Fluid Flow in the world of linearity

"How big is it? How long does it last? These are the most basic questions a scientist can ask about a thing. They are so basic to the way people conceptualize the world that it is not easy to see that they imply a certain bias. They suggest that size and duration, qualities that depend on scale, are qualities with meaning, qualities that can help describe an object and classify it.(...)

It is hard to break the habit of thinking of things in terms of how big they are and how long they last. But the claim of fractal geometry is that, for some elements of nature, looking for a characteristic scale becomes a distraction. Hurricane. By definition, it is a storm of a certain size. But the definition is imposed by people on nature.(...) Categories mislead. The ends of continuum are of a piece with the middle.

It happens that the equations of fluid flow are in many contexts dimensionless, meaning that they apply without regard to scale." - (Gleick, J., 1998 - p. 107-108)

"Still, Scholz considered the tools of fractal geometry indispensable.

'It's a single model that allows us to cope with the range of changing dimensions of the earth,' he said. 'It gives you mathematical and geometrical tools to describe and make predictions. Once you get over the hump, and you understand the paradigm, you can start actually measuring things and think about things in a new way. You see them differently.  You have a new vision. It's not the same as the old vision at all--it's much broader.'" - (Gleick, J., 1998 - p. 107)

 

Comment:

The problem of bias. In every linear interpretation of reality, we are assigning discrepancies to nature. To think that dimensions are stable scales that you can fix on a linear equation is to dwell on illusions of reality. Even if we can explain how a rock rolls down a hill, doesn't necessarily mean we know how to start the movement of the rock rolling down the hill. We may have some idea, but not the whole picture. As, for example, we cannot even grasp the meaning of gravity. We can only assign discrepancies to it and hope we are getting closer to understanding the problem of space and time.

Lápis e abismo

 

Pomba gira

Dois rios ressoam

"Abismo, abismo!" - Cantam.

Uma roda e uma boca

Ressoam também.

 

Estrelas caem sobre cabeças.

Lua lacunar e agulha.

Nós todos.

 

K. Alves G.

 

Reference: Gleick, James, 1998 - Chaos, The Amazing Science of the Unpredictable. Vintage Books.