OptikaNET wrote:...And that's without getting into the strong-anthropic arguments that mathematics is a human construct, or the semi-Sheldrake territory of thinking that maths works because we believe it does!!! After all, without encountering another intelligence and comparing notes, we have no way of independantly verifying it.
The answer to this is also the answer to the next paragraph, but to add a couple of extra observations to the discussion below, (a) mathematicians almost universally believe that they discover
maths, rather than invent
it. That's because it "kicks back" - doesn't just easily fit their preconceptions. For example, if they invent it, why didn't they just solve the 4-colour problem or the Goldbach conjecture or Fermat's last theorem by making up an answer? Why were they so put out be Godel's theorem showing no sufficiently rich system of arithmetic can be complete or consistent (or whatever it showed) if it's all just invented? The simple answer: because it isn't. It's "out there" in some real sense, even if it isn't soemthing we can see or touch.
And (b) why does maths work so darn well in the physical sciences, if it's "just a human invention" ?
OptikaNET wrote:And physics assumes that the universe follows the same rules throughout, no matter where you look; which is a necessary assumption for the science of cosmology to progress, but it's still an untested assumption. And with us constantly having to "multiply our entities" to create things like "Dark Matter", "Dark Energy" and "Dark Flow" to explain things we can see that don't follow the maths, it's not unreasonable to spare a bit of thought for a universe which follows different rules in different areas. Modified Newtonian Gravity is already treading that territory...
That just isn't true. We can see
that physics works the same way in other parts of the universe by looking at distant objects. For example we can work out what stars are made of by using spectroscopes, which work because the laws of physics are the same inside stars as they are on Earth. It is a very well tested
assumption, all astronomcal observations to date have tested it, a point which is illustrated by the discovery that the expansion of the universe is accelerating, which required incredibly careful measurements of distant objects. This was an unexpected result, no one set out to prove it, and indeed they checked their results very carefully before publication because they could hardly believe them! If science was a tower of cards based on our own assumptions - i.e what we'd like
to be true - we'd never find unexpected stuff like that.
We don't "constantly" have to multiply entities, either. Dark matter was discovered in 1933, dark energy in about 1995. That's 2 unobserved entities postulated over the course of a century in a rather large universe. If that's the only things we don't know about we're doing rather well. (Dark flow is not an entity, by the way, they just got used to using "Dark" for everything. It's a possible irregularity in the uniformity of the expansion of the universe.)
Modified Newtonian gravity has a LONG way to go before it has the explanatory power of general relativity. It's a completely ad hoc revision with no justification except to fit observations without postulating dark matter. But there's no reason why all the components of the universe SHOULD interact with light (dark matter is better called invisible matter).
More generally, Emmy Noether explained very well why we should expect the laws of physics not to change across time and space due to symmetry considerations, and observation backs this up, because if the laws of physics DID change that would create gradients in the universe which would be able to do work. (This is exactly what dark energy seems to be doing - pushing the universe to expand faster. Since DE is thought to only be effective in large matterless voids, it's effectively a "change" in the laws of physics in some regions, and it has a visible effect. We'd expect that if say c varied in different areas, that would also cause visible changes).
Maths and physics only appear to leave large explanatory gaps if one is desperate for them to do so, perhaps for religious reasons. To most scientists they appear to be doing a damn fine job of explaining 99% of the universe, and closing in on the other 1%.
If you really want to find real gaps in our knowledge, you'd do far better to forget the "Einstein was wrong and I can prove it!" crowd and instead talk about consciousness
. See http://thecrazystuff.wordpress.com/
for further discussion of this interesting and by no means settled topic.