Economy & Energy
Year VIII -No 46:
October-November 2004  
ISSN 1518-2932

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The technological prospective: prediction with a simple mathematical modeling (2)

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First Part in e&e No 45

The Technological Prospective: Prediction with a Simple Mathematical Modeling (2)     

Technological and scientific quantitative time behavior: predictions.

José Israel Vargas(*)

Let us now finally proceed to the examination of the evolution of some techno-scientific and a few associated industrial practices, with a view to assemble useful information that might help the formulation of more cogent Science and Technology Policies. As remarked before, the model has proved to be valid for the analysis of thousands of systems of interest. It asserts as a basic tenet, quantitatively verifiable, that in the competition between systems (or between species) the winner is always the most efficient one. Efficiency itself – the concrete and most precise measurement of the technical progress – also grows following a logistic path, as shown beautifully in Figure 30. It represents, in truth, the thermodynamic efficiency as observed for several kinds of techniques, involving different modes of energy and light production. Actually, for producing work with growing effectiveness. It also describes the increasing efficacy of the synthesis of ammonia, first carried out by Fritz Haber. The conversion of energy among its different forms does also obey the same pattern, as shown in Figure 31, calculated from data in Starr (21). Studies such as these have demonstrated that there is no valid example of a less efficient system conquering its place in the market, which always displays a Darwinian behavior. This means that “appropriate technologies”, poor or “soft” ones, which became popular thanks to Schumacher’s book “Small is Beautiful” (22) have no future, nor any practical value… Despite this, it continues to play significant role in the adopted policies of some developing countries, under the influence of many international organizations, even in those parts of the world that should already have overcome such temptations. The application of thermodynamic criteria in the search and development of new materials - a goal often cited as a priority in numerous science policy formulations - should reveal itself most useful. The minimizing of entropy growth, Q/T (Q is the variation of quantity of energy used in the process, and T is the prevailing absolute temperature), should always be sought. It guides the choice for materials capable of working at the highest temperatures and the consequent minimum energy expenditure (and higher efficiency). In addition, the close connection between entropy and information theory principles, made evident in the present model as already pointed out, while dealing with the connection between energy fluctuations and the invention/innovation production – should also be applicable to abstract activities. Hence it should also reveal itself as a good guide for the choice of best alternatives as regards the rate of evolution displayed by  scientific findings themselves or to the examination of the performance of educational systems, as well as to the exploration of some special feature of still more abstract activities.

Historical evolution of efficiency for three Technologies, D T50% is the time to go from 1% to 50%.

Figure 30

Figure 31

Since smaller entropy leads to minimal noise – and therefore maximum of information transmission – the entropy evolution examination, that reflects the intrinsic efficiency of the system under examination, is also helpful when choosing useful materials, for this kind of application. The demand for minimizing entropy change should, for instance, also illuminate the past development of optical fibers, of silicon, germanium, and of other materials needed for faster transmission of digital data

In this connection, the study of the evolution of both scientific creativity, measured by the rate and extent of the number of published research papers, as well as of the number of registered relevant patents on new technologies, would help decide whether the approaching exhaustion or the extension of the research concerned would still merit attention and additional effort from the technical-scientific community. The contention that appropriate decisions can be induced by the model constitutes the corner stone of this presentation. In fact, certain examples, chosen at random, from the large number of those studied by Marchetti and his group, and also by the present author, report on fields that either have been exhausted and hence became useless for further work or, on the contrary, should still merit additional attention. Examples of both categories are given bellow

1. As shown in Figure 32, no additional study should be devoted to the  study  of the  metabolism of vitamin D,  since 90% of the “niche “ involving this  field of investigation has  already been  occupied;

Figure 32

2. Basic research on cobalt-rare earths magnets (evaluated by the reported number of related publications, Figure 33), reached maturity by 1976, with a ΔT of only 10 years. Thus additional research in this field is risky. However, the analysis of the number of registered patents for the field indicates, as shown in Figure 34, that it would still be possible, and perhaps, profitable to dedicate another ten years of research to the field, particularly  to those concerning  their potential applications.

