Thursday, August 05, 2010

How can Mathematics be the Language of Nature?

I am reading this wonderful book about Physics (and history and philosophy of Physics) "Tao of Physics" by my all-time favorite Physicist and author Dr. Fritjof Capra, a contemporary of Werner Heisenberg. Incidentally, Dr. Capra's other famous book "Turning point" has really introduced me to the concept "systems thinking" while I struggled to grasp the subject by reading another influential legend and Guru of software (testing) Jerry Weinberg. James Bach and Michael Bolton introduced me to the subject of "systems thinking" as science of complexity.

Well... coming to the point, this post is not about system thinking but about a paragraph from the book "Tao of Physics". Here goes the text ...

"... The words of our language are thus not clearly defined... Science, on the other hand aims for clear definitions and unambiguous connections. Therefore, it abstracts the language further by limiting the meaning of its words and by standardizing its structure in accordance with the rules of logic. The ultimate abstraction takes place in mathematics where words are replaced by symbols... In this way scientists can condense information into one equation, into one single line of symbols. The view that mathematics is nothing but extremely abstracted and compressed language does not go unchallenged...mathematics not just a language to describe nature but is inherent in nature itself. Originator of this belief was Pythagoras, who made famous statement - "All things are numbers" …

This puzzles me ... considering(or conceding) that mathematics is an abstract language used by scientists to represent theories, models and scientific thought in a precise and unambiguous way, how can such an abstract language be suitable to describe nature (even in parts) ?

Nature is live, rich and multi dimensional where as mathematics is at other end of the spectrum - abstract, precise and single dimensional. Did Pythagoras and for that matter Galileo make mistake by saying "book of nature is written in the language of mathematics". I am certain that mathematics does not be to be interpreted where as nature and its manifestations need to be. Am I making sense?