Re: Database design

Mark Johnson wrote:
> Christopher Browne <cbbrowne_at_acm.org> wrote:
>
> >Cleveland served BOTH before and after Harrison, which means that
> >there is NOT a clear order on a by-president basis.
>
> No, not in terms of a non-network tree. A list. A roster.

There are partial order relations and total order relations. There are other kinds of order relations as well but let's not lay it on too thick.

For any list, we can construct a pair of relations that contains the same information. We do not need the use of an ordered collection to do so.

In fact, let's pull a basic set theory book off the shelf and look up "list."

"A 'finite sequence' over set A is a function from {1,2,...,m} into A, and
it is usually denoted by:

    a_1, a_2,...,a_m

Such a finite sequence is sometimes called a 'list' ..."

In other words, we can use set theory to define lists without reference to any ordered collection.

> >According to the theory, relations are unordered sets of facts.
>
> But according to someone else, here, sets are always unordered.
> It's simply redundant to speak of unordered sets, by that thinking.

That's right!

> And the
> relation, itself, is said to correspond to a set, though I'm not sure
> that's true.

A relation is a kind of set.

> It contains entities, or tuples, instances, records, what
> have you, which consists of fields, attributes, again, what have you.

"Elements" or "members" are the usual terms for what a set contains. "Attributes" is what we usually speak of the subparts of a relation element as consisting of, although I prefer the simpler "fields" these days.

> So you would phrase it, a relation is a set of sets which members are
> 2-tuples each being a name and value.

Um, no. A binary relation is a set of ordered pairs or, equivalently, a subset of a product of two sets. The more general n-ary relation used in database theory is a subset of a product of n sets, n >= 0. In n-ary sets, we usually speak of the attributes as being identified by name rather than by one of {left, right}.

> In other words, the tuples are not in any order.

Right.

> >Your need for "proper order" is a fabrication in your own mind.
>
> My need for my own that is mine, etc. Look, let's take this very
> sentence.
>
> Your need for "proper order" is a fabrication in your own mind.
>
> If those words appear in any other order then they will say to you
> something else, or nothing at all. Let's experiment:

These experiments don't show anything that isn't obvious: namely, that there is information in the order of the words. But no one ever said a sentence was a set of words!

And anyway, the value of paragraph order is being overstated. There are tons of things that can be done with text without reference to word order. An index springs to mind.

As per your earlier request, here are four paragraphs of text out of order. I have reversed the order of the paragraphs that the author intended. I picked a Housman poem, "The New Mistress". Housman doesn't have a lot of four stanza poems, but this one is nice.

The New Mistress (in reverse stanza order) A E Housman

I will go where I am wanted, where there's room for one or two, And the men are none too many for the work there is to do; Where the standing line wears thinner and the dropping dead lie thick; And the enemies of England they shall see me and be sick.

I will go where I am wanted, for the sergeant does not mind; He may be sick to see me but he treats me very kind: He gives me beer and breakfast and a ribbon for my cap, And I never knew a sweetheart spend her money on a chap.

I will go where I am wanted, to a lady born and bred Who will dress me free for nothing in a uniform of red; She will not be sick to see me if I only keep it clean: I will go where I am wanted for a soldier of the Queen.

'Oh, sick I am to see you, will you never let me be? You may be good for something but you are not good for me. Oh, go where you are wanted, for you are not wanted here.' And that was all the farewell when I parted from my dear.

As you can see, the poem works perfectly well with the paragraphs in reverse order, as I had predicted.

> Everything in its proper order. And that seems to be considered not
> merely a luxury in such a model that you defend, but an irrelevancy.
> And that makes such a model - itself - rather irrelevant. Does it not?

You are noting the definition of set, and assuming that it is thought that this definition is intended to describe all collections; it is not.
You have reversed the process.

> There is a reality. By comparison, theoretical physics may appear to
> be a lot of assertion and imagining and such. But there is something
> against which the theory is tested, something that makes the equations
> right or wrong. And that's physical reality.

Physics is science; it is bound to physical reality. Math is not. Math is only bound to math. Objecting to a mathematical theory by analogy to the physical world is invalid. Were we to limit ourselves to that, we would have to discard most of math, including negative numbers, complex numbers, infinities, the axiom of choice, and more. Heck, even fractions; you can't show me half of anything. That's not half an orange; that's a huge collection of atoms. We would also have to get rid of zero, because you can't show me zero of something, either; I don't see it!

You may think I'm being facetious, but I'm not--all of these advances in math were initially objected to by analogy to the real world. But, as it turns out, analogy to the real world is not a useful way to reason about math. (Although the reverse, using math to reason about the real world, does turn out to be useful. This is why math is useful.)

Marshall Received on Thu Feb 23 2006 - 09:30:11 CET