Re: Mixing OO and DB

On Feb 22, 12:47 pm, "Dmitry A. Kazakov" <mail..._at_dmitry-kazakov.de> wrote:
> On Fri, 22 Feb 2008 12:20:02 -0800 (PST), Marshall wrote:
> > On Feb 22, 11:36 am, "Dmitry A. Kazakov" <mail..._at_dmitry-kazakov.de>
> > wrote:
> >> On Fri, 22 Feb 2008 08:13:10 -0800 (PST), Marshall wrote:
>
> >>> Earlier your threw around the word "uncountable"
> >>> a few times so maybe you have some related meaning in
> >>> mind. But it doesn't matter; if we limit our context to what
> >>> is computable, then mathematical relationships don't somehow
> >>> vanish;
>
> >> Of course they do. For example this vanishes:
>
> >> forall x, circle exist y, circle twice as big
>
> > Does this mean that you are claiming that given a
> > computable specification of a circle, it is impossible
> > to determine a computable specification of a
> > circle with twice the radius? Or maybe area?
>
> No, you claimed that a set of computable circles retain the properties of
> the set of all circles. This is wrong, as my example shows.

You example is sufficiently fuzzily worded that it cannot be said to show anything. I asked some clarifying questions and you didn't answer any of them, so I have no alternative but to ignore it. Please feel free to clarify your example at any time.

Let us be clear to distinguish between all properties holding and some properties holding.

Specifically:

The subset relationship is transitive. So:

Given:

1. the set of all circles is a subset of the set of all ellipses
2. the set of all computable circles is a subset of the set of all circles

We can conclude:

3. The set of all computable circles is a subset of the set of all ellipses.

Informally, every circle is an ellipse, even if we restrict ourselves to discussing only computable circles.

Agree or disagree? Please include the words "yes" or "no" in your answer. If you answer no, please indicate which of 1, 2, or {1, 2} -> 3 you disagree with.

> > It appears you are somehow claiming that multiplication
> > is not defined on computable numbers.
>
> Sure. Multiplication (addition, subtraction, division) is incomputable and
> thus cannot be defined.

The claim "multiplication is uncomputable" is amusing.

Ordinarily, I would ask you some clarifying questions at this point, but perhaps that would not be a productive use of my time. Instead I will point out that multiplication is computable (and closed to boot!) over ZxZ, QxQ, over the algebraic numbers, and over the computable numbers. So again there can be no objection to discussing mathematically faithful models of circles parameterized on these domains.

> >>> a computable circle is still an ellipse, just as much
> >>> as an uncomputable circle is. Also: every countable set of
> >>> circles is still a subset of the set of all ellipses.
>
> >> So what?
>
> > So what?! It's what we're discussing. So you agree then?
>
> > What did you think we were discussing?
>
> Whether a set of circle values can have the structure of the set of
> circles.

I thought we were discussing whether a circle is an ellipse or not. I claim that the set of circles is a subset of the set of ellipses. I further claim that computable models of circles using some computable subset of the reals is entirely feasible, and that all such models are subsets of the set of circles, and therefore a subset of the set of ellipses.

> In order to prove that you have to show an isomorphism, which
> trivially does not exist.

"Circle values" is synonymous with "circles" so your question can be reworded to "whether a set of circles can have the structure of the set of circles" which is trivially true. I perceive that you are trying to express some idea about computability or countability but lack the vocabulary. If the specific idea you're trying to express is whether some countable set of circles is isomorphic to the uncountable set of circles defined over the reals, then yes, no such isomorphism can exist, given that they have differing cardinality.

> So far your single argument was that you could
> find a circle for each circle value.

That would not be my argument since I do not recognize the term "circle value" as being distinct from "circle." If you wish to supply a specific definition for this or some other term, please do so. However, merely saying something "as defined in geometry" does not qualify.

And of course, none of this has anything to do with whether subtypes are subset under a mutable C++ class model.

Marshall Received on Fri Feb 22 2008 - 22:26:14 CET