6.12.1913  -  12.12.2002

Books of N.M.Amosov

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Digression. System, Models, Heuristies

I have described what we do in the cybernetics department in articles and books. Now I would like to write about it once again, adding something new that I have devised. I want to tell it simply: this is important for me.

Strictly scientific literature is intended for specialists. In the meantime, curiosity increases in proportion to education. It is satisfied by popular science books. And this is reasonable: specialists study their subjects using scientific books.

My cybernetic half is occupied by "eternal questions": The Truth, Wisdom, Man, Society, Mankind, The Planet.


Let's begin with the main postulate. What is The Truth? The truths of different peoples contradict each other. Demonstrating or proving the truth is a problem. I am not a philosopher, and for me, the truth about something is its model. To understand the structure and functioning of a cell, an organism or a society we must visualize all this in their structures and functioning, in other words, we must devise a model, possibly a complete and correct one.

We are so accustomed to these terms — system and model — that it seems there is no need to explain them, although they are not a hundred percent true. A system is a certain set of diverse elements with multiple relations and an integral function which has its own peculiar qualities. A model is a system with its own structure and function reflecting the structure and function of the system — the original. The model is a simplification of the original and is usually a distortion of it. The elements of the system consist of atoms, and energy circulates along the relations.

However, such a simplified interpretation is applicable only to simple systems, such as a stone, a car, or even a solar system. And if these are sophisticated and living systems, then the answer cannot be monosemantic — yes or not. Yes, elements are made of atoms, yes, the energy circulates in the system. But not only heat or electrons. Also circulating are the signals coming from the elements of the system controlling the physics and chemistry of its more simple working parts. These signals are specific organized portions of energy or substances, and the control parts of the system are complex structures which incorporate all the information about the system — its model.

Here are the examples to explain it.

A cell. Its working organs — mitochondria (the power station), lyzosomes (digestion — preparation of fuel), membranes (division, protection and external ties). The control of this mechanism is concentrated in the DNA of genes, in the nucleus. They incorporate the models, in other words, the structures of all proteins and the programme for how and when they should be produced. Control signals are represented by information RNA.

Take an organism. Its working organs are well known: the muscles, lungs, heart, stomach, etc. Control organs — the nervous and endocrine systems. Signals — nerve impulses and hormone molecules. Models for control are found in nerve ties.

The term "model" is widely used at present. A "model car," a model of a house or a dam are all simple. The structure and appearance are merely reproduced. A toy car may run; this means its function has been reproduced. A model car can be made close to the original. But the concept of a model is much broader. A verbal description of a model is itself a model. So are drawings, calculations, and function graphs. They can all be models of one object with different means of representation (different codes).

The main property of a model is its accuracy and the completeness of reproduction. Take a simple object — a car. A brief description of a car sufficient for driving is given to a driver. To repair a car, one needs a detailed description. To build a new one we need a set of drawings, schemes, calculations, and technology. All these models are about one object. The difference is in the depth of detail. There are detailed and generalized models which incorporate only structural blocks. Both models are necessary for a thorough understanding of the object.

Another example from electronics. Take a circuit design of a radio set: it contains a block circuit — several squares and arrows. There is a schematic diagram: conventional signs reflect all parts and connec­tions. There is a wiring diagram where the parts are represented in their appearance and mutual location.

Quite possible is an uneven model where one part is presented in detail, and other parts are presented in a general form so as to reflect the attitude of the main part to the other parts. Sometimes the main part is depicted in a drawing in heavy lines, and other parts, in lighter lines.

The model may represent either the whole system — in which case it is a complete model — or only part of it (a partial model). Different sets of signs and means can be used for models — from mathematics and words to diagrams and figures, to physical models made of metal, plastics, or electronic parts. Moreover, a model can be expressed by a conventional code in the memory of a computer.

