Pythagoras was a dab hand at the maths. He was also a tall man. On top of all that he was strong like a bull. You either loved him or hated him. He was intelligent. He had a cool name and people just cottoned to him naturally. You couldn't ignore him. He taught few people many things. Let us not forget that he himself had teachers and that many of the best things he knew and taught had been circulating in the underground stream long before he was potty trained.
Another thing to bear in mind is that many of the most useful, confounding, and profound things he taught were the simplest. In fact, they were and are laying in front of everyone's noses, they are universal, ubiquitous and freely available. That is their camouflage and thus they elude most of us.
Cuidado Piso Mojado. What? These three words are usually found on a yellow sign to warn you of a wet floor. Usually in a place where Spanish is not spoken. The obverse has the same warning in French. If you are an Anglophone it is assumed that you can see that the floor is wet. Or is it?
If we repeat the three words three times we will have added a jewel into the crown of our medium term memory. If the words are chosen carefully so that they “go together nice” we will have made the deposit to the medium term memory bank even easier. Now, if we sing the words, say, to the tune of a simple childhood rhyme, we will have put these three words and many other things way back into our long term memory or the term deposit of the mind which generates interest.
Those of you readers who at this point ask, “ Why would I want to do that?” are obviously born of noble parentage. Read on. Consider that, perhaps someone else wants you to do that. You may want to do something similar for a completely different project for your own reasons. The important thing is to see it and to understand that it works.
In feudal Japan there once were warrior clans who liked to fight on horseback. Their chosen weapon was the bow and arrow. The problem they had was getting pierced by arrows. They made armor and their opponents made better bows and arrows. One fellow simply looked at an old Chinese book and managed to see the principal of three. He applied the principal and came up with a simple solution.
The solution itself served three purposes, simultaneously. He made beautiful silk drag-chutes embroidered with the gang logos of the various proto-Yakuzas. These were tied in such a way to the bodies of the warriors, that they billowed out behind one when one was galloping across a field of battle. In about seven out of ten cases the silk would deflect an arrow harmlessly to the side. The three that got through were so velocity-challenged as to not penetrate to a dangerous degree. It must be remembered that magic is science that is not yet understood. People were freaked by the whole thing.
Three things are at work in this apparent magic. The arrow's point, the silk cloth and the air molecules behind the cloth are the three things. The weapon itself has three components, namely the bow, the string and the arrow. I would imagine that whatever the source credited with the invention of this miracle was far older, even at the time, than they were led to believe. Its like saying that you “invented” the ice-cube. Sorry, patent seeking entrepreneur dude, water has always frozen at 32 degrees Fahrenheit, give or take, depending on the salts content. You put it in a square frame and got some poor bastards in the Middle Kingdom to mass produce it. As Shania Twain aptly says in the song, “That don't impress me much.”
This brings us to frames. I was talking to a colleague the other day who is a musician. We were discussing how songs are composed. When you look at a sheet of music, you are looking at a two dimensional chart of time. It is marked off with scratches to represent bits of time. The raw material is all of time. You, the composer, simply put it in a frame of your own choosing. You may apportion it to give the effect of happiness, sadness or anything else. The medium is still unchanged, superabundant and free for you to use. People may say, “Wow, neat ice cubes” or “Ewwww, gross.” Beethoven could see the music on three dimensions, he simply had to mark it off.
I know a man who never finished reform school. He can't spell many words and if he greeted you “Good morning,” he would use “fuck” five times in the sentence as ligatures to glue the whole thing together. His appearance is unkempt and he would be underestimated by nearly anyone. He has a gift. It is something that we all have, he just has it in an uncluttered state, due to not being cursed with education”.
His gift is the ability to see and visualize. His medium is metal. His hobby is welding. A person can tell him of a problem of a physical nature. An object that is broken or that needs to be “invented” to make something work for them. This fellow can see the needed object in his mind's eye exactly like a draftsman's three-sided drawing Front-view, top-view and end-view. He doesn't need to name the parts or fret over any aspect. He can take this picture and rotate it in his mind to any and every angle or perspective. He can go to his shed and fabricate the object with the same ease that you make a sandwich.
Children could sit in a stuffy classroom and “learn” about geography, history and economics. They could spend years at it. They could memorize this information and be tested on it. Or they could ride in a small plane at low speed and altitude during a field trip. In their ride they could be taken along a coastline and across an ocean. Then they could approach another coastline and along it until a river delta was encountered. They could fly up this river to the headwaters and across the mountains forming the watershed of that river system.
When they got back to class they would be able to see that all their previous knowledge had been two dimensional. Maps, charts and such. They may grasp that by adding a third dimension, that of height, to their perspective, that they could easily have seen everything that they had so strenuously learned in their two dimensional tutelage. The finer points would only require little bit of extrapolation. This is fine, as long as you don't do it too much and balance it with some interpolation.
Our brains are already set up properly to do what they are supposed to do. We need to let them. What I mean is that a person cannot consciously fight and struggle mentally through a problem with strength of will. This is an illusion. Simply look at what confronts you. Take in all the details you can. Then by doing nothing consciously, your computer will start running down the answer. It does help if one is sober, well rested and well nourished. Johnny, why did you say “Damn!”
As I pointed out earlier, Pythagoras told those who begged him that all problems have three components. Simply identifying these three things renders any problem halfway solved. This information was old long before the Greeks got a hold of it. Why? Because it is the nature of reality. It is just there and you step in it everyday. Let's think about that.
A chair has three legs, that is if is to stand alone. It can have only two legs, if you agree to supply the third. It can have only one, if you agree to provide the other two. A bird has two wings. It also has a sharp beak and can peck the shit out of you if you are busy watching the two wings. One, two, three. Three little pigs and three blind mice. A triangle does not a pyramid make. But a pyramid is made of four triangles and a square. It has five faces. A triangle is two dimensional and a pyramid is three dimensional.
If you are still reading, you may have grasped that three is important. If you are religious, you may have bumped into three before. If you are interested in comparative theology, you may have had exquisite, stimulating arguments with people of similar interests about three. Is the three actually one? Is the one made of three. Should I worship the three individually or as one? Triune or monad? Remember that a triangle is made of three points, but a point is not a triangle. A point is not much use of itself but with only three of them, you get a useful triangle. You wouldn't believe what you make out of a bunch of these.
This stuff is older than whatever your definition of old may be. There have always been some who knew it in any given slice of time. This is key. Think about all the threes you encounter everyday. Think about all the twos that are thrust at you by others. This or that, black or white, yin or yang. The threes are there in nature. The twos are pushed on you by people. Why would they do that? I wonder.
If you are satisfied with the music of the spheres, it is free. If you want the universe to play your request, you have to pay the DJ.
As I close this essay, I leave you with a picture. It is a boy about nine years old. He is walking up a steep rocky trail. Over his shoulder he has a strap, looped around three books with no titles. He is smiling and looking over his other shoulder. He has a slingshot sticking out of his back pocket.
Michael Hawes was born in Texas, raised in Louisiana and lives in British Columbia.