Another Sunday meditation of sorts today, about the Albert Einstein quote I employ in the right-hand column of this blog...
"... As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. "I've always loved those thought-provoking lines. Once or twice a year someone emails me with some sort of question or complaint about them. Often readers don't realize they can simply click on the quotation to go to the fuller speech Einstein gave from which the words come.
Anyway, since it's a famous quote, I decided to check around the internet to see what sort of discussion it may have generated elsewhere.
It arises in a lot of places, but one of the best treatments I came across was entitled "Unpacking An Einstein Aphorism" with a lengthy discussion of it (and its possible meanings) here:
It's a bit heavy on philosophy and semantics, but introduces many points I hadn't thought about. For one thing, I hadn't even thought about the fact that Einstein originally gave this talk in German, and so what we commonly read is of course an English translation… which immediately raises some uncertainty because of the imprecision of translation, especially of a word like "reality." The piece is a bit of a slog by the end (but no more so than any philosophical piece addressing subtleties and nuances of language), and makes interesting points along the way. If the quote interests you give the above piece by J.N. Nielson a whirl...
[elsewhere... if you know who blogger Mike Lawler is, get to know him better by visiting MathTango now, or if you don't know of Mike, by all means, go there to learn about him.)]