You will probably know that Leibniz and Newton, working independently, came up with that torment for schoolchildren and an invaluable aid for engineers, the infinitesimal Calculus. However, did you realise that the formulation of the Calculus, at least that due to Leibniz, had a mystical, rather than a mathematical foundation? Also, were you aware that Newton, during the same period of time, was studying the Bible trying to discover an underlying secret code?
For those of you who have played with fractal producing programs, it can hardly have passed your notice that we have fortuitously stumbled across something truly “magical”. How can such short pieces of very simple code generate such complexity? Why did it require us to enter the Computer Age to make this fantastic discovery when history reveals that our past great mathematicians were easily up to the task? Can other pieces of not-so-simple code generate any other wonders?
Have you read Sir Arthur C Clarke’s “The Nine Billion Names of God”? If so skip this paragraph and move on. Briefly, a computer is used to print out all the permutations and combinations of God’s name as revealed in an ancient text, that is all nine billion of them. The computer is set to the task, and as the last permutation is printed off, the stars start to go out!
Let us return briefly to Leibniz. What was he actually trying to do when he came up with the Calculus? Leibniz was attempting to link special symbols to all essential notions of thought. These symbols or characteristica could then be mathematically manipulated to solve any problem, mathematical, social or even spiritual. You may have heard the phrase “Let us calculate” associated with Leibniz. This did not mean let us sit down and sort out a difficult mathematical problem using the Calculus. In fact this actually meant, instead of us going to war and killing each other over these differences in Religious interpretation, let us use the Calculus to tell us what this passage of Religious text is really telling us! What a project! This was a mathematical way of manipulating thoughts and ideas.
All very well and good, but where is this leading us? Please bear with me for this last part of my account.
Apart from a deep interest in Physics, Optics, Mathematics and Astronomy, I have always been fascinated by Ancient Egypt and Ancient Greece. On a trip to Luxor over 15 years ago I took a felucca across the Nile to a little visited set of cliff-tombs called “The Tombs of the Nobles”. In one of these tombs were an amazing set of hieroglyphics, unlike any others I had seen before (or since). Clearly much of the text was mathematical (I has seen similar symbols on the famous Rhind papyrus) but a great deal of the text was completely unknown. Having paid my (Egyptian) pound to be able to take photographs, I took a complete set of photos of the wall for later study. I had not appreciated at that time that it would take 15 years to translate those hieroglyphs. With help from well-known Egyptologists who were given little (isolated) sections of the text, I now have the complete translation. The translation not only required help from the Egyptologists, but a key component for their understanding was knowledge of the mystical roots of the infinitesimal Calculus!
The text is basically a spell, but it is unlike any spell you will find in the “Book of the Dead”. The text gives full detail for the production of an iterative incantation for “The re-establishment of Order and the Removal of Chaos from the Universe”. Having taken 15 years for the translation it was a relief to have only taken the past six months to convert the spell into Mathematica code.
I have now run the code for a couple of days and have a graphical output routine to indicate how far the iteration has proceeded. I estimate the iteration will terminate on the 6th July 2008 around mid-day. However, I must admit to being a little nervous about letting the program run its full course.
Should I let the computer finish the iteration? What would you do?