t is its center?” -- “Trivial”; “What is the order of its Weyl group?” -- “696729600” (but you already knew that) …
Now: Suppose that spacetime does turn out to have six extra compactified dimensions, and that heterotic string theory is indeed the gospel truth. Now, those in a position to know, inform us that in that case there are only two possible choices for the gauge group of our world. Recall that earlier gauge groups we’ve met were things like the rotation of a wheel, things whose reality is familiar even prior to their employment as gauge groups: but now we must choose between SO(32) and E8 X E8. The choice must be made on the basis of certain physical predictions. Assessment-dimension lambda, for instance, might turn out to be physically measurable (specifying, say, the spin of a graviton, or the mass of a magnetic monopole, or what have you); lo and behold, lambda-0 in E8 X E8 turns out to correspond what we have measured, whereas the different value that falls out of SO(32) does not; and so forth for some other assessments.
All right then: The Realist thesis in this case says simply that adoption of E8 -- which is, in this view, pre-existent, and independent of physics just as it is independent of politics -- is a package deal. Not every fact and feature about E8 will be physically interpretable, let alone measurable; but for any that is -- say, omega -- the value as measured experimentally must turn out to be omega-0. If it doesn’t, we have a problem. E8 being pre-existent, and not invented by ourselves for our own convenience, it cannot be toyed and tinkered with, selecting some features and rejecting others in a Procrustean attempt to match experiments. And Synge’s picture of using Newton or Einstein, merely as the mood moves us, as though one were an Allen wrench and the other a pair of pliers, won’t do at all. If the mathematical structures we seem dimly to glimpse behind the veil of the world were analogous, not to mountains, but to man-made tools, then we could always kludge one up for the occasion. Then physics would be the theoretical equivalent of toenail clippers and pinking shears.