The Arab Center for Research and Policy Studies has published Mathematics as an Intellectual Pursuit: A New Way of Cognitive Thinking by Mahmoud Bakir (368pp.) and fact-checked by Muwaffaq Dabul. The book explains the reasons why mathematics ought to be transformed into an “intellectual pursuit”, how some mathematical ideas can be used to approach an array of general issues, and how to devise a general “system” to use in the fields of politics, sociology, international relations, business, and so on. Thus, it presents a mathematical approach to “conflicts from the perspective of gestalt” and discusses the “butterfly effect” historically, using the Arab case as a model.
The book examines whether the proverbial butterfly’s movement has had any effect on the stability of the universal system, answers whether this has any relationship to the social or political system, then addresses events taking place in the Arab context and considers whether it is possible to mathematically “model” the behaviour of individuals or society. The author highlights the role played by the nature of mathematical proof in crafting any “logical system” of discourses, literary innovation, philosophical perspectives, or even ordinary conversation and discusses one of the benefits of mathematics for political science and understanding, and sometimes predicting, the behaviour of a social group, as well as the impact of mathematics on moral development when studied as an intellectual pursuit.
Across space and time, many have posed the question of “what is mathematics?”, along with other questions that appear within this framework, including “what use is mathematics?”, “how did it come about?”, and so on. Yet “what is mathematics” remains at the forefront of these questions. It is rarely discussed or addressed in university lectures on mathematics teaching, or even in school curricula, because most mathematicians accept that it is not an easy concept for beginners, and that it becomes easier to answer as one advances in the study of mathematics. Still, these are legitimate questions in urgent need of answers. Mathematicians joke that the average person might be able to remember the names of numerous artists, political leaders, and perhaps even fashion designers, but could he recall the names of just three 20^{th}-century mathematicians, numerous as they are? Could he relate eminent mathematicians such as Carl Friedrich Gauss (1777-1855), Georg Friedrich Riemann (1826-1866), and Kurt Godel (1906-1978) to the mathematical concepts through which they impacted human civilisation? Mathematics, thus, has become significantly isolated from ordinary people: there is a large cognitive gap, growing larger with time, between the concerns of mathematicians and the rest of the world, even though there is significant misunderstanding among a wide segment of people as to the nature of mathematics, especially in its modern form. To this day, most of these people believe that mathematics is a set of procedures and algorithms used for certain calculations.
The formulation of the prevailing concept of “structure” in mathematics came as a consecration of formalism, established by the mathematician David Hilbert in the early 20^{th} century and one of the more widespread of the three major schools of thought in the philosophy of mathematics. It is derived from the principles of Euclidean geometry, known as Hilbert’s Axioms, that Hilbert proposed in 1899 in his famous work Foundations of Geometry (Grundlagen der Geometrie). Mathematics, for formalists, is interested in the structural characteristics of symbols more than their meanings. The meaning of a symbol appears when its “relationship” to other symbols becomes apparent; a symbol in itself is free of any meaning or import.
Next, the author discusses the “butterfly effect” in the Arab context, based on the notion that most of life’s phenomena are subject to a particular kind of general law that stipulates that any changes they undergo, no matter how insignificant, will eventually lead to radical transformations that appear unrelated to the beginning—or perhaps we have forgotten how things began. Thus, the primary values on which “dynamic systems” are based quickly become unrelated to what is happening, as in the case of social phenomena.
On the human level, Bakir argues that any change in human choices, no matter how small, will lead to significant changes over a period of time. The shape of this change becomes clearer the longer this period is, and things may appear insignificant then grow larger and larger to such a degree of complexity that it becomes difficult to unravel them or even understand their causes. The book attempts to explain the “mechanism” by which many things arrive at a great deal of complexity, as awareness of this “mechanism” makes it easier to address things or at least might prevent them from reoccurring in certain contexts.