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"Куда идет мир? Каково будущее науки? Как "объять необъятное", получая образование - высшее, среднее, начальное? Как преодолеть "пропасть двух культур" - естественнонаучной и гуманитарной? Как создать и вырастить научную школу? Какова структура нашего познания? Как управлять риском? Можно ли с единой точки зрения взглянуть на проблемы математики и экономики, физики и психологии, компьютерных наук и географии, техники и философии?"

«NONLINEAR DYNAMICS AND THE PROBLEMS OF PREDICTION DISCUSSION AT THE RAS PRESIDIUM» 
G.G. Malinetskii and S.P. Kurdyumov

Now, when we at the Institute of Applied Mathematics requested from the Gref center the models on which the Gref program relied, they responded with silence. I believe it says something about our culture if people regard it as normal that someone puts forward a program without backing it by any forecasts and serious models.
Also note the following fact. Seismologists have learned to predict earthquakes because they have vast data files, which every forecaster can analyze. Nothing like this is found in economic statistics. It is bad enough that every department of any size that maintains some inhouse statistics is not liable to make them available, and often seeks to sell them. Many important data are simply not collected or discarded.
To my mind, the Duma should pass’a law, not on forecasting, but on statistical data, which are a strategically important resource.
Academician G.A. Mesyats: I should like to note that three RAS institutes gave their opinion on the Gref program. The main question was whether or not i( was possible, within the framework of the proposed concepts or models, to assure a 5-percent growth fot the GDP, as envisioned in the Gref program. One institute gave one-percent growth, another gave zero growth, and the third, one-percent growth. You are absolutely right; nobody shows their models. The models that our economic theorists have are, of course, more realistic.
Academician A.F. Andreev: The word prediction was repeatedly used here. However, prediction is what science is always concerned with: given particular starting conditions, to determine what will happen to the system afterwards. Therefore, our talk about prediction is actually a talk about the destiny of science in contemporary society. When the Duma enacts a prediction law, it thereby enacts a science law. Prediction cannot be separated from science, nor science from prediction. They are one and the same thing.
Recently, the prediction problem has been used in reference to something vitally serious for the economy and for life; therefore, the general attitude to prediction is entirely human, being somewhat different from the attitude to science. I totally disagree with this view.
I liked the report very much. It shows that when we take up a forecast problem, i.e., a prediction about what will happen to a structure, or a system, we must have in mind some technicalities, which are very many. A system can be described with high accuracy by simple equations, and they will be a model of the system. No simple model ever completely describes a system. Something is always left out. A simple model has a certain degree of accuracy, and its accuracy may happen to be quite high. But as a system develops, it may enter an unstable region. It can be the model’s own instability, which is apparent to all, or instability with respect to some parameters not recognized by the model. Then, however long you analyze the model you are not likely to see any instability. The rapporteur gave an example of an electromagnetic field in a pendulum, whose action is not visible at first sight.
I do not agree that, until the 1960s, people did not understand any of these things. What happened is that, starting in the 1960s, the science of prediction has experienced rapid growth. This very important research area is finding ever new applications in all fields of science and society. These predictions are essentially not different from all those problems that have been solved by science long ago, and we must accord them the same esteem that we generally accord science.
Izrael’: I shall make some observations. As far as meteorological forecasts are concerned, their prediction limit is two to three weeks. In climatology, as Academician Golitzyn said, scientists even gave up the word forecast, using the word projection instead. They make these forecasts for 50 or 100 years ahead, without computing every single path. We should realize, therefore, that there are two different approaches to forecasts.
Now to the extradesign accidents that Academician Subbotin mentioned. These accidents are, as a rule, considered in projects. They are accepted as they were. But there are other accidents, which are, as the rapporteur said, so rare as to be ignored. However, they are precisely our main interest. The Chemobyl disaster was not included in the extradesign category. All the fantasy that designers incorporated in their nuclear power plants never lived up to the situation that occurred in the Chemobyl disaster; it is a well known fact. It would seem, therefore, that where we refer to power statistics, to rare events, we should examine once again what extradesign accidents these data refer to.
