Re: Mixing OO and DB

From: Marshall <marshall.spight_at_gmail.com>
Date: Sat, 16 Feb 2008 08:57:59 -0800 (PST)
Message-ID: <17402b67-e5f1-4455-ba27-fe540bb1a42c_at_e25g2000prg.googlegroups.com>


On Feb 16, 3:39 am, "Dmitry A. Kazakov" <mail..._at_dmitry-kazakov.de> wrote:
> On Fri, 15 Feb 2008 17:49:38 -0800 (PST), Marshall wrote:
>
> > Mathematically, a circle value is a set of points, and an ellipse
> > value is a set of points.
>
> Geometry does not operate "values".

All of mathematics operates on values. In fact it is pretty much devoid of anything like a mutable variable construct as used in imperative programming.

> It deals with plain circles and ellipses.

These are usually understood to be sets of points. Is there some reason you don't think sets are values?

> In a computational system that models geometrical
> objects a circle value serves as a model of circle.

What is the point of such complexity? "Circle" and "circle value" denote the same thing. So you're saying a circle is a model of a circle.

> > Mathematically, we can describe a set of points
> > with an equation, and the equation that describes ellipses reduces
> > to the equation that describes circles in certain cases. Do you want
> > to say that two different appearances of the same equation may be
> > different depending on what they were reduced from? That dog
> > won't hunt.
>
> It can also define a circle using its center and radius, or as a conic
> section, or via complex exponent, or by an uncountable number of other
> ways. All these definitions are said equivalent. It has nothing to do with
> being "same value".

Whatever equation you use, that equation will reduce to an equation that specifies a circle in some cases. So now you have arrived at the same equation from two different directions. Do you still object to the "same value" idea after we have the same equation?

Every circle is an ellipse. This fact might be inconvenient you one wishes to view every bit of mathematics from within a specific type theory that cannot capture this.

> > I happen to think type systems are just about the most interesting
> > thing in computer science, but I don't make the mistake of thinking
> > that they are somehow fundamentally necessary, or worse, that
> > the state of the art of today's industrial languages (which is decades
> > behind the state of the art of today's academic languages) is
> > somehow the end of the road.
>
> Just a comment, mathematicians understood need in typed systems
> hundred years before us.

As I understand it, type theory arose from Russel's desire to patch up Frege's naive set theory after his discovery of what is now called Russel's paradox. However most set theories today are untyped; there turn out to be easier ways to deal with Russel's paradox than types.

But again, I love type theory. I just happen to think it's usually done in a way that is substantially too complicated.

Marshall Received on Sat Feb 16 2008 - 17:57:59 CET

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