Re: Mixing OO and DB
Date: Fri, 22 Feb 2008 23:34:26 +0100
Message-ID: <1xshqdm4wq2c8.1v7un9kf2thsk.dlg_at_40tude.net>
On Fri, 22 Feb 2008 13:26:14 -0800 (PST), Marshall wrote:
> 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.
No, it is worded precisely enough to show that properties are not preserved by the model. Do you object that?
[... irrelevant and obvious stuff about geometrical subsets ...]
>>> 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.
Really? Show me a DFA model of multiplication in R. Let's laugh together.
>>> 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.
No, we don't discuss this. We do whether circle values and circles constitute the same set either per construction of or else per isomorphism.
Nobody ever claimed that a circle is not an ellipse.
> 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.
Models are subsets of the sets of circles? How exciting.
>> In order to prove that you have to show an isomorphism, which >> trivially does not exist.
>
> "Circle values" is synonymous with "circles"
[...]
Who said that? Please provide a quote from a textbook on geometry.
Again, circle value is a model for circle. Period.
>> 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.
Geometry is a commonly accepted mathematical discipline
http://en.wikipedia.org/wiki/Geometry
which part, called "Euclidean" defines the term circle.
http://en.wikipedia.org/wiki/Circle
As such a reference to it certainly qualifies as a definition of circle. If you need a book on geometry, I can recommend Marcel Berger's Geometry:
http://www.amazon.com/Geometry-I-Universitext-Marcel-Berger/dp/3540116583/ref=cm_lmf_tit_9_rsrsrs0
-- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.deReceived on Fri Feb 22 2008 - 23:34:26 CET