The last observation. I did not read the prediction bill being discussed in the Duma. If it is about the order of the use of forecasts, it is quite natural, but if it preaches some scientific truths, then, I believe, in principle, there must not be such a law.
Kuznetsov: I shall name yet another reason for prediction limitation. It is connected with the fundamental limitation of computers.
If a system’s path fills some area of the phase space, this path cannot be predicted by computer «path by path.» The fact is that computers have their capacity. Every equation is converted into digits. For example, we use discretization to reduce a set of partial differential equations to a set of ordinary derivative equations, then computation follows. However, when we wrote our set of ordinary derivative equations, we assumed that some of the coordinates are continuous; we discretized some coordinates leaving others continuous. A computer has no continuous coordinates, all of its coordinates being discrete. We have at every time slice a finite set of points where the system may find itself, in other words, there can, in principle, be no nonperiodic motion, and we must be fully aware of this. We can predict distributions but not every individual path.
Methods have been developed in the last two to three years, which make it possible to judge, from the resulting semihyperbolicity, conditions of whether or not we can in principle simulate a particular path on a discrete computer, and if we cannot, what must be done to compute the path distribution. In other words, we cannot say what course a path in a phase space will take, but we can say in what neighborhood of this point it will remain one time, and in the neighborhood of another at another time. This is a prediction too, albeit a peculiar one.
Subbotin: I have a very short remark about Chemobyl. Today, it is generally admitted that its design was faulty. Besides, it is important that the control system be self protected: If someone initiates operations that are contrary to logic, they must not be executed. Unfortunately, this was not implemented. I call your attention to the fact that the terms «extradesign accident» or «hypothetical accident» often hide a faulty design.
L’vov: I found the report extremely interesting because of its multidimensionality, which also includes the study of economic processes. In my view, such studies could be of great applied value. Therefore, it was with a purpose that I asked to speak.
It grieves me, as an economic expert, to say what I must say, but the information we manipulate is thoroughly individualized, with a great many overruns. For this reason any experimenter wishing to use my model to replicate my result will arrive at a totally different one. We allow ourselves wonderful levity to handle key statistical indicators. The problem of statistics is typical everywhere, but it is only in this country that the measuring system we use has a prediction period close to zero is from the start from the start. However, we believe such predictions and create heightened expectations of economic theory. We believe that it ostensibly knows how to do something, and is doing something, instead of analyzing the models underlying this or that construction. This is my first point.
My second point is that it seems to be quite obvious that our academy-and the report we have heard is vivid proof-has a fairly large scientific backlog, which can be used to analyze economic information and assess economic development parameters in order to make a significant step forward. Today, the academy stands aloof of these efforts (I beg to be understood correctly), demonstrating the destitution of all principles. We know this: what is incorporated in the development of our economy has no scientific verification. And what do we do? We raise our hands and give our support.
In conclusion, a few words about the expectations we create in our students. Any textbook on economics describes a model proposed by a winner of the Nobel Prize in economics. But the model is not confirmed by reality, because if you take different time intervals, or different countries, the model will not work. These are the facts, and something must be done about them.
Malkov: We are concerned with the matters of provision and prediction of the strategic stability of this country in the military field. Recently, we expanded our scope to include research into information stability, and social-psychological, economic, and other kinds of safety. In cooperation with the Keldysh Institute of
Applied Mathematics and other organizations we are modeling social processes, specifically historical processes.
We established that a closed society, bounded by its territory and resources, has a steady-state condition, being a closed-loop system. If it is an open-loop system, i.e., it has neighbors and no clear boundaries, it is inherently unstable, as feudalism was in its time. A steady-state condition does exist for a capitalist society, but the domain of attraction is continuously changing, and certain correlations of parameters give rise to several attractors, which can, for the same level of productive forces, lead to a feudal-type society with an uneven distribution of earnings. This social structure is also stable.
