I guess it just depends on the math your using. Numbers like any other symbol in mathematics are used to imply value, which follow a given set of rules when manipulated. Change the value and give the rules a little tweaking and PRESTO! 2+2 could equal a honey-baked ham. Sound silly? Both Gauss and Riemann invented mathematics in which 2+2 equaled 3 and 5, respectively. Although, we can thank Fermat’s editor for also screwing us out of the proof for 2+2=5 under Euclidian Arithmetic. I think that Dex was a little off calling it “a joke about rounding and estimating” (Does 2 + 2 = 5 for very large values of 2?"), seeing as the Pythgoreans, Fibonacci, and Frege took it pretty seriously.
I have edited the link to the staff report so that it works. – CKDH
[Edited by C K Dexter Haven on 04-19-2001 at 07:11 AM]
The key phrase is “for very large values of 2.” The expression is very different from just “2 + 2 = 5” and the search for (or invention of) different numbering systems or different group operations within the Real Number system.
Thus, the Staff Report was not about the mathematics of group theory (among others) but about the common English-language expression… which is clearly jocular, and not a statement of a mathematical theorem. Not even a lemma.
Also, please note, I did say it was a joke with a serious underlying point.
Interestingly, I had always heard that this expression had its origins in physics, not math, and had nothing to do with rounding. Often, physicists will say things like “for small values of hbar, quantum mechanics looks like classical mechanics”, or “for large values of c”, or something similiar. Of course, hbar and c are fundamental constants of Nature, and can no more have “large values” than can 2. What those statements really mean is that everything else in the problem is large, relative to hbar, or small, relative to c.