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Re: Operationalize orthogonality

From: Pickie <keith.johnson_at_datacom.co.nz>
Date: 7 Jun 2006 14:16:38 -0700
Message-ID: <1149714998.719221.45840@f6g2000cwb.googlegroups.com>

paul c wrote:
> Pickie wrote:
> > Booleans don't in themselves convey order. Marshall elsewhere in this
> > thread said "The RM doesn't have anything about order as part of its
> > definition; one defines order on top of it." and I don't think there
> > was any controversy over that.
> >
> > Individual bits can represent booleans, but where is the concept of
> > order coming from that turns a set of bits into a coded string of bits?
> > If Marshall's statement quoted above is true, then it cannot come from
> > relations, therefore Tony's contention that it is possible to "model
> > everything from there on up in terms of relations and booleans" is
> > untrue.
> >
> > So, to answer your question. Not only do I not see it, I do not
> > acknowledge it is possible. Obviously there are systems that do it,
> > but _not_ by building _solely_ on booleans and relations (even
> > theoretically).
> >
>
> At the end of the day, order is in your head and doesn't seem to be
> necessary to the rm though you could choose to express it with a
> relation. Even physical machines fake it, eg., opcodes that return
> 'greater than' are usually just subtraction circuits in disguise. There
> is a big difference between slavishly emulating such a relation and
> taking a short-cut to get its logical equivalent. Even though I'm not
> one of them I'll stick my neck out and state that that's part of what
> rm's deep thinkers have in mind when they talk about implementing an
> abstraction, which is not at all about emulation or imitation (which
> were certainly part of the motivation for C++, plus maybe other oo
> languages). You don't need to materialize a relation in order to adhere
> to it (which some of the oo people seem to forget, can't comment about
> the pickies). My impression is that the rm people consider the "coded
> string of bits" as a mere representation, ie. carrying meaning only in
> the eyes of the beholder.
>
> p

I too consider the "coded string of bits" as a representation, although possibly not 'mere'. Do I have to put a silly emoticon or tag set here so no one is offended? Hope not.

My difficulty is with a highly limited aspect of Tony's post that is, as far as I can see, unrelated to the "relational model".

Your statement about order, viz. that "...you could choose to express it with a relation" is just about the same as the one in Tony's with which I have trouble. Is this use of the word "relation" the same as that in the relational model; that is, the thing Date calls a relvar? If it is, I have the same problem understanding just how this can be done. Received on Wed Jun 07 2006 - 16:16:38 CDT

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