“Prediction is very difficult, especially about the future...”
Niels Bohr (1885–1962)
Danish Physicist

This book on technology, in the sense of a discourse of thought on a technique or an art, focuses on numerical modeling. It is used by engineers in the industry and by many researchers in various scientific fields in order to understand different physical phenomena or to design some of the objects we use every day. It uses the computing power of computers in order to represent the world around us through mathematical models. These consist of equations formulated to report observations. Numerical modeling is the result of a human construction, engaged in its modern form since the 16th Century. At that time, the English physicist Isaac Newton and the German mathematician Gottfried Leibniz developed mathematical concepts that gave access to an abstract representation of movement. In the 21st Century, numerical modeling is part of the family of digital techniques and one of its primary uses concerns mechanics, the science of motion and energy, contributing to understanding the world.

Like all knowledge, mechanics is also an opening, alongside mathematics and the physical sciences, to philosophy or history. In the form of writing with light and movement, it also interacts with the visual arts (cinema, drawing, painting, photography, etc.), to which we will sometimes refer in order to illustrate our point. Mechanics is also a way of thinking that can contribute to political action, the organization of economic life, etc., in a word, to the choices of society. We will therefore begin our presentation with it, before opening our discussion to other areas.

The notion of modeling is the guiding principle of this book. A model refers to an abstract representation of a process (physical or other, for example biological, economic, demographic, psychological, etc.). Developed using equations* or data*, it makes it possible to understand or experiment – and potentially predict changes in the observed process. Starting with examples from physics and engineering, therefore, we will broaden our focus by reflecting on attempts to model human processes. This will lead us to mention, among other things, artificial intelligence*. Before we get to this point, we will show what a mathematical model is, what forms it can take, how it serves a numerical simulation and how it is used by engineers. We will use this framework to discuss how other sciences also use models and simulations, the latter being, as in mechanics, based on equations or data.

Understanding makes it possible to decide and act. This book on technology also aims to contribute to the understanding of numerical simulation and modeling – and some of their principles, uses, limitations, promises and challenges. Any reader interested in this technique and its applications can therefore find here an introduction to understanding them. However, it does not require any special scientific knowledge.

The book is partly the result of the experience of its author, an engineer and industrial researcher, who has contributed for nearly 20 years to the development of mathematical models and numerical methods for applications in shipbuilding. The presentation borrows many examples from this and other areas to show how simulation algorithms are designed, developed and used. They serve industrial applications and many others which cannot be covered exhaustively by a single book!

However, the perspective we propose is intended to be as broad as possible. In a context where some applications of the techniques are presented in an anxiety-provoking way, we wish to show applications that concretely benefit humans in the 21st Century. However, we will not avoid legitimate questions associated with the use of digital technologies and their purposes.

Three sources of information have contributed to this objective:

• – scientific articles and books directly related to the physics and mathematics used by engineers. These references have accompanied an experience acquired in this field and of which we transmit some principles;
• – exchanges with engineers or scientists using numerical modeling in industry or for research purposes. In collaboration with them, we looked at their scientific practice and how digital simulation contributes to or modifies it;
• – additional readings (books, newspapers and generalist websites), the references of which are provided in the bibliography. They concern subjects beyond the framework of mechanics and we nevertheless found it interesting to put them in contact with it in order to broaden our reflection.

The book is structured into two volumes:

• – the first provides an overview of numerical simulation and some related techniques (such as statistics, computer science, algorithms, etc.);
• – the second details examples of use in many fields: agriculture, industry, earth and universe sciences, meteorology and climatology, energy, the human body and, finally, individuals and societies.

The few mathematical formulas used – because it is also necessary to learn how to use them – are accessible to a first- or second-year level in science. It is not necessary to know them before entering into the subject. The presentation comments on them in plain language and explains what they represent. Moreover, it is also possible to read the book without dwelling on certain theoretical questions, placed, for this purpose, in boxes. We also give some definitions in a glossary at the end of the first volume; the terms or abbreviations concerned are indicated in the text by an asterisk*.

The presentation sometimes deliberately takes a few paths which are intended to be, hopefully, pleasant to read. It thus proposes:

• – figures with informative captions proposing to enhance the meeting with some of the scientific personalities mentioned in the text, or to establish links between mathematical modeling and other scientific and artistic disciplines;
• – remarks and boxes to detail a subject or present a concept or application in relation to the theme developed in the relevant chapter;
• – statements from interviews or excerpts from books and conferences to illustrate the presentation¹.

The algorithms used in numerical modeling perform a rigid succession of mathematical and computer operations. Perhaps it takes all the writing talent of French writer Georges Perec (1936–1982) to breathe life and humor into them. With L’Art et la manière d’aborder son chef de service pour lui demander une augmentation (The Art and Craft of Approaching Your Head of Department to Submit a Request for a Raise), he gives us the keys to an algorithm that guarantees the success of this endeavor. Perec liked complexity very much but nevertheless writes: “you must always simplify...” [PER 73].

Reality is always more complex than what we can write in a book. The presentation we propose thus simplifies many of the scientific bases and technical aspects of numerical simulation. If some concepts have been simplified, possibly beyond what is reasonable for experts in the field, it is in order to make them accessible to as many people as possible, encouraging the reader to go further. Simplifications result as much from conscious choice as from ignorance, which in its assumed form can be conceived as one of the qualities necessary for scientific research [FIR 12]. In any case, they are our responsibility and do not engage the contributors, personalities or organizations solicited during the research work accompanying the writing of this book. Any comments regarding an error or approximation are welcome: simply contact the author via his website².

Jean-François SIGRIST
September 2019