On 7/18/07, Anthony W. Youngman <[EMAIL PROTECTED]> wrote:
In message <[EMAIL PROTECTED]>, Mats Carlid <[EMAIL PROTECTED]> writes
>Anthony W. Youngman skrev:
>>
>> At which point, you hit my hobbyhorse ... "In the real world ..." -
>>relational database theory has ABSOLUTELY NOTHING whatsoever to do
>>with the real world. It's an exercise in pure maths.
>>
>>
>
>And You hit my hobbyhorse or rather one of them :-) ...
>
>RDMS theory is absolutely not pure maths!
So you'd say it's applied maths?
Sorry to be so chatty lately (still trying not to get sent to
u2-community with every topic that interests me ;-) but you (Wol)
know you are hitting my buttons now too.
It is a fact that many "relational theorists" try to keep their
"realtional theory" work to the realm of pure mathematics. If you
read Date or Pascal, for example, they would suggest that relational
theory is pure math which may be applied to databases.
The term "relation" is a mathematical term. "Relationship" is another
mathematical term and through language misuse combined perhaps with an
attempt to use a term that might not get confused with the English
meaning of "relationship" (which it does anyway), Codd opted to talk
about "relations" and that was close enough for his purposes.
One can do relational theory while working exclusively within
mathematics, originally remaining within set theory but predicate
logic is another branch of mathematics in which relational theory is
done today.
When this theory from set theory or predicate logic is applied to data
modeling or databases, it becomes applied. So, from a purist
standpoint, I'll vote with Wol on this. However, the Computer Science
community also uses the terms "relational theory" or "relational
modeling" or "relational databases" without placing any of these
strictly within the domain of pure mathematics. So, as used by the CS
discipline, it is applied mathematics. Applied mathematics has no
such claim to objectivity in the sense that if one chooses an
inappropriate mathematical model (many examples of this in the history
of science, but none popping to mine immediately), your applied
mathematics is flawed.
For example, if we say that Elmasri wrote a book on the fundamentals
of database systems and Navathe wrote a book on the fundamentals of
database systems and you decide to model this by assigning "1 book on
..." to Elmasri and "1 book on..." to Navathe and then decide to use
the + operator and conclude that "Elmasri and Navathe wrote two books
on the fundamentals of database systems" you would be wrong if they
are co-authors of one such book.
I know that you (Wol) and I both think this is biggest issue with
database theory--they came up with a mathematical "relational theory"
that had single-valued attributes, e.g. and then applied it to
databases. Many theorists have since worked with more complex
mathematics, while the applications of the simpler models or residue
thereof remain throughout "applied database theory" in SQL, Oracle,
etc.
Getting off-topic, but I've never
really understood the difference (as in how it is defined) between pure
and applied.
Did my above help to clarify that? In pure mathematics you can
"prove" mathematically (ignoring some fringe debates) from primitives
(axioms) that your result is accurate. With applied mathematics, you
can prove that the mathematics involved is accurate (1+1=2 which comes
from axioms/defs for these), but there is no mathematical proof that
you are applying it properly.
I know you can look at a problem and "know" which is which,
but how do you define it?
>
>In pure maths a relation is the set of tuples (ordered lists of n
>elements {e1,e2,e3...en } where the first element e1 belongs to a set
>S1 and e2 to set S2 etc.
>and there are no limitations on the nature of theses sets.
>Not even that the elements must be atomic - in contrary they may be
>sets themselves
>or lists ( like our multivalues ) or even relations ( like our
>associations ).
>
>Pure maths doesn't limit the nature of the defining sets at all -
>a set consisiting of my car, the north pole,the number pi and the set
>of all real numbers is valid.
>
>Thats a long way from rdbms integers,date, fixed length strings etc..
>.
>The explicit goal of Codds rules ( at least in the paper where I read them)
>is to limit this to something that is possible to handle on
>computer hardware (of the 70-ies!?) as well as allowing a relative
>easy formulation of select criteria,
>constraints etc.
and a desire to decouple application iprogramming from physical
database storage for large shared databanks.
>
>From an u2 or pick view Codd choose to include unecessary contraints on
>relations
>for the RDBMS,
Yes.
>But that doesnt make it more or less mathematical than the pick model..
This is where I agree with Mats, if I am catching onto who wrote what.
Actually, I'd say Codd made the RDBMS a damn sight *more* mathematical
than the Pick model :-)
He was explicit in the mathematics he used. One can (and does) still
apply mathematical models whether they are aware of it or not. It is
not more mathematical for a child to make a one-to-one correspondence
putting one toy on each book that is on the floor than for me to do
so, understanding that it is an application of a mathematical function
or map.
The relational model is defined in terms of axioms, constraints, and -
as I pointed out - a flat-out BAN on empirical testing
The theory itself does not ban empirical testing. Those who think
that relational theory is pure even after they apply it, try to put it
on a pedestal where it is immune to being tested even in its
application. It is true that the theory (mathematics) can live
outside of any usefulness it might have. There is a lot of money
ruding on ensuring that our industry keeps thinking that the
application of this theory to databases should not be tested. The
term "database" might need to be surrendered (replaced over time) in
order to get past this. Then we can benchmark the various ug-a-bungas
(or whatever) instead.
in that the
"users" building their system on top of an RDBMS are presented with a
"black box". That places it extremely firmly in the world of Maths.
The Pick model is far more scientific, as it actually makes some attempt
to model reality.
I would say that it was designed to more closely model language. XML
was also designed as an imlementation of a language model (which is
why there are similarities to Pick), but language in documents. SQL
was designed to implement a mathematical model that IMO was an
unfortunate application of mathematics to databases (particularly 1NF
and 3-valued logic). Just my ten cents. --dawn
--
Dawn M. Wolthuis
Tincat Group, Inc.
Take and give some delight today
Cheers,
Wol
--
Anthony W. Youngman <[EMAIL PROTECTED]>
'Yings, yow graley yin! Suz ae rikt dheu,' said the blue man, taking the
thimble. 'What *is* he?' said Magrat. 'They're gnomes,' said Nanny. The man
lowered the thimble. 'Pictsies!' Carpe Jugulum, Terry Pratchett 1998
Visit the MaVerick web-site - <http://www.maverick-dbms.org> Open Source Pick
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