I was reading a paper concerned with the comparison of Karl Pribram's holonomic theory of mind with other models (though there seem to be no cogent other models, but rather a systematic collection of data with a pre-assumed notion that a theory will somehow pop out of all of it). While I was reading the paper something was said with regards to the ultimate reality of mathematical 'truth', in a way that as soon as I read it made me wonder at how I had not noticed the logic and depth of the question before.
Our scientific laws are, of course, written in the language of mathematics, and any serious scientist needs to develop their arguments mathematically as well as conceptually. It is something of a mystery that our mathematical language appears to describe physical laws so accurately, in as much as there is a correlation between mathematical equations and the physical results we obtain with them in experiments, and their consequent predictive qualities.
It is not surprising, then, that mathematics seems to be the natural language of the universe. It has troubled me that many of the mathematical arguments regarding the classical physical world are more often thatn not statistical in nature, particularly as we measure more and more at the quantum level of 'reality'. At the most extreme end of the belief in mathematics as the true nature of 'reality' Max Tegmark has proposed that the universe is mathematics. Truly the predictive power of mathematics is compelling and like most people I really didn't put too much thought into how convenient it was that a language devised by humans (for that is what it is) should so (seemingly) exactly match the base of reality.
But, what was drawn to my attention was the fact that our mathematics is based upon algorithms which are fed initial conditions and by means of the algorithm produce some predicted result. All seems well...except, does it seem likely or reasonable to think of the universe as being made of objects interacting with each other by means of algorithmic equations? The natural corollary of such a position is that of a dualism, that there are physical entities and an idea-like realm of laws; in other words the mathematical models we use cannot really be the 'reality', but are simply models which describe events pretty well. They are, in other words, contingent upon context. Actually we know this to be true, because the simple mathematical rules which have worked so well with regards to the classical realm are found to be inadequate to express the quantum realm - such that apparently simple summations (2+2, for example) become contingent, commutability not being a basic and necessary function of the quantum realm.
It strikes me, then, that we ought to keep in mind that mathematics, like any other form of language, is contingent; that a methematical argument in and of itself is not the thing itself but rather an approximation of how things are like, from a particular perspective. It is little wonder, then, that string theorists have tied themselves in knots as their arguments are pretty much entirely mathematical constructions - as if the mathematical equations themselves held truth/are truth. It always struck me as odd that extra dimensions should be invoked, without any real explanation of what a dimension actually is.
In the same way it has always puzzled me why anyone would talk of what 'shape' the universe is, as if somehow 'shape' and 'form' are objective entities - as if such concepts have any reality outside of a subjective purview (which links with such questions as how 'old' the universe is).
Just something more to think on, in terms of the search for scientific truth..... whatever that may mean..
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