Alternative approach to problem statement, V.M.Gerasimov, L.A.Kozhevnickova

Alternative approach to problem statement

V.M.Gerasimov, L.A.Kozhevnickova; Russia


The process of improvement of any system usually starts with understanding of what should be changed in it for the best. And the goal of such improvement often consists in elimination of only one particular disadvantage or few disadvantages that create the greatest hindrance. However, even when improvement has been successful, after some time the remaining disadvantages become more aggravated and again it becomes necessary to formulate and solve a new inventive problem. Let us consider another approach to the formulation of problems.

What is primary?

The following words of Karl Marx are quoted in the book by G.S.Altshuller "Algorithm for Inventing" [1, p. 238] in the chapter "Psychological barriers": "... Humanity always formulates only the problems, which it is able to solve because on closer examination it always appears that a problem appears only when the material conditions for solving it already exist or at least are in the process of emergence". Well, everything is clear here – first the material conditions should appear and then the problem could be formulated. Or, in other words, the substance is primary and the conscience is secondary, we leant this at universities. Let us analyze this situation in greater detail.

Long waiting

Could it be like that – the conditions for solving a problem exist, the problem has been formulated, but still there is no solution for it? Yes, such things happen. For example, a lens telescope (refractor) was invented by Galileo in 1609, mirror telescope (reflector) was proposed by Isaac Newton in 1671 - after quite a short period of time, taking into account in what period of history it happened. And the meniscus telescope, which is widely spread nowadays, was invented by Dmitry Maksutov only in 1942, i.e., almost 300 (!) years after that [2]. Why was it necessary to wait for so long, - all material conditions required for solving this problem were already in place? 

A version of an answer and its analysis

Maksutov gives the following version of an answer: "If at the dawn of astronomic optics an elementary simple principle of meniscus systems were known, basically understandable for the contemporaries of Descartes and Newton, then astronomic optics could take quite a different pathway and we could have achromatic short-focus optics with spherical surfaces (based on the single type of optic glass) irrespective of constants" [3, p.15].


A conclusion could be drawn that a fundamental invention appeared three centuries late only because of the fact that the "elementary simple principle of meniscus systems" was not known during all this time? If this is right, then it is necessary to analyze this principle, which is able to exert such immensely powerful braking action upon the progress. To avoid the distortion of the truth, we shall give full-scale quotations.

Thus, to protect an open tube of mirror telescope from the action of temperature plus from penetration of dust and extraneous objects, D.Maksutov proposed to cover it with a thin lens - meniscus, which was known even in the Ancient China.  But what would it give? The author writes: "Such approach is very good, but wouldn't a meniscus introduce harmful aberrations? Most probably, it would, but what aberrations – this should be found out. It was clear from the very beginning of the analysis of this issue that it is always possible to select such curvature for the meniscus, with which it will be highly achromatic. The issue of spherical aberration remained unsolved.

Close reasoning showed that such meniscuses may introduce significant spherical aberration (both positive and negative) remaining in this case still quite achromatic. And here I nearly missed an important discovery - drawing a conclusion that in this case a meniscus could be calculated, which does not introduce aberration, i.e., n o n-a b e r r a t i o n  m e n i s c u s.  I kept thinking about that for several hours until an idea came to my mind that it is much more beneficial to choose such a meniscus that would introduce p o s i t i v e aberration into the system, i.e., aberration that is able to compensate n e g a t i v e aberration of a spherical mirror or system of spherical mirrors. It was at that very moment that the m e n i s c u s systems were invented" [4, с.314].

A spherical mirror is characterized by harmful negative aberration (image distortion). The meniscus may also have harmful aberration (both negative and positive), therefore it is advantageous to compensate one type of harm with another. This is the "elementary simple principle of meniscus systems", or, in other words,  "a method of compensation", which is surprisingly similar to a technique, which is well known to us: "converting harm into benefit". It is difficult to agree with Dmitry Maksutov that a 300-year delay in the appearance of such an important invention could be explained only by the fact that this technique was not familiar to anybody during all this time.

An eternal idea

G.S.Altshuller writes: "If a problem remains unsolved during a long period of time, it means that the chosen direction of scientific search is wrong. In this case even a simple problem may become an "eternal" one. This is, for example, the thing that happened with the meniscus telescope."...[1, p. 238].

