Complexity and intransitivity in technological development

Abstract

This paper investigates the existence of a fundamental link between two disciplines that emerged during last few decades: complexity science and advanced engineering. During this time many industries, especially those related to the high-tech end of technological development, have faced the problem of increasing complexity of design, production and operation. Industrial projects have grown to become multidisciplinary, tightly interconnected, costly and difficult to control and predict. Two trends can be identified in this respect: one is the consistent effort of systems engineering in reducing the uncertainties of complex industrial operations and the other is the effort undertaken in complexity studies to account for uncertainties present in the real world.In this work, we provide a brief overview of recent developments in advanced engineering and give a consistent interpretation of technological evolution from the perspective of complexity science in general and complex competitive systems (CCS) in particular. CCS is a general framework that was recently developed for analysis of complex systems involving competition. Transitivity of the decision-making process and the cyclic nature of technological progress are considered. Correctness of intransitive decisions is inherently relativistic: the same decisions can be seen as correct or incorrect when considered from different perspectives. When treated simplistically, intransitivity may seem to be illogical but, nevertheless, it is common in nature and needs to be studied. CCS provides a formalised scientific framework for analysis of intransitivity and establishes the existence of an important connection linking complexity and uncertainty with intransitivity. Implications of intransitivity for engineering decision-making and strategic planning are considered in the context of CCS. A working example of intransitivity in competition between major car manufacturers is presented.

A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings

“…In addition, in [76], the author claims that: <<When treated simplistically, intransitivity may seem to be illogical but, nevertheless, it is common in nature and needs to be studied.>> Taking into account these last comments encountered in the aforementioned references, as well as the study made in Section 3 in [1], we can give some answers to the problem of intransitive behavior encountered in several physical or chemical processes. To do so, our main tools are the concept of an interval order and its numerical representability through two real-valued functions, when available.…”

“…Those additional axioms lean on additivity properties, and the aim here is finding entropy functions that are unique up to linear transformations. In a similar way, a battery of papers by Klimenko (see [38,[73][74][75][76][77]) deals with concepts as mixing (see also [78]) and competition of systems. It is not our intention here to make a criticism on those papers.…”

Entropy of chemical processes versus numerical representability of orderings

“…Those problems are mainly related to intransitivity. In the same way, some other problems related to mixing and competition have also been considered in [27][28][29]34].…”

“…Since then many other authors have followed this approach and improved Carathéodory's setting (see e.g., [19][20][21][22][23][24][25]). Besides, applications to particular situations in Physics and/or Chemistry consequently follow (see e.g., [26][27][28][29]) and a wide sort of uses of concepts related to Entropy are typical when analyzing the behavior of some chemical processes (see e.g., [30][31][32][33]). …”

“…An important case, already considered in [27,29,34], appears when intransitivities are involved in a chemical process. Apparently, when some kind of intransitivity is observed in a chemical process (see, e.g., [35,36]), one may tend to interpret that there is something wrong in all what concerns the existence of an entropy function that could control the process, and, consequently, something coming directly from Carathéodory's axiomatics that explains why an entropy function exists, seems also to have a flaw.…”