Re: Mixing OO and DB
Date: Fri, 22 Feb 2008 12:24:21 +0100
Message-ID: <1tddqe4aavxs.yalu6gr9opv7.dlg_at_40tude.net>
On Thu, 21 Feb 2008 20:37:09 -0800 (PST), Marshall wrote:
> 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.
This is an invalid argument. You claim that circles drawn by pencil are equivalent to ones in the program. I don't know, but let them be. From this does not follow that either is equivalent to mathematical circles. It is just like to argue that the set of integer is finite because you don't know anybody who could count it.
-- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.deReceived on Fri Feb 22 2008 - 12:24:21 CET