And what particular task was set by the mankind, or, to be exact, by that part of mankind, which dealt with the astronomic optics?  To answer this question, let us once again get back to the history of creation of meniscus telescope. Maksutov came out with an idea to create his "school telescope" – both a high-quality one and inexpensive one, i.e. the one that was affordable for every school (even to the one that is not rich) already in the 1920-ies.  It was a reflector-type telescope with a spherical mirror. Such Newton telescopes - with a diameter of 140 mm, well made in terms of mechanics and equipped with a high-class optics - were manufactured under his guidance in 1929-30 in the number of over one hundred. And still, as an author, he was utterly dissatisfied with the results.

"Is everything well in the developed design of school reflector?" – Maksutov asks himself and bitterly admits: "No, not everything is well, because the mirrors in it, though they are aluminized, will soon fail to function properly and this would result in inevitable consequences - such as criticisms from schoolteachers and requests to re-aluminize the darkened and malfunctioning mirrors. And the prestige of school telescope would be ruined.

What should be done to improve the design? – asks D.Maksutov. – It could seem that the only way is to make the design more complex by introducing a flat parallel protective window in the front part of the tube. This window would convert the telescope into a hermetically sealed structure that is resistant to dusting, condensation (fogging) and mechanical damaging of the mirrors. The introduction of flat parallel window made of optic glass will make the telescope much more expensive; but what's to be done, if only in this case a school telescope will win wide popularity, which the telescope richly deserves" [4, p. 312].

Straightly speaking – this is not a very concise formulation of an inventive problem. G.S.Altshuller formulated this problem much more accurately: "Is everything well in the developed design of school reflector? No, not everything is well, - in particular the mirrors in it, though they are aluminized, will soon fail to function properly. It is hardly probable that a reflector with an uncovered tube will function at school for long. Suffice it for a charwoman to rub off the dust from the glass and it will be spoiled. Is it possible to cover the tube with glass? This would protect the mirror, of course. But what should the glass be made of? Simple glass is inexpensive, but it absorbs a lot of light. Optical glass is good for this purpose, but its cost is high." [1, p.16].

An erroneous opinion is widely spread that Maksutov managed to resolve this contradiction. This is not so, though he spent over 13 years trying to solve this particular problem. The problem still has not been solved - 66 years later, and there are no chances that it will be solved in the nearest few decades. The solution of this problem presupposes that high-quality optical glass, which is unbelievably expensive, will be available at the same price as that of window glass. Therefore, using the terminology of G.S.Altshuller, the problem of glass for the school telescope can be easily called "eternal". But Maksutov invented a meniscus telescope! How could it be - he did not solve the problem, but he invented a telescope?…. We will discuss this issue later and now let us see what problems were set by the specialists in the field of astronomic optics during the entire period "from Newton to Maksutov"?  

Thorny way

D.Maksutov writes in this connection: "Working on the theory of meniscus systems and seeing their advantages, one inadvertently recollects the thorny way of history of optical instruments construction.

So many swords were crossed in the struggle between adherents of reflector and adherents of refractor! How much energy was wasted, on the one hand, on mastering the methodology for manufacturing and exploring of precision non-spherical surfaces and, on the other hand, – on solving the problems of achromatic glass lenses! How much flint glass and other labor-consuming types of glass was made for such cases, in which one could easily do without these types of glass! And finally, how many expensive, cumbersome and imperfect telescopes with no less expensive and cumbersome mechanical equipment and expensive rooms with huge rotating cupolas were built!" [3, p.15].

The key phrase here is: "...struggle between adherents of reflector and adherents of refractor". The forces, means and human lives were spent for many years on improving EITHER ONE OR ANOTHER optical instrument. And the work with one system implies the identification of disadvantages of only this system, how could it be otherwise? This method is so customary that it might seem to be the only existing method.

A specific feature of this approach is that it is relatively simple to identify disadvantages, but it is extremely difficult to eliminate them. Here is one example only: it is obvious that the greater is the diameter of the lens of the telescope-refractor, the better. It is easy to formulate the problem: it is required to obtain a lens of large size, but it is very difficult to solve numerous problems, which arise in this case. As of today, there are only two large visual lenses, the diameter of which are 91 cm and 102 cm. Both lenses were manufactured back in 1888 and in 1896 by American opticians D. Clark and A. Clark. All subsequent attempts to create something similar failed.

The same situation is observed in all other areas of engineering. Does it mean that this way for improving the devices (i.e. through identification and elimination of disadvantages) is wrong or erroneous? By no means. Simply this way is not the only one.

How it could be done differently?

