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The best most amazingly wonderful boss I ever had was a mathematics professor named Ed. Once he tore off a strip of paper, twisted it and then joined the ends to show me what a mobius (or moebius, or moëbius) strip is. In case you don't know, as I didn't, it's a surface with only one side. That's right, if you run your finger along any surface, you'll see that there is only one. It is one of those deliciously annoying impossibilities that tells me I can't be a scientist. I just can't get my head around it, and that bothers me. If I couldn't get my head around it and it didn't bother me, I might be scientist material. (You scientists are going to correct me now.) A mobius strip is also a non-orientable surface. If you want to understand that physical concept, try this. "Orientability is a mathematical property of surfaces in Euclidian space measuring whether or not it is possible to make a consistent choice of surface normal vector at every point dot dot dot"
Whatever. So this is a mobius strip bangle.
I have this friend, a person in authority and power. This is her bracelet, which I admired on her wrist. One day many months later, she publicly scolded me very vehemently over something I thought trivial, and I didn't deserve it. After that I had to seriously consider whether I wanted her to remain in my life as a friend. It took several days and a mini vision quest of sorts to really search out my heart about her and what had happened. I decided I did want her in my life, in spite of her sometimes abrasive ways. There are many things I love about her and our relationship, so I talked with her about it, we patched things up better than before, and a few months later she came for a gathering at my house on my birthday. She handed me a gift box, and when I opened it there was the bracelet. The significance of its twisting and single surface touched me as a symbol of our friendship, one that was pliable enough to go on after a rift that almost tore us apart.
I love it so much that if a fire broke out I would grab it with the photo albums, camera and the external hard drive with all my photographs - after making sure Don is out ok.
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68 comments:
It's a really lovely piece.
There are certainly a lot of things we have some great difficulties to understand, some that we (I) will never understand… , not even referring to the extreme questions of what was before the beginning, what will be after the end, what is beyond the last limit...
What we MUST learn is to keep good friends!
I've unintentionally knit a few mobiuses in my time...tricking thing knitting in the round. What I love best about your bracelet is the simplicity of it.
Also in the last few years I've gotten to work with some scientists. Even though I consider myself intelligent these people utter words that I've never heard before and totally understand concepts that I struggle with.
Doesn't the twist in the bracelet feel irritating?
Oh, that's right, it only has one surface, so you wouldn't feel the twist at all, dot for dot.
Great explanation, Ruth! I understood every word.
;->
It is wonderful that your friendship was strong enough to stand the test! Your friend is a keeper if she put enough thought into such a beautiful, yet simple piece of jewelry. Congratulations!
wonderful post about friendship....the older our friendships get, the easier to separate the wheat from the chaff...great jewelry helps too...
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Beautiful bracelet - & I love it's symbolism. I'm glad you patched things up with your friend. I would probably not have dumped the friend, but my hurt would have festered & damaged the friendship. Sometimes (most times!) it's better to just get things out where they can be examined.
True friendship takes the bad with the good. Lovely bracelet. good that you were able to talk to her about it.
My eyes started glazing over when I got to Euclidian space - remembrances of past math nightmares!
The bracelet is gorgeous. You Lionesses are very forgiving and loving - you are a good friend to your friend and the bracelet shows that she knows it.
Hi Ruth, It seems that the older i get the more difficult it is to make new friends. I count you as a new friend:)
One of my friends is able to make new friends everywhere he goes. He is always getting involved in new relationships but keeps his old friends close too. His get togethers are fun simply because of the great mix of people.
As for me I love my friends and hold them close to my heart. Misunderstandings are few but I am with you, take time to think and weigh the importance of that person in your life,and have a converstion.
The bangle was a wonderful and symbolic gift. A treasure as are our friendships and human connections.
Beautiful, Ruth! What an apt symbol for a strong friendship--and a lovely bangle, too! Thank you.
Hi Ruth,
Now I understand your surprise re:when is a line a shape! Amazing coincidence.
Your post has a deeper meaning, however...how our relationships can twist and bend, a remarkably, survive.
Okay, I got a migraine after reading that first part. Do you have any Excedrin?
The second part, however, was very lovely and a testament to the strength of the bonds of friendship. You are like an orb-weaver when you write, and I love orb-weavers.
You are like me I always believe in going to the source and saying 'what exactly happened' and fixing it up or letting it go, but not until I at least have tried.
Beautiful bracelet.
Love Renee xoxo
That is a beautiful bracelet, and great that it means more than just a bracelet to you :)
The works of M. C. Escher always amazed me.
yeah, right, whatever. beautiful bracelet. you could save time (in a fire scenario) by wearing the bracelet always. then you could also grab your camera...
word verification is 'airever'.