Figure 33

Figure 34


3. Scientific and technical research results on a plastic building material, essential component of water transportation systems, of many home appliances and widely used in the chemical industry – polyvinyl chloride, PVC- are presented in the usual format in Figures 35 and 36. The pertinent data comprises two waves: one indicates maximum research activity focused around 1976, while another saturates itself by 1986. On the other hand, Figure 36 (ΔT=22 years) also suggests that purely technical applications of the material are still feasible;

Figure 35

Figure 36

4. Figure 37 supplies the number of papers published on the role of CO2 (a main greenhouse effect inducing gas) on climatic change, which is being extensively examined by the scientific community involved with  these  researches shall probably end, unless new scientific discoveries emerge, to induce the initiation of a new wave of novel results, presumably much latter on.

Figure 37

5. The number of papers on superconductivity, listed by the present author, is given in the usual model presentation in Figures 38 and 39. Apparently by the middle of the fifties, the activities concerned were exhausted. Two waves of research publications can nevertheless be noted (Figure 38) indicating a renewed interest in the challenging subject: the latest one, having ended by the nineties, suggesting a renewed interest in the subject. In fact this behavior should not surprise practitioners of the present modeling exercise: a novel, exciting phenomenon did emerge with the discovery of the ceramic high temperature superconductors in the beginning of the 1990s. Incidentally, this spectacular discovery may change the whole fabric of the electric sector, starting off an absolutely new and revolutionary innovation wave. The major inflexion on the evolution curve describing the number of publications on the subject of superconductivity, since the discovery of this phenomenon by Kammerlingh-Ohmnes, should also be remarked. It occurred around the middle fifties, at the end of the first wave, and coincides with the publication of the famous Bardeen-Schrieffer-Cooper paper (23). The extraordinary acceleration displayed in the curve (a thirty five fold increase in the number of publications); this illustrates the enormous impact that a theoretical understanding of a previously unexplained phenomenon may exert on a nevertheless challenging, classical and interesting sunject. To conclude this topic it should be recalled that chances for new discoveries in this area involving national groups is deemed  improbable; opportunities may however remain for the development of practical, and as yet unforeseen applications, particularly in the fields of instrumentation development. Nevertheless a caveat, often expressed by the late Abdus Salam, should be kept in mind: these limitations should not let us loose sight that fundamental research remains essential, for “there is no applied science without science”.

Figure 38

Figura 39

         Figure 39 dealing with classic superconductors indicates that high transition temperatures would never be reached through traditional technological approaches for, in fact, 90% of the available research “niche” had already been attained by the end of the eighties. A new wave had therefore to start. It did in fact occur, and as already remarked, is bound to revolutionize all technical sectors with undreamed of discoveries and innovations. It would be worthwhile to pay attention to the fact that such new developments could already have been surmised, if the data saturation of the number of published papers that had been treated by the present model, had been duly extrapolated in Figure 39. In fact, if this exercise had been carried out, it would have been possible to guess as early as 1970 the onset of a new wave of discoveries.

         Let us now direct our attention to systems so typically anchored in past American and European developments: the automobile industry saga throughout the past century, illustrated in Figures 40 and 41. It should be pointed out that in both cases two waves may be clearly identified, illustrating, once more the Kondratiev cycles existence. Similar phenomena may be perceived for Brazil (Figure 42); only in this case, the elapsed time from the inception of the national industry was not sufficient to show more than a fraction of a cycle.

Figure 40


Figure 41

Figure 42


         It is however interesting to verify that what is valid for the whole of the automobile sector, is also valid for large firms, such as Mercedes Benz, as displayed in Figure 43. It indicates that Mercedes’ image is in people’s minds; it recalls a dream car that stands for elegance, comfort, quality and status.

Figure 43

 One should note that the “fractality” implied in the logistic approach for the automobile industry is also clearly valid for the USA, Germany, as well as for Brazil.

         The analysis of the growth and demise of the American car industry is spectacular and very instructive: it may set the inexorable destiny of the majority of the industrial sectors, constituting a key facet of the global market. This pattern is, of course, the result of fierce Darwinian competition that governs both the most characteristically material assets (ordinarily associated to economics), as well as among those labeled “soft”, or immaterial: the creative scientific, artistic and all cultural sectors that therefore can be dealt with by the model under examination. Figure 43 shows the growth and almost complete collapse, as far as the number of “actors” involved with the automobile industry, in the last century.