There are two types of models: quantitative and qualitative. The former are presented by verbal descriptions. They are subjective and inaccurate, uneven in terms of the reflection of the parts of the system, and in terms of generalization. They are suitable for approximate control of the system, but the object cannot be built anew by these models: each man has an arbitrary interpretation of them. On the contrary, quantitative models present an object at a certain "scale." These are drawings, figures, formulas, mechanical or electronic models and the latest — sophisticated models generated by computers. These models, if they are detailed ones, allow us to build the system itself.

Another division of models: static and functioning ones. A verbal description, a drawing or a set of formulas are static. From them, we can only visualize how a model moves. Such models do not function without our intervention. But there are functioning models as well. An example — moving automobile models or a hydropower plant model. These are simple examples. But we can make complex operating electronic models. They can be reproduced in a computer. Such a model can control an object without human intervention.

Many generalized models can be derived for each more or less complex object — it all depends on the "taste and skills" of designers. This is true not only of descriptive but also of functioning models. Fancy how many models can be made for just one automobile.

It is no coincidence that I have taken these examples from engineering — its objects are rather sophisticated and at the same time much more simple than "living" systems — from viruses to communities and the biosphere itself. Any engineering system has "complete" models — drawings, diagrams and descriptions which are used to design them. As yet, we cannot do the same for biological systems. We do not know biology to an extent which will allow us to model nature.

So should we limit ourselves to descriptions and verbal models in this case, while quantitative, to say nothing of functioning models are not suitable for living systems even in principle. Nothing doing. It is impossible to create complete models, but it is both possible and necessary to create generalized models. Without them, cognition is incomplete, and control is limited.

It is not sufficient for an engineer to look at a new machine and have a detailed lay-out in order to understand it. He will need generalized models — block-schemes, a line diagram, performances and curves. The same is true for living systems.

It is impossible to understand an organism using a microscope alone. We need description of its major parts and generalized models as well. This is necessary for an understanding not only of the structure but of its functions as well. For instance, to comprehend the physiology of an organism, we need a model of interaction of the heart, blood vessels, lungs, kidneys, etc. This can be created without a model of the cells that are elements of these organs. This model will help us to understand the mechanism of functions disturbance in some diseases — in heart diseases, for instance, and even to control these functions after an operation. But such a generalized model cannot show us how cancer occurs, since it takes place at the molecular level within the cells. With this purpose in view, we need a complete model, something which is not possible at present.


Thus, we come to know the truth through modeling — the creation of models. At the same time a set of models of diverse generalization or detalization is necessary for sophisticated models.

The problem of vital significance here is the correlation between the complexity of a model and an object. It is impossible to express complexity through simplicity if you are aiming for completeness. There is no need to draw a cell to show all its molecules. Until now, we have been using only generalized models with different levels of detalization — lopsided and uneven very often — for complex objects. By the way, this problem of reflecting the complexity of a model is far from being simple. We cannot be too categorical about it. Take nature, for example. The genes, the DNA of the germ cell, incorporate a model of the future organism. There are about one hurdred thousand genes in an organism, and each consists of a thousand of nucleotides — letters. That's too much for us. But still the living model of the genes is much simpler than a whole organism.

How can we explain this? The genes contain a compact model which reflects their structure and technology. Therefore, in principle, it is possible to create artificial models that will accurately describe an assembly of extremely sophisticated objects. However, they do not dare to compete with Nature.

Now let's take technology — how to create a model.

The construction of a model represents the process of reproducing an object while you look at it or hear it. Like the lenses of a camera which create a negative on film, the eye "draws" the patterns of a neuron in the cortex. But obviously, not exactly like that. First, there is the tuning of a receptor — a selective fine interpretation of details. So we receive uneven models. Second, there is the choice of objects. Wisdom comes into action during the process of interpretation and selects information. By what criteria? Under what influence? Let's make it brief (before we analyze human wisdon). Primary selection of information or objects for modeling is motivated by feelings ("This is interesting") and convictions ("This is important"). In this way subjectivity is present from the moment of perception. That is precisely why each of us perceives similar sophisticated objects as different and therefore interprets them differently.

