Mobius: where time becomes a loop


Mobius tattoo

I have been thinking about Mobius Strips lately.   These tricky little mathematical shapes are described in Wikipedia as:


The Möbius strip or Möbius band (UK /ˈmɜrbiəs/ or US /ˈmoʊbiəs/; German: [ˈmøːbi̯ʊs]), also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.


(Hmmmmm.  So it really could have been called “The Listing Strip” and then we all wouldn’t have to feel bad about not having umlauts on our keyboards.)


But a written description can’t possibly give you the full strip experience, so those of you who have never actually made one yourself, here is a video that will have you running for a piece of paper, tape and scissors (no, please don’t run with the scissors!)  so you can prove to yourself that there really is an object that has only one side…and dazzle others who may be uninitiated.


I first encountered this phenomenon, when I was in high school although Mobius Strips were not in any curriculum of my formal education at Earl L. Vandermeulen High School in Port Jefferson, New York.  No, it was when I was doing a little part time work for a famous sociologist, Dr. Benjamin Nelson, who at the time was on the faculty of the New York State University at Stony Brook.  My mother, Rose, worked for him in his home office as his secretary.  She was soon joined by her very dear friend Elsie in support of Dr. Nelson’s accounting, and over the years I, my sister Barbara, and my soul-siblings, twins Carol and Jim Winkler, who are Elsie’s children, all found ourselves in the Nelson home office, editing, organizing, filing, and having lunch with Dr. Nelson.  He was a fascinating person, professor, social science researcher, author and mentor.  I still clearly remember him telling me one day over dessert that there was blood in my tea which was pretty horrifying to my naïve self as he drew the longitudinal connection between my teabag and tyranny in developing countries. So, then there was an article he asked me to edit (by this time I might actually have been in college at Stony Brook,) for the Journal of  the American Psychiatric Association called ”The Onion and the Mobius Strip” (I am sure they had an umlaut.)  I have realized that there are limits to our searches on the Internet because although I have found many other journal articles and books by and about Dr. Nelson, I have yet to mine this one.  I do believe the article was about two conflicting models of personality studies, but it has been a pretty long time.  I, however, clearly remember looking up Mobius Strip in his (you won’t believe this but it is true) Encyclopedia Britannica.  (Just to give you a time reference on all of this Dr. Nelson died in 1977, in his sleep on a train in Italy.)


So why have I particularly had Mobius Strips on my mind?  It’s the US government shut down.  Here’s how that is going:


(If you want to read the most current details, here’s an article in Forbes )

In short, because the Democrats support President Obama’s Affordable Care Act, the Republicans are refusing to approve the United States budget which expired on September 30.  And the Democrats won’t negotiate. Since the budget isn’t approved, federal employees who are considered “non-essential” are out of work and some of them actually would be providing health care but can’t because the agencies they work for are shut down.  Here are a couple of examples from an article in the Washington Post


Health: The National Institutes of Health will stop accepting new patients for clinical research and stop answering hotline calls about medical questions. The Centers for Disease Control and Prevention will stop its seasonal flu program and have a “significantly reduced capacity to respond to outbreak investigations.”


Women, Infants, and Children: The Department of Agriculture will cut off support for the Women, Infants and Children program, which helps pregnant women and new moms buy healthy food and provides nutritional information and health care referrals. The program reaches some 9 million Americans. The USDA estimates most states have funds to continue their programs for “a week or so,” but they’ll “likely be unable to sustain operations for a longer period” — emergency funds may run out by the end of October.


So here’s the Mobius loop of the Affordable Care Act based on people needing health care looping back on itself to people needing health care while our government fights with itself.


I am aware of another more local Mobius Strip health loop.  Flu season is almost upon us and the New York State Department of Health has mandated that all health care providers receive the flu vaccine (or wear a mask in the presence of patients and other health providers.)  There are some health providers, the lowest paid who provide direct care but don’t have health benefits themselves from their employers.  Their employers will not pay for the vaccinations so they have to pay for the vaccine themselves.  If they can’t afford it they will be removed from their jobs and then they really won’t be able to afford the vaccinations and won’t be able to go back to work…well at least not until flu season is over.  And they may very well get sick and require the health care they can’t afford because they are out of work.  Dr.  Mobius, I presume.


And here is a more personal health Mobius.  A friend of mine works for a health care company.  She is required to work long days often into the evenings and on many weekends.  She has been very stressed and not feeling well and so has been seeing her doctor and a therapist who both have advised her to work shorter  (normal) hours and have some time for her health care, recreation and relaxation.  She however, can’t do this because of the requirements of her job.  And she often misses the therapy because she has to stay late at work, making her more stressed.  Here’s the Mobius one sided one edge shape: the health care company she works for is also her health insurance provider paying for her health care.  So, it’s a one-sided shape, the deterioration of her health is being caused and paid for by the same company!  Loop de loop.


