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Originally Posted by tommac
Even by design I believe that Einstein avoided the math ... but Grossman tricked him into using it for GR.
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Not by a long shot. The popular myth of Einstein being somehow lousy at math is just that, a popular myth. He was in fact quite good at it. It was Einstein who was the driving force behind the mathematical development of GR, going to Grossman and others for help when he knew he needed new tools to develop the necessary math. Newton solved the problem by inventing calculus for himself. Einstein did not need to do that, he only needed to find the right tool already in the hands of mathematicians.
Quote:
Originally Posted by tommac
I guess a better way to word the problem is ... how to approach a problem, start with the math or start with logic?
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Logic & math are inseparable, at least in the context of the natural sciences. Math is the natural language of logic, so in order to understand the logic at any level beyond the most rudimentary, you must do the math.
Quote:
Originally Posted by tommac
But you can understand some of the concepts without understanding the complicated math.
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For the most part, this too is a popular myth. You may
think you "understand" an idea without the "complicated math" (which is often not really all that complicated, ust specialized). But in reality there are always key points left out or skipped over because the math, complicated or not, is still missing. This is something I have come to learn from years of trying to design talks and articles explaining those very ideas to totally non mathematical audiences. I have become quite skeptical & critical of almost all of the popular explanations I see because they are so over simplified that they just get it wrong, or get it so misleading as to make it essentially wrong.
if you can't or don't do the mathematics then you have literally no hope at all of ever really understanding general relativity, or really any other aspect of modern physics, beyond the legendary "cave man" level.