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Split Möbius

  • created 2008
  • granite
  • 24” H x 12”W x 12”D (61cmH x 30cmW x 30cmD)
  • collection of Dr. D. Thomson, Saskatoon, SK, Canada

Sculptor Michael Binkley received a request to create a complex abstract sculpture for Dr. Thomson’s garden on the Canadian prairies. The environment of the city of Saskatoon, Saskatchewan is very cold in winter and hot in summer and this is relevant to the proper type of stone for an exterior sculpture. Although Dr. Thomson liked the look of Italian Carrara marble, it just was not the best stone for the project as marble will deteriorate in these extreme elements. Binkley recommended using a light grey granite, as this silica based stone is almost impervious to the elements and with the proper finish, it looks almost white in bright sunshine. Dr. Thomson acquiesced and Binkley began work.


This original fine art granite abstract sculpture is a möbius that has been cut in half. It is best to describe a möbius first:


A möbius is a complex conundrum, being a three dimensional depiction of a two dimensional object, and therefore essentially cannot exist in our world of three axis space. It is a form consisting of a strip of material that is closed into a loop with one half a twist in it. It was invented by a German mathematician, A. F. Möbius in the mid 1800’s and there is a long, very complicated equation with many variables that describes it. The numbers that are plugged in determine the shape of the möbius.


If one were to take a strip of paper, and join the ends, you would get a loop, or wheel that had two sides (inside and outside) and two edges. And if you draw a line down the middle of the strip, like the painted line in the middle of the road, you’ll only draw on one side. Cutting completely along that line will result in two separate loops. But if you put one twist in the paper before joining the ends, a side and an edge mysteriously disappear. The outside is the same as the inside and there is only one edge. Try drawing a line down the middle of the strip, and you will find that without lifting the pencil, you will come back to where you started.


Now try cutting that line with scissors. Instead of two separate loops, you will find that you still have one loop. It is twice the length of the möbius, but it has two twists in it. The form is no longer a möbius, as the figure again has two sides and two edges. If you draw a line down the middle of this figure and cut it completely, you will discover you have two loops as before, but they are linked like a chain.


Binkley began buy carving a möbius and then cut the figure down the centreline of the strip. Since the sculptor carved this sculpture from the rigid medium of granite, once this cutting process was complete, the resulting split möbius does not move as the paper example described above. From certain angles, it appears that one form is mysteriously floating in space. Binkley mounted the abstract sculpture on a tailored square highly polished charcoal colour granite base by way of a single steel pin. The pin is free of the sculpture, so one can turn the abstract to any desired viewing angle. Binkley used a smooth, matte finish for the split möbius’ surfaces. This gives contrast to the base and gives the granite the ability to successfully hold shadow.


Dr. Thomson is very pleased with the sculpture and it holds a place of honour in her garden.