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Monday, December 23, 2013

In the Mobius Strip of Life, A Little Twist is Needed


     This is Math Month with 14 brilliant kindergarteners. We've gone from Fibonacci Numbers to Golden Spirals to Mobius Strips. The kids watched the following jaw-dropping, 3-minute video linking a Mobius Strip to the music of J. S. Bach:

     They watched the Jos Leys video transfixed. I heard more than one soft "Whoa!"

      The kids then drew on and cut their pre-made Mobius strips in half length-wise to learn more about the amazing looping properties of the Mobius strip. Then I created one more extra-long Mobius strip, expecting to cut one-third of the way into the strip creating one long loop intersecting with a shorter loop.

     I got two disconnected loops of green construction paper.

     Hysterical laughter ensued as Ms. Steph had forgotten to twist the loop. 

     It was GREAT!

     It looped perfectly into a discussion of scientists making mistakes and to the wonderful book I am reading (thanks, Jan!): Brilliant Blunders by Mario Livio (2013).




      In the preface, Livio starts by noting his standard answer to what his book was about: "It is about blunders, and it is not an autobiography." So far, it is a finely-woven quintuple helix of the biggest mistakes of Charles Darwin, Albert Einstein, Fred Hoyle, William Thomson (Lord Kelvin) and Fred Hoyle. Rosalind Franklin (see October 29, 2013 Partial Ellipsis of the Sun blog post here:  Rosalind Franklin: DNA Photograph 51) and her contribution to the discovery of the DNA double helix (not triple helix as Pauling hypothesized) are discussed in great detail. There are photos, letters, journal notes, and diagrams detailing the errors of these scientists. One reviewer wrote, "Even Einstein was no Einstein sometimes."  

      The word "blunder" according to Merriam Webster is from the  Middle English blundren, probably of Scandinavian origin; akin to Old Norse blunda to shut one's eyes, doze, Norwegian dialect blundra.Here's hoping that you will open your eyes to the beauty of these holiday Mobius strips:

and to this very creative person, Jos Baldwin, who blended (and surely blundered along the way) to this creation of 36 Mobius strips creating a Chambered Nautilus:




There are more photographs of this Mobius Nautilus here: Mobius Nautilus

      My world is looping back on itself as I remember the thrill of reading a first-year (ok, we called it freshman) English book that connected with my Geology 101 textbook. A chambered nautilus made of Mobius strips? W h o a . . .

     Wishing you all a good holiday (whichever you celebrate--or not) and winter filled with colossal mistakes, many children, and much laughter. . .and, perhaps, a Mobius tree:



 I look forward to our loopy conversation. (Sorry about the lack of an umlaut over the "o" in Mobius; I know you'll pronounce it Mer-bius not Moh-bius. . .)

Posting on a Monday this week, back to Tuesday next week,
Word Woman (Scientific Steph)



  1. I would enjoy hearing about your colossal blunders and minor boo-boos!

  2. You could store your Möbius strip in a Klein bottle, its 3-dimentional equivalent, more or less. Dissect a Klein bottle to get 2 mirror-image Möbius strips.

    In the words of mathematician Leo Moser:

    A mathematician named Klein
    Thought the Möbius band was divine.
    Said he: "If you glue
    The edges of two,
    You'll get a weird bottle like mine."

    Happy holidays!

    1. And then there's the Aperiodic Penrose Torus at Smith:

      (if you are so inkleined ;-)).

      Happy holidays to you, too, Jan! Thanks for checking in every seven days. . .


    2. SS,
      Great blog this week. That Mobius Nautilus is a keeper. Thanks, jan, for the Leo Moser limerick. What a wonderful blending of words and science!

      As a child I looked forward each month to Martin Gardiner’s columns in Scientific American. Recreational mathematics is one of life’s great joys. Those who don’t agree just haven’t been exposed to it yet (Keep doing your part with those kindergartners! BTW, I have committed the same tape-the-strip-sans-the-twist blunder you committed. My audience was puzzled, but when I finally did it right the effect was enhanced because of the contrast with the mundane they had just witnessed.)

      As for other blunders/booboos, I could write a book. Mine would be the autobiography Mr. Livio did not write. My title: “A Busload of Blunders,” or “Blunderbuss,” for short, befitting one who is prone to shooting himself in the foot that is in his mouth. Brilliant blunders? No. Glaring errors? Yes. And a Jellystone Parkful of minor Booboos. My colossal but unbrilliant blunders are painful to relate, so I will disclose instead a booboo:

      Twenty years ago, my mother, Helen, then 86, was arthritic and homebound. My brother and sister, who lived in the same Wisconsin city as she, would routinely look in on her. I often drove from Minnesota to visit her on weekends because I, of course, was her favorite child.

      Although I am only putterer around the kitchen, I would cook comfort food for mom, the same simple dishes she made for us as kids -- corn chowder, tomato bisque soup, cheese toastwiches… She loved desserts, pumpkin pie in particular. But for me, pies were not a piece of cake to make, nor, for that matter, were they easy as pie. So I bought a recipe book from the Norske Nook, a regional west-central Wisconsin restaurant chain known for their pastries. The recipe I was interested in, written in a down-home style, read in part, “You can never really put enough salt in a pumpkin pie.” Hmmm, I thought. Where’s that economy box of salt?

      After the pie baked and cooled, I hoisted a generous steaming slab from the pie tin onto a plate. I paused Mom’s VHS movie, “African Queen,” and placed my fruit-of-the-gourd creation onto a tray next to her recliner. “Joey, this is a real treat.” she said, her dimpled face expressing a blend of gratitude and anticipation. With fork clenched in fist, she lopped off a triangle of pie, fumbled it past her lips and into her mouth, and chewed it the best she could with the teeth she still had. As she ruminated I intently studied her face, seeking feedback.
      “Is it OK, Mom?”
      “Delicious,” she said, a little garbled, like she still might be savoring a remnant of that first golden morsel, letting it linger lingually before swallowing. “I think I’ll eat it while I watch my show,” she said punctuating her slightly slurred words with a muffled choke and throat-clearing. I unpaused her movie and went about my business of being the favorite son.

      About a half-hour later I checked back in on my maternal gourmand. On the TV, Bogie and Kate were grappling with leeches. My mother, fork still in hand, was snoring through that unpleasantness, probably with visions of pumpkin pie dancing in her head. As I reached to bus her pie plate I was puzzled to see slab still intact, save for the missing triangle at its tip. Hmmm. With my forefinger I scooped a dollop of the filling and touched it to my tongue. It went no further. For there, kissing my taste buds ever so fleetingly, was a pure distillation of all the water in the Seven Seas (plus one Great Salt Lake)!

      Booboo number 1: I might have put a “pinch” too much salt into the mix. Booboo number 2: I did no taste-testing during the entire pie-making process. Boob number 3 (that’s me): I served my sainted mother a slice of pie that would have served well as a salt lick for livestock or deer.

      Have a joyful holiday season, and may the new year be blessed with just the right mixture of salt and pumpkin.


  3. Hi Lego,

    I enjoyed your very readable and enchanting story about Helen and the pumpkin pie. She truly was a deer (:-)) to say it was delicious...and you were truly a dear to make it for her.

    Merry Christmas!


  4. Speaking of deer, I thought this an appropriate Christmas card for this group:

  5. Speaking of deer, I thought this an appropriate Christmas card for this group:

    1. Jan, kinda funny/sad (funad?). I didn't know the Limbo was a Trinidad and Tobago dance performed at wakes.

      Or that the state of Wyoming was named for the Wyoming Valley in Pennsylvania (memorialized in the 1809 poem Gertrude of Wyoming.