G.S. Altshuller writes: "Two ways are combined in the evolution of engineering –evolutionary (within the limits of one level) and revolutionary (implying the transition from one level to another). Schematically this evolution could be presented as a zigzag line with a large number of turns. A narrowly focused specialist sees well the direction of one section of this line. Thinking about the future he is inclined to imagine this future as a continuation of the present; in his thoughts he sort of continues the finite section of the line further. Understanding the limitations of the existing engineering means, the specialist clearly sees the insolvable problems, i.e. a wall against which bears the imaginary continuation of the given line section.  However the dialectic of evolution is such that the insolvable problems are solved in a "roundabout way" – through fundamentally new engineering means" [1, p. 243].

There are numerous examples of situations, when a problem is formulated not for one, but for two engineering systems at once. And they are well matched to one another – they perform one and the same function and have opposite advantages and disadvantages. These are the problems aimed at the SYNTHESIS OF A NEW SYSTEM, which has the advantages of both prototypes and which is free of their disadvantages.

Typical is the variant when one prototype system performs the function better than another, but it is more expensive, while the second system is a simpler and less expensive one, but it operates worse than the first one [5, 6, 7, 17]. One more variant, which is met very often, is when the cost of both systems is approximately the same, but the first one performs better one part of the work, while the second - another part; and it is necessary to achieve such state of things when the entire work is performed well [8, 9, 10, 16]. There are examples, when the problem is formulated not only for devices, but also for two technological processes at once  ("Laminated magnet core"; the material is currently being prepared for publication).  

A specific feature of this approach is the fact that psychologically it is rather difficult to formulate a problem. Here is an example [16]. An electric razor invented in the 1930-ies had only one shaving head. In 1948 Philips marketed a razor with two shaving heads. Then came the razor with three heads and recently razors with four heads were advertised on TV. Remington managed to manufacture a "nested doll"– two shaving wire nets and two blades were placed inside each head, i.e., figuratively speaking, an electric razor with six shaving heads was created... It seems that this situation is close to its limit because further evolution would imply non-surpassable engineering difficulties. Since the very beginning of this race the following goal was clearly visible - namely, to increase the area of surface shaved. This goal was accomplished, but at what cost? During 50 years (starting from 1939) Philips released 120 models of electric razors, the complexity of design growing from one model to another. Narrow blades are used in all these razors and they cut the hairs well, but the goal was to cover a larger area.   

However, at the same time spring and inertia razors with broad blades existed, which could operate at once on an area that is several times larger, and had only one (!) shaving head. Honestly speaking, the shaving quality was lower and therefore, they disappeared 25-30 years ago, having failed to withstand severe competition. A classical variant: "either – or". The razor either shaves well but operates on a small area or operates a larger area, but shaves not so well. And it is desirable to have a simple design with one head, which does both tasks well – i.e. shaves well and operates on a large area... 

The problem is formulated "through pluses" in the following way. It is required to keep wide blades in the razor. This would enable to use the operating surface of the shaving net more efficiently. At the same time good conditions for cutting should be provided over the entire surface of the shaving net, therefore the blades should be narrow. Or, in brief wording: The blades in the razor should be wide and at the same time they should be narrow.

The specialists dealing with the development of new designs of electric razors from numerous companies with the names known all over the world failed to formulate this problem, - psychological inertia was a hindrance.  Therefore the solution of this problem appeared "extraneously", as an initiative, not in the course of work, - rather as hobby, to have one more example of stating a problem "through addition of pluses". It appeared to be quite simple to solve this problem, which is characteristic of the problems of such type. Based on the idea obtained as a result of solving this problem and protected by a US patent No. 6,584,691, several dozens of different designs of shaving heads were proposed (the material is being prepared for publication).

One could only repeat the words of Maksutov with sorrow: "When considering a shaving head with rotational blades and seeing its advantages, I involuntarily note this very thorny way, which was characteristic of evolution of optical instrument making".

So many swords were crossed in the struggle between adherents of narrow blades and those of wide blades! So much energy was wasted... so many expensive and imperfect models were made... what a high cost was paid by that half of mankind, which needs to shave!".

This example allows to offer a much more truthful version of an answer to the question: why was it impossible to invent a meniscus telescope for three centuries? Only because of the fact that before Maksutov, NOBODY SET the task (or problem) of integrating the advantages of lens type telescope with those of mirror type telescopes. Psychological inertia was the hindrance.

Correct problem

This problem was really formulated for the first time by Maksutov for his "school" telescope.

It is required to make a telescope-reflector. This would make it possible to use a spherical mirror and would result in a low cost of the instrument. At the same time the open tube of the reflector should be covered by a protective window made of expensive optical glass to obtain a hermetically sealed design - similar to that of telescope-refractor. Or in a shorter wording: It is necessary to cover the tube with a protective window to obtain a high-quality instrument and the tube should not be covered with anything to avoid increasing the cost of the telescope.

