This section will present three examples (among others), which correspond to three famous problems, well-known in Literature:
i) The Three-Body Problem (Classical Mechanics)
ii) The Protein Folding Problem (Biology and Pharmacology)
iii) The Three-Good and Two Factor Problem (Economics)
Such a choice is substantially due to the fact that their consideration corresponds to their logical (and also chronological) sequence of solution, obtained on the basis of the Maximum Ordinality Principle. At the same time these examples allow us to show the vast applicability of such a Principle, because the afore-mentioned problems pertain to three completely different “fields” of analysis: “non-living” Systems, “living” Systems, and “thinking” Systems, respectively.
The rational that led us to the solutions of such important problems is synthetically illustrated here below:
1 – A preliminary solution to The Three-Body Problem was obtained by introducing the concept of “incipient” derivative into the well-known equations of Classical Mechanics, still maintaining the traditional hypothesis of a supposed independence of the space variables (x, y, z) from each other.
However, the most appropriate solution to the “Three-body Problem” was obtained when the proper Space of the System was considered as being one sole entity. Such a solution was then easily generalized in the case of N bodies (see Eq. (4) in the section devoted to the mathematical formulation of the Maximum Ordinality Principle).
At this stage, instead of considering some direct applications to Celestial Mechanics such as the Solar System or, better, some particular Galaxies (in order to analyze, for instance, the real presence therein of the so-called “Black Holes”), we decided to primarily devote our attention to a problem which appeared (and still appears) as being much more important, at least in terms of Human Health: the Problem of Protein Folding.
2 – The Protein Folding Problem
Such a problem was faced in two subsequent steps, which precisely correspond to two different papers presented at the Third and Fourth International Conferences on Bioinformatics, held in Valencia (2010) and Rome (2011), respectively.
In the first paper (see Protein Folding 1 ), after having recalled the relevance of Protein Folding and the fact that it is one of the most important “intractable” problems, we showed that its “intractability” can be overcome by adopting the Maximum Ordinality Principle as a reference criterion. In such a case, in fact, the folding of even a macroscopic protein, such as Dystrophin, made up of about 100,000 atoms, can be carried out in a few minutes, when the model is run on the most updated computers (1 Petaflop).
In the second paper (see Protein Folding 2 ), we showed that the same problem (the folding of Dystrophin) can also be run on a simple PC in less than two hours, as a consequence of those very profound “symmetry” properties of the Ordinal Matrices that characterize its solution, when this is obtained on the basis of the Maximum Ordinality Principle.
Such results represented a fundamental step in order to face the third problem:
3 – The Three-Good and Two Factor Problem
This problem is strictly related to “The Three-body Problem” precisely because Fundamental Principles in Economics and, in particular, in Neo-Classical Economics (NCE), represent a direct transposition to economic activities of the Principles of Classical Mechanics (CM) and, even more, of Classical Thermodynamics (CT). The rational that guided us to the solution to this problem can be summarized as follows:
i) the first step consisted in the passage from “two” to “three” factors. This is because one of the major criticisms addressed to NCE is that of neglecting Nature as the third fundamental factor and, consequently, the intrinsic value of Natural Resources;
ii) a this stage, the transposition of the topological space (x, y, z), usually adopted in the case of “The Three (N) body Problem”, into a new Space of analysis (the Space of goods), represented by the three new “co-ordinates” K, L, N (Kapital, Labor, Nature), enabled us to obtain the solution to “The N-Good and Three Factor Problem ”;
iii) Under these conditions, “The Three-good and Three Factor Problem” represents a particular case of the former, whereas “The Three-good and Two Factor Problem” is nothing but a particular case of the latter.
It is worth adding that the research for an Optimum Reference Criterion for making strategic choices in the Energetic-Economic-Environmental field had started about ten years before (as clearly shown by papers and articles listed in References). Such a research, however, had always been carried out under steady state conditions. This is because the considered case studies were always analyzed on the basis of the Maximum Em-Power Principle. The real novelty of the Maximum Ordinality Principle is that all such examples can now be reconsidered under dynamic conditions too.
4 – An Additional Ostensive Example: the case of Smart Grids
This example shows how the Mathematical Model of a Smart Grid, based on the M.O.P., is able to suggest the best strategy to maximize the Ordinality of the System, so as to improve its large scale “intrinsic” instability and the consequential strong vulnerability to “cyber” attacks (Paper to be presented at the 7th Biennial Emergy Conference, Gainesville, Florida, USA, January 12-14, 2012).
Giannantoni C. Thermodynamics of Quality and Society. In Proceeding of International Workshop on “Advances in Energy Studies” 2004, Campinas, Brazil, June 16-19, 2004, p. 139-157.
Giannantoni, C., Lazzaretto, A., Macor, A., Mirandola, A., Stoppato, A., Tonon, S., Ulgiati, S., 2005, Multicriteria Approach for the Improvement of Energy Systems Design, Energy, 30; 1989-2016.
Giannantoni C. Emergy Analysis as the First Ordinal Theory of Complex Systems. In Proceedings of Fourth Emergy Conference 2006. Gainesville, Florida, USA, January 17-22, 2006, p. 15.1-15.13.
Giannantoni C., Boccardelli P., Luongo S., Zoli M., Ulgiati S. 2006. The Code POLIDEMACO (POLIcy DEcision MAking COde) for Strategic Choices based on Circulation of Benefits. In Proceedings of Fifth Workshop on “Advances in Energy Studies” 2006, Porto Venere, Italy, September 16-18, 2006.
Giannantoni C., 2007. Ordinal Benefits vs Economic Benefits as a Reference Guide for Policy Decision Making. The Case of Hydrogen Technologies. In Proceedings of 20th International Conference “ECOS-2007” , Padua, Italy, June 25-28, 2007, p. 1629-1636. Afterwards published by Energy, as an updated version.
Giannantoni C., Zoli M., 2008. Ordinal Maximization Principle vs Pareto’s Optimum Conditions in Policy Decision Making. The Case of Hydrogen Technologies. Proceedings of the 6th International Workshop on Advances in Energy Studies, Graz University; 333-344.
Giannantoni C., 2009. Ordinal Benefits vs Economic Benefits as a Reference Guide for Policy Decision Making. The Case of Hydrogen Technologies. Energy n. 34 (2009), pp. 2230–2239. Giannantoni C., Zoli M., 2010. The Four-Sector Diagram Of Benefits (FSDOB) as a Method For Evaluating Strategic Interactions Between Humans and the Environment. The case study of Hydrogen Fuel Cell Buses. Ecological Economics 69 (2010) 486-494.