In order for me to understand math, it has to be in the context of a story, preferrably with lots of emotion. I'm right-brained, so when someone tells me a story where calculations and numbers are needed, but there's elation or heartbreak involved, I have a decent hope of understanding the math.
That's why, when I first heard about the Enneagram- a personality typing system that ascribes a personality type to each of the numbers between 1 and 9, a spark of interest was lit. Fours years after my workshop with him, I still remember a line our teacher said that has nipped at my heels this whole time, "When they discovered irrational numbers, there was an inherent horror in this idea that you could be stuck forever in a repeating decimal that never ended", the repeating decimal a metaphor for being stuck in one of the nine personality ruts. It was an incredible fusion of left- and right-brained principles for me on a topic that meant so much. So begins today my search for answers around this connection between math and the transformation of our souls. And in order to understand irrational numbers, first we have to understand the importance of the discovery of zero.
It's wierd to think that the number 0 didn't always exist- that it had to be thought up by mathematicians in response to a problem they didn't really know how to define until hundreds of years after Christ. It was the Indians who first solved the riddle in the context of the place-value system- before that, the Babylonians just left a space where the zero should be (Pickover, 80) and Egyptians used the symbol Nfr- the symbol for beauty and completeness- for zero (source). But that was cuneiform and hieroglypic math respectively- the kind where you draw a line or symbol for one, and two lines or symbols for two, and so on.
The number system most cultures use today is a place-holder system called the decimal system with a base of ten and a 0 to distinguish the tenth place from the first, a Hindu invention that changed history forever.
The introduction of the zero into the decimal system ... was the most significant achievement in the development of a number system, in which calculation with large numbers became feasible. Without the notion of zero, the ... modeling process in commerce, astronomy, physics, chemistry and industry would have been unthinkable. The lack of such a symbol is one of the serious drawbacks in the Roman numeral system" (mathematician Hossein Arsham quoted in The Math Book by Clifford Pickover).
The oldest undisputed documentation for the Indians' use of the 0 is in from a tablet in Gwalior, India, dated to 876 AD. Their mathematicians used a small, raised circle to hold its place. The Bakhshali manuscript, found around Pakistan in 1881 might be older than that, but nobody agrees on how old it is. Mathematician Amir Aczel just came out with a book that describes his search for an even older zero, and he says he found it in Cambodia inscribed on a stone listed as K-127, which would date to 683 AD, about 200 years older than the Gwalior one.
From India, the idea of the zero spread to the Persians, then to the Arabs who traded with India, then finally to Europe in the 12th century when the Moors conquered Spain. It wasn't until Fibonacci, an Italian merchant and mathematician, translated the 9th century works of Mohammed Ibn Musa Al-Khowarizmi into Latin for other businessmen that Europe started to "see the light" and abandon its awkward Roman numeral system (source). Slowly, over the next three hundred years, the use of the zero spread from its tight bankers' and mercantile circle outward to the common European, enabling Europe to shed the shackles of the Middle ages and enter the thriving Renaissance period.