“The most incomprehensible thing about the world is that it is comprehensible.” – A. Einstein
“The eternal mystery of the world is its comprehensibility.” – A. Einstein
I have always wished that I could appreciate the beauty of pure mathematics in the same way that brilliant mathematicians and physicists do. Truly. I was reminded of this last night when I watched a special on one of my lifelong heroes, Albert Einstein.
For people like Einstein, mathematics is art. Numbers on a page are akin to Leonardo da Vinci’s “Mona Lisa.” In fact, the “Mona Lisa,” was painted based on a mathematical premise known as the Golden Ratio:
The Golden Ratio, also known as the Golden Number or the Golden Section, is defined as the ratio of the lengths of the two sides of any Golden Rectangle. That is, if you take a Golden Rectangle and divide the length by the height, you will have the Golden Ratio. Traditionally, mathematicians have denoted the Golden Ratio by the Greek letter phi (φ). (http://library.thinkquest.org/27890/goldenRatio2.html)
Leonardo da Vinci is regarded as a Renaissance man because of his integration of art and science. He is not only famous for his paintings and sculpture, but also for his drawings, such as “The Vitruvian Man,” as well as his sketches of a flying machine, a hang glider, and numerous studies of human anatomy, all based on mathematical and physical principles of angles, lines, arcs, and relational gravity.
Of course, da Vinci was predated by the Greek Archimedes, whose studies in mathematics and physics are thought to be the origins of pi as well as the principles of the lever. Archimedes was working around 250 B.C. in Sicily. Then, of course, following da Vinci, was Galileo, who was perhaps the first to posit that the laws of nature were dictated by math. In The Assayer, Galileo stated that “Philosophy is written in this grand book, the universe … It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures” (http://en.wikipedia.org/wiki/Galileo_Galilei).
“Anyone who has never made a mistake has never tried anything new.” – A. Einstein
But getting back to Einstein, this man spent almost a decade on his General Theory of Relativity (not to be confused with his theory of relativity), which he presented in 1916. This was the subject of the show that I watched last night. What I found the most amazing about the entire show was how this man with the beginnings of his wild hair would fill pages and pages with these long equations and know, just know that they were incorrect. But then I tried to relate his equations to words, and in a way it made sense to me. His numbers were a writer’s words. His numbers had their own elegance and truth for him. They were truth.
He could look at a page of numbers and see something larger. I can stare at a page of numbers, equations, and see absolutely nothing, I mean, absolutely nothing. That has always made me feel stupid: the way in which numbers come alive for some people. I know that it is a brain function thing: some people work with one side of their brain; other people work with the other side of their brain. And then there are some people, like da Vinci, who manage to tap into both sides of their brain and encompass all of it. That is what I have always been so jealous of: I want to tap into both sides of my brain. I want to work with words, and I want to see the beauty of numbers so that I can look at space and see not just the beauty of the stars, but also the beauty of reaching the stars.
“Great spirits have often encountered violent opposition from weak minds.” – A. Einstein
I have read countless articles on how human beings only use a very small portion of their brain function, that scientists are always looking for ways to open up that untapped potential. It’s the stuff of sci-fi horror movies—The Manchurian Candidate and others, depositing information into that unused portion of the brain only to have it come alive at some later time, usually inconvenient to real life, but great for the plot line. But you know that there are individuals who have tapped into part of that potential. We have seen and heard about them all throughout time, and they have come from all walks of life: Leonardo da Vinci, Michelangelo, Shakespeare, Alexander the Great, Dante, Beethoven, Einstein, Frank Lloyd Wright, Dorothea Lange, Le Corbusier, Bill Gates, Mozart, etc.
They are people who have achieved greatness in different fields for different reasons. I have only named a minute few. They have contributed in great ways and in horrible ways to our history because they have had the ability to see beyond the here and now. They have had the ability to tap into just that small part of their brains that most people use. They have melded the words with the numbers to put it into the crudest possible sense. In other words, they have touched greatness and changed the world and changed history.
Granted, Einstein was myopic when it came to his work. He had very little time for his family. He did, however pay attention to events around him. He was a pacifist, and he hated the events of WWI and the participation of colleagues of whom he had once greatly sought respect and admiration. He was very certain that his ideas were correct, so certain in fact, that he bartered for a divorce from his first wife on the condition that when he won the Nobel Prize, she could have the money if she would grant him a divorce. His biggest concern was getting what he wanted when he wanted it and being allowed to do as he wished. But no one who worked with him doubted his dedication or his genius.
“The important thing is not to stop questioning. Curiosity has its own reason for existing.” – A. Einstein
Which takes us back to general relativity and one of my favorite concepts: an event horizon. Somehow, and don’t stick me on the particulars because I won’t even pretend to understand it all, when an object becomes sufficiently compact, general relativity predicts the formation of a black hole, a region of nothingness in space. In general relativity no material body can catch up with or overtake a light pulse. The study of spacetime is called global geometry.
Now, as I understand it, using global geometry, some boundaries can be identified, and these boundaries are called horizons, and a black hole is one of these horizons because it is cut off from the rest of space time (bear with me here, I think that I’m almost there). There are other types of horizons in the universe because the universe expands. Horizons from the past are called particle horizons and cannot be observed. Horizons from the future cannot be influenced and are called Event Horizons! I finally understand the term. I really do. How cool is that?
“The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science.” – A. Einstein
So while I look at a painting such as Botticelli’s “Birth of Venus” and I may not see the Golden Mean, and I cannot appreciate the culture of pi and the fact that people spend time trying to carry it out beyond a trillion digits or why this is important, I don’t discount the art involved in this pursuit. As to myself, I am gloriously appreciative of the fact that somehow I have come just a little bit closer to understanding the mathematical definition of what an Event Horizon is, although I know that in actuality, I probably haven’t.
I do know that space and time are on another dimension, one that I cannot comprehend, just as I cannot truly comprehend the space between quarks. The closest that I have ever come was how it was explained in the movie “The Adventures of Buckaroo Bonzai Across the 8th Dimension,” which made complete sense to me” . . . perhaps because it was visual and utterly nonsensical.
Ah well. Just remember, “no matter where you go, there you are.” More later. Peace.
Lola's Curmudgeonly Musings 