Imagine, expression is based solely on algorithmic processes in our brain. How would we use this insight to reduce the complexity the modern information society provides, or how could we make learning difficult subjects such as physics or expression itself more effective ?
I am currently looking at lambda calculus, which is based on one transformation rule only: Substitution of variables. It is interesting to think on functions as basic components in expressions, and substitution of parts as one of the most simplest approaches to transform expression.
In lambda calculus, there are three possible forms to specify ideas:
(1) expressions := can be names, functions, applications
(2) functions := lambda name. expression
(3) application := expression expression
The idea of recurrence, expressions in terms of itself, simplifies tremendously the expression of repeating structures, or structures with so many details that make it impossible to keep track of everything. It also reminds me on the idea that mathematics is an artform, the art of expression, an artistic endeavour in itself.
