The 9 classical windows of TRIZ are the views on the past, present, and future of a system, its subsystems, and supersystems. There could be other views, e.g. from inside and outside of a system. That is why a few years ago I proposed to expand the classical 9 windows to 18 windows. Today I propose to further expand the number of windows to 36 by inclusion of anti-system.
The rationale is that while looking at a system it is not only important to take a look at its subsystems and supersystems but also at anti-systems. The expanded number of windows should provide a look at the past, present, and future of a system, its subsystems, supersystems, and anti-systems, as viewed from both inside and outside. Mathematically it can be expressed as follows:
(past, present, future) of (system, subsystem, supersystem, anti-system) from (inside, outside),
or as the product
(past, present, future) × (system, subsystem, supersystem, anti-system) ⊗ (inside, outside),
where × is "of" and ⊗ is "from".
There could be even further expansions like this:
(past, present, future) × (system, subsystem, supersystem, anti-system, anti-subsystem, anti-supersystem, subsystem of anti-system, supersystem of anti-system) ⊗ (inside, outside)
At the very least it is useful to see anti-systems for systems. An example of such an approach is presented in this issue in the article titled "On the viruses driven species' evolution".