Let me remind the reader that Maksutov failed to solve this problem formulated as indicated above. Nevertheless, it is this particular formulation that enabled him to create his meniscus systems.

In order to explain this paradox, let's first analyze the possible variants of solutions for problems involving "integration of advantages of alternative systems". There are only three of them.

  1. The solution of the problem is obvious at once [8, 9, 10].
  2. The problem needs to be solved, but it is easy. [5, 6, 7].
  3. The problem cannot be solved [2, 11].

The boundary between items 1 and 2 is practically diffuse. In any case, these problems are always easy problems, and for solving them it is often enough to have common sense or simple inventive techniques. The problems remained unsolved for a long period because of the fact that nobody ever set the task to solve them. Strong psychological inertia of the specialists prevented the solving of problems. To help specialists to step over the psychological barrier, V.V.Mitrofanov and B.L.Zlotin already in the 1980-ies proposed to formulate "system contradiction" that is related to two systems concurrently (later on, it was called "alternative contradiction"): "Probably, in many cases, when we work with "live" systems, one shouldn't aim to aggravate the contradiction till it reaches the physical level, but staying at the system level it is possible to formulate a system contradiction – a vehicle should be a train to move by rails and should be an airplane to have high speed.  And instead of resolving the contradiction, systems should be integrated - in other words, "symbionized". The train of aerodynamic shape with a jet engine.  It should be system 1 in order to... and system 2 in order to..." [12]. Numerous examples of such "symbionized" (or, to use modern terminology – "hybrid") systems are given in publication [13]. 

What's to be done in the third case? G.S.Altshuller writes: "with rarest exceptions there are no problems in engineering that people would fail to solve at all (even in future). It is impossible to violate the main laws of nature – laws of conservation and laws of dialectics, if everything else is impossible, it is only temporary" [1, p. 238]. Then what do we mean, when we say: "It is impossible to solve this problem" ("The problem is unsolvable")?

Two cases could be singled out. In the first case it is understandable in general how to solve a problem, but there are powerful constraints (e.g., financial). In the example with impregnation of the rotor of a large electric machine [11], the problem consists in the fact that the existing impregnation chamber is too small for a rotor to be placed in it. It is clear how to build a chamber of a larger size, but it is also clear that it will be very expensive and would never pay back. Since it is also economically unprofitable to cut the rotor and to impregnate one part after another, it is easier to acknowledge that it is impossible to solve this problem. However, nothing prevents a problem-solver from ASSUMING that this problem is solved and from tracing the consequences.

This is exactly what Maksutov did [2], being unable for 13 years to invent a method of making optical glass inexpensive. At a certain moment he stopped to rack his brains over a method for producing such glass and simply ASSUMED that he has such glass already. Then it took him several hours only to perform several simple steps and to create his magnificent meniscus systems. Of course, some time in the distant future the problem of producing inexpensive optical glass will be solved, but why wait for so long, if it is much more advantageous to assume that it is impossible to solve this problem and to make use of a hypothetical "ideal" answer?

The second case presupposes that there are real constraints imposed by the laws of nature. However, joint use of the method for alternative systems integration and technique "admit the inadmissible" enables to circumvent these constraints as well. Yes, the problem cannot be solved, but, as it has been just demonstrated above, it is not always necessary to do it. It is possible to track out the consequences - as if the problem has been already solved. In particular – to add together the advantages of an actual system and an "impossible" one. The practice shows that as a rule, it is easy to obtain a solution in this case. This is one more advantage of this approach.

Let us sum everything up. From our standpoint, a "hybrid" of these two tools – namely, the method for alternative systems integration and technique "to admit the inadmissible" – not only enables to set non-traditional inventive problems through summing up the advantages of different systems, but also dramatically simplifies the search for a solution for these problems.  Besides, one can always expect a significant improvement in the supersystem even in such cases, when the attempts to solve the set problem fail. However, it has to be noted that such an approach in no way eliminates other inventing tools, it only supplements them. The work in this direction goes on, a series of publications has been planned.


Working on this article the authors used analytical reviews [14, 15] written based on the materials from the TRIZ funds of Chelyabinsk Regional University Scientific Library. These reviews describe in detail the history of the idea to integrate alternative systems, the application of this method to problem statement (formulation), and psychological problems that are encountered by problem-solvers.

