Portraits of Wildflowers

Perspectives on Nature Photography

Sunday sunset 4

with 32 comments

On each of the four Sundays in January you’ve seen sunset pictures from the state whose license plates proclaim it the Land of Enchantment. Now that today’s post concludes the series, you’re welcome to look back at the other photographs that have appeared here from June 10, 2017, at Camel Rock, 11 miles north of downtown Santa Fe.

Because the first Sunday sunset picture this month appeared on January 7, and because there are 7 days in a week, all of the January pictures in this sequence came on dates divisible by 7:  7, 14, 21, 28. Speaking of divisibility, if you divide 1 by 7, and then 2 by 7, etc., to convert the fractions to decimals, you’ll find that the sevenths give the following infinitely repeating six-digit cycles:

Do you see the cyclical nature of those decimal expansions, with each one consisting of the same digits in the same order, only starting at a different place in the cycle?

But wait! The columns want some attention, too. Notice that reading down the first column of decimal digits is the same as reading up the fourth column? Likewise for the second and fifth columns, and also for the third and sixth columns.

There’s more that could be said, but for now I’ll let the sun set on these mathematical pleasures and not take you further into seventh heaven.

© 2018 Steven Schwartzman

Written by Steve Schwartzman

January 28, 2018 at 4:58 AM

32 Responses

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  1. The top shot, which could be a called a “Top Shot”, reminds me of Stieglitz’s Equivalents series.

    Steve Gingold

    January 28, 2018 at 5:08 AM

  2. Nice and interesting. Thanks!

    José Manuel

    January 28, 2018 at 5:52 AM

  3. Mind is well and truly boggled now. I shall just gaze at those pretty wisps of cloud for a while…


    January 28, 2018 at 6:57 AM

    • And not the pretty wisps of digits?

      Steve Schwartzman

      January 28, 2018 at 9:18 AM

      • Much as I enjoy figures, I shall pass on these, though I do appreciate the pattern 😉


        January 28, 2018 at 9:55 AM

        • Your comment reminds me how hard it must be for a non-native speaker of English to distinguish the almost opposite meanings of “I’ll pass on these” and “I’ll pass these on.”

          Steve Schwartzman

          January 28, 2018 at 10:15 AM

  4. Only you could start my day this way.

    Jim R

    January 28, 2018 at 8:21 AM

    • I immediately thought of the song “Only You,” which led to an article about the guy who wrote the song and others that the Platters had hits with.

      Steve Schwartzman

      January 28, 2018 at 10:11 AM

      • “…also known as Ande Rand, Lynn Paul or Jean Miles.”

        I remember the Platters. My older sisters played them a lot.

        Jim R

        January 28, 2018 at 10:31 AM

        • I noticed all those aliases and wondered why the guy went by so many names.
          I remember hearing “The Great Pretender” playing at Jahn’s Ice Cream Parlor in Rockville Center (Long Island), probably in 1956.

          Steve Schwartzman

          January 28, 2018 at 10:42 AM

  5. I cannot look at clouds without trying to find shapes and figures – – the top shot looks to me, like someone swimming underwater. But mathematics, on a weekend !?! I won’t even stick my toes in. 🙂

    Robert Parker

    January 28, 2018 at 10:22 AM

    • I think the human mind is predisposed to find figures in clouds. My mind adds the figures of arithmetic. I figure on a non-weekend you’ll more likely swim over from the first kind to the second.

      Steve Schwartzman

      January 28, 2018 at 10:37 AM

  6. I am caught up with you again, Steve. Lovely clouds, and mathematical patterns!

    Lavinia Ross

    January 28, 2018 at 10:40 AM

    • Happy catching up, Lavinia. The patterns in clouds and math are different types, but patterns nonetheless.

      Steve Schwartzman

      January 28, 2018 at 10:44 AM

  7. As I have dyscalculia the maths’ sequence is lost on me, but I love the sunset!


    January 28, 2018 at 1:24 PM

    • Well, as they say, the glass is half full for you. It’s possible that in person, with enough of the background filled in first, I could explain the math patterns clearly enough that you would come to see them.

      Steve Schwartzman

      January 28, 2018 at 1:35 PM

  8. I have only been through New Mexico on the way to and from Oklahoma. It was too quick. I did not get to see much.


    January 28, 2018 at 5:05 PM

    • Then I highly recommend it to you whenever you get the chance to go back and spend time. If you’d like, you can scroll down through some of the pictures I’ve taken in New Mexico over the past few years:


      You can make note of any places that particularly interest you so you’ll have some prime locations to check out when you visit.

      Steve Schwartzman

      January 28, 2018 at 6:54 PM

  9. I can’t believe I saw the cyclical pattern right away. After you pointed out the pattern in the columns, I saw that, too. I can’t figure out the “why,” but at least I can see the “what.”

    Last month, I surprised myself by solving this Futility Closet problem in logic before reading the explanation. At the time, an odd question occurred to me, and the number patterns you’ve presented today brought it back to mind: is there a relationship between logic and mathematics?

    Speaking of patterns, that’s quite a skeletal wraith with upstretched arms in that first photo. Once again, it’s the vertical I found most compelling.


    January 28, 2018 at 10:16 PM

    • I was confident you’d take the time to look for the cyclical pattern. Seeing it right away is even better. In fact you’re only the second commenter who’s mentioned appreciating.

      Good for you for getting the logic problem quickly, too. I think it’s pretty well accepted that there’s a relationship between logic and mathematics.

      Originally I planned to show only the vertical photograph. At the last minute I added the second one, even though I think the first is a better picture. I’m with you in seeing a wraith with arms upraised (or shall I say upwraithed?).

      Steve Schwartzman

      January 29, 2018 at 5:02 AM

  10. Hahaha, seventh heaven indeed! Math is really so beautiful, isn’t it? As for the delightful first photo, I saw a creature diving.


    January 29, 2018 at 9:56 AM

    • I’m glad you caught the “seventh heaven” play on words.
      For me the first picture has always had an upward movement, so it’s interesting that it led you to think of diving.

      Steve Schwartzman

      January 29, 2018 at 10:26 AM

  11. This is fascinating, Steve, but far beyond my grasp.


    January 29, 2018 at 8:48 PM

    • As I said in reply to Val’s comment: “It’s possible that in person, with enough of the background filled in first, I could explain the math patterns clearly enough that you would come to see them.” I don’t think this would be beyond your grasp.

      Steve Schwartzman

      January 29, 2018 at 10:21 PM

      • ….maybe I could follow the explanation, but I am amazed that anybody ever thought of this, or knew to look closely enough to determine or even predict a pattern!


        January 29, 2018 at 10:31 PM

        • Then here’s to the mathematicians of the world; we profit from their quest for patterns.
          And here’s to the good teachers of the world, who expose children to these things from an early age.

          Steve Schwartzman

          January 29, 2018 at 10:41 PM

  12. Maths was never my forte .. love your second image Steve, delicious colours 🙂


    January 31, 2018 at 12:15 PM

    • You’re not alone, Julie. Few of the people who come here for nature photography have shown an interest in math—and I’m not surprised.

      No one else but you has mentioned the second sunset picture, so I’m glad to hear you like it.

      Steve Schwartzman

      January 31, 2018 at 12:38 PM

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