Of Myth and Math

To a large extent modern philosophy—Transfinite Theory included—is the result of a reassessment of Classical Greek philosophy that took place toward the end of the Enlightenment (in the late 1700s and early 1800s).

This means that—to understand the modern age—one must investigate this re-interpretation of the classical world.

The upcoming chapters of Rich Theory will present a version of classical history from ancient times, through the invention of Transfinite Theory, and to its aftermath.

The reason that so many math and philosophy books start with a chapter on prehistory or with the Ancient Greeks is that by beginning the work with reference to the ancient past emphasize this coming into being. The language, logic and mathematics that we know today did not just happen. The systems evolved over time.

There is not a written history detailing the evolution of language. We can only speculate as to how humans learned to talk. I surmise that language arose as a group activity. People within a group would use sound and gesture to indicate vital information to benefit the group. Groups that were good at this process had an advantage over those that did not.

The system of communication would become more and more complex as people assigned different sounds to the people, things and actions around them.

For a language to work, people need to assign similar meanings to the same sounds. It is likely that groups developed mechanisms to train the members of the tribe in the common language.

These techniques involved into the stories and myths of the culture.

An interesting thing happens when people share common stories. They develop the ability to communicate complex ideas by referring to parts of the story.

For example a person in Athens might say: "I had a run in with Dionysus" rather than "I drank too much wine and have a headache."

As language evolved, the ability to reason improved. Once you have abstract sounds assigned to the things around you, you can start reasoning about them. The next big step in the development of culture was the invention of writing.

Since there is no written history detailing how people learned to talk, the subject is up to supposition. There is archeological evidence of an evolution of symbols.

One of the highlights of the evolution of languages was the appearance of the Phoenician phonetic alphabet circa 1050BC. The Phoenicians lived in the area of modern day Lebanon. The Phoenicians were a sea faring people and their language quickly spread. The alphabet became the foundation of Aramaic languages (Hebrew and Arabic). The alphabet also traveled north to Ionian (in modern day Turkey) where the Ionian Greeks modified the script to fit the Greek language. Further modifications produced the Latin alphabet that I am using at this moment.

The Ancient Greeks had a well developed mythology with a cast of gods that affected everyday life. There was also a long tradition of epic poems. Notably, the Iliad and Odyssey by Homer chronicled events from the mythical war with Troy.

On the subject of myth, many ancient Greeks believed that Homer was a real person and that the war with Troy was a historical event. However, there is no evidence to prove that Troy existed, and Homer may have been a fictitious name used by storytellers to enhance the tale.

The Ancient Greeks also had a proud military tradition. Famous battles include the Battle of Marathon during which the fabled Pheidippides ran some twenty six miles from Marathon to Athens with news of the war. The 480BC Battle of Thermopylae is another heroic event in which 300 Spartans are said to have held off the army of Xerxes I of Persia giving the Greeks time for the evacuation of Athens and preparation for the naval battle that ended the war.

The history of the Persian war was chronicled by the respected historian Herodotus of Halicarnassus (Ἡρόδοτος Ἁλικαρνᾱσσεύς ) who lived from 484 BC to circa 425 BC. Herodotus is heralded as the first true historian and people give merit to his words. However, one most note that he was born during the war; so his tale is a compilation of second hand accounts.

The Greeks had historical information of varying degrees of authenticity which makes for lively discussion of what is and is not myth.

Separating myth from fact is a primary concern of historians.

Oddly, it is far less important to the mathematician, the logician or even the ethicist. In some cases, groups are keenly interested in preserving myths because the myths provide the foundation for later works.

Mathematicians are often more concerned with the form of ideas than in the source of the idea. If I developed a sound idea by contemplating a myth, the soundness of the idea would not falter if the myth were proven false.

One of the more exciting disciplines in mathematics is the field of "mathematical archeology." A Mathematical Archaeologist is interested in the way that different cultures approached mathematics and how mathematical knowledge affected the success of a culture.

Mathematical Archaeologists work with other scientists to analyze the meanings of known facts and the artifacts of different cultures.

Mathematicians outside the field of mathematical archeology look to this field for inspiration. The interplay of mathematical archeology demonstrates the way in which myths evolve.

A true mathematical archaeologist is interested in the hard science and facts of ancient cultures. They analyze new artifacts and discoveries in light of what is known of the culture under study.

Writers of popular math books take these discoveries and work them into math textbooks. This process involves filtering. The writer of a Geometry textbook is likely to only look at the archeologist's work as it is relevant to geometry. The process of filtering gives the students who read the geometry book an incomplete view of the archaeological record.

By taking the steps necessary to make the textbook relevant to audience of the book, the textbook writer is engaged in the myth-making process.

In teaching science, professors will elucidate on the discoveries that they find most relevant to the message they want to students to learn. This process filters out much of the best science.

The boring and dull truth of science is that for every great discovery, there were a thousand other minds running in different direction. The teaching of science has created a mythology of science with wonderful discovery piled on wonderful discovery. Science classes fails to give proper credit to the many dead ends that great thinkers took before finding the successful path.

Understanding the interplay of myth and the writing of popular science is important. Myth-making appears to be a necessary part of life.

In the last chapter on perspective, I mentioned that visual perspective reduces a three dimensional space to a two dimensional surface. The very way that space and time works means that we have a reduced view of what has happened in the world.

The chapters to come will speak of the myths of the ancients and how what we know of the ancients is also myth.

My homage to mathematical archeology begins with a mention of a pressing problem of the ancients: allocating farmland on the delta of the Nile.

It appears that many ancient cultures had developed intriguing ideas about mathematics. The Egyptians, for example, had developed skills sufficient to build huge pyramids and to raise towering obelisks to the sky.

I've come across texts that alluded to one of the great challenges of the ancient Egyptians: