# Re: Operationalize orthogonality

Date: Tue, 06 Jun 2006 09:22:25 GMT

Message-ID: <lPbhg.38715$YI5.14318_at_tornado.ohiordc.rr.com>

Pickie wrote:

> Tony D wrote:

*>
*

>>By describing integers using booleans. Once you have integers >>described, you can (assuming you've defined the > operator on them) >>explicitly maintain order, wherever it's necessary to have order. >> >>We start from ground zero (booleans, relations, type generator). From >>ground zero, we can get to the basement (booleans, relations, type >>generator, integers). From the basement, we can clamber to the ground >>floor (booleans, relations, type generator, integers, characters). This >>is the point where things might start to get recognisable as a usable >>system, assuming generous helpings of syntactic sugar. >> >>It isn't a cop-out, but I did use in an earlier post the phrase >>"frightening degree of circumlocution". Hopefully you can now see just >>how frightening. But it is doable. >> >>This is very good news, because if we can reason about ground zero, >>then everything above it is on a very sound foundation. If we start >>building at the ground floor with no foundations or without thinking >>about the foundations, then sooner or later our reasoning about how the >>building is hanging together won't work anymore leading to >>unpredictable or difficult results trying to build additional floors >>(or heaven help us, an extension) or even collapse of the building.

*>*

*>*

> OK Tony.

*>*

*> As I understand you, there are three things you are saying (in the*

*> thread in general).*

*>*

*> The first is that the relational model requires only the boolean type.*

*> Fair enough, although I would have said that booleans underpin the*

*> relational model, as they do logical methods, structure, processes,*

*> etc. in general.*

*>*

*> The second is that something else should provide types and the type*

*> generator because this is orthogonal to the relational model. Again,*

*> fair enough. No problem there. Can I assume that information defining*

*> the types is held somewhere available to the DBMS?*

*>*

*> The third thing is that other types _could_ be defined using only*

*> booleans and relations. This is the part with which I am having*

*> difficulty. I understand that bits (zeros and ones) in particular*

*> order, using specified codes, can be used to represent integers, text,*

*> video, etc. I understand that a boolean can be repesented by one bit.*

*> Just how does one get from the sub-sub-basement (booleans and*

*> relations) to ground zero (booleans, relations, type generator)?*

*This* is what you're hung-up on? You seem to be assuring us that you understand how collections of bits can be used to represent integers and text and video and that you understand how some collections of bits end up as music in your ears - but you're having trouble understanding how these bits can represent attributes, tuples, and relations?

> On re-reading your first post of May 30, my only problem is with

*> something you said _could_ be attempted but ought not to be. You
**> thought it would "require a frightening degree of circumlocution",
**> while I just can't see how it's possible at all.
*

Okay, let's start with the fact that you "can't see how it's possible at all." Do you acknowledge that it is possible, despite the fact that you can't see it? (Obviously, there are systems that do these things.)

> However, since you

*> re-assert it's doable, my question remains. How?
**>
*

Received on Tue Jun 06 2006 - 11:22:25 CEST