Playing with Dimensions

A photograph of a green paper Möbius strip. Da...

Sometimes the simplest things are the best.

I’ve long been fascinated by the Möbius strip.  It was one of those synchronous discoveries – ‘found’, if that’s the right word, in the same year (1858), in the same country (Germany) by two mathematicians working completely independently of one another.

Johann Benedict Listing.

Johann Benedict Listing. (Photo credit: Wikipedia)

That’s strange to begin with, isn’t it?  Yet ideas often emerge spontaneously in different places like that.  One of its discoverers was August Möbius and the other Johann Listing.  So it might well have been called the Listing Loop (and perhaps it is in some alternate universe).

In case you’ve never taken the trouble to examine one, when you start with a long, narrow strip of paper, and lay it flat on a table, it has two dimensions – length and width.  The rectangle has four sides and one visible face.  There is, obviously, a second face underneath which can’t be seen until you lift it up.

If you pick the paper strip up and stick the two short ends together, forming a simple loop, and you have a 3D shape.  The new shape – a shallow cylinder – has two faces and two sides.  (There is a point to all this, bear with me.)

However – I love this bit – if you were to twist the strip before sticking the ends together, you would end up with the shape shown here:

It's a rather wonderful infinity symbol of a shape.  How many dimensions does it now have?  Still three?  It's certainly more complex than the loop, yet if you watch the animated ants there, you'll notice that the Mobius loop has only ONE side and ONE face.  Head over here to watch a short, rather cheery demonstration or (if you're so inclined) try making one yourself, then drawing a line down the centre, cutting it in half lengthways and so forth.

The point (finally!) is, the more strange and complex the shape we create, the simpler it’s geometry becomes.  Maybe it’s approaching Unity….

 

This is a short summary of the material on the Möbius strip in LIFE: A Players Guide.

 

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7 comments on “Playing with Dimensions

  1. Hi Jan,

    My life seems to consist of mundane domesticities while your mind is beyond the clouds! While I am sweeping up kitty litter you are thinking great & creative thoughts. Do I envy you? Well, perhaps in some respects, but alas, my mind is more earthbound. Hopefully I have other qualities which make up for the lack of scientific knowledge and curiosity.

    Right now I would love to be making some ceramic objects, but must settle down and start my tax returns, which I have left until now-procrastinating. I am very lazy in many ways, preferring to read over doing housework or paperwork, but the time has come (altho I have already applied for an extension). Taxes are more complicated for me this year with the condo expenses and small income.

    Also, I am quite depressed having just lost another friend to Cancer, and a very old & dear friend with the same kind(ovarian-stage3) is leaving today for a clinic in Germany with the hope they can cure her, as she has run out of treatment options here. We have all been contributing prayers, love and $. She is only 60 and deserves more time.

    I have to remind myself that every day is a good one when I can wake up and get up!

    Hope that you are well and will have a marvelous birthday.

    All Best Wishes, Wendy

    “A smile can be contagious for miles~ share your smile Today!”

    • Good to hear from you Wendy. Believe me, I have tax returns to file too. Creative thoughts have to squeeze in amongst the mundane stuff.
      So sorry to hear about your friends. Hard as it may be to understand, I believe that each of us leaves physical life when we have chosen, at soul level, to do so. This can so often feel wrong to the people left to grieve, though.
      Yes, all those days when we can get up and wake up are good… but I’m certain there are wonderful experiences beyond our days here.
      Thanks for the birthday wishes!
      Jan xx

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