Pythagoras was a dab hand at math. 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 a few people many things and many people a few 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 underground streams long before he was potty-trained.
Another thing to bear in mind is that many of the most useful, confounding, and profound things that he taught were the simplest. In fact, they were and are yet, laying in front of everyone's noses, universal, ubiquitous and freely available to apprehend. 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 location 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? Is it so the person who is most likely mopping the floor can read it?
If we repeat these three words three times we will have added a jewel into the crown of our medium-term memory. If three words are chosen carefully, so that they “go together nice,” we will have made our deposit to the medium-term memory bank even easier. Now, if we sing the three words, say, to the tune of a simple childhood rhyme, we will have placed those three words and many other correspondent things deep into our long-term memory, aka, the term deposit of the mind, which generates steady interest.
Those of you readers, whom at this point ask, “Why would I want to do that?" you 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 of 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. When they made armour, their opponents made better bows and arrows. One bright fellow, after looking at an old Chinese book, managed to apprehend the Principal of Three. He applied that principal and came up with a simple solution.
His solution served three purposes, simultaneously. He made beautiful silk drag-chutes embroidered with the gang logos of various clans. These were tied to the bodies of the warriors in such a way that they billowed out behind when galloping across a field of battle. In seven out of ten shots, 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 out 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 source was credited with the invention of this miracle shield at that time, was far older than people were led to believe. It’s like a person saying that they invented an ice-cube. Sorry, patent seeking entrepreneurs, water has always frozen at 32 degrees Fahrenheit, give or take, depending on the salts content. Putting it in a movable cubic frame is beside my point.
As Shania Twain aptly said in one of her songs, “That don't impress me much.”
This naturally brings us to the topic of 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 time chart. It is marked off with scratches representing bits of time. The raw material is eternity. You, the composer, simply put apportion this all into a frame of your own choosing. You may apportion in such a way as to elicit an effect of happiness, sadness or anything else your skill allows. The medium, however, remains unchanged, superabundant and free for everyone to use.
Beethoven could see music in three dimensions and simply had to mark it off. I once knew a man who never finished reform school. He couldn’t spell that many words and when he greeted you, he would use the word “fuck” five times per sentence, as a ligature to glue the whole thing together. His appearance was unkempt and he was underestimated by nearly everyone. He had a rare gift. It was something that we all have, but he possessed it in an uncluttered state, due to never having been hindered by education.
His gift was the ability to see and visualize. His medium was metal. His hobby was welding. A person could tell him about a problem of a physical nature, such as an object that was broken or something that needed to be invented to make something else work for them. My friend could see the needed object in his mind's eye, exactly like a draftsman's three-sided drawing, with a front-view, top-view and end-view. He didn’t need to name the parts or fret over any other aspects. He could take his mental picture and rotate it in his mind to any and every angle or perspective. He could then go to his shed and fabricate the object with the same ease that you or I would make a sandwich.
Children can sit in a stuffy classroom and learn about geography, history and economics. They can spend years at it. They can memorize information and be tested on it. Or they could ride in a small plane at low speed and low altitude during a field trip. During their ride, they could be taken along a coastline and across an ocean. Then, they could approach another coastline and fly along it until a river delta was encountered. They could then fly up that river to its headwaters and across the mountains that form the watershed of that river system.
When they got back to their classroom, they would be able to see that all their previous knowledge had been only two dimensional. Maps, charts and such. They might now grasp the fact that by adding a third dimension, that of height, to their previous perspectives; that they could easily have apprehended 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 do. We need to let them be. What I mean is, that a person cannot efficiently and consciously struggle through a problem mentally with only strength of will. That is an illusion. Rather, simply look at what confronts you. Take in all the details you can. Then by doing nothing consciously, your computer will start running down your answer. It does help if one is sober, well rested and well nourished.
As I pointed out earlier, Pythagoras told those who listened to him that all problems have three components. Simply identifying those 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 always settles firmly onto three of its four legs. A chair can have only two legs if you supply the third. It can also have only one leg, if you agree to provide the other two. A bird has two wings. It also has a sharp beak and can peck you if you are busy watching only 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 of much use itself but with only three of them, you get a useful triangle. You wouldn't believe what you can make out of a bunch of those.
This lore of three is older than whatever your personal definition of ancient might be. There have always been some humans who knew it in any given slice of time. This is key. Think about all the threes that you encounter everyday. Think about all the twos that are thrust at you by other people and by institutions and governments. This or that, black or white, yin or yang. The threes are always organically there in nature. The twos are pushed on us by other people. Why would they do that? I wonder at this along with you. If you are satisfied with the music of the spheres, it is free to enjoy. If you want the universe to play your requests, you have to pay.
As I tuck this essay into bed, I leave you with a picture. It is a boy about nine years old. He is walking up a steep, rocky, pine-clad mountain trail. Over his shoulder, he has a strap looped around three books with no titles. He is smiling and looking over his other shoulder. There is a slingshot sticking out of his back pocket.
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