The understanding of the truth... What is it? Can it be an identification in terms of figures? More or less. We identify the unknown by comparing it with the familiar — wholly or in part. These known figures — models taken for comparison — have been fed into the memory of wisdom through training. They are associated with other figures, with destination, designation and evaluation by feelings. We "know" them. And, on the contrary, the unknown figures do not have a name, or use and there is no place or thing to "associate" them with.

Each wisdom tries to see the familiar in the unknown. Each has in his memory his own set of generalized and particular models (figures). It associates them with a new one. At the same time it is not important if there is not a complete coincidence. Our new-found confidence helps us identify incomplete coincidence with complete. And this is the manifestation of the subjectivity of identification or understanding the truth.

Cognition (modeling) of simple systems is relatively simple. The problems emerge in interpreting "living" systems. Their descriptive models are similar to children's drawings or toys. We find a multitude of details and unreliable generalizations. The level of generalization and the list to one side or the other are determined by the qualifications and convictions of the author, that is by a set of standard models that his memory possesses and which he is "in favour of." Psychologists label this "attitudes." I am not a psychologist, therefore I call them "biased ideas." Each has his own level of preconceptions, since each intelligent being has its own feelings and memory. There are no absolutely objective researchers when we are dealing with sophisticated systems in which we have to use generalized models.

The mechanism of human wisdom employed for the cognition of sophisticated systems is limited. Bookish verbal models cannot be used as a code for quantitative modeling. Similar models for simpler objects — in physics and engineering — are derived mathematically and are represented by systems of equations.

A cell or a community is another thing. They contain a multitude of structural units, and they are arranged in a multi-layered hierarchy. Therefore, it is difficult quantitatively to determine the dependencies between their elements. Digital data are insufficient and contradictory. Therefore, quantitative models are limited by particular problems.

At the same time without complete, or at least generalized models we cannot always understand the principles of action of a system. Therefore, they are necessary.


I give here a simplified diagram to show what this "functioning" model of a certain system is like.

Each square (A—E) is a structural element, an organ for instance. Each arrow (1—-6) is a function. The "output" of one element is the "input" for the other. Some arrows form feedback loops. Positive feedback (a-f-) enhances the "input" and rapidly brings the function to maximum. Negative (b —) feedback reduces it and promotes smooth transfer from one mode of operation to another...

The designer must wrack his brains to create such a model.

Begin with an objective — what do you need this model for? Monitoring or perhaps elucidating the hidden mechanisms of interaction of elements, for instance. Then evaluate your "know-how" — what do you know of the structure of the object, and is there any digital information concerning its functions?


system model


To what extent can you use your computer? All this influences the choice of the generalization level which helps us to reproduce the object as a model. For instance, the organism could be modeled, beginning with the cells or the organs, or, in general, it may be taken as a whole, as a "black box" with external "inputs" and "outputs." Practically speaking, models can be derived only at the level of organs. There is digital information for their equations and the amount of information that can be processed by a computer.

The choice of the level of generalization is the first rough approx­imation of the model scale. The next step is to derive a non-contradictory hypothesis about the structure and functions of the object at the given level. To do this, a diagram like the one shown in the figure must be drawn. This is far from being simple. Libraries of books have been compiled for each sophisticated system, be it a type of knowledge, an organism or personality. They all incorporate a multitude of facts, both correct and misleading. Something out of this multitude with a minimum of contradictions must be selected. It is impossible in this case to avoid the likings of the author.

The hypothesis is the qualitative basis of a model. Computers need digital information alone. Therefore, the arrows in the diagram should be replaced with equations. This is the most difficult and arbitrary stage, since one is short of credible quantitative information. Approximations, corrections, and even invention of some dependencies banking on verbal descriptions are in order here.

When all the equations have been compiled, a tormenting "adjustment" of the model to the hypothesis begins. It is namely at this stage that all the contradictions of the hypothesis and incorrectly derived performances (equations) come to the surface, and much must be changed.

