Physicist John Moffatt has a new book out called 'Reinventing Gravity. ' In it, he offers his take on the phenomena of dark matter and dark gravity. According to his theory, working with a variable quantity for the gravitational constant, both phenomena, which have not been observed, are no longer necessary.
Since I'm not a mathematician or physicist, what I found most interesting about the book was Moffat's approach to current assumptions in mainstream science, particularly regarding verifiability and paradigm shifts. His book fairly easy to read, and I haven't gotten to the chapters where he finally spells out his theory, but it appears that he is willing to let observed data have the last say. It will be interesting to see how it all falls out.
Perhaps my favorite part of the book so far is his exposition of the astronomical fascination with the planet Vulcan, a world that was theorized initially, with some authority and even logic, to explain the pertubrations in Mercury's orbit. Moffat likens Vulcan to current theoretization of dark matter.
It is interesting to see scientists grapple with some very fundamental problems in science theory these days. Moffat and Wilczek seem very willing to call things as they see them and not pull any punches.
My own feeling is that the current reliance on symmetry as a guide through today's research will turn out to be overused. It looks as if mathematics itself is in for an overhaul, because our current notation doesn't deal with the dimension of time very well. In simple equations, time is equivocated upon, and Moffat indirectly acknowledges this by refusing to take commutativity as an absolute property of some processes. Another absolute that hasn't been dealt with very well (in my opinion) is pi. This constant is an observed local phenomenon of our particular corner of the universe, and implies a flatness that could easily be violated elsewhere.
Finally, I think the concept of dimension needs to be taken even further than Mandelbrot has carried it, which physicists have implicitly done, but which hasn't made it into our explicit apprehension of the world. Scientists are still relying on Euclidean Geometry of three dimensions for interpretations and explanations of their math, when it is obvious that dimension is the wrong word for what they are calculating.
Dimension is too strongly associated with what we measure as length depth and width, which are entirely Euclidean and simply a construct that ignores other measurable continua in the Universe, such as heat, mass, and others which I might go into at a later date. If we replace the word 'dimension' with 'translation' or some other noun, then an order greater than three or four ('dimensions') becomes intuitively much less confusing.
