Re: Mixing OO and DB

From: Marshall <marshall.spight_at_gmail.com>
Date: Thu, 21 Feb 2008 20:37:09 -0800 (PST)
Message-ID: <e3ce5986-ab1c-43f9-ae94-ed8c1c031722_at_d4g2000prg.googlegroups.com>


On Feb 16, 10:53 am, "Dmitry A. Kazakov" <mail..._at_dmitry-kazakov.de> wrote:
> On Sat, 16 Feb 2008 08:57:59 -0800 (PST), Marshall wrote:
>
> > 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.
>
> The point is that a computational model is sufficiently weaker than
> geometry. Circle is an uncountable set, and the set of circles is even so.
> For this reason no computational model can be equivalent to geometry and
> thus the claim that circle value is circle is mathematically invalid.
> Because there is no bijection between the set of all circle values and the
> set of all circles.

Mathematics contains within in the idea of computable functions, computable reals, etc. Computers can of course only compute computable functions. A person with pencil and paper has the same limitation. The person with pencil and paper, drawing a set of equations, using geometry, whatever, is said to be working with circles. Software can work with circles as well. A computer cannot perform calculations on a circle whose center is a pair of uncomputable reals; neither can a person. However a person can recognize the fact that the equations describing circles are special cases of the equations describing ellipses, and a computer can be programmed to take advantage of this as well.

The distinction between "circle value" and "circle" is without merit: the two terms have identical denotations.

Marshall Received on Fri Feb 22 2008 - 05:37:09 CET

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