In other words, transitions to local chaos and the multiplicity of attractors are characteristic of social systems with the same macroparameters. When we speak about forecasts, we should realize that accurate predictions for any reasonably long period are not possible, and it is self-deception to believe otherwise. We can only speak about short-term forecasts, about the presence or absence of steady-state conditions, there generally being several steady-state conditions. In conclusion, our prognostication strategy should be as follows:
we need to ascertain what parameters and in what combination (because the combination of parametric changes is also a very important thing) must be changed in order to arrive at a needed limiting condition. Our country is currently located in an attractor with a low-productivity state of economy, characterized by a feudal societal structure.
It would be a good thing if the Academy of Sciences paid more attention to interdisciplinary research, and colleges and universities trained students who are at home in both soft sciences and nonlinear analysis techniques. If this does not happen, we must not expect any significant progress in prognostication.
Nigmatulin: I think that today’s meeting is a rare example of a case when every word said by the rapporteur and the speakers is extremely interesting. I will not speak on the gist of the matter but, as a State Duma deputy, I deem it necessary to touch on the prediction law now on the floor at the Duma. I, too, have given it some thought.
It is common knowledge that state budget figures are based on forecasts. The most fundamental forecast says that the 2001 GDP will be 7.5 trillion rubles and the state budget, nearly 1.2 trillion rubles. The tax code is being adopted, which also allocates rates. The government states that it will keep the state budget. But what is the basis for this statement? Figures change depending on the methodology used in the computation of the GDP. There must be certain standard methodologies. They are not partial-derivative equations, they are a group of simple (perhaps ten to twenty) arithmetic operations. We do not need dozens of figures, what we wish to know is whether or not we shall collect one or two trillion rubles worth of taxes. In this connection, I believe that government should be put within the prediction law framework. We need limitations on the particular state budget figures that are confirmed every year. However, the method of their acquisition-especially as some of them are fundamental-should, I feel, be regulated by the prediction law.
Ganiev: Nonlinear mechanics is a field our team has worked on all its life, especially in recent years in connection with the need for development of science-, intensive processes. There will be people aspiring to create a new science. They will coin a name, take an example from the biology of something like a self-oscillating system: many hares, fewer wolves; many wolves, fewer hares. This is what the new science of synergetics is all about. No sir, a science becomes a science when it has common mathematical models, common mechanisms, and common methods. And there are none in synergetics! There are various applications, there are fine analogies that physicists can take from mechanics and biologists can take from physics. But models in biology are very complex, and they should be studied specifically and seriously.
Incidentally, I read an article by Mathematician V.I. Arnol’d the other day. He attempted to predict some social processes using simple mathematical systems. This is all very interesting, but with all due respect to this distinguished mathematician, these questions should be the concern of students, maybe sociologists, in order to get the feel of the trends. The models that were considered today are very simple, therefore, professionals in the fields of sociology and economics ought to regard them with great caution. Much work remains to be done on the development of mathematical models themselves. I should like to hear more about attractor models and chaos.
When this trendy theory first appeared, we mechanics knew perfectly well that in deterministic systems, along with regular processes, there are always unstable processes in evidence. Let us take a glass filled with water and begin to sway it. At certain frequencies the surface of the liquid in the glass will execute plane oscillations, at other frequencies it will gyrate, i.e., spatial motions will oscillate in two distinct planes. Between these two states there is a nonstable domain, where the whole liquid is in chaotic motion. This phenomenon is described by simple mathematical techniques, without recourse to terms like attractors, chaos. and the like.
In conclusion, I want to emphasize once again that models related to social phenomena or economic phenomena are very complex. Therefore, we must be very cautious in basing far-reaching conclusions on them.
Plate: I am glad that the report provoked such a good reaction, because I was among those who had initiated its presentation at a RAS presidium meeting. In truth, there is food for thought here, and for the interaction of specialists in different fields.
