I remember fondly an episode of Mayberry, with little Opie exclaiming, “a BATH?! This is turning out worse than I thought!” That came to mind when I opened this post, and my mind balked. “MATH?!”


    August 31, 2014 at 6:33 PM

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