The Idea of Equations between the Infinite and Discrete

The Idea of Equations between the Infinite and Discrete

Sometimes a picture is enough in our insight into geometry. But equations work well also, our shifting across a mirror or mirrors can have their own perspectives of how we relate to design and measurement. Where I have toyed with the trivial problems of proportions involving the golden section and the third CSA flag I could have just as well wrote the series of powers of phi to see that in one dimension of the flag we have some multiple of phi with the Fibonacci numbers and a value added to it as an excess of similar and recursive numbers. But as with all such mathematics it is a relaxing recreation although some of our saints in the field like Lucas were essentially hobbyists. I use the variant of little theta to represent phi which can be replaced by a Fibonacci number (hence digamma) for a more general continuum.

I have always been bothered by the need for a quasized continuum as sort of a parallel offshoot of what seemed a reasonably complete series of continua. Now these seem to have a relationship more concretely in my mind.

We should have expanded some of our notations long ago. What is the negative root of a positive number? To ask this is a question of linguistic ambiguity as much as one of our idea of limits and numbers. Surely in general space there exists a point between zero and one which uniquely describes the irrational number yet it in reality is a number or limit that in some sense is never reached. But it can be described in the greater concept of dimension and space and spaces as a dynamic relationship between what is continuous and discrete in the virtual structures of the worlds design and its vigorous lifelike evolving.