Copyright © 1983-2008 Yevgeny Karasik

Presently TRIZ has two independent tools of betterment of the
__structure__ of technical systems:
SuField analysis and analysis of dualities.
The former is based on the rule: if there is an incomplete SuField in a
technical system,
then it can be improved by completing this SuField.
In contrast, analysis of dualities is based on the rule: if there are dual
objects in a technical system then it can be
improved by decreasing
the degree of their separation and ultimately merging.
None of these rules taken alone is sufficient to explain all transformations
of a technical system in the course of its betterment.
But jointly they do the trick.

Consider, for example, the stages of betterment of the cooling system of such electrical machines as motors and generators. The first stage is neatly described by the following SuField formula:

In other words, in order to eliminate the harmful impact of the heating of
machine S_{1} by the field of
temperature F_{T}
the incomplete SuField has to be completed by
introducing the other substance S_{2} which cools the motor or
generator.
Normally, S_{2} is water.

But water can only be poured onto the external surfaces of the machine. This results in not uniform cooling which causes thermal stresses in the machine and breaks it down. In order to uniformly cool the machine not only its external surfaces have to be cooled but also internal ones. But even this is not enough because to avoid stresses non-surface portions have to be cooled too. In other words all parts of the machine have to be literally saturated with water. Then evaporating water would cool it uniformly.

But how to saturate metallic parts with water ? It was proposed to build them not of continuous pieces of metal but of metal powder particles welded together with the help of the powder metallurgy techniques. Such powdered metal parts would have numerous pores which could be filled with water or other fluids and cooled uniformly (see USSR invention authorship certificate #187135).

This improvement cannot be already explained by SuField analysis. But analysis of dualities explains it easily: the cooling and the cooled are dual objects. Hence, the system gets improved when one of them becomes part of the other.

Unfortunately, analysis of dualities so far did not have a graphical
notation, which would facilitate its use along with SuFiled analysis.
To fix the situation I propose to modify SuField notation to
reflect that substances and fields are geometric objects and have dimensions. It can be done by replacing S_{1}, S_{2} and F in SuField formulas by geometric figures as follows:

Rectangles around S_{1}, S_{2} and F are purported to show that they are
not only physical but also geometric objects
(not necessarily of rectangular shape, of course, but of any shape). Then
rectangle inside rectangle has an obvious meaning:
one object is inside the other. And the above formula means that a tool (S_{2}) tends to become a part of the product (S_{1}), which is one of the basic rules of Analysis of Dualities. Thus, the modified SuField notation allows us to write down both rules of SuField Analysis and of Analysis of Dualities.

It has to be noted that "inside" should not be meant strictly.
The following ways of putting S_{2} "inside"
S_{1} are possible:

- If S
_{1}is hollow and/or has pores then S_{2}can be put into these pores or into the empty space inside S_{1}; - If S
_{1}is not hollow and does not have pores then it first gets modified to have them and then S_{2}gets put into these cavities and pores; - Alternatively, S
_{2}just gets forcefully embedded into the continuous mass of S_{1}; - A portion of S
_{1}gets modified to function as S_{2}.

Consider, for example, the problem of coating the interior surface of a rectangular metallic pipe with a uniform layer of glass. SuField analysis suggests the first step on the way to a solution:

where S_{1} is the pipe, S_{2} is glass but S_{3} and F could not be figured out by SuField analysis alone. One has to resort to analysis of dualities to make the next step on the way to a solution (and determining S_{3} and F):

From the formula on the right of ===> it follows that S_{3} has to be located
inside glass S_{2}, which has to be located inside pipe S_{1}.
Moreover, S_{3} from inside of S_{2} has to uniformly distribute it along the interior of S_{1}. To achieve it, the glass mass has to be made hollow (as a pipe),
expandable (in order to uniformly distribute it along the interior surface of the pipe) and sticky. To this end S_{3} could be a compressed hot air
which would soften the glass pipe inside the metallic pipe, inflate it and
spread uniformly along the interior surface of the latter.

Thus, the modified SuField notation allows one to write down both rules of SuField analysis and analysis of dualities and facilitates their joint use in problem solving. This, in turn, makes problem solving easier and more focused.