The statement 2+2=4 isn't true if you are doing your arithmetic modulo 3
On the contrary: 4 is by definition what you get if you add 2 and 2, and 2 in turn is by definition what you get if you add the multiplicative identity to itself. It just so happens that in GF(3), 4 is equal to 1 :-)
Indeed, many statements about the universe are explicitly stated to only apply in restricted areas or to particular materials (Ohm's Law being another good example), and are still useful, and it's missing the point to talk about whether they're "true". The thing about Newton's laws in particular, though, is that they were claimed to be universally applicable, and it is that which turned out to be untrue. In particular, they were claimed to be what governed the motion of the planets round the sun, and even that is untrue (Mercury's precession is only explicable by the relativistic correction).
Re: Newton's Laws
Date: 2006-12-22 01:12 pm (UTC)On the contrary: 4 is by definition what you get if you add 2 and 2, and 2 in turn is by definition what you get if you add the multiplicative identity to itself. It just so happens that in GF(3), 4 is equal to 1 :-)
Indeed, many statements about the universe are explicitly stated to only apply in restricted areas or to particular materials (Ohm's Law being another good example), and are still useful, and it's missing the point to talk about whether they're "true". The thing about Newton's laws in particular, though, is that they were claimed to be universally applicable, and it is that which turned out to be untrue. In particular, they were claimed to be what governed the motion of the planets round the sun, and even that is untrue (Mercury's precession is only explicable by the relativistic correction).