Ed's last name isn't Palmer is it? Because that would make our world WAY too small!
This is beautiful on so many levels -- certainly the tactile element of the bracelet you captured in the photos and the science (which blows my mind). But mostly because it deals head on with something I think so many of us have encountered at one time or another -- and the choices we have to make with relationships. I'm glad you were able to work it though and remain friends. The fact that you would take this bracelet with your photo albums is such testament to that friendship.
Gee Monee, I don't understand any of that. My husband is always trying to explain quantum physic principals to me and my eyes cross and roll back in my head.
oh I love this Ruth... I love the story... both sides.. I love the pictures.... I love the actual gorgeous bracelet... I love the whole entire wonderful thing!!!!!
Thank you, Snappy.
I'm with you, Peter. Now that I'm on the other side of 50 (53) I'm losing interest in understanding certain things. But human relationships interest me a lot.
NJ, you made me smile, knitting mobiuses. And what you said about scientists? My nephew is brilliant, works in Artificial Intelligence. But he says he is not bright enough to be a real AI scientist - he just assists them in their work. Yikes.
Heh, Barry. It may have only one surface, but yes! Sometimes that twist digs into my wrist a little, especially when I'm slipping it on. I still like it, the weight of it, and it doesn't annoy enough to avoid it. Maybe a good reminder of my friendship with its former owner.
Now that you've mastered the Mobius, you're ready for a Klein bottle!
http://www.kleinbottle.com/
I love mobius strips! MC Escher did some mobius strip illustrations with ants endlessly marching along its side:
http://www.worldofescher.com/gallery/A29L.html
I used to teach mobius strips in little math groups at my kids' elementary school. When they didn't believe that it only has one side, I would ask them to draw a long line along its surface and then they quickly became believers.
I worked with a man who had a mobius wedding ring - he liked that it had no beginning and no end.
Beautiful. Simple yet complex.
I also had a friend who was unfair to me. Our friendship lasted for years though as it had more pros than cons.
A twist in the story Ruth.
If the foundation is weak the building would collapse with a gentle push. Long friendship is weather proof, earthquake proof, tsunami proof, nothing can shake it. But there is a thing called third party damage. Most of the friendships are damaged by a third party. i have this bad habit of not clarifying things, i tend to keep quiet and withdraw.
Your bracelet is beautiful, and the relationship moreso....
But you've done it to me. I'm sitting here with scissors, tape and strips of paper cut from the WalMart ads, trying to figure this out. Oh, and the Wiki page, too.
There just are certain things I CANNOT get my mind around. But I did love that someone's written a story about a subway system built like a Mobius strip, and that the subway cars kept disappearing.
OK... now... back to my puzzlement. How can it have only one surface when there obviously are two sides? (An hour on this, can you believe? Sigh.)
CottageGirl, I find that it takes a lot of getting into someone else's shoes to try to understand them.
Jean, I was a loner most of my life. I haven't been a very good friend. I didn't know how. I learned something with this friend - about myself.
Dana, it's a good thing we have a lifetime to learn some things. If I were the same girl I was 20 years ago, I probably wouldn't have taken this in hand as I did. I was on a spiritual journey at the time, and the 3-hour vision quest was just what I needed to think and feel it through.
Ellen, agreed for the most part, but even though it would have been painful, I could have decided to part ways with her. There are times that is necessary, when the bad is just too painful for the other person.
Delphyne, math is nothing but ache and moan for me. I got a D in geometry, and I have no idea how I ever got through Algebra II. Thankfully math was not a university requirement when I got my degree, or I would have had a stack of dummies books around me and maybe I could have passed with a 1.0. I feel sorry for my English students who are not good at math now and struggle and have to finish it to get their degree.
Cathy, I am going the opposite way and making more friends as I get older. I count you as a friend too, and I find these friendships that are not face to face, that are placed in typed words and images to be fulfilling a need I had but didn't know. There is still nothing like sitting with a friend over coffee and letting the conversation dance. This lacks that. But I like what I have here, although at times I am daunted by it too.
Thank you, DS. I do like it when I have little items that represent a friend - especially if they are far away. They make me feel connected.
Patricia, the work your students are producing is quite inspiring. We can give anything meaning, I suppose. It's all in our minds.
Susie - I am so sorry about the headache. Yes, I have some Excedrin PM - took it the other night so I could sleep. Haven't been sleeping well.
I had to look up orb weaver, wanted to be sure it was a compliment. :) What an honor to be compared to those talented spiders! Thank you.
Renee, I'm glad to hear that. It isn't good to let anything stew inside, best to be free. Love to you today.
