Multi-factor Experimenting Methodology

Recall the basic principle of the study of complex systems: the more diverse the experimental effects, the fuller and many-sided knowledge of the system being studied. Diversify the impact in two ways.

First, you can use or invent previously not used methods of influence. This is a completely new impact, not limited to the combinations already tested. (For example, if an object has not yet been tested in x-rays or in zero gravity, you can do this.)

The second way is a combination of effects in various combinations. As shown in the theory of systems and the theory of experiment, combination is the most important universal direction of unfolding a variety of experimental actions. Whenever we know at least two or more methods of influence, we can begin to combine them in various combinations according to the rules of combinatorics. In this case, although fundamentally new methods of influence are not invented, fundamentally new and important information is acquired - information about the interaction of factors, about internal connections in the system. Multifactorial experimentation is based on this.

Multifactorial experimentation allows us to study such a fundamental property of systems as emergence - the irreducibility of the properties of a system to the sum of the properties of its individual elements (non-additive, non-summatic).

The simplest physical metaphor of nonadditivity (or non-summability), manifested in the experiment, is the weighting of several objects [Pyatnitsyn, Vovk, 1987]. Suppose there are 3 objects: A, B, C. When we weigh them separately, we find, for example, that object A weighs 2 g, B weighs 5 g, and C weighs 10 g. But when we weigh two objects A and B , then we get not 7 (2 + 5), but, for example, 25 g. When we weigh A and C, we get not 12 (2 + 10), but 1 g. When we weigh B and C, we get not 15, but 3 d. The explanation of such facts is that the objects to be weighed enter into various interactions with each other and with the environment (for example, chemical or any other). After weighing all three objects together, we can get a negative weight (-120 g): the weighing pan begins to pull up. (If A, B, C are, say, three blocks of a self-assembling helicopter).

At the same time, the possibilities of inter-factor interactions are not absolute. According to the credibility argument, the effects of variables taken one by one are considered more likely than the effects of interaction between two variables, and the effects of interaction of two variables are considered more likely than the effects of interaction of three, etc. In other words, the main effect is more likely than the interaction effect. If higher-order interaction effects were just as significant and probable as the effects of the interactions of previous orders, then any generalizations and predictions would be impossible - every next factor would completely change the whole picture, entering into new, completely unpredictable interactions with previously existing factors. . That would make the existence of science impossible. Generalizations are possible, because the set of potentially determining factors can still be neglected - this is the postulate of the ultimate causal connection.

But the finiteness of causality is a postulate, not an axiom, and not a proven theorem. It remains an open question about how this postulate of ultimate connection correlates with the fundamental philosophical concept of universal connection, which is the result and manifestation of the universal interaction of all objects and phenomena among themselves.

Obviously, this postulate works best when analyzing closed stable monosystems. In the limit, in a closed and stable system, the chains of causal connections are minimal, if any, the system is frozen, “frozen”. When analyzing the open, dynamically changing complex systems, one has to reckon with the fact that the list of potentially significant factors that can come into play in certain situations is not just finite, but “essentially endless” is indefinitely large. No matter how big the final list of factors to be taken into account, there will always be a situation in which a factor appears, either considered extremely unlikely or unrecorded, but consideration of which will turn out to be a matter of life and death. This means that the list of factors to be taken into account will have to be increased, etc.