Pi as a period of time

1 09 2010

This is a bit of a revelation. And I read this revelation from a book. I have started to real Lakoff and Nunez book, Where Mathematics Comes From. It was given to me by Leon for my trip to Maderia; I intend to spend the rest of my thinking life exploring XQ and this is a good start.

I was reading with a certain trepidation: what if these guys have explored the space already, more rigourously and comprehensively than my meandering and intuitive forays? That would make XQ an incidental eccentricity destined for obscurity… But it is also relieving to know that hard-core academics are exploring the space.

I read the preface and the introduction with interest. Some big claims, the abstract universality of mathematics as purely embodied in the human experience. I also benefited from reading Leon’s written commentary, such as his exploration as to mapping his notion of stance to a mathematical framework. What caught my attention was their new interpretation of Euler’s remarkable equation, e^Pi*i = -1. So I turned to that section of the book, the final section.

Very interesting. It made clear how their use of metaphor works. I remember noting that mathematics used metaphor, and exemplified it with pointing out that a graph was a metaphor. They use it rather more precisely, stating that an angle is metaphorically described by a number. That is, as far as I can tell, they use metaphor to describe a mapping of anything to number. That is measure is a metaphor.

Anyhow… in their explanation of what they call the Unit Circle Blend, they combine simple circle in Euclidean space with Cartesian co-ordinates, with enumerated angle, with Pythagoras theory. It is simple and beautiful. They then follow this with The Trigonometry Metaphor, and thereby map length of side a to the function of cos theta, and length of side b to the function of sine theta. And on page 397 state:

Where Pi was previously only the ratio of the circumference of a circle to it’s diameter, 2Pi now becomes a measure of periodicity for recurrent phenomena, with Pi as the measure of half a period. This is a new idea: a new meaning for Pi.

Actually, it is a new meaning for me! Not only does this give my query as to the significance of special numbers such as Pi new material to think about, it might even shed some significant light on Euler’s equation and the “shape” of consciousness!

That is, if some young genius studying AI were to come across these guys and combine it with the jump I have made with XQ… and maybe another piece out there…

Honestly, Pi as a period of time. Wow. That’s huge. At least in my mind. Thanks Lakoff and Nunez :)




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