Re: In an RDBMS, what does "Data" mean?

"Paul" <paul_at_test.com> wrote in message news:gfjtc.7896$wI4.912834_at_wards.force9.net...
> Anthony W. Youngman wrote:
> > So if you use Newtonian Mechanics to prove where Mercury was 400 years
> > ago, your proof is more accurate than Tycho Brahe's observations - which
> > place it somewhere else?
>
> The proof will still be 100% accurate.
> Newtonian Dynamics assumes certain axioms, which we now know to be
> slightly wrong.

If talking about mathematical axioms, they are not right or wrong -- they just are. It is the use of those axioms in some setting or another that could be inappropriate, not useful, or lead one to draw incorrect conclusions due to applying a poor mathematical analogy (metaphor) to the situation.

> The first-order logic is still perfectly accurate; it's
> just your starting assumptions have changed.

So the mathematics is right, but the science is wrong -- and I think that is a major point of this thread.

> > You are making exactly the mistake that made me start this thread - you
> > are assuming that the DBMS *defines* reality, rather than carrying out
> > experiments to show that the DBMS accurately *describes* reality.
> >
> > What you should have said is "IF the dbms is an accurate model of real
> > life then ...". Which is basically what I said - if the dbms and real
> > life disagree then the dbms model must be wrong. You seem to be saying
> > that it's reality that's wrong ...
>
> I'm just talking about the system of logic that enables us to talk about
> our database (our "theory" if you like). Whether our theory has axioms
> that correspond to the real world, or whether our interpretation (or
> "model") of our theory is accurate, is a totally different question.

Exactly -- so I think you and Wol (and I) are in agreement on that. It is why whenever anyone suggests that the best way to set up a databases is by employing relational theory BECAUSE relational theory is based on mathematics, I laugh (then cry). I have an appreciation of what mathematics is and what it isn't. How do we determine whether a mathematical model is a good metaphor for what we are doing? We have to step outside of mathematics to do that. So, the proof that various aspects of relational theory have been good for use with DBMS's is not within mathematics.

> > The problem I have is that the mathematicians seem to have taken C&D's
> > idea of "data" and built this wonderful theory on top of it.
> > Unfortunately, what they have not done is to define "data" in real-world
> > terms (rather than mathematical), and as such there is no way we can go
> > from a "proof within the model" to a formal description of the reality
> > that that proof represents. So you can come up with all the proofs you
> > like within the dbms, but you cannot show that the equivalent real-life
> > scenario is true because you cannot describe that scenario accurately.
>
> What I'm saying isn't really relying on DBMSs at all, it's just pure
> logic. A DBMS is just an example of a system that uses it. We have
> several layers:
>
> 1. First-order logic itself (our meta-language)
> 2. Our theory (all the relations and tuples in the database, our axioms)
> 3. Our model (how we interpret our theory in the real world)
>
> All I'm saying is that we know that part 1 is guaranteed to be complete
> and consistent. Parts 2 & 3 can be totally wrong, which is when your
> database will give answers that diverge from reality.

Additionally, the metaphor we choose might limit us so that what we say is true, but not the whole story. And another possibility is that our metaphor is useful and provides accurate answers, but does so in a clumsy fashion so as to cost more than it needs to. The cost of one metaphor might be higher than another because the human brain or people in a particular culture might find one metaphor easier to grasp. If I tell a person on the street that I have data in a relation (using a mathematical metaphor), that might not be as good as telling them I have data in a folder (a non-mathematical metaphor), for example.

[Slight digression: If we could the 1st-order predicate logic behind the "folder" metaphor (ah ha -- how 'bout a function?) we could make some progress perhaps?]

> > So by definition the theory is unscientific because you cannot show that
> > the dbms proof is true (or false) in real life.
>
> Given that your axioms and your interpretation are correct, then I think
> you can show the DBMS proof is true in real life (for the reasons given
> above and in previous posts).

And how do you show that your interpretation is correct -- by not showing it to be incorrect, by showing many cases where it is correct? I think that is central to this discussion. I'm about to read the book someone mentioned, "Data and Reality," and perhaps that will shed some more light on that question.

Summarizing -- three questions:
1) (How) can we prove that our mathematical model (e.g. relational theory) aligns with what we are applying it to (e.g. databases)? I think we can only disprove it or fail to disprove it.

2) Are we missing some important aspects of databases (e.g. mountain man's concerns) if we limit ourselves to a single mathematical metaphor (e.g. to what relational theory can tell us, or can tell us today)?

3) Are we applying the best, most effective, most efficient, etc metaphor or is there something better to either supplement or replace it?

--dawn
<snip> Received on Thu May 27 2004 - 13:11:24 CEST