Re: theory and practice: ying and yang

erk schrieb:
> Alexandr Savinov wrote:
>

>>By the way, I also think that real numbers is non-sense. I strongly
>>believe that the world is finite and discrete.

There are many points in the classical science where people can find inconsistencies or fill dissatisfaction. The list is very long and includes very general (and well known) points and very specific ones. For example, in most theories infinity (of any type) is an illegal element and hence it is an obvious defect - recognition of failure of the theory to explain some phenomena. We can continue and add other defects but after that we can come up with some proposal how to overcome them. And here everybody invents his own weapon. I gradually came to some other principles where having a discrete universe is much more natural (i.e., productive, simple symmetric etc.) In particular, there is hope that we can get rid of illegal elements and make our picture more symmetric. Of course, I do not have a complete theory but I have enough informal principles which show a direction for further development.

> And why do you leap from "real numbers" to "the world"? "Real" has no
> bearing on reality - real numbers are useful intellectual inventions,
> as are integers. Unless I'm missing some relevant theory - this is
> outside my realm.

Yes, for mathematicians real numbers are a useful abstraction defined by its properties. However, this abstraction is then used in practice (and vice versa), i.e., we start accept things from the world in terms of real numbers. For example, we assume that a stick may have its length measured in real numbers or diagonal has a real length. Just like armed with relational model we think of our data as rows in tables (although there might be other views).

> Even if the world is, in some sense, finite and discrete, that has no
> bearing on the value of theories addressing reality "statistically"
> (quantum theory, for example, describes the behavior of communities of
> individually ineffable phenomena). Light being seen as waves and
> particles, etc.

In any good theory we need to have an explanation of uncertainty. Statistics (of different types) is one way. There could be also other approaches for explaining uncertainty and may be they could be used to explain the classical statistics. Having a discrete universe (instead of continous) might be one way to explain fundamental uncertainty of some events.

> Even if it ain't continuous, it's sure easier to handle when you treat
> it that way.

I think that the concept of continuum was invented in order to make the life of mathematicians easier. Try to transfer elementary mathematical notions onto discrete case and you understand that it is impossible. Having continuum solves the problem.

>>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.

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.

-- 
alex
http://conceptoriented.com