Re: The IDS, the EDS and the DBMS

"Paul" <paul_at_test.com> wrote in message news:414745d8$0$13400$ed2e19e4_at_ptn-nntp-reader04.plus.net...
> Mikito Harakiri wrote:
> >>But irrationals, or even the subset of them that is the nth roots of
> >>integers, don't have such a canonical form - for example consider
> >>sqrt(2) + sqrt(3). So after a few simple addition or multiplication
> >>operations the representation will rapidly get very unwieldy.
> >
> > When adding integers the representation grows as well, so there is
really no
> > difference.
>
> Well if I add two integers the result is usually not much bigger in
> terms of space e.g.
> 28594564654655 + 56467986465464
>
> but if I add two "surds" I get an expression that takes up at least
> twice as much space e.g. sqrt(2) + sqrt(3). Also there could be
> complicated ways to simplify the expressions which would be
> computationally expensive compared to integers.

The complexity of finite object can't be specified in absolute terms. Colmogoroff's complexity measure is defined as length of a program that builds the object, but since one program can model another one, then complexity measure is defined up to an arbitrary constant only. Therefore, your argument might not hold in some other representation for integers and radicals, or at least you have to prove that addition for integers is less complex than that of for radicals *in any representation*. And for integer representation in 1-based system we indeed witness that the complexity of the sum can be as big as the sum of the arguments. 1-based system is unconventional, of course, but you have to make sure that there is no other representation for radicals that is more compressed. Received on Tue Sep 14 2004 - 22:29:11 CEST