The role of contradictions in the creative process, especially in scientific research and engineering is well known. It has been emphasized not once by prominent scientists and engineers. For example, P.L. Kapitza used to say that "the main engine of advancing physics, as well as of any other science, is revealing contradictions ..." .
However, the mechanisms to overcome contradictions received little attention. It remained an open question whether there are any patterns in overcoming contradictions or not and if there are patterns then which ones? Below we attempt to fill up this gap. We first turn to a specific example of overcoming a contradiction in the art of war.
Napoleon's contemporaries often marveled at how he was often able to defeat an enemy who had numerical superiority. But there where the contemporaries saw just a contradiction - the opponent has to have fewer soldiers, so that it could be defeated, but has more - Napoleon also saw a way to overcome it. Many times and on different occasions he said that all of the art of war is to be able to concentrate more force than the enemy at the right place and the right time. Napoleon did it by attacking the scattered forces of the enemy with the lightning speed and beating them piecemeal. And in every such a separate engagement, he turned out to be stronger, although the total number of soldiers in the enemy's entire army was greater than the total number of soldiers in the army of Napoleon.
Let us analyze this formula of overcoming the contradiction that since then entered all textbooks on the art of war – one can be weaker on the whole, but must be able to be stronger in any particular engagement. It is easy to see that in this formula, along with one pair of opposites, namely “weak and strong”, there is another pair, “the part and the whole”. As they say, fight fire with fire.
It turns out that it is no accident but rather a manifestation of a general rule: overcoming of a broad class of contradictions is accomplished by introducing yet another pair of opposites in addition to that pair which was already present in the statement of a contradiction. If the conflicting requirements that make up a contradiction, are denoted as A and "not A", and the added opposites as B and “not B”, then the contradiction gets overcome because entity B is given property “not A” and entity “not B” is given property A. Analysis of a large number of examples of overcoming contradictions, taken from various fields of science and engineering, has shown that there is a limited number of standard opposites, B and “not B”, which are used to separate the conflicting demands A and “not A”.
Below is the list of such standard opposites to separate contradictory requirements with examples of their use from the history of science and technology.
The properties of an object are called substantial if it possesses them in a free state. The properties are called functional if the object acquires them when it is incorporated into some system.
The use of these opposites to separate the contradictory requirements "the object must have property A and should not have property A" results in the following method of contradictions overcoming. Property A has to be functional, and property "not A" has to be substantial. In other words, in a free state the object has to be "not A" but being included in an appropriate system it has to acquire the property of A.
For example, in 1934 the Joliot-Curies bombarded aluminum atoms with alpha particles and obtained phosphorus-30, which spontaneously emitted positrons and turned into a silicon-30. This could only have happened if the conversion occurred in the nucleus where one proton emitted a positron and converted into a neutron. However, this assumption run against the fact that proton is lighter than neutron and could not convert into it due to the law of mass-energy conservation. Thus, there was a contradiction: on the one hand, the proton had to convert into a neutron, so that the experiment of the Joliot-Curies could be explained, and on the other hand, could not do so, as it was contrary to the law of conservation of mass and energy.
This contradiction was overcome when it was found that proton is indeed lighter than neutron when it comes to free particles. Inside the nucleus, however, the masses of nucleons are slightly changing, and the transformation of a proton into a neutron becomes possible. Thus, in a free state, a proton cannot really turn into a neutron, but in some nuclei the transformation is possible.
This way of overcoming contradictions is especially prevalent in engineering, where objects often have to be given certain properties that they themselves do not possess. There are many ways to give the desired properties to an object: introduce additives; apply fields; immerse it into a special environment ... Here is a concrete example of the application of the above method to overcoming a contradiction in agricultural engineering .
It is known that 99% of the water consumed by a plant does not affect its growth. It is just pumped out of the soil and evaporates into the ambient air. In this way, one hectare of wheat during the growing season pumps out about 5,000 cubic meters of water. If we take into account that by 1980, the irrigated area is expected to double, then there is a problem: where to get one million cubic meters of fresh water? You can try to find the millions, but it does not eliminate the problem, but only postpones its solution. Therefore, irrigators were not afraid to put the problem radically: find a way to overcome the contradiction consisting in the fact that the soil should be watered abundantly, and you cannot do so, because of the limited water supplies. After a long search, it was suggested to consider the soil not in isolation from the rest but as part of the system "soil + air" and to irrigate not just the soil but the entire system. If the air layer above the ground is made humid, then the soil evaporates much less water, and hence requires less watering.
