Re: Database design

"Marshall Spight" <marshall.spight_at_gmail.com> wrote:

>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.

Alright. But that's what you'll speak of, some ordered set.

>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.

While necessarily, as a necessary condition, being able to retrieve in proper order:

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

> a_1, a_2,...,a_m

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

However denoted:

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

Someone touched on this, before.

They said that (a,b), was an ordered pair. But what if we say that (a,b) is also a set. What if we show that we could define (a,b) in terms of the elements and an unordered pair in a set. But if we have an order, (a,b), why not add c at the end, and d, up to say a total of nine and then substitute in the names on the roster? It preserves the proper ordering, however you might otherwise expand the notation. There it is. It suggests, almost, an ordered tuple. If the 'new math' creates a sense that order is not maintained in ordered data, let that superstition depart. In fact, wasn't it said at one point that the attributes in a tuple are ordered the same way in each relation? almost if one were still speaking of punch cards? In other words, one might simply say, but that's a different 'kind' of order, a punch card field order, which never represents any ranking of the data. That is, and in this very example, the tuple isn't the entire batting order at any point in the game. It's not a relation of batting orders. It's one batter. It's ordered, perhaps, but not the order from the data, until one begins to name attributes, insisting upon a name/value pair, a 'keyword search'. In practical terms of a database implementation, I believe column/positional reference is still typically used. But then one will say, that 9-tuple can never describe a relation of nine members/elements. That, at least, is not in its proper order, all is saved. But if the tuple is one attribute, and this unique type of ordering/sorting attribute, then at what point does one say that you have an ordered relation?

>> >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!

Unless it's an ordered set, and which you say is not possible. A list cannot be a set. A batting roster cannot be thought of as a set of names, because it is in proper order. But don't let me put words in your mouth either. Do you agree?

>> 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 is a set.

>"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.

That's progress. Same thing, in different contexts. The ER people might call it all something else, besides. But this is good.

>A binary relation is a set of ordered pairs

A set of sets.

>a subset of a product of two sets.

A set of sets, or specifically subset of same.

>In n-ary sets, we usually speak of the attributes as being identified
>by name rather than by one of {left, right}.

As I suggested above, the implementation might depart from a model that insists upon an order attribute pair.

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

Unless they are in some order.

>> 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:

>> Your "proper" mind for "order" fabrication is in your own need.

>These experiments don't show anything that isn't obvious: namely,
>that there is information in the order of the words.

Does the second sentence make sense, to you? At the very least, is it the same information? That's the point.

If I go to store a database of cat show winners, or even contestants, and I store the results of the Wednesday races at the horse track, instead, won't the cat show people say it is more than "don't show anything" or that it is somehow otherwise equivalent? I would suspect so. So would you. But what if, instead of that, I do save the cat show winners, but I put first place as second, third as first, and mismatch the names to boot. What would the cat people say?

>ever said a sentence was a set of words!

A sentence may be stored as a table of words and phrases, in their proper order.

>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.

An index in which the categories are not in alphabetical order might be one kind of index. But a name or categorical index which is not alphabetically sorted would strike some as rather being a printer's error, than anything else.

Your objection almost seems to be to the idea of - proper order. Almost.

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

Let's try this. You wrote this, just above. But allow me to take it out of order:

>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.

Becomes:

Any construct that contains relations we can pair with a list for the same information. To do we so ordered an not need use of the collection.

At the very least, it is not what you said, but something different, and verging on incoherent and useless. It's not in its proper order. It's not the original data. That was never stored, it seems. And what about those cat show people?

>> 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.

My point was that you are defending a scheme, as you've described it, that need not store ordered information in its proper order. But that is an important aspect of the information, itself. That must be the touchstone. However represented, even if not in some straightforward fashion, that information, and not something else, must be represented. Again with the cat show people.

>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.

You can speak of halves. It's done all the time. I have to half, have?, half of the charge required to set off the 'orange', if they had not chosen compression. Somewhat less or more than half for the little boy, then. But still halves.

>You may think I'm being facetious

I didn't care, really, if I was to be Abbott or Costello. I just wasn't sure which.

>the real world. But, as it turns out, analogy to the real
>world is not a useful way to reason about math.

And:

>This is why math is useful.)

And all I was saying is that a database would be less useful, or useless, if it applied a math that claimed to represent one thing and instead represented it as something else, another way. We'll definitely be hearing from those cat show people. Unplug the phones? Or is the cardinality of the avenues for contact set simply too large for all that? Received on Thu Feb 23 2006 - 22:13:13 CET