Re: what are keys and surrogates?
Date: Sun, 27 Jan 2008 20:02:45 -0800 (PST)
Message-ID: <5a760728-9b0d-417b-a9d3-df08ae8cd8f9_at_u10g2000prn.googlegroups.com>
On Jan 28, 8:42 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> Jan Hidders wrote:
> > On 19 jan, 02:48, David BL <davi..._at_iinet.net.au> wrote:
> >>On Jan 19, 8:35 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >>>Jan Hidders wrote:
> >>>>On 18 jan, 18:33, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >>>>>Jan Hidders wrote:
> >>>>>>On 18 jan, 16:55, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >>>>>>>Jan Hidders wrote:
> >>>>>>>>On 18 jan, 00:55, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >>>>>>>>>Jan Hidders wrote:
> >>>>>>>>>>On Jan 17, 10:29 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >>>>>>>>>>>Jan Hidders wrote:
> >>>>>>>>>>>>On 17 jan, 14:40, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >>>>>>>>>>>>>Marshall wrote:
> >>>>>>>>>>>>>>On Jan 10, 7:07 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >>>>>>>>>>>>>>>Marshall wrote:
> >>>>>>>>>>>>>>Possreps! That's the one!
>
> >>>>>>>>>>>>>Having multiple possible representations for the same type allows data
> >>>>>>>>>>>>>independence--especially physical independence.
>> >>>>>>>>>>>>possible ways to store something in memory or on disk are related?
> >>>>>>>>>>>>You think the number of possible representations and the number of
> >>>>>>>>>>>>Why?
>
> >>>>>>>>>>>The latter grows linearly with the former.
>> >>>>>>>>>>(something which a matter of definition and/or convention) have any
> >>>>>>>>>>Why? Seriously. Why do you think there is a relationship at all? Why
> >>>>>>>>>>would the number of ways a value can be represented to the user
> >>>>>>>>>>bearing on how many ways there are to map it to 1's and 0's?
>
> >>>>>>>>>Why do you think representations are limited to representing to users?
>> >>an appropriate definition of "user". Otherwise what is the logical-
> >>Badour seems hung up on this, but it seems reasonable to assume the
> >>logical-physical distinction has very much to do with distinction
> >>between representations that are visible or not visible to users, with
> >>physical distinction about?
>
> Logical representations are representations to users. Physical
> representations are representations to the machine.
>
> From that, I conclude representations are not limited to representing
> to users.
>
> I repeat: Why do you think representations are limited to representing
> to users?
It seems Badour assumed "possible representations" meant physical and logical representations whereas Jan assumed it was only logical representations.
> >>>I don't see any need to respond to straw men beyond observing that they
> >>>are straw men. So, you want to assume that "possible representations"
> >>>relates exclusively to human users to what end? To prove your axiom?
> >>>Your axiom is false in the first place.
>
> >>>Assuming it to prove it is mental masturbation. If you want to engage in
> >>>such activities, please do so in private.
>
> >>Jan simply asked Badour to clarify what is meant by a representation
> >>and Badour responds with the straw man defence.
>
> Jan simply constructed a straw man to burn, and Badour obligingly
> pointed out the deficit of his sophistry.
This discussion is bordering on meaningless because of poorly defined terms.
> >>>>>Indeed. However, every mapping to the physical level starts with a
> >>>>>possible representation. Double or triple the number of possible
> >>>>>representations, and one doubles or triples the number of possible
> >>>>>physical representations.
>
> >>Note this well!
>
> Indeed. One would do very well to contemplate the point made.
Badour is as skilled at self promotion as handing out insults.
> >>>>No, it doesn't. Increasing or decreasing the number of possible
> >>>>representations does not influence the number of ways you can store
> >>>>it.
>> >>>representations for a data type. What's possible is always possible and
> >>>You are talking nonsense. One cannot increase or decrease the possible
> >>>what's not is not.
>
> >>On its face that contradicts Badour's earlier statement where he talks
> >>about doubling or tripling the number of possible representations.
>
> >>Perhaps he would say his previous statement concerned comparisons of
> >>*different* data types;
>
> Of course, it does. I thought that would go without saying. Apparently,
> I was wrong.
>
> however it seems remarkable to claim that
>
> >>unrelated data types would always exhibit such a similar ratio of
> >>number of logical to physical representations.
>
> >>For a given data type the possible logical representations are *user
> >>defined*,
>
> Hell no! The possible representations are all possible regardless of
> declaration to the dbms. What the possrep concept does is provide a way
> to declare some subset of them to the dmbs.
Doesn't Badour realise that according to that definition of "possible representations" its cardinality for any given data type would surely be infinite? How does one make sense of the following statement by Badour
Double or triple the number of possible
representations, and one doubles or triples
the number of possible physical
representations
Does Badour think one can compare infinities like that?
> >>>>>If one has six ways of storing it, presumably one has six ways of
> >>>>>storing each of the possible representations. Thus, the number of
> >>>>>physical representations grows linearly with the possible representations.
>
> >>Am I reading this right?
>
> No, you are not.
>
> Badour seems to assume that a given physical
>
> >>representation coincides with (only) one of the logical
> >>representations.
>
> Hell no! Stick to what Badour actually says. If one has 6 physical ways
> of storing an arbitrary representation, presumably one has 6 physical
> ways of storing each possible representation. If I had meant to say the
> number of physical representations exactly equals the number of possreps
> that's exactly what I would have said, you fucking moron.
Badour should stick to what I said! I never suggested he thought the number of physical representations exactly equals the number of possreps.
I would like to see Badour more carefully write down the point he is trying to make. I shall make an attempt...
Let's define some terminology. Let 'T' be a given data type. Let 'db' be a given database on which a user has provided particular definitions of physical and logical representations of T.
LR(T) = set of all (possible) logical representations of T. PR(T) = set of all (possible) physical representations of T.
ULR(T,db) = set of user defined logical
representations of T for database db
UPR(T,db) = set of user defined physical
representations of T for database db.
I don't believe LR(T) and PR(T) can be mathematically well defined. Even if there is some sense in which one can define an absolute concept of "possible representation", I imagine that for all T, LR(T) and PR(T) are infinite sets, because there is nothing to constrain a representation's complexity, redundancy or aesthetic quality.
Mathematicians tend to use the isomorphism concept to determine whether two mathematical systems are for all intensive purposes equivalent. For example, there is a sense in which the reals are uniquely defined given the usual axioms, and trivial differences like the choice of symbol used for zero are accommodated by an isomorphism.
I don't see any well defined approach for using isomorphic equivalence to reasonably count some finite set of possible representations (at least in any absolute sense). The problem is that at the outset we know all representations are isomorphic by definition!
Therefore I shall assume Badour is ignoring LR(T) and PR(T) (even though amazingly that doesn't appear to be the case).
Here's a guess at what he's saying: For a given database db, for a given T, for each element of ULR(T,db) every element of UPR(T,db) is available for its physical representation. Therefore, for all given T1,T2
|UPR(T1,db)| / |ULR(T1,db)| = |UPR(T2,db)| / |ULR(T2,db)|.
using |S| to denote cardinality of set S.
Clearly that doesn't follow. So what is Badour actually saying?
[snip] Received on Mon Jan 28 2008 - 05:02:45 CET