Pi: a History of Progress
The story of π is the story of people and our struggle to build a better world through trial and error. It is a story of growth through tiny changes
Descartes’ expression “I think, therefore I am,” was the origin of the Enlightenment, a time when reason and individualism challenged traditional ways of thinking. Enlightenment era thinkers from Ukraine to Scotland argued that liberty and equality form the basis of progress – and that everyone should have an education . Up until that point in time, education was reserved for the nobility, who argued poetically in defense of the tradition that not all men are created equal. An algorithm that computes π gets closer and closer to the truth by tirelessly making small corrections - just as our societies have slowly become more peaceful over our long history, as we learn from our mistakes and make small improvements.
The poetic arguments made to defend kings and despots used elaborate language and ambiguous concepts. These arguments could not be challenged by anyone without an education – which was pretty much everyone. Even if you were lucky enough to be educated, these arguments were difficult to challenge – especially without an army at your back. Before Descartes, mathematical arguments were made the same way; they were very wordy and difficult to analyze.
Descartes made his famous argument in favor of rational inquiry over tradition in a treatise called Discourse on Method. This same treatise also introduced the western world to the Cartesian grid and algebra. The term ‘algebra’ comes from Arabic ‘al-jabr’ , which means “the reunion of broken parts”. Descartes recognized the technique of algebra – developed by Islamic philosophers - was a powerful tool for discerning the truth. After that, the story of π takes a right turn , as mathematicians drew circles on Cartesian grids, and used algebraic symbols to reason about π. The ability to analyze arguments by using rules governing symbols, rather than interpreting words and phrases, made it possible to develop much more accurate approximations of π.
In the late 19th century, Ferdinand von Lindemann proved that π is a transcendental number , which means π is infinitely long, and all-encompassing. If you look long enough, you can find any number somewhere in the digits of π. I don't know whether it's possible to even comprehend a world of infinite possibilities, where we have the abundance of energy and resources to create anything we can imagine. I do believe that without honesty, open communication and collaboration we won't get there.
Because π is infinite, you need to use a symbol to express it. Likewise, the size of software systems is simply astounding, and without symbols, we would not be able to reason about them. Fifty years ago, the Apollo 11 space shuttle had 2.5 million moving parts. Today, the software in the Mars Rover hasover 5 million lines of code. The immense complexity of software systems requires a lot of people who can work together. Mathematics makes that possible.
This π day - Friday, March 14 - if you share anything with your friends, share with them the message of mathematics; not as arcane and confusing theorems, but as a language of collaboration . Social progress and mathematical progress go hand in hand. Although we may disagree over what we would like to see happen and the direction we would like the world to go, we can all agree on some very basic things: A2 + B2 = C2 . And more importantly, we are all part of one genetic family.
This Pi day, we’re working with ThinkerSmith to host Pi Day For Kids, where a group of children will have the chance to work as a team to build with symbols. They will see and understand that communication, while sometimes difficult, is both the most crucial and rewarding part of building with thought. If you're in the Eugene, Oregon area this Friday- come say hi!
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