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ABCB TOPOLOGY: CONTINUOUS / DISCRETE        1
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The dichotomy continuous / discrete is one of the oldest of human 
thinking. It has been formulated already in the presocratic Greece 
and its first versions had astonishing depth, scope and maturity.
The discrete term of the dichotomy was represented by the atomistic 
view of Democrit, the continuous by Heraclit's "everything flows". 
Democrit's view is very close to a physical corpuscular kinetic model. 
In Heraclit's allegory you cannot step in twice into the same river. 
The river, the continuous flux represents his view of the world. 
It is less precise, more intuitive than that of Democrit, but taking 
into account that the concept of flux is harder to grasp and handle 
than that of particle, it represents the continuous term of the 
dichotomy, worthy of its atomistic complement.

Let us note, that the dialectic character of the dichotomy appears 
in the historic perspective more clearly than it did to the first 
involved authors. We may almost certainly assume that Democrit and 
Heraclit believed to create "unified theories", while actually dealing 
with what we see as one term of the dichotomy.

The beginning of our century saw one of the most ambitious, deepest 
trials to create a unified theory: Einstein's relativity followed by 
his later works destinated to extend it over the entire domaine of 
physics. The importance of his partial achievement is universally 
known and admitted. Nevertheless, his most ambitious trials failed 
and towards the end of his life he became discouraged as to the very
possibility of a unified theory whether centered on the continuous, 
or on the discrete term of the dichotomy. His models were centered on 
the continuous term, but he most fairly estimated the chances of the 
opposit side, the quantum theory. We shall return to his ideas 
concerning the problems involved by an eventual unified theory starting 
concentrated on any term of the dichotomy in ABCX. 

Let us note for the moment that: 

1.the dichotomy formulated in presocratic Greece survived till us, 
2.its terms supply bases for complementary or, more often, competitive 
  models, 
3.none of the terms seems to be capable to assume by itself the 
  responsibility of a unified theory.

ABCB TOPOLOGY: CONTINUOUS / DISCRETE        2

We would like to point out a feature of the dichotomy.
The only way to conceive, to imagine, to consider in any way the 
continuous consists in cutting out lumps of it, to discretise it. We 
grasp intuitively the continuum, when we can cut out of it arbitrary 
lumps which, in turn, can be further divided without limitation. 
The continuous asserts itself via the discrete.

A similar thing happens when we consider the discrete. A discrete object
is unconceivable in isolation from any context. Even in my imagination 
it has to have some position and some size, it has to be determined in
space. It has to occupy a part of space and to negate the complementary 
part. It has sense only as a lump of continuum.
The discrete asserts itself via the continuous.

We recognize here the principle of alternative orientation introduced
in AB.