**What in a system is non-linear?**

The question is what in a system is non-linear? Linear chemical interactions
of atoms and molecules, drive life which is essentially non-linear. Peptide
polymerization is linear. Yet only when peptides interact they create proteins
(enzymes) , exhibiting non-linear structure and behavior. The same applies
the CA systems. Indeed the CA are linear, as you wrote, however their**
interaction initiates non-linear structure and behavior. **You have
to **distinguish between a linear engine consisting of CA, whose manifestation
is a non-linear change of structure and behavior. **

You might liken the CA to isolated peptides. Once interacting they generate the
complexity which we observe in life. There are two pre-requisites for this
kind of non-linearity: Interaction and death (turnover).

**The non-linearity of life cannot be
captured by current mathematical tool**s.

There is a** broader definition of non-linearity than mathematics has
to offer**. When you encounter a system what you perceive is **change**.
Then you ask yourself where is this change going to? In order to find out
you decide that this **change is a process **and your task is
to capture the essence of this change in order to predict where it is going
to. You know its past and would like to predict its future. You obviously
start with mathematical tools:

1. Assume that the change is linear and find out that you can’t predict its
future.

2. You turn
to non-linear mathematical tools, and still the future of this process is
unpredictable.

3. Then you transform the observed change to make it linearly or non-linearly
predictable. And the process is still unpredictable.

4. In short none of the mathematical tools known today may foretell the future
of this process.

5. Then your teachers turn to Plato and say that this change which you observe
is a corruption of how really this process ought to behave . They beam with
self-confidence and are ready to face a corrupted future which current mathematical
tools foretell.

**The non-linearity of an ant’s nest**

In order to see what I mean do the following:

Look for an **ant’s nest** and study it for some time. What
you perceive is change. You already know that this nest is a process with
a past and a future, yet you don’t have the tools to study its past. You can’t
even define its today’s initial conditions on which you might construct a
conceptual model for predicting the future. This is the non-linearity I am
talking about. Yet the nest is an organism which experienced its past and
has inborn expectations of what its future might be. Its “swarm –intelligence”
outsmarts any scientific intuition.

It is my humble belief that CA may capture a tiny bit of this non-linearity.