Finally, the model has been balanced. Both ends have met, the programme is valid, and the model can be studied. The "game" is on. Different conditions manifest in external "inputs" are set, and all functions and total "outputs" are calculated — that is the way the system-model functions.

And this is the most interesting stage — we make an experiment not on a living object, but on its model. This shows the great potential of modeling. First, you cannot experiment on all objects. An example of this is a community. Second, stimuli can not always be used. (As in the case of man.) And, third, models can be experimented with as long as we like, quickly and cheaply.

The main purpose of working with a model is to compare it with the same experiment on an object when such an experiment is technically possible. If adequate similarity is discovered in several experiments, this means that the model is correct and can be used in controling the object. For instance, in treating a patient...

A skeptical researcher, on reading my primitive statement may say: "Bosh. It's wishful thinking. How can it be? You have spun half your data out of thin air, drawn your curves by hand, and come up with a model which you say is reliable? How can you seriously trust the results of such a model study?"

Well, the skeptic is correct — it cannot be done. But I will try to explain.

The technique of finding the truth which has just been presented with simplifications is called "heuristic modeling" of sophisticated "living" systems. Its task is to model hypotheses, not via verbal descriptions, as is the norm, but in mathematical form — in digital information and graphs. Our cybernetic section has been working in this area for almost twenty years and has experimented on many objects.

Why do we bother, you may ask. Why should we wrack our brains over a model when there are no credible quantitative data? Perhaps we should wait until experiments are made, hypotheses are cleared, and contradictions are eliminated.

I'm afraid it's useless to wait — nothing will come of it. The technique for deriving the truth from sophisticated systems which was effective up till now can be defined as analytical. Specific dependencies are artificially derived from the object and are studied in pairs or by threes, seldom more than three. It is assumed that a group of scholars can, in this fashion, analyze all the possible combinations and ac­cumulate digital information which will later promote the automatic formation of the whole. Vain hopes. The number of specific dependencies is innumerable, they cannot be found by an exhaustive method without a plan, which is the present method of working. We are drowned in particulars. Such a plan can give only a synthetic approach.

The synthesis of the complexity is made possible only on the basis of digital, and not verbal information. Therefore, we need quantitative models.

Both synthetic and analytical methods should be used in tandem. Synthesis points the way to experiments; analysis gives the "bricks" or elements, since they are derived from the programme which accounts for the whole system.

In this way, heuristic models, although they cannot give the whole truth about the system and its theory, nevertheless are necessary for progress of science. Here are the reasons for it.

They allow us to chose, when possible, a non-contradictory hy­pothesis and to modify it.

They indicate the direction of the experiment: first you have to study whatever is in doubt, taking due account of all interrelationships and conditions. New data are incorporated into models and gradually advance it to form a hypothesis to the theory.

They provide a new language for science — the language of mathematics so unusual to biologists and humanitarians. However, we cannot do without it.

And, finally, they can be used for practice — within the boundaries of satisfactory coincidence with an object. This practice consists of management and advice-giving.

I'm convinced that in this or other form, heuristic models (you may call them simulation models) are necessary for scientific progress with respect to sophisticated systems.

And what shall we do at present? Up till now, both physicists and chemists have come to a common agreement by 90—95 percent. The remaining discrepancies advance research. In the case of biologists, these discrepancies make up approximately 30—40 percent of our total information.

Sociology? I'd better not expatiate on it. It is no concern of mine. Intil we have quantitative models of sophisticated systems, it will be impossible to prove the truth in biology, psychology, or sociology. There is no mechanism of proof; it is difficult to conduct standardized research to derive compatible data. The path to real models, in other words, to the theory of sophisticated systems, is the construction of heuristic models. I'm comfident of this. However, by no means, do I want to say that models will solve all our problems. We're a long way from complete models (like drawings of machines) whereas generalized models are always subjective and, therefore, disputable.

But this is much easier to prove in disputes on figures than in disputes on words.