Re: theory and practice: ying and yang

From: Alexandr Savinov <savinov_at_host.com>
Date: Fri, 03 Jun 2005 14:37:33 +0200
Message-ID: <42a04f1c$1@news.fhg.de>

Paul schrieb:
> Alexandr Savinov wrote:
>

>>>>For any naïve
>>>>(classical) thinker real numbers is something really existing but if we
>>>>look at the problems deeper we will see that they are not needed.
>>>
>>>Do you have any support for this somewhat startling revelation?
>>
>>Real numbers do not help in solving contemporary problems and this why I
>>find this apparatus almost useless. They are used and will be used by
>>inertia.

>
>
> They are useful for standard calculus surely? Which has practical
> applications. Maths is only used as a *model* of reality, and often a
> continuous model is simpler and more useful in practice that a discrete
> model, even if the discrete model is actually more close to the reality.
> e.g. in general an civil engineer will find Newtonian physics more
> useful than quantum physics.
>
> I think the issue of whether or not real numbers "exist" is a bit of a
> red herring. Ultimately all maths is just symbolic manipulation.

Absolutely agree.

I just wanted to emphasize that even if we have some dominating theory or approach there still exist alternatives so that the dominating approach should not be considered a dogma but only a kind of useful (productive) illusion or convention. Considering the earth the center of the universe was rather natural and very productive illusion. Real numbers and relational model are also very natural and highly productive solutions. But they are not dogmas. Inventors of such theories normally very well understand their conditional character however their followers normally consider it a religion and aggresively fight with any revision or even doubt in their validity (history of relational model is a very good example).

> You're not a fan of Wolfram's book A New Kind Of Science, by any chance?

No.

-- 
alex
http://conceptoriented.com

Received on Fri Jun 03 2005 - 07:37:33 CDT