Number patterns

The first memory I have of loving patterns was when we had to start learning our times tables in grade 2. I found maths relatively easy, I think in hindsight because I was able to understand the way numbers worked in patterns. For me learning times tables wasn't about rote learning, it was about the number patterns. It was about, for example, with the 9x table how the first number went up by 1 and the second number decreased by 1; 18, 27. 36 etc. It was about how for the 11x table it was simply the repetition of numbers; 11,22,33 etc. 

So-called magic squares were (in the simplest form) a 3 x 3 matrix where all the rows and columns needed to add up to the same total. I was less interested in figuring out the solution than understanding the pattern of the numbers in a solution, which, once cracked, could be applied to a magic square of any dimension. In my high school text book the largest magic square I could physically fit onto a page was something like 30 x 30; a matrix with 900 cells, so the entries in the cells were the numbers 1 to 900. I remember filling it out so that numbers in each column and row added up to exactly the same total - just because I could because I'd cracked the pattern. Expanding ridiculously large equations such as (a + b)30 using Pascals triangle was another pointless but immensely satisfying waste of my high school time.

As well as loving mathematics, I also loved art. I had a hobby creating what were called 'string pictures'. patterns created by weaving cotton between rows of tacks into shapes; a series of lattices. I similarly loved playing with another very 70s educational toy called a spirograph. All of these developed in me a fascination with geometry and numbers.

But none of that compared with the joy of discovering patterns associated with the Golden Ratio, Calculus, and the Fibonacci Number which would come later. The beauty of the symmetry associated with paper sizes A4, A3 etc, where folding a piece in half maintained exactly the same proportions (√2 pattern), being intoxicated by Newton's genius in developing calculus as a way of modelling anything in nature that changed. I was especially interested in modelling motion. And the wonder of seeing the shape of sea shells matching exactly the set of Fibonacci numbers. I was amazed at how maths worked, how these number patterns could help us understand and predict so much of what we experienced in the world.

I had an eccentric (left handed, as I recall) lecturer in one of my 3rd year maths subjects. He had just filled the entire blackboard (yes, still used chalk in those days) with unfathomable scribble in arriving at a solution to a complex calculus problem. In the same way a gymnast flings their arms open at the end of a routine, he turned to us exclaiming 'Beautiful!' and was so excited by what he'd just done he dropped the chalk. I remember feeling his pride.

More recently I have been poking around in E8, an ambitious theory to integrate all known physical forces and interactions in a single unified theory based on an 8 dimensional pattern which has been described as the most beautiful ever.

I think there is such a thing as pattern number intelligence. It is the appreciation of proportions, of layout, of geometrical design and of applying mathematic methods in everyday life. I'm not so sure about number pattern wisdom? To be considered ...