In one of the letters written to the Infeld group in Warsaw Einstein wrote:
"A new manner of thinking is essential if humankind is to survive."

  
     A_Entropy. 

This chapter requires some familiarity with the rudiments of physics and
mathematics. Readers lacking this familiarity may skip it and proceed
to "B_Morphogenesis" on condition, however, to accept:
-the physical foundations of Informatics as granted and
-a loose definition of the concept of order.

In physics, the customary way to express the probability of a given 
heat distribution is the ENTROPY E defined by the BOLTZMANN expression 

(1):  E = k ln(S) 

where k is the Boltzmanns gas constant and S is the number of 
microscopic states in which the macroscopic state E may be realized. 
The concept of entropy may be generalized by extending the expression
over all forms of energy. Setting in the generalized expression 
k = 1/ln(2) we get:

(2): E = ln(S) / ln(2) = log2(S)  (where log2 means log base 2).

(2) allows to express the entropy of the system as the number of 
digits of a binary string capable to address all possible system's 
states. Each digit of this string determines a degree of freedom of 
the system.

Entropy represents the part of energy of a system unfit for doing 
mechanical work. 

Replacing entropy E with information I we may say that the complete 
set of system's states may be addressed with help of I binary bits:

(3): I = log2(S)

(2) and (3) express the analogy between entropy and  information.

The second law of thermodynamics, the "LAW OF ENTROPY" which may be 
generalized over all practical energetic systems states that any change 
of the system state increases its entropy. In the limit, for the purely
theoretical reversible system, entropy stays constant. It never decreases. 
NOTE: This holds for closed systems. As we shall see in "B_Morphogenesis"
entropy may decrease in local open systems. Such systems may get ordered 
and their ordering is foundation of the cosmos, of life and of human 
reason. 

Analogically, as result of a communication some of the I bits necessary
to describe the S possible system states may get corrupted in which case
the amount of useful information contained in I decreases. For each 
corrupted bit half of the possible system states S is excluded from the 
information I. This is the customary way of representing the analogy 
between entropy and information.

Another way of presenting the analogy, which we find more appropriate
for the present study is to consider not the information, but the
information carrier as analogous and say that for each corrupted bit 
a new must be added in order to describe all S possible states of 
the system. In this context the analogy becomes strictly isomorphic
and we may refer to I as to the ENTROPY OF INFORMATION, or shortly
ENTROPY, when no misunderstanding about the nature of the involved
system is possible.

Entropy may be considered as the measure of disorder and its inverse 
as measure of order. In information systems entropy represents the
degree of uncertainty of a message.

NOTE: We shall further use the term Chaos as synonym of Disorder which
differs from the definition used in certain Chaos Theories, where "Chaos"
points to some "hidden order" concealed by apparent disorder.
"Disorder" contains a suggestion of having necessarily emerged from some 
preliminary Order by its destruction. "Chaos", on the contrary, is, like
"Order", just a system's state not prejudging any direction of emerging.
We shall see in B_Morphogenesis that Order may under certain circumstances
emerge from Chaos, which sounds better than talking about Order emerging
from Disorder. For instance discussing the Big Bang we shall admit Chaos
as the original state of this Cosmos Model while the negative term 
"Disorder" could hardly pertain to this context.

Based upon the notion of entropy we define the ORDER of an information
system:

(4): O = I1 / I

where I is systems entropy in a given situation and I1 = log2(S) 
is the minimum possible entropy of the system.
Consequently, the highest possible order is 1. When entropy increases 
order decreases. Its value range is between 1 and 0.

After introduction of the concept of order the law of entropy extended 
over information systems may be called DISORDERING PRINCIPLE and 
formulated: any spontaneous change of a system decreases its order.
In the limit case of an ideal "reversible system", the order stays 
constant. It never increases. (With exception of local open systems
which we mentioned above. We shall discuss them in the next chapter
"B_Morphogenesis".)

With respect to entropy and order Informatics is analogous to Physics.
By virtue of this analogy we shall consider Informatics as a domain 
which may be investigated, ordered and processed with help of rigorous 
scientific methods.