Figure 44

It can be seen that at the beginning of this century there existed 1400 automobile enterprises. The dotted line represents the observed mortality rate of car enterprises, leading, today, to the survival of not more than one dozen - less than one percent of the number of pioneers that started the industry. This figure also shows that, at the summit of the development process, the average life expectation of the pioneering enterprises was in fact reduced to four years.

The examination of the situation of the very paradigm of modernity – the computer industry - displays analogous behavior, as indicated in Figure 45.

Figure 45

         Ferocious competition prevails: the number of   manufacturers remaining in 1991 was 700, while for 1987 it had reached 3.000. In fact, also for this case, it is highly probable that only a dozen computer makers may survive. Innovation is highly valued in this field, as can be judged by the cumulative number of new models offered to consumers in 1987: it reached 3.000 and will attain probably twice as many by 2010, as shown in Figure 46. It may still be possible to participate in this dangerous game - at least as regards the versatility of model design - possibly displaying a rather superficial technology that nevertheless may be charming in their presentation (design). This may also happen with other kinds of technological gadgetry. It seems appropriate to conclude these remarks, advancing the following statements:

Figure 46

1. It is possible to anticipate the outreach of the new scientific and technological “development throbbing”. For this purpose it is necessary to collect and duly analyze the existing information relevant to inventions and innovations, even if still only incipiently introduced into the market. A minimum level of 2 to 5% would be deemed desirable. It would be perhaps more profitable to use other people’s processes, inventions and innovations, rather than investing to obtain original results for in general, innovations require much time and money for their market acceptance when facing the competition filters barriers - a phase that involves obstacles rather more arduous obstacles to overcome. Acquisition, or the establishment of some form of partnership in cost sharing, may be more profitable. Attention must however be paid to intellectual property limitations. Japan’s success story after World War II should not be forgotten. Also leasing at early stages of product diffusion may constitute an acceptable approach from the strictly commercial point of view.

2. Clearly it is not at all possible to anticipate the occurrence of any emerging invention which could appear at any time. It may, however, be expedient to consider that an invention (or innovation) follows another invention (or innovation). If this is kept in mind, then deliberations to be timely taken for actions may be called for, particularly as regard those aimed at merely improving the newly described invention.

3. Whenever two actions   decisions (solutions to problems involving inventions and innovations) are in competition, the one presenting the higher efficiency - preferably of higher thermodynamic efficiency - will prevail. This may constitute a good initial query preceding a choice.

4. Diffusion of major heavy technologies - and not only the heavy ones - as already indicated in Figure 22 taken from a study of Fisher and Pry – indicates that it takes around fifty years for them to firmly establish themselves, conquering and playing a commanding role. The development of nuclear energy, as previously remarked, constitutes an illustration worth considering. The first reactor started in 1941, but it was only in 1990 that this kind of primary energy source was to respond to 5% of the total energy consumption and reach 15% of the total world electricity production.

5. This sluggishness in the introduction of major technological systems opens the possibility of evaluating their relative market share. For example, from Figure 11, we may infer that natural gas will become the major fossil fuel in use in the next fifty years. It would, therefore, be wise to act accordingly. Fortunately Brazil has started importing massively gas from Bolivia and Argentina while developing prospecting within its own boundaries.

         It may equally be foreseen that future steel production will be carried out mainly in electrical furnaces utilizing mostly pre-reduced iron ores (perhaps by natural gas, thanks to its flexibility and abundance) and increasingly by the use of available scrap iron, as shown in Figure 47. The product generated in the so-called mini-steel mills will dominate the future steel industry, as foreseen by the present modeling technique. Brazil therefore would be well advised to follow closely this trend that will probably become the dominating technology in the American market which is the main buyer of Brazilian steel. Thus the displayed data indicates that the American  mini -steel mill production is growing rapidly, tending to successfully overcome the L.D. process, the most widely used process in Brazil, as well as in other American suppliers, such as Japan, Mexico, China, and so on.

