Re: Basic question?What 's the key if there 's no FD(Functional Dependencies)?

NENASHI, Tegiri wrote:
> vc wrote:
> > NENASHI, Tegiri wrote:
> > [...]
> > > The advantage is a lot: evolution from functional datamodel DAPLEX to
> > > the functorial data mode: class is a category;
> >
> > The FDM does not appear to offer much in comparison to the old fdm
> > except the obscure categorical jargon, fdm/NIAM in its turn does not
> > offer much in comparison to the r.m. (see old fdm discussions in this
> > group).
> >
> >
> > >. Zinovy Diskin said that category theory
> >
> > Your favorite chap Zinovy's article are pretty hollow unless he wrote
> > something more substantial elsewhere.
>
> It is not very fair but you can be probably right that his articles are
> more easy for the beginners.
>
> >
> > The only interesting reference you've provided is the universal view
> > updatability property. The author apparently knows what he is talking
> > about, not jus tries his best to get published. I need to take a
> > closer look though.
> >
> >
> > > and Lawvere who solved the mystery of what natural number is
> >
> > Could you like explain this n.n thingy ? Don't we all know that the n.n
> > are just 1,2,3, and so on ? Statements like that sort of undermine
> > your credibility.
>
> The natural number in the set theory can be build in many facons: von
> Neumann numerals, Zermelo numerals et cetera.

That's right, but as soon as you showed that a construction is possible, you can discard it and just use the algebraic properties, or specification, of a specific mathematical structure. I do not see much difference between the Peano axioms and the Lawvere NNO. In fact,  the Peano axioms are much much simpler to understand and explain. Besides, the NNO relies to a great extent on Dedekind's "Was sind und was sollen die Zahlen ?" and hardly can be considered an "invention" (see below).

> Lawvere invented the
> natural number object in the category theory that is independent of the
> implemenation. It is a pure specification without not important
> details. There is a very good article by the Harvard professor Barry
> Mazur "When is one thing equal to some other thing?" that explains the
> natural number very well. But it can be very simple for you like the
> articles of Diskin, no ? ;)

Mazur's article contains a lot of stuff that I disagree with, but as an intro to the category theory I guess it's better than some others. Anyway, I do not think this categorical mumbo-jumbo is very relevant to the newsgroup although the sketch model might be interesting to some people.

>
>
> --
> Tegi
Received on Wed Nov 08 2006 - 22:44:14 CET