Re: Interesting article: In the Beginning: An RDBMS history
Date: Sat, 08 Apr 2006 12:25:29 GMT
Message-ID: <ZYNZf.133$ee6.86_at_trndny01>
>
> As soon as it does change (e.g. add/scratch an
> attribute/column/field/whatever horizontal thingy)
> the /number/ references have to be re-examined whereas the /name/
> simply continues to refer to the correct (as
> correct as it was to begin with) data.
>
The above is true if the numbers are determined by a position in a list. If
the numbers are simply assigned
sequentially, as if they were "names", you could alter relational tables
or relations without regard to the
"column numbers". However, since attributes in a relation are written down
by POSITION, and not merely by numerical name, your point is valid with
regard to mathematical relations.
Going back to the original question which was (roughly) "what's the difference, in mathematics, between a relation and a relationship", the question you raise may not arise. I declined to offer either Codd's answer or my own. I didn't offer Codd's because I don't know it. I didn't offer mine because I'm not a mathematician.
All of the answers that have been since advanced do not relate to the mathematical consequences of "relation" vis a vis "relationship". They relate to the software engineering problems of building a DBMS, and to the human problems of sharing data without losing meaning. These problems are real, but they aren't "mathematical". (That's not to say that mathematics cannot be usefully applied to addressing these problems. I'm not offering an opinion on that, either).
What mathematicians who read Codd tend to overlook is that Codd was not writing mathematics. He was proposing a data model. The fact that his model maps tightly onto the mathematics of relations was part of Codd's intention, and one of the reasons for the durability of the model. But the purpose wasn't to advance the frontiers of mathematics. The purpose was to advance the frontiers of the human art and the engineering discipline of building and using large, shared data banks. Received on Sat Apr 08 2006 - 14:25:29 CEST