Above we have already considered an example of the use of this opposition to overcome the contradiction in the art of war. Consider now the use of this opposition in resolving contradictions in science.
When in the late XIX century, cathode rays research led to the discovery of the electron, which, as it turned out, could be extracted from any matter, a contradiction emerged between these experimental results and the well-established fact of atoms’ neutrality and to the assumption of their indivisibility.
As it is known, this contradiction was overcome by J.J. Thomson, who suggested that atom is not indivisible but consists of parts, which are not neutral although on the whole it is neutral. In other words, the contradictory statement
charge-of(atom) = 0 & charge-of(atom) ≠ 0
was replaced by a not contradictory statement
charge-of(the-whole(atom)) = 0 & charge-of(the-parts-of(atom)) ≠ 0
Let’s denote the property “charge-of(x) ≠ 0” as A(x) and “the-whole(y)” as B(y). Since the opposite of “the whole” is “not the whole”, i.e. “part(s)”, then not-B(y) is “the-parts-of(y)”. Hence, the above contradiction can be symbolically written as A(atom) & not-A(atom) and its solution as A(not-B(atom)) & not-A(B(atom)). Thus, transition from contradiction to its solution can be written as follows:
A(*) & not-A(*) → A(not-B(*)) & not-A(B(*))
Here “atom” is replaced by * for the sake of generality as the formula could be applied to other entities, not atoms only.
Since A(*) & not-A(*) = (A & not-A)(*) and A(not-B(*)) & not-A(B(*)) = (A(not-B) & not-A(B))(*) and since A(not-B) in another notation is A•not-B, the above formula can be rewritten as
(A & not-A)(*) → (A•not-B & not-A•B)(*)
By assuming the convention of omitting (*), the formula can be further simplified as
A & not-A → A•not-B & not-A•B
which means that in order to resolve a contradiction the contradictory requirements have to be applied to opposite entities, i.e. separated between them.
In engineering it is also pretty often that contradiction “something has to have property A and has to do not have property A” is overcome by replacing a continuum object with a structure which elements have property of A and the structure on the whole has property not-A. For example, to accurately measure the acoustic field the fiber of the acoustic sensor has to be thin. But to cover as much area of the field as possible the fiber has to be thick. The contradiction is resolved by replacing one continuum thick fiber with a bundle of many thin ones .
Suppose that we face a contradiction that something has to have property A and has to have property not-A. Then the contradiction turns out to be resolved if the form of this "something" turns out (or made) to have property A, whereas its content turns out (or made) to have property not-A. Here is an example of such separation of contradictory requirements between the form and content in science.
When in the mid 1920's Heisenberg et al put forward matrix mechanics and Schrödinger put forward wave mechanics, it appeared that these are two unrelated theories - so different they were in their postulates and used mathematical apparatus. However, it turned out that they were applicable to the same phenomena in atomic physics, and produced the same results. Thus a contradiction emerged: how come that the two completely different theories produce the same results?
To explain this contradiction, and thus overcome it Schrödinger has showed that, although by its form (A) matrix mechanics is quite different (not-B) from the wave mechanics, in terms of their content (not-A) the both theories are identical (B). In both not the measured values played the major role but their operators. The theories only differed in how these operators were represented. In matrix mechanics they were represented as matrices and in wave mechanics as differential operators.
Consider now the application of "the form vs. the content" dichotomy to overcoming a contradiction in technology. We first have to keep in mind that in technology the content often means the substance or the composition of an object, and the form means its geometric shape/ configuration or the shape of an object in which the substance is distributed or dissolved.
In conducting the accelerated wear-testing of engines a variety of bulks (such as quicksand, dust, clay particles, etc.) have to be fed into the engine’s filters. The number of the materials is generally high, they should be fed on schedule in certain portions, and they cannot be mixed. Dispensers/feeders cannot be used to feed the materials as too many dispensers/feeders are needed which results in a too big and cumbersome set up. To serve them by hand is also impossible as it is impossible to manually measure out and feed too small portions of the materials. Thus, a contradiction arises: the portions of the material have to be big enough so that they could be measured out and served manually and the portions have to be small so that not to kill the engine right away. The contradiction is resolved by separating the contradictory requirements between the form and the content. The small content of the material is uniformly spread over large areas. Specifically, long tapes are used to spread the materials over them (each material has its own tape). Then it is not difficult to manually measure out small portions as they occupy large portions of the tape, which can be easily measured out and cut off .