Babs, wow, I had to look up Escher's mobius images - they are breathtaking. Thank you so much for that nudge.
Hi, Violetski, you make a good point. I could never wear the mobius to bed though, it is a little heavy, and I'm afraid I would wake up in pain from it somewhere.
Jeanie, nope not Palmer.
My friend Ed loved art too, and music. I think he found mathematics beautiful in those ways, as well as scientifically. He was a big opera buff - used to be married to an opera singer.
Thanks for the big smile, California Girl. It took me a couple seconds to understand what Gee Monee was. Had to say it out loud. Who said Jiminy Cricket! - ?
So, google nerd that I am, I looked it up. It was first an expletive for "Jesus Christ!". I never knew that Jiminy Cricket in Pinocchio is based on the Talking Cricket from the book Pinocchio by Carlo Collodi. I love blogging.
Now I ask you, Gwen, have you ever designed jewelry with the mobius strip?
Loring, next time I need "an inferior mousetrap" I will order one! Ha! Those are WEIRD. And I would not exactly say mastered.
Dutchbaby, thanks to you and Babs I saw the Escher mobiuses. Oh I think it's wonderful you showed that to elementary students. I told Don about it to see if he might like to do that in his 3rd grade class.
I wonder how a mobius ring would feel, that turn might poke a bit. But it is good symbolism of an eternal bond.
Annie, sometimes there is greater freedom and openness after a row and good head to head conversation about it.
No I never have Ruth, but your presentation is certainly inspirational...
Have a great weekend dear Ruth.
xoxo
Next steps, Klein's bottle, Boy's surface... and some Lacan's lessons.
A powerful post Ruth. I'm not mathematical in the least but I really got it. A touching symbol of your friendship. Beautiful bracelet.
rauf, I never liked it when Lesley brought two friends to spend the night. A group of three was always a problem. Two would side against one. I felt this growing up too. I was usually the third one - odd, outside. So I became a loner. I did not know how to be a friend. Actually I have only started learning about friendship in the last 10 years.
Oh shoot, Linda, I feel for you. The story sounds ingenious though! I guess a mobius strip is like the Twilight Zone for those subway cars. I guess science fiction is when science goes bad.
Gwen, your designs are beautiful and full of life - in jewelry and in your home.
Renee, thank you, I am looking forward to doing almost nothing productive.
Daniel, oh dear, now I have two more to learn after Loring told me about Klein's bottles.
Sue, I'm lucky a real person showed this to me first. But it didn't really help me really appreciate how it can be.
Ruth,
What a heart-warming story of friendship. It's not easy to share such personal experience, but of course, your story ends with a happy ending, and I'm glad. That is one beautiful bracelet. I admit I haven't heard of the mobius strip. It makes me think of M.C. Escher's artwork... most intriguing!
Arti - you're the third person to mention Escher. Thank you, I had not seen those mobiuses of his before this post.
Love bracelet and lovely sentiment.
Dear Ruth
I admire you for taking the time and effort to work through your feelings for a friend who hurt you...I'm not sure that I would have been able to do that and I would have lost a friend...and never received such a beautiful token of friendship...
I love how you have compared relationships to this intriguing, never-ending, non-orientable strip...
...as for math...all my life I have felt plagued with the fact that I have done best at math and science - which I don't care for much...and have done poorly in literature and the arts - which are my first loves...a tormented soul!
Thanks, Bella.
Oliag - your response to math is similar to many of my advisees - English majors who do well at math but don't like it. The ones who have both sides of their brains working that way make me quite jealous. I am unlike you and have been good in literature (sort of), and abysmal in math (or as the Brits say, maths, which makes sense).
The thing is, Ruth, we're not dumb! So why can't we figure this out!!! HA! I have sat here tracing my finger around this bracelet over and over again. It's mystifying! And I love the story that goes with it!
Hehe, Boots, I can see you trying. :)
I'm an artist, and avoided math and science in college, so have only my high school level with me at age 51. Can you ask your math whiz people if the moebius strip is explained, mathematically or geometrically, simply by drawing two parallel lines on a tubular form, twisting in the same way as a flat strip, and connecting the opposite lines' endpoints into a donut form?
R. L. Croft
croft58@gmail.com
www.rlcroft.com
Robin -
Thank you for your interest in the mobius strip on my blog post. I'm afraid I don't know anyone who knows the answer. I hope you might connect with someone who does, or can find it online.
Your gallery is impressive. All the best to you in your art!
Ruth
i make mobius bracelets if anyones interested! lovely story.
www.anniecracknell.com
Beautiful your work is, Annie!
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