None of this should be so complicated, convoluted and twisty.  In spite of all of this the health exchanges sites are so busy with people registering and buying affordable health care insurance that there were some crashes the first day.  There is a clear straight line between health care and the health and well being of individuals, communities, populations, the people of the United States.  The Affordable Care Act is a pretty simple straight line.


Getting back to the government shut down, a twist in the fabric of space where time becomes a loop.  It does seem that this isn’t quite a Mobius Strip, after all there are two sides, the Democrats and the Republicans.  But actually as the strip loops around, until these two sides get it together, there really is only one side to this situation:  everyone is losing.


If you need some cheering up after that, watch this and have a healthy, happy heart:


Beautiful to the Bone

The fine black line that diagonaled through the bright white shaft against the dark background was the reason we were looking at this picture.  It was cause for concern, for necessary interventions, for my fear.  And yet my attention was also drawn to the lower area of this study in black and white where delicate lines and sensual little spheres connected, designed like an intricate and elegant piece of jewelry.   These were the bones of my right ankle and foot.

I soon came to have a great appreciation for my ankles, the right one in particular.  I have of course enjoyed them and they have held me up in ever so many of my endeavors:  running on my pier out into the Hudson River; climbing along a precipice in the foothills of the Himalayas; standing in Proud Warrior; kicking away the blue and green and aqua of oceans and rivers and swimming pools; holding me steady as I bounced a baby (mine or anyone’s else’s I could get my hands on;)  dancing and leaping into a silly pirouette; rocking forward on a tennis serve, sloshing through the Mumbai Monsoon; supporting me as I sauté-ed and fried and roasted and peeled and mashed and whipped in my kitchen.

But I never learned to really appreciate my ankles until my right foot slipped from a wet stair onto a wet tiled floor and slid sharply (much too sharply) to the left on a wet San Diego morning.  Snap.  Alas, the ominous black diagonal line running through my lovely fibula poised above the delicate bones of my foot.  Despite the diagnosis, the picture of my ankle and foot was quite beautiful.  Perhaps if I ever decided to take online dating seriously I would post, instead of the requisite head shot, this foot shot with the caption, “Not just another pretty face.”

So while I have certainly enjoyed the structure and support of my bones, I haven’t really thought about them all that much, as is probably true of most of us.  Sure, I am pretty compulsive about getting my calcium; cheese is after all one of the great pleasures of life.  And then there is all of that low fat yogurt:  plain, Greek, frozen, and in smoothies.  Ice cream.  Zero Percent Over the Moon Milk (with Oreos, of course.)  Pizza with fresh mozzarella and anchovies.    I haven’t exactly indulged in all of these calcium rich foods for purely medicinal purposes.  I do also love all those green leafies: broccoli, Brussells sprouts (an odd early acquired taste during my childhood,)  spinach (preferably creamed. ) I have done exceedingly well on my bone density tests with very little advance study.

Now I think about my bones all the time; now that the thin black line has resulted in my right ankle being permanently adorned with some titanium.

I have also been thinking about why we don’t typically think too much about our bones.  In fact bones actually get kind of a bad rap.  Halloween: scary skeletons.  One annually adorns my front door kept company by the Jack O’Lanterns.  Pirate ships:  Skull and Cross Bones.  The dangling marionette of bones in a medical lab in a science fiction thriller.  Malicious King Richard found under a parking lot.  Creepy, but bones intact.  The pejorative terms:  bag of bones, bad to the bone,  bare bones and bone head.

I looked through a few magazines to do some research on the fashion value of bones.  More seemed age appropriate for me.  Here are the survey results of attention to body parts  beautiful as depicted in advertisements:

Skin:  18

Hair: 8

Eye lashes: 4

Lips:  3

Nails (fingers and toes):  2

Bones:  0 (except for a minor mention among heart, joints, muscles, digestive tract, immune system in an ad for Shiff vitamins.  Not very glamorous. )

Of course there were lots of ads for beautiful clothes, and shoes (I long to wear two matching shoes; high heels are yet a dream for the future…although mostly I would love to be wearing my tennis sneakers on the courts.)

Where would those clear unwrinkled skins, exotic eye lashes, lavish hair styles, luscious lips, and sassy finger and toe nails be without the beautiful bones holding everything up.

I was thinking that maybe to attain beautiful bones it just doesn’t take a lot of chemical research (certainly not like what it takes to have those exotic eye lashes.)

Here’s what the NIH has to say:

Get enough calcium and vitamin D in your diet at every age.

Be physically active.

