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?


Anonymous said...

Ask this question to Computer gfx people. They will tell you whether maths is the language of nature or not.

Chris M said...

Ah but Mathematics is the language of nature. One of the goals of physics is to derive a core set of laws from which all behaviour in the universe will follow. The language that these laws will be written in will, of course be mathematics.

For an example take Newton's law of gravity which can be expressed as F=G*m1*m2/r^2. This is a simple bit of mathematics but from it comes the entire movement of the solar system along with a n ice explanation as to why we can all inhabit this planet without floating off into space!

Interestingly at the start of the last century, the laws of physics as then known implied that if you could somehow precisely measure the position and velocity of all of the particles in the universe then you could work out what all past events had been and what all future events would be. The discovery of quantum mechanics and its inherent randomness put a stop to that idea (to the great relief of those who liked to believe in free will), but the fact remains that with enough data and a bit of fairly simple maths, you can describe nature quite well!

Shrini Kulkarni said...

Hi chris,

Thanks for dropping in and commenting. This blog probably is an unusual place for physics/maths discussion. But that is fine.

To me, the nature at macroscopic level, manifests itself in multitudes of dimensions. No one model or formal representation can be considered as appropriate. That is the basis of my confusion. While Newton quantified the force of gravity, apparently could not explain why there is gravity in the first place. We had to wait until the start of 20th century for Einstein to provide a plausible explanation.

Nature like a piece of music or poetry or painting - needs interpretation. Maths, on the other hand claims "self evident" and "self explanatory". Do you see a disconnect here? I do.

Physicists for their all glorified quest for finding out "essence" of nature, constantly seek simple unified solutions for "complex", "messy" and inherently contradicting - nature. But Nature, as demonstrated in Quantum theory, has surprised them at every instant.

To me, using the language of mathematics, physicists can "stage" the nature (reductionism)and observe a specific part.

I am not sure if there are any mathematical representations of rain, smell of a flower, sound of a bird, roar of a Lion. All voices of nature - akin to poetry, painting, music and multidimensional human emotional representation.

what do you say?


yomero said...

Unfortunately our senses ( that means the way we personally perceive or understand nature) are not a reliable as a source of scientific knowledge, and until we find a better way to represent nature we'll have to stick to reductionism.

Remember that every unexplained thing usually seems a lot more complex before the explanation comes.

This reminds me of a fragment from a interview with David Albert I watched recently:

"... if physics comes to this point, and I don't know that it will, but if it does, there's gonna be a very acute question - this other stuff you believe in, soul, spirit, or whatever it is, ..., What does it do?, What is it for? We've got the account for everything in terms of the motions of these particles, okay.... We've already established that it is not what makes you say what you say, is not what makes you write what you write, it's not what makes you marry who you marry. What work does it do?... Things could come to that."

Anyway, whatever the answer will be to our existential questions, the journey promises to be very interesting.