The subject of our study are the mechanisms/methods to overcome contradictions in specific areas of science and technology. So it may seem strange that in the wording of these methods philosophical concepts such as "the substantial and functional", "part-whole", "form-content", "cause and effect", etc. are used.
This discrepancy has its justification and explanation. Philosophical opposites are the most common opposites. Each of them is the quintessence of many similar specific opposites characteristic of a particular field of science and technology. For example, to be the cause of something is a generalization of such concepts as "to be derived from something", “to be produced by something”, “to be generated by something”, “to be converted from something”, etc.
In general terms, a method to overcome contradictions considered in this section boils down to that cause having property A entails a consequence with property not-A.
Consider its application in chemistry. At the beginning of the XIX century, after the victory of Proust in a controversy with Berthollet, chemistry embraced the view that in all chemical reactions, substances always combine in constant and definite proportions. So when it was later discovered that in catalytic reactions the Law of Definite Proportions does not hold, this could not do not cause a lively interest. But at the same time, it was not enough to stimulate revision of stoichiometric ideas, which has got a tough win. In this way chemistry was confronted with a contradiction: the law of definite proportions should hold in catalytic reactions too and should not hold, as evidenced by some of the facts. W. Henry, A. de la Rive, H. Hess, A. Khodnev tried to overcome this contradiction by explaining the violation of the law of definite proportions in catalytic reactions by the very same law (i.e. by deriving "not A" from "A"). According to them the catalyst C takes exactly the same part in the reaction as reagent R1 to form compounds of constant composition: R1 + C = R1C. This compound reacts with the second reagent R2, which results in the release of the catalyst: R1C + R2 = R1R2 + C .
Although these ideas turned out to be wrong, it does not diminish the value of this example. The use of a particular method to overcome a contradiction, as any theoretical construct, does not guarantee a solution adequate to the reality. It only guarantees the production of such a hypothesis in which the contradiction is removed. A hypothesis must be tested in practice. And if it turns out to be wrong, it is necessary to change a way of overcoming the contradiction and to formulate a new hypothesis.
In technology, especially computer technology, the above method of overcoming contradictions is frequently used too. For example, in computing it is often the case that it is easy to write a simple program that runs long but it is difficult to write a sophisticated program that runs fast. This contradiction could be removed by creating a simple program that generates a sophisticated one, which otherwise would be hard to come up with (i.e. a program with property A generates a program with property not-A). Writing generators is sometimes the only way to obtain the error free convoluted fast programs.
Use of this opposition to overcome the contradictions of "something must have property A and should have the property of not-A," is that this "something" splits into deterministic and random parts. The deterministic part has property A, but the random one has the property of not-A.
Here is an example of a contradiction in science which could have been resolved by this method . When it was proved that thermonuclear fusion reactions go in the Sun, this immediately raised the question: why does the Sun not explode? There is a lot of matter in the Sun and a high temperature. Hence, the number of interactions between atoms with energy sufficient for the synthesis must be huge. But the Sun does not explode. Hence, the number of interactions is much smaller that the calculations show. Let’s separate the contradictory requirements, the number of interactions has to be high and has to be low, between "deterministic" and "random." In other words let’s split the interaction into deterministic and random parts. The deterministic part has to happen in the Sun frequently but the random part has to happen rarely. And indeed it turned out that for the synthesis to happen it is not enough for atoms with sufficient energy to collide. Something else has to happen. This "something else" turned out to be random, not depend on external conditions, and extremely rare. It was called the weak interaction. This is how it was explained why the Sun does not explode.
Overcoming contradictions are not necessarily related to separating the conflicting demands between opposites. Conflicting requirements could be separated between different objects, different conditions, different parts of space or time and other differences. The opposite is an extreme case of a difference. But if one strives for unification, it is easy to discern opposites in every difference. For instance, two objects are different just because one has something which the other one does not have. Opposites are entities which are opposite in everything, whereas differences are entities, which are opposite in something.
Here are a few examples of separating contradictory requirements between differences in science.