A few short comments. Of course, extradesign, ill-predictable disasters should perhaps be our primary concern. Many of those present will remember that epoch-making presidium meeting two months after Chemobyl in this room, where Valerii Alekseevich Legasov spoke; Anatolii Petrovich Aleksandrov was also here. At the time, the likelihood of that disaster was estimated at less than 10У7 a year. It did occur nonetheless. The design, which might have been faulty, had, of course, contributed to the disaster, but there was also a crazy conjunction of many other things. It seems to me that we must be in a position to estimate the likelihood of such events by means of models, to predict them, and to give some advice for their prevention.
As for the direct application of the modeling approach in economics, I think that this possibility should be discussed. The nation has for decades invested heavily in its agribusiness. The Soviet Union could not be fed, and now we cannot feed Russia either. Every year, we have a battle for the crop, a battle for the seedage, procurement, etc. Maybe it is simply an imperfect policy. I set apart all manner of ideological and political things, which are abundant here, but these things must be looked into.
Georgii Gennad’evich Malinetskii showed us a drawing, which demonstrates how the funding of science and education affects the economy. A very important conclusion follows from it. We are now rejoicing that the Duma and government promise to increase the 2001 science budget by 30%. But if our models and computations are correct, it may turn out that this 30% will not affect any qualitative change in the present situation, and then disappointment and disaffection will follow; we are investing in science, but it has no effect on the economy. We must assess the critical magnitudes of appropriations for science in fractions of a percent of the GDP, which are purposeless in terms of our future strategy. Perhaps what we need is to demonstrate in quantitative terms that an increase in appropriations by 300, not 30%, will bring about economic growth in two years’ time.
This is the kind of educative work with government officials, the Duma, and others that should be carried out by our economics and spokesmen for the group headed by Georgii Gennad’evich Malinetskii and Ser-gei Pavlovich Kurdyumov.
Rundkvist: It was with great expectations that I
came to hear this report, because prediction is the number one question for geology and seismics. Regrettably, I am leaving without the clarity that I had hoped to gain.
The rapporteur set a singularly important task: to consider the prediction of all processes and phenomena in the social sphere, in nature, and in the technogenic sphere. It would seem that, having posed such a super-general problem, we should have made supergeneral conclusions, to be detailed by us in particular areas. Unfortunately, his conclusions (which I tried to faithfully record) will not be easy to use.
I am not at all objecting to those who highly appreciated the report. The aim of my intervention is simply to state that when such reports are made, one wishes more clearly formulated conclusions on fundamental issues, which we can be applied in the future. A super-generalization such as the we one just heard is from a small perspective.
On the whole, I am glad that this report took place. This is an exceptionally important field, and I hope that future contacts will help us, including myself, to better understand what precisely is of use for geologists today.
Mesyats: Most likely, it not easy to deliver a report from which something new could be derived by both nuclear scientists, mechanics, and economists. I think that this is quite a natural reaction.
Malinetskii: I wish to thank you for a very interesting discussion, and above all else, for your understanding. It was only once that the speaker’s understanding of my words was the direct opposite to my meaning. When I spoke about accidents, I said that there are engineering systems where extradesign, or hypothetical accidents, can be ignored. This can be done, in particular, with regard to car breakdowns. But there are complex systems where we cannot act in this manner and where we must count on the worst. Our institute, jointly with the Institute of Control Problems, is currently engaged in the scenario modeling of precisely the worst possible situation we can face.
As far as the conclusions from the report are concerned, I should like you to-realize the following: There are general fundamental limitations in prognostication. Science has established essential restrictions on predictions for most diverse systems. Prediction is becoming major technology in many fields. As for the fields where it is most effective, I think that this is a subject for a general study. Thank you very much for a very exciting discussion.
Mesyats: I believe that many of us have gleaned from this report new and necessary information. At any rate, a feeling has emerged that there is much common ground between the different fields of knowledge.