The first thing we need to understand is that 'physics' tries to explain the way matter and/or energy interact with themselves or each other. In a sense, science explains 'natural' phenomena, provided we understand that everything that happens in nature must be termed natural (God, ghosts, etc. for which there are no observational evidence, don't fall in the purview of science as a whole), but physics restricts itself to inanimate things. A living organism as an unit, cannot be the subject of a physical law. But there are physical laws which explain how the atoms and molecules of which the living being is built, behave. The three stages of physical (or scientific for that matter) studies are, trying to explain various observations, building up a database of 'things' found out, and applying this hard earned knowledge to build objects of everyday use (technology).
Now let us try to figure out how mathematics came to be. It started with the effort to quantify objects found in nature, and gave rise to natural numbers. After this quite a few leaps of imagination were needed. The first one was taken by the hindus, who figured out the power of zero. Now we had the set of whole numbers, and in turn moved to the set of integers, real nubers, and then complex numbers. The arab mathematicians discovered how to do things without actually using numbers, but symbols to represent them (algebra). The dark age in europe ended soon after, and since then mathematics has progressed a lot, and today it's a highly abstract discipline, with a myriad of structures and sub-structures.
What was interesting was that everytime a physical law was to be stated, it found a mathematical structure appropriate for itself. The laws gave predictions which could be verified, which means we come back to natural phenomena and quantifying them (measuring them, whatever you like). The leaps of imagination that we were taking all this time couldn't take us very far away from what we perceive as reality, through physics we found a way to link the abstract structures of mathematics to phenomena we see around us. This search for a connection with something 'real' even made us 'see' things we didn't notice before.
All this makes you wonder whether a discipline whose origins lie in the quantification of physical entities/phenomena will always be linked to physical reality in some way? Even the most complex strucures that can be thought of, will actually be used to describe physical phenomena, albeit at a much more profound level in terms of understanding why things behave the way they do. Can physical laws be described any differently? Or is it just that we have a bias towards mathematical structures?
P.S. : two excellent papers to read which discuss the above topic and more ...
http://www.galileivr.it/docenti/Fisica/articoli/Effectiveness.pdf
http://arxiv.org/pdf/0704.0646
Now let us try to figure out how mathematics came to be. It started with the effort to quantify objects found in nature, and gave rise to natural numbers. After this quite a few leaps of imagination were needed. The first one was taken by the hindus, who figured out the power of zero. Now we had the set of whole numbers, and in turn moved to the set of integers, real nubers, and then complex numbers. The arab mathematicians discovered how to do things without actually using numbers, but symbols to represent them (algebra). The dark age in europe ended soon after, and since then mathematics has progressed a lot, and today it's a highly abstract discipline, with a myriad of structures and sub-structures.
What was interesting was that everytime a physical law was to be stated, it found a mathematical structure appropriate for itself. The laws gave predictions which could be verified, which means we come back to natural phenomena and quantifying them (measuring them, whatever you like). The leaps of imagination that we were taking all this time couldn't take us very far away from what we perceive as reality, through physics we found a way to link the abstract structures of mathematics to phenomena we see around us. This search for a connection with something 'real' even made us 'see' things we didn't notice before.
All this makes you wonder whether a discipline whose origins lie in the quantification of physical entities/phenomena will always be linked to physical reality in some way? Even the most complex strucures that can be thought of, will actually be used to describe physical phenomena, albeit at a much more profound level in terms of understanding why things behave the way they do. Can physical laws be described any differently? Or is it just that we have a bias towards mathematical structures?
P.S. : two excellent papers to read which discuss the above topic and more ...
http://www.galileivr.it/docenti/Fisica/articoli/Effectiveness.pdf
http://arxiv.org/pdf/0704.0646
