Throughout the centuries, mathematicians developed unique conventions to develop and discuss their ideas. For example, they would usually use a single character to represent a variable. They would also give each of the most important constants a unique symbol. For example the symbol pi (π) universally represents the one half the circumference of a circle with a diameter of one.
Mathematicians had tremendous success in using symbols to represent complex ideas. By using symbols to represent ideas, they could quickly forge ahead and express extremely complex ideas on a single piece of paper.
With interesting combinations of symbols and lines, professors learned to take full advantage of the two dimensional surface of a chalkboard, and the symbolism used by mathematics professors quickly developed into its own unique, international language.
At the beginning of the twentieth century, mathematicians under the lead of Cantor, Frege, Hilbert, Russell, et al., began the detailed development of a formal new language called "Symbolic Logic." Mathematicians the world over began dropping even the pretense of speaking in their native tongues, and began doing all of their work in this new and rather esoteric language filled with symbols and bold fanciful script.
The creators of the new symbolic logic portrayed it as a superior language. Symbolic logic firmly placed mathematics on a sound logical framework. As a language, Symbolic Logic was no longer subject to the vagaries and ambiguities of the vulgar tongues.
Yet despite the hundreds of thousands of hours vested in creating a new tongue. Symbolic Logic, it failed to achieve in full promise of a complete, consistent language. For the matter, the logician Kurt Gödel proved that an internally consistent language capable of describing the Integers could not be internally consistent.
Despite major setbacks, Symbolic Language continued to grow. The people who were took part in the creation of the language raved about its merits. Those who stood on the fringes kept silent. Unfortunately, the language too quickly surpassed the common man. It became impossible for all but a few to even read mathematical journals.
Symbol logic as a language became far more elitist than Greek and Latin. I fear that many mathematicians took greater pride in how few people could read their work, than in how many people had read their work.
I remember spending thousands of hours at the University library, trying to fathom the meaning of different articles in the Mathematics library. I felt like a dolt when faced with the new Symbolic Logic. I could read most of the work written at the beginning of the twentieth century, but the only way I could understand an article was to ask a professor to translate the article for me. (I had a feeling that many professors had the same problem.)
In many ways, I felt overcome with despair. I wanted to find ways to use mathematics to improve people's lives. I wanted to live in a world where people used their ability to reason to create a better world. But at the heart of the subject, I did not find people trying to communicate. I found reams of papers that seemed to have not purpose except for the academic exercise of proving who is the smartest and most detached from the common man.
Recently, I walked into the mathematics library at the local university. I could remember how sad I felt when trying to read the mathematics journals. I always found the place intimidating.
Yet this day, when I walked into the library. I found a different scene. An old professor pleaded that I leave the magazines I read on the table. Apparently, I was the only person to visit the library that week. His budget was going down, while the cost of subscriptions was increasing. He had to figure out which subscriptions to cancel.
I looked at the shelves in the library. There was perhaps ten thousand volumes on the shelves. There was so much work invested in this collection that I felt humbled. But I realized that not even full percent of these pages would ever be viewed again. These works seemed destined to die on the dust heap of history.
Perhaps the language of Symbolic Logic is destined to be dismissed, just as we've dismissed the long, involved treatises of the Scholastics.
I made my selection, and tried to read an article or two. Again, I felt dismay. The mathematicians writing these papers did not even give me an entry point to read and enjoy their work. I felt a surge of anger. Yes, the authors did a wonderful job of demonstrating their intellectual superiority, but they failed completely at communicating their ideas.
I tried to speak to the professor. He was distraught at his decision. Which journals would he cancel. The price was going up, and the number of readers going down. Everybody was doing the Internet, and studying programming languages. There was no time to learn the subtle nuances of the mathematics journals.
The professor looked at the impression collection of the library. These volumes represented his life's work. He saw me struggling against the language. "All is lost" he said.
I closed my eyes and imagined the story of two wanderers entering the kingdom. They convinced the emperor that they had a shiny new language. It was a language pure in nature--a language in which no-one could tell a falsehood or lie. It was a language that only the purest in heart could understand.
The wanderers squeaked some syllables. The king not wanting to show his own weaknesses applauded. The courtiers and court jesters eagerly mimicked the sounds and squeaks of the wanderers. Each wanting to pretend that they were pure in heart.
The wandering con men were clever. Not wanting to admit his own weaknesses, the emperor would proclaim all of his laws in the new tongue. The wanderers would careful interpret these proclamations to the courtiers of the kingdoms. (Oddly enough the proclamations seemed to include transferring large amounts of jewels and gold to the wanderers).
Finally, during the great feast of the Fall harvest, the king stood before his subjects, and began to babble forth in the emperor's new language. He squeaked, squawked and hissed. It was a speech the wanderers carefully taught him. He felt terrified that he did not know the meaning of the words he spoke. The crowd stood hushed in a greater fear that they did not understand.
The people tried to applaud at the correct places, but when the speach ended, the people were hushed. It was a deafening silence. No one wanted to admit that they were impure of thought, but were careful not to applaud until the others applauded. The king began to sweat. He had mimicked all the words of the wanderers, and had no more to give. To try to speak further would result in humiliation.
The world was silent, all except one small child with the bravery to stand forth and proclaim: "The emperor is speaking gibberish!"
Just then, the palace guards realize that the wanderers had left with the jewels and gold of the kingdom.
When Bertrand Russell finished writing his Principia Mathemitica, he wondered if the work would still be read in a century. He spoke of an image of a librarian pulling the last copy of the work from a shelf. The librarian would stare at the strange symbols on the pages, and making the decision of whether or not to place it in the recycling bin.
There have been some wonderful advancements made with the language of symbolic logic, and modern mathematics. Unfortunately, many of these efforts might suffer the fate of Russell's nightmare--not because of the subject or meaning of the work, but simply because the mathematicians failed to write their works in a fashion that could communicate the meaning of their work to others.
Although the use of symbols and mathematical conventions can greatly aid in the communication of ideas. Creating symbol logic as a separate, foreign language places the longevity of the entire body of these works in jeopardy.
In many ways, I feel the current challenge of mathematicians is not too simply come up with far out ideas, but to struggle and find ways to communicate their ideas to the people. With descriptive mathematics, I do not intend to ridicule the fantastic work of mathematicians. But I want to extend the challenge of communicating this work to the world.
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