Re: Operationalize orthogonality

J M Davitt 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).
> >
>
> (Too bad you snipped so much... Wait: you snipped *everything!*)
>
> Hmm... I'm not sure you responded to everything.
>
> My follow-on was to have been, "How far do we have to go before you
> see the light at the end of the tunnel? A half-adder, perhaps?"
> No problem. "You want more?" Can do!
>
> Some time ago - and for a different purpose - I put together an
> octal digit implementation with operations for most of the C-style
> arithmetic and bit-fiddling stuff.
>
> But I'm done with this...
>
> (So sad.)

I don't think I over-snipped. You asked two rhetorical questions and one actual one. I answered the actual one.

However, I think you are still 'off' in terms of my original question.

Tony made an assertion that I read as saying that one could build a type generator using only booleans (which are not bits) and relations and I cannot see how this can be done. Tony may have been using the word 'relations' in the mathematical, rather than the 'relational model' (as used in DBMS theory) sense. if so, it's up to him to clarify that; but I would still struggle to understand the 'how' because I don't think he is correct.

I am not making any sort of attack on the relational model. As far as I can see, it's 'orthogonal' to my question. As is my work history and education. Received on Wed Jun 07 2006 - 22:51:41 CEST