Moderation Note: The first two posts in this thread were split from "Bang/Crunch Revisited" where they were off topic.
Maddog,
This may come as a wake-up call for you on all those extra dimensions in string/M-theory.
From near the end of the "The Ontology and Cosmology of Non-Euclidean Geometry"
essay we are discussing in the spacetime thread:
The Ontology and Cosmology of Non-Euclidean Geometry
Quote:
Just because the math works doesn't mean that we understand what is happening in nature. Every physical theory has a mathematical component and a conceptual component, but these two are often confused. Many speak as though the mathematical component confers understanding, this even after decades of the beautiful mathematics of quantum mechanics obviously conferring little understanding. The mathematics of Newton's theory of gravity were beautiful and successful for two centuries, but it conferred no understanding about what gravity was. Now we actually have two competing ways of understanding gravity, either through Einstein's geometrical method or through the interaction of virtual particles in quantum mechanics.
Nevertheless, there is often still a kind of deliberate know-nothing-ism that the mathematics is the explanation. It isn't. Instead, each theory contains a conceptual interpretation that assigns meaning to its mathematical expressions. In non-Euclidean geometry and its application by Einstein, the most important conceptual question is over the meaning of "curvature" and the ontological status of the dimensions of space, time, or whatever. The most important point is that the ontological status of the dimensions involved with the distinction between intrinsic and extrinsic curvature is a question entirely separate from the mathematics. It is also, to an extent, a question that is separate from science--since a scientific theory may work quite well without out needing to decide what all is going on ontologically. Some realization of this, unfortunately, leads people more easily to the conclusion that science is conventionalistic or a social construction than to the more difficult truth that much remains to be understood about reality and that philosophical questions and perspectives are not always useless or without meaning. Philosophy usually does a poor job of preparing the way for science, but it never hurts to ask questions. The worst thing that can ever happen for philosophy, and for science, is that people are so overawed by the conventional wisdom in areas where they feel inadequate (like math) that they are actually afraid to ask questions that may imply criticism, skepticism, or, heaven help them, ignorance.
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It fits Modest's overblown estimate of 'the more math the better' (not a quote) as well.
Michael