This article is the third in a series of three publications, the two of which were already published as papers for International TRIZ conferences in Saint Petersburg  ("Admit the inadmissible", 2005, see  and "Transfer of Resources", 2006, see ). Both approaches are match one another well and supplement each other, thereby forming a completely finished system.

We are thankful to V.V.Mitrofanov, A.Zakharov and D.Kutcheryavy for their remarks, proposals and for their attention to our work.

May 2007.


List of References

1. Altshuller G.S. Algorithm for Inventing [Text] / G.S. Altshuller– 2nd ed. – M.: Moskovsky rabochy, 1973. – 284 p.

2. Gerasimov V. М. Meniscus Telescope of D.D. Maksutov: History of Invention [Manuscript] / V. М. Gerasimov– 2005. – 30 p. – The manuscript is deposited at Chelyabinsk Non-Governmental University Scientific Library 13.07.2005 No. 3046. – [Electronic resource] – Access mode: – Title from the screen.

3. Maksutov D.D. New Catadioptric Meniscus Systems [Text] / D.D.Maksutov. Publication of State Optical Institute.  – V. ХV1. –Issue.124. – 1944.

4. Maksutov D.D. Astronomic Optics [Text] / D.D. Maksutov. – M.-L. : OGIZ, State publishers of theoretic engineering literature, 1946.

5. Gerasimov V. Nail and Screw: (a training inventor's tail) [Electronic resource] - Access mode: – Title from the screen.

6. Gerasimov V. Meat grinder, my love: (inventive diptych) [Electronic resource] – Access mode: – Title from the screen.

7. Gerasimov V. Heat Exchange Intensification: a Case Study [Manuscript] / V.M. Gerasimov, M.D.Barkan. – 1998. – 8 p. – Deposited at Chelyabinsk Non-Governmental University Scientific Library 26.04.2007. No. 3134.

8. Gerasimov V. M. Hybrid: a Story from the Inventive Seminar [Manuscript] / V. M. Gerasimov – SPb, 2006. – 7 p. – Deposited at Chelyabinsk Non-Governmental University Scientific Library 23.11.2006. No. 3128. – [Electronic resource] – Access mode: – Title from the screen.

9. Gerasimov V. M. Fence: (Inventive Tale) [Electronic resource] – Access mode: – Title from the screen.

10. Gerasimov V. M. Pink Washbasin or How to State a Correct Inventive Problem? : (Inventive Tale) [Electronic resource] – Access mode: – Title from the screen.

11. Gerasimov V. M. Rotor of Synchronous Polar Electric Machine: Inventive Story from Real Life [Manuscript] / V. M.Gerasimov– 2005. – 25 p. – Manuscript is deposited at Chelyabinsk Non-Governmental University Scientific Library 12.07.2005. No. 3045. – [Electronic resource] – Access mode: – Title from the screen.

12. Mitrofanov V.V. Manifestation of Unity and Struggle of Oppositions in Engineering: (Symbiosis in Engineering Systems) [Manuscript] / V.V.Mitrofanov, B.L.Zlotin. – 3 p. – Deposited at Chelyabinsk Non-Governmental University Scientific Library, 26.09.1989.   No. 791.

13. Zlotin B. Reading Old IR (Information Resources)  [Manuscript] / B.L.Zlotin. – 6 p. – Deposited at Chelyabinsk Non-Governmental University Scientific Library, 12.07.1990, No. 972.

14. Kozhevnickova L.A. Alternative Approach to Problem Statement: Review Essay  [Manuscript] / L.A. Kozhevnickova. – Chelyabinsk, 2007. – 11 p. –Bibliography: p.7-11 (49 titles). – Deposited at Chelyabinsk Non-Governmental University Scientific Library, 10.05.2007, No. 3138.

15. Kozhevnickova L.A. Integration of Alternative Systems: Historical and Analytical Review [Manuscript] / L.A. Kozhevnickova – Chelyabinsk, 2007. – 35 p. – Bibliography: p.32-35 (55 titles). – Deposited at Chelyabinsk Non-Governmental University Scientific Library 10.05.2007, No. 3138.

16. Gerasimov V. Electric Shaver Evolution. [Manuscript] / V. Gerasimov. – 1998. – 22 p. – Deposited at Chelyabinsk Non-Governmental University Scientific Library, 26.04.2007, No. 3136. – (text is in Russian and in English).

17. Gerasimov V. Intensification of Heat Exchange : (Case Study)  [Manuscript] / V. Gerasimov, M. Barkan. – 1998. – 8 p. – Deposited at Chelyabinsk Non-Governmental University Scientific Library, 26.04.2007. No. 3135.