[renormalised (Carl)]

You seem to be implying that Einstein was a failure.

Einstein wasn't a failure, and I never stated that explicitly. What I said was that SR had problems and that he had a hard time trying to understand Quantum Theory.

Einstein's self admitted biggest blunder (The piece of fudge called the cosmological constant)may yet prove to be his biggest truimph.

Yes, and you're correct in that assumption, providing that what we observe as an apparent acceleration of universal expansion is actually occurring. Rather ironic, don't you think??. Einstein would probably laugh about it, if he was still alive.

If you look at string theory, the mathematics are also having to be made simpler by making a lot of assumptions and mathematical compromises.

You make a point saying that any theory that introduces infinities into its equations is meaningless and incorrect in its assumptions. Well, mathematics introduces infinities as one of its basic axioms (n+1) so does that mean that mathematics is incorrect.

Yes, there are a lot of assumptions and compromises in String Theory and in other related theories. Much of it due to the appearance of infinities in the equations of the theories. That's why I explained about renormalisation....it's to remove the infinities from the equations, otherwise the equations don't work. They produce nonsense or undefined answers. If the infinities were OK, then the mathematicians and physicist wouldn't bother trying to get rid of them!!!. N+1 is only infinite if you take the value of N to infinity. N can be defined in any way you choose, depending on the system you're working with...and when it approaches infinity, the answer to N+1 becomes undefined, It's an impossibly large number.

As far as saying that I am not thinking and accepting Einsteins theories at face value without applying any thought, then the same could be said for people like:
1. Owen Gingrich.
2. Steven Hawking
3. Brian Green
4. Jeremy Bernstein
5. Gerald Holton
6. Shimon Malin
7. John Stachel
8. John Archibald Wheeler
9. Richard Feynmann
10.Julian Schwinger
12.Roger Penrose
The list grows much longer and these are well known authorities in Astronomy, Mathematics and Physics of every persuasion.

So...they can only go by what they have learned and know. However, it doesn't mean that they can't questions Einstein's basic assumptions and the veracity of any formulations he made...and most of those guys have. Why do you think most of these guys have come up with various Quantum Theories.....why the great push for a theory of quantum gravity. It's because Einsteins theories only work so far... it's the same with Newtonian physics. Good for some situations and not for others. Now, even these new theories have run into trouble along various lines. Not just for infinities cropping up in equations, but it's one reason why.

Space as far as we know is infinite so any theory that discards infinity surely then must be incomplete. The mathematical universe has infinite complexity and is not fully comprehensible to us humans and this is why Godel came up with his theory of incompleteness.

These assumptions are entirely due to our lack of knowledge and understanding. We believe things to be infinite because we can't see any other way that they can be... all due to a lack of the complete facts. Essentially why Godel came up with his theory. It's the old axiom:

"The more we think we know, the more we realise the less we actually know and understand"

To quote Richard Feynmann "I can safely say that no one understands quantum mechanics"

I totally agree with him!!!!

Randomness is upsetting to mathematicians but only an outsider to mathematics would venture this statement. Just because infinities makes things more difficult to understand and compute doesn't make it incorrect and meaningless.

The first sentence you wrote here, about randomness, is rather odd. If something is upsetting to someone, then why wouldn't that someone venture the fact that it upsets them??!!. If someone from outside maths said that randomness upsets mathematicians, then he/she is only stating a fact that the mathematicians already concur with!!! Why would mathematicians want to try and renormalise equations that produce infinities if those infinities didn't create problems for them. Since they do try to renormalise their equations, then it's safe to say that having infinities crop up in your theories does cause problems and is a cause for concern amongst mathematicians (and physicists).

Suffice to say, your assumption that it took so long before someone could see the obvious mistake in SR is incorrect itself. They've known for decades about the problems with relativity. However, it doesn't mean that the entire theory should be thrown out with the bathwater, so to speak. Like Newtonian physics, it works...upto a point. But then the problems with the theory crop up and it no longer works (or works rather difficultly) in those situations where the theory is stretched beyond its limitations. Having infinities crop up in your theory is a sign that you're reaching those limits. All mathematicians and physicists recognise this, otherwise they wouldn't try to use methods such as renormalisation to get rid of them.

If you want to read a reasonably well written piece on renormalisation, go here:

http://en.wikipedia.org/wiki/Renormalization