Reduce hazards in your home that could increase your risk of falling and breaking bones.

Talk with your doctor about medicines you are taking that could weaken bones, like medicine for thyroid problems or arthritis. Also talk about ways to take medicines that are safe for bones. Discuss ways to protect bones while treating other problems.

Maintain a healthy weight. Being underweight raises the risk of fracture and bone loss.  (hmmmm here’s something those fashion models might need to know.)

Don’t smoke. Smoking can reduce bone mass and increase your risks for a broken bone.

Limit alcohol use. Heavy alcohol use reduces bone mass and increases your risk for broken bones.

Surgeon General’s Report on Bones

I thought it was interesting that it didn’t say anything about don’t do crazy stuff like skiing, playing tennis, skate boarding, bike riding,  bungie jumping, mountain climbing, running Marathons. Take it from me, done a lot of those things and never broke a bone.

Most of these recommendations are pretty easy for us here in the United States, but may be more difficult in developing countries.  In some countries dairy products are either expensive, difficult to acquire or in places like India and Nepal not a dietary desire.  When I was planning my trip to Nepal, I asked the Director at the US Embassy what he might like for me to bring him from home.  He didn’t hesitate for a nano second:  “Cheese.  Please bring me cheese. “ And it was true there was no cheese in Nepal.  There are other ways of getting calcium.  It is in those green leafy vegetables, nuts, herbs, soy and seeds (including, yes, Amaranth!!!!!)  But 4 cups a day of that zero fat milk will give you 100% vitamin D, 120% of your calcium, at only 360 calories.

So get your exercise, don’t smoke or drink too much, definitely don’t be underweight, be careful at home, and get your calcium and vitamin D.

But here is something a little tricky and it’s about the vitamin D.  Would you ever think that being out in the sun without sunscreen and eating sausages would be good for you.  Seems a little counter intuitive.  And yet one of the most important ways we get our vitamin D is why it is called the “sunshine vitamin.”   Yes, we get it from sunshine.  It’s also in some things we might find kind of odd:  Cod Liver Oil (ick!:) Fish (yum;) Fortified Cereals (think Cocoa Krispies;) Oysters (sexy;) Fortified Soy (meh!) Eggs (: ) Mushrooms (exotic;) Fortified Dairy (there’s that milk again:) and!!!!!! Salami, Ham, Sausage (get down and make yourself a good hoagie!)

As we know, sunshine is much maligned and for some good reasons like skin cancer.  But we do need some.  An editorial in the Indian Journal of Medical Research by Sarath Gopalan and Prema Ramachanandran (March, 2008) states:

Adequate exposure to sunlight can provide

sufficient vitamin D to children and adults. It is therefore

imperative that nutrition and health education to

improve exposure to sun gets due attention. These

efforts will also result in increase in physical activity

(play in schools and walks for adults) which will reduce

risk of overnutrition and associated risk of non

communicable diseases and improve muscle and bone


The article also notes that the preference for light skin in Indian and Asian cultures can keep people particularly women out of the sun, increasing the possibility of vitamin D deficiency.

If you want to read the whole (very interesting) article here’s the link:

So these are just some ideas about bone health.  Mostly, we all need to think about our bones more, love them, honor them, respect them.  I have been assured that my right ankle will once again be strong.  I will walk (without crutches,) swim, run, dance, balance, pick up and cradle babies, wrestle with my grandchildren.  I will climb mountains again.

And for this I have many people to thank:  My daughter Kierra who rescued me from Newark Airport and the hospital and nurtured, fed me and kept me smiling; my daughter Alex who will stay with me next week and get me off to my new job, I am sure with her typical sweetness; my grandchildren Nico and Sonoma who love me even in a cast; daughter Kristin who has cheered from the sidelines; Lauren who was able to make me laugh even when I was about to be wheeled into the hospital for surgery; Julie who kept me calm and brought me sushi the night before; Pat who is adopting me for (hopefully) almost the last of my days on crutches; Deb, Purna, Carol, Rochelle, Dan, Jon, Terry who have kept me company; Enrique who is always an Epic; and San Diego Steve who was there.

I am thankful to the health professionals at Englewood Medical Center and Englewood Orthopedics who are the finest and kindest I have ever known in any health facilities; Dr. Perlman who put me to sleep (and made sure I woke up;) and Dr. Adam Becker of Englewood Orthopedics who expertly put my lovely fibula back together (and called me “Princess” when I was wearing a shower cap, hospital gown and my glasses.  Sometimes it’s the little things that get us through.)

To all of the above, who have truly healed me, bones and soul, and to all of you, I raise a glass of Zero Percent Over the Moon Milk in a toast:

“To Our Beautiful Bones.”