March 16, 2021
Having survived both Pi Day and The Ides of March I would like to start this screed off with a thought experiment, which may be a new way to look at mathematical knots.
To begin you’ll need to visualize a strip of material that is three inches wide and three or four feet long. This material must be flexible yet rigid enough that the side don’t collapse. A piece of sheet metal will do, or a long strip of that flexible magnet stuff that goes on the back of things so you can stick them on the refrigerator. Or maybe a piece of plastic.
I was thinking of a plastic strip when I came up with this idea. What I wanted to do was to make a traveling protective wall for stuff I might buy on a trip. I have used plastic coffee containers in the past. They are bulky but perfect for a coffee mug to go into, stuffed with dirty laundry. I thought, “What if I had something that was just the wall of the container?” When not in use it could lie flat on the edge of my suitcase. If I cut a slit halfway on either end such that the two slits could fit into each other I could then create a round strip to hold something. (This would require the slits be cut starting at the opposite sides on the strip.)
Now I played in my mind with how to attach that strip. The standard way would be to fit the notches together such that the strip had two little ears sticking out. Or you could attach them such that the whole strip was flat and the notches would them lay flat to the surface.
Okay, here comes the thing I got to, “What if I needed a a slightly higher container, say for one of those tall thin coffee mugs?”
I could take my strip and put a loop in it like you see on those plastic racing tracks for kids cars – a loop de loop. This would require you put a 360 degree turn in the strip before attaching the notches.
Okay. Okay. Here’s the mind F*cker. I mean the mind meld. What happens if you grab the joint where the two notches are and twist it 180 degrees? That is you turn it inside out?
I was picturing a strip that had raised portion due to the fact that when you put the loop in the strip there had to be a point where the sides were bumping against one another. If I laid the construction on a flat table there would be part that was sticking up.
Now if I twist the thing 180 degrees, the part sticking up goes to the other side of the construction!
So what? ( “Sew buttons, you can’t glue them,” I always say to that. )
Now imagine that you have your strip but instead of being notched it is magnetic so you can just snap the two ends magnetically in place. This allows you to do something new. You can now take the strip and before you attach the ends you can twist the strip 180 degrees and now you have a Möbius Strip, a continuous surface, whereas before you had two surfaces.
“Is that the same as what I described in my loop de loop?”
I’m not sure.
This gets into that study of surfaces where an object with a hole in it could be a donut or a coffee mug.
However, it also gets into the study of quarternions and octonions. A rather forgotten corner of math until Cohl Furey (don’t you love that name?) revived it a few years ago and said that it could explain The Standard Model of the Universe and if so we don’t need no mo’ stinkin’ leptons, quarks or other particles. The advantage of octions is they can describe another characteristic that vectors can’t, spin. In the Standard Model it can be shown that we got all we need to describe the universe.
With my mind experiment have I tripped over something that knot theory (not string) has missed? That is the twisting of surfaces? With a rope, imagine it like my strip, but the top and bottom sides have been fused together to form a sheath. Therefore the question of the sides is ignored. At least I haven’t heard anyone talk about a rope in terms of it being a sheath, having an inner and outer side.
Oh well, moving on.
Two more arrests have happened on the Jan 6th Insurrection. They nailed two guys that were using bear spray. They are shown spraying the officer who was killed.
The CDC has announced, ever so quietly, that they are investigating, and taking down, all the crap the previous White House administration put up in the name of the CDC.
The CDC is back! Hooray!
Checks are going out to people.
The Republican state legislatures are busy passing voting suppression laws that are so egregious it is now being called by some “The Second Jim Crow Era.” Having lost the past election, and realizing they don’t have a chance in a fair fight, they are doing everything they can to rig the game.
If this is not stopped it is not the end of the world as we know ( I quoteth Mad Magazine and their take off called “The Daily Dirt” in reference to nuclear war having started.) No, it is just THE END OF OUR DEMOCRACY. No biggie. Right? It’s just a bunch of good old boys and girls doing their racist thing. That’s the cover. The truth is some more malevolent forces are at work.
To be continued …
PS Part of a maithuna frieze, north wall, Vishwanath Temple, Khajuraho, India. Circa 1000 C.E.
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