Re: Mixing OO and DB
Date: Fri, 22 Feb 2008 20:36:05 +0100
Message-ID: <1olhnzcol6vjz.1it2d8rtxcm88.dlg_at_40tude.net>
On Fri, 22 Feb 2008 08:13:10 -0800 (PST), Marshall wrote:
> On Feb 22, 3:24 am, "Dmitry A. Kazakov" <mail..._at_dmitry-kazakov.de>
> wrote:
>> On Thu, 21 Feb 2008 20:37:09 -0800 (PST), Marshall wrote:
>>
>>> 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.
> > Since you haven't defined "mathematical circles" I can't evaluate > your claim.
mathematical circles = as defined in geometry
> 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
> 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? Moreover, forall P, program there exists a unique circle [*]. This does not make programs any circular.
- Take the binary code of P and write it after "0.". The number obtained is the circle's radius.
-- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.deReceived on Fri Feb 22 2008 - 20:36:05 CET