When Altshuller published "How to learn inventing" in 1961, the editor of the publishing house decided to send copies of the book to various members of the Soviet Academy of Sciences with a request to comment on it. He hopped that after learning about TRIZ, the academicians would embrace and support it, which would enable him to continue publishing books on TRIZ without being accused of disseminating the anti-scientific literature.

Altshuller did not like the idea. He felt that the result would be not what the editor was hopping for. But he could not start dissuading him because he understood that the editor was in a precarious position.

As Altshuller foresaw, there were no positive responses, almost. Only one letter was supportive. But it came from the world renowned mathematician A. N. Kolmogorov. But even he expressed doubt that such a goal as algorithmization of inventive thinking could be attained by engineers and inventors themselves. He suggested setting up a team of various specialists, which would include as a must a mathematician. Altshuller did not tell whether Kolmogorov backed his views with arguments or not, but it is easy to understand his train of thoughts.

Algorithmization of anything is nothing else but mathematization. It cannot be accomplished without first giving notions the mathematically strict definitions. And for such a complex area as thinking only mathematicians can do the job.

Consider, for example, the notions of mono-, bi-, and poly-systems. Altshuller never defined what a mono-system is. Consequently he could not consistently define what bi-systems and poly-systems are. Do they differ in the number of components, or in the number of functions they perform or both ? Most of his examples point to the first:

- a single page of paper is a mono-system but a note-book is already a poly-system;
^{1} - boat is a mono-system, but catamaran is a bi-system and trimaran is a poly-system;
^{2} - a slab of material is a mono-system but a pack of identical slabs is already a poly-system;
^{3} - a single pencil is a mono-system but a set of pencils is a poly-system.
^{4}

But any boat also consists of many elements. Why should it be then related to mono-systems ?
If catamaran is the union of two boats, then boat is the union of other parts !
So, what is the difference ?
The only one is that catamaran consists of two ** identical** boats
whereas boat consists of many

__
Thus, if we want to base definition of mono-, bi- and poly-system on
the number of parts they have, then poly-system has to be defined as
a union of several IDENTICAL mono-systems (plus something that keeps them together, such as a coil in
a notebook, for example).
__

But such a definition runs against Standard 3.1.3, which says that poly-systems only originate as unions of several identical
mono-systems but then they become not identical ! Thus, due to Altshuller, a poly-system is
not necessarily a union of IDENTICAL mono-systems.
__But defining it as a union of not necessarily identical objects eliminates
the difference between mono- and poly-systems ! Indeed, boat consists of various not necessarily
identical parts, and trimaran also consists of various not necessarily identical parts. Why should
the first be called mono-system and the second - poly-system then ?__

__Altshuller could not answer these questions. Algorithmization of inventive thinking remained unattained !__

By the way, Altshuller's theories are not only logically inconsistent (e.g. Standard 3.1.3 made poly-systems indistinguishable from mono-systems) but even his examples aimed at illustrating certain concepts in fact contradict them !

Indeed, he wrote that a mono-sectional turbine is a mono-system whereas a multi-sectional turbine is a poly-system
^{5}. He should have known that different sections of multi-sectional turbines
are neither identical functionally nor constructively. Their construction and functions differ.
But that's fine. Standard 3.1.3 allows poly-systems to consist of different objects. However, it stipulates that
this only happens at a latter stage of poly-system evolution. Initially all poly-system have to originate as
unions of identical mono-systems, and then they become less and less identical. This theory implies that
multi-sectional turbine had to have originated as a union of identical sections. But that was not the case !
Multi-sectional turbines were never composed of identical sections. From the very beginning they were composed of
not identical sections !

But let's try to save Altshuller's theory of mono-bi-poly by giving the notions not contradictory definitions. There are only three ways to consistently define mono-, bi-, and poly-systems:

- A poly-system is a union of
__identical__mono-systems; - A poly-system is a union of
__similar (rather than identical)__mono-systems; - A poly-system is a system with many functions whereas a mono-system is a system with one function (in the spirit of the last month's Editorial).

Of these three definitions, the last one is the widest. Indeed, I) is a particular case of II). The latter requires defining the limits of similarity and how to measure it. If a limit is not imposed, then poly-system degenerates into union of any objects, which makes the definition logically inconsistent as was shown above. As for measuring the degree of similarity, it could be based on measuring either structural or functional similarity. So far, nobody found a measure of structural similarity, which would work in all cases. It is one of the open problems in pattern recognition. Thus, we have no choice as to pursue measuring the functional similarity. But then poly-system has to be defined as a union of functionally similar mono-systems, which makes it a particular case of III).

Thus, definition of poly-system as a system with many functions is the WIDEST possible amongst the
LOGICALLY CONSISTENT definitions of poly-system. But even so, it does not cover all Altshuller's examples !
__Hence, no consistent definition of mono-bi-poly can cover all his examples !__
What is to be done in order to save the theory then ?

__There are only two approaches available. The first one is to exclude some Altshuller's examples of mono-, bi-, and
poly-systems by declaring them irrelevant. The second one is to preserve all examples but
repudiate all definitions of mono-bi-poly and search for another paradigm that would cover the
examples without resorting to the notions of mono-, bi-, and poly-system at all.__

Surprisingly, such a paradigm is not difficult to find (as soon as the objective became clear, of course). Here it is:

- Some systems originate as the result of union of several functionally identical systems;
- Some systems originate as the result of union of several functionally different systems;
- Some systems originate as the result of union of functionally opposite systems;
- The number of subsystems in a system may both increase and decrease over time.

(As a result, the number of*identical*subsystems in a system may also both decrease and increase over time;) - Identical subsystems may become not completely identical over time;
- Identical subsystems may become very different over time;
- Identical subsystems may become even functionally opposite over time;
- Different subsystems may become even more different over time;
- Different subsystems may become even completely opposite over time;
- Different subsystems may become less different over time;
- Different subsystems may become even identical over time;
- Opposite subsystems may become not opposite over time;
- Opposite subsystems may become even identical over time.

All these trends can be confirmed by examples of real inventions. And all Altshuller's examples
on his mono-bi-poly "trend" fall into one of the above categories ! But they are wider in scope and more
universal than his theory.
And, which is the most important, __nowhere we used the notions of mono-, bi-, or poly-systems
to formulate the above trends! They turned out to be redundant!__

The theory that mono-systems are grouping into bi- and poly-systems with subsequent differentiating of the originally identical subsystems sounds as a revelation only for those who does not see the whole picture. For those who see it, such a theory is nothing more than a partial truth and not especially a novel and correct one.

So, what is the morale of the story ?

- The most comprehensive schemes (such as the above list) seem to be obvious after one eventually stumbles upon them;
- Revelations are revelations only when such more comprehensive schemes are unknown.
- The comprehensive schemes that include everything and which seem to be obvious after they are found, are the most difficult to find !