Figure 47

6. It would also be worthwhile to examine a few examples, taken from a large number of studies carried out so far - over 3.000 - dealing with applications of the model. This would offer the opportunity for understanding the internal logic of the System and perhaps to devise better policies for the developing of novel technological applications. For instance, the present author (using this model) has examined the opportunities for describing the development of and the capacity for competition by the following Brazilian systems:

·clarification of the past evolution and the future market for television sets in Brazil (Figure 48);

Figure 48

·Brazil’s communication infrastructure evolution (Figure 49);

 Figure 49

·description of the evolution of telegram sending in this country during the last 100 years (lasting for about 2 Kondratiev cycles), shown in Figure 50;  


Figure 50

·examination of the remaining market potential for the Flandres sheets fabrication  in Brazil (Figure 51). Supposedly this material could not face the growing competition by the newly developed aluminum, paper board and steel sheets used in the packing industry as well as other applications. The study has concluded that while competition was indeed growing, with the diminishing relative participation of the product therein, its absolute production could still be sustained for many years to come.


Figura 51

·projections for cement production and uses might have disastrous economic consequences if a too short time database for the past G.N.P. evolution would have been adopted. Such an approach was indeed utilized to estimate the future Brazilian electricity demand; this resulted in a surplus and costly capacity installation. It so happens that “the system” has taken over to correct this ambitious planning, setting the process back to its natural logistic tracks, as shown in Figure 52

Forecast for 2000:            Curve A 60 million ton

                                           Curve B 68 million ton

Figure 52


● as a last example, the crash of the world financial system could have been predicted and perhaps avoided if an appropriate (and early) treatment of the registered numbers of American companies and banks that had so far collapsed (Figures 53 and 54) had been carried out.

Figure 53

Recession is a period of readjustment, change, and revolution. The firms which are not elastic enough to adapt to new circumstances fail. Rates of failure are a good indicator of the tensions in the economic system. We have analyzed bankruptcies in the USA larger then $300,000. Their center point has just passed, in 1991, and the process should reach 90% in 1997 and end (99%) in 2003, implying a final total of 5.5 million bankruptcies


Figure 54

         Taking these features into account, Marchetti remarks that looking at the real human actions through the lenses of this modeling technique, all that seemed to be irregular, incongruent or even seemingly chaotic becomes faultlessly organized - following an inflexible logic.

         For our purpose, it seems prudent and indispensable for our government to develop an institutional mechanism capable of examining existing databanks on inventions and innovations, particularly of those relative to patent applications. These analyses could provide potentially interesting information on techniques applicable to our market, provided they relate to a still early development stage, thus allowing for timely initiatives. This would offer the opportunity of building up more pro active science and technology policies, to the benefit not only of appropriate capacity building but also to reinforce the existing and new research laboratory infrastructure.

The human capital resulting from this process would be prepared to face the challenges of the 21st century. Lacking these measures (as it has hopefully been made clear) it would be necessary to wait for another half a century to participate in the next innovative waves, should we decide to do so. In fact the innovations that define the present wave have already been determined (having gone through a maximum intensity by 1978). However, participation in the next wave may perhaps still be feasible, for it may be extended to 2005-2010.

It is remarkable that most Brazilian systems that so far have been analyzed, through the model just described, reveal that this country remains one Kondratiev (55 years) behind the major industrialized countries, particularly as compared to the United States. This is made evident when comparison is effected as regards a key indicator - energy consumption in both countries: 41 MW for the installed capacity in the U.S. by 1940, as compared to the 43 MW installed in Brazil by 1985! We may probably have missed the boat much earlier, by about 4 Kondratiev cycles, leading us roughly to 1780-1790, when we failed to get rid of the Portuguese colonial yoke. In contradistinction, the United States at the same epoch, became independent, and Europe, that was liberated from feudalism by the French Revolution. Thus the industrial revolution practically coincided with this epoch making events that led to the demise of the old empires, like the Iberian ones, which ruled over our country for 300 years. I hope that these reflections will prod us into action. The opportunity of speaking to the executives of the Federal Government Special Secretariat for Strategic Issues may perhaps contribute to the diffusion of the methodology briefly herein described; perhaps it may even find utilization in the ongoing planning exercise aiming at the examination and formulation of policies capable of facing our country’s truly complex circumstances.



21.          Starr, C., Scientific American 225(3):36-49, 1971.

22.          Schumacher, E. F., “Small is Beautiful”, Hartley&Marks, 1999.

23.          Bardeen, J. R., Cooper, L. N., Schrieffer, J. R., Phys. Rev., 1175, 1957

(*) This article resulted, in part, from a previous extensive research study carried out within the ambit of UNESCO’s Participation Program Nº 5136 (1990/91).

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Tuesday, 11 November 2008

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