# Intensive or Extensive? LO27031

From: Dressler, Winfried (Winfried.Dressler@Voith.com)
Date: 07/23/01

>...whereas the form refers to extensive factors.

Dear Leo,

I hope you had a nice holiday with a good balance for body and mind. When
you are going to be back, I will be on holiday with my family and learn
some lessons on creativity and learning from my children.

>One thing which I take with me in my thoughts is the question: is colour
>an intensive or an extensive factor.

wish to clarify my understanding of intensive and extensive factors and
why I refer to the former as quality/form and to the latter as
quantity/content.

I seldom refer to definitions, but here I will: A system can be described
by many factors. These factors may be categorized in many ways. One
possibility is by observing how the factors change when the spatial size
of the system changes. Those factors which remain unchanged are called
"intensive", those which scale with the size are called "extensive". This
is a most important categorization, because without it the very
encompassing term "energy" could not have been formed in the way we know
and use it today. In order to know about the energy of a system, one has
to measure two factors: an intensive and an extensive one and then to
multiply them so as to calculate the energy.

Think of the room around you, filled with air. In this room imagine a box.
This box is also filled with air. What distinguishes the box and the room
is the spatial size of both. Thus to distinguish intensive from extensive
factors, you may ask: What is the same in the box and the room (for the
intensive factors)? What is different in the box and the room (for the
extensive factors)? Typically intensive are: pressure, temperature.
Typically extensive are: volume, number of molecules.

A slightly different example: You hand out soup for lunch and you hear by
your dear wife: "May I have another ladle full of this delicious soup?",
but you think, after tying: "Ow, this soup is too hot!" The first question
asks for more quantity, more volume, thus focuses on an extensive factor
of the soup. Your sentence states too much of a quality of the soup, its
temperature and thus focuses on an intensive factor of the soup. Back to
the question of your wife for "delicious soup". Because already the first
spoon was delicious, she asked for more, expecting that this more will not
be less delicious. Thus more of the content, the soup, was asked for
because of it's favouable form, that what makes it delicious. This example
also shows how intimately form and content are connected.

Two remarks to end with:

First, although I am very comfortable with identifying intensive factors
with quality and extensive factors with quantity using above definition of
scalability, this is not so easy for form and content. Those instances
when we start to speak of form are already so complex, that the
Gedankenexperiment (thought-experiment?) of scaling becomes very
difficult. The more a form is unique (law of singularity of complexity)
the more it is also shaped by the size of a specific content. This is as
true for pieces of art as it is for the character of people. A small bush
has another form as a centuries old oak tree.

Second, the scaling must not be thought of as a thermodynamic process.
Scaling does not mean to increase the volume of an isolated system. In
that case, all the quantities remain the same (the system is isolated -
nothing goes in, nothing out) but all the qualities change. So, Leo, when
you think about colour, don't inflate a balloon in your mind and observe
how the colour goes pale.

Now I will go for the energy of a delicious meal!

Liebe Gruesse,
Winfried

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