In 1935, Japanese physicist H. Yukawa predicted the existence of a particle with a mass intermediate between the mass of a proton and of an electron. Soon particles of this mass were found in cosmic rays. They were called mesons. It was found that mesons are unstable, and therefore could not come from the space, but formed in the upper layers of the atmosphere under the influence of cosmic rays. Surprisingly, it turned out that mesons in the lower layers of the atmosphere were absorbed approximately 100 times less intensely than in the upper layers. This was contrary to the Yukawa theory, according to which the meson must intensely and quickly interact with matter. In order to overcome the contradiction – according to the theory meson must be rapidly absorbed by the substance, but in reality this does not happen - the American physicist Marshak in 1947 firstly suggested the existence of two types of mesons. One of them interacts strongly with matter (this is the Yukawa meson), the other don’t. Secondly, Marshak suggested that in the upper layers of the atmosphere, we are dealing with the Yukawa meson, and in the lower - with another meson. The third assumption by Marshak was that the less intensively interacting meson is formed by the decay of more rapidly interacting Yukawa's meson, pervades the atmosphere and reaches the Earth's surface, where it is recorded by our instruments. Subsequent experiments confirmed the validity of this hypothesis.
This example is interesting because the mutually exclusive properties separated not between one pair of opposites or differences but between three of them at once. Firstly, they are separated between different particles. Secondly, they are separated between different areas of space (specifically between different layers of atmosphere). And thirdly, they are separated between cause and effect (specifically between the parent particle and the daughter particle).
And here is an example of separating the mutually exclusive properties between different points in time . It is known that the system of Sirius is a double star - Sirius A and Sirius B. It is reasonable to assume that both stars were formed at the same time. Yet Sirius A is in the prime of life (one of the brightest stars) whereas Sirius B is a very old guy (it shines 8000 times weaker than Sirius A and is barely seen, even though its mass is only half the mass of Sirius A). If the age of the both stars is the same, it can only mean that Sirius B lived much faster than Sirius A. For this to happen, according to the Mass-Luminosity relation, Sirius B must have greater mass than Sirius A. In fact, it has half the mass of Sirius A. This contradiction was resolved when it has been suggested (and then theoretically proved) that white dwarfs, which is Sirius B, are the result of stars’ explosions. Thus, the contradiction was explained by the fact that the earlier Sirius B (before explosion) had a much larger mass than it has now.
And here is an example of separating contradictory requirements between different points in time in technology. To protect the radio telescope antenna from lightning it must have a lightning rod. But the lightning rod absorbs radio waves, creating a radio shadow. Thus, in order to pass the radio waves, a lightning rod must be nonconductive, but in order to catch the lightning it has to be a conductor. This contradiction was overcome in the invention , where a lightning rod is an insulator in the absence of a lightning but turns into a conductor when lightning strikes.
An interesting technological example of overcoming a contradiction by separating between different objects is found in . In the second generation of computers the speed of the whole machine was limited by the speed of its slowest component. On many computers expensive CPUs were idle most of the time waiting for slow peripheral devices, performing IO. An excellent solution to this contradiction - the machine is able to work quickly, since has a fast processor, but cannot realize its potential because of the slow work of input-output devices - was found by IBM. It developed a computer system consisting of a fast "main" machine IBM 7090 and one or more small slow machines IBM 1401. The first carried out the calculations, the rest - input-output.
In this country and abroad the theory of inventor’s problem solving (TRIZ) grows in popularity [10, 11]. The apparatus of identifying and resolving contradictions is one of the main parts of this theory. Therefore, the results of this work may be the use of clarifying and advancing this apparatus.
Besides, from the above it is possible to draw an important conclusion about the similarity of the basic mechanisms of scientific and technological creativity, which was first argued within TRIZ framework back in . In this age of specialization, this conclusion may reflect the fact that, in the future, perhaps not too distant, the history will again turn around in a spiral and the age of all-round craftsmen will return. The previous era of all-round craftsmen was an era of encyclopaedists. A person could productively work in various fields of science and technology because of their encyclopedic knowledge. This time is over, because the body of knowledge has grown so much that is no longer fit into one person's head. The desire to know everything, or almost everything in his field led to specialization. Now, however, the growth of knowledge turned into its opposite: more often you can hear that the information explosion has created the hunger for information, that it is easier to re-discover the needed results or reinvent some device than looking them up in an avalanche of information. That is why it is not the analysis of the huge number of secondary and tertiary facts specific to a particular area that is becoming increasingly important, but the knowledge and ability to apply the tools of creativity that are the same for all areas of science and technology. In the future, it appears, the main emphasis will be laid upon the education of scientists and engineers who have basic polytechnic knowledge in conjunction with the perfection of mastering the tools of the theory of solving scientific and engineering problems. This combination should allow one to easily switch from one area of science or technology to another, as the highly specialized corollaries of the fundamental concepts will be almost obvious for them.
In the meantime, on the agenda is the problem of utilization of the discovered similarity of the basic mechanisms of scientific and engineering creativity in mirroring the high potential of TRIZ in a similar theory of scientific creativity.