Page 274 - Mechatronics for Safety, Security and Dependability in a New Era

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MODEL OF ACTING POTENTIALS

The collection of the common attributes which all the elements in a set equally share beyond their own
peculiarities is called intensity of the set, while the collection of the members is the extension of the
set. The intensity is reciprocal to the extension (Russell and Whitehead 1910). There are two ends in
the universe of the set theory, the empty set and the universe. Taking limits towards both ends, the
intensity of the empty set is °° and that of the universe is 0. The universe has no intensity, i.e. no
common ascribable attribute as long as we stay inside the universe (unless from outside, i.e. from a
view of a larger whole, it cannot obtain any attribute A, for the attribute requires the existence of its
opposite ~A for A to be defined).

On the other, the empty set could be deemed to contain all the possible pairs of opposite attributes,
since <f> = A D ~A for any attribute A relevant in the universe currently dealt with. Any attribute A that
predicates the empty set is necessarily cancelled out by its opposite attribute ~A in the view of
extension, whose cancellation does not however evade that the empty set contains both opposite
attributes in the view of intensity. The empty set therefore transcends all and contains all - in short, 'it
is empty, but plenum'.
The two extremes in the set theory, the empty set and the universe therefore may be deemed as the two
opposite wholes, the intensional whole and the extensional whole respectively. The extensional and
intensional wholes were shown as two reciprocal modes of the Whole. They are two modes of
existence, to which the domains of events and of potentials correspond respectively.

The Whole must thus satisfy the double-fold requirements in its unity; (1) the requirement that the
Whole is one, and (2) that there are two distinct reciprocal modes of the Whole. A Mobius strip as
shown at Figure 1 can give a plausible model for the Whole so defined to satisfy the double-fold
requirements above. The universe £1 yields its copies with different dimidiated partition according to
every possible pair of opposite attributes. A series of (infinitely many) copies with different
partitioning, Q A, Q, B, Q. c, ••• is thus obtained. Let these copies raise perpendicular to the Mobius
surface and align along the surface, whose intersections equally represent the empty set, e.g. <f> = AP\
~Afor any attribute A on the surface.
In this regards, the Mobius model constitutes the null </) along its surface as just one single surface
globally, and rends all the possible opposite attributes across its two local faces everywhere. It unifies
the reciprocal modes of the Whole, the intensional whole along the null surface and extensional
wholes across the surface; (1) The Mobius null surface models the Potential as the intensional whole,
pure being of potentials as plenum of attributes. It renders existence to the extensional universe of
events and its constituents, (2) an event occurs, when a choice is made out of every attributable
opposite. It is because collapsing over the null direction determines the unique accumulation of
attributes relevant to a particular event, (3) whenever and wherever an event occurs, holding itself
existent extensionally, the Potential acts on the event intensionally to render existence to the event
from behind.

DYNAMIC INTERACTION OF OPPOSITES
The innate dynamic interaction of opposites for decision making is thus found well represented by the
Mobius model. Given that both wholes, intensional and extensional, are reciprocal opposites, when the
one covers the whole surface as it should, there remains no room for the other whole. Immediately
after the one whole covers the whole surface, it cannot hold itself, for the one requires its opposite to