This book provides an overview of the mechanistic approach to science from
historical, philosophical, computational, and other viewpoints. This approach
arises from the fact that, in real life, most objects remain the same (at least
locally) almost all the time: objects move, parts may break off,
rubber objects may change shape, but local properties mostly remain the
same. There are exceptions--water boils, wood burns--but these are
relatively rare. We can break most objects into smaller and smaller pieces
until we cannot, so it is reasonable to imagine the world as a collection of
not-further-divisible parts--what Greeks called atoms.

Interaction between objects is also usually local: to move my desk, I need to
stand next to it and either push it or lift it. There are exceptions, like
magnetism, but they are rare. So, it is reasonable to conclude that atoms
interact only when they happen to be next to each other, that is, when they
collide. Such a description of the world as several (possibly moving)
particles is the original mechanistic description (see chapter 2). The main
advantage of such a description is that mechanical motion and mechanical
collisions are ubiquitous; we have developed intuition about such processes, which helps us to make predictions based on such models. Also, from numerous
observations, we can deduce equations of motion for such interacting
particles, and this allows us to apply standard algorithms for solving these
equations, and thus for extracting numerical predictions from such mechanical
models.

Success of this approach led to the idea of representing seemingly
action-at-a-distance processes, like magnetic attraction or gravity, in the same
way, that is, as caused by an exchange of special particles. Until Newton, this was
the usual explanation for gravity, for optical phenomena, and so on.

This naive mechanistic model of the world was broken by Newton (see chapters
2 through 5). Newton came up with explicit formulas and algorithms for describing
action-at-a-distance. Thus there was no longer any need for a mechanical
model. Physicists still used mechanistic atom-based models, for example, in
statistical physics, but these models were perceived as a useful way to
derive observable equations, not as a description of physical reality.

Somewhat surprisingly, a revival of the mechanistic approach came in the 20th
century with the emergence of relativity and quantum mechanics (see chapters
2 through 5). Relativity (discussed in chapter 7) showed that
immediate-action-at-a-distance is impossible; all interactions have to be
local. For simple particles, relativity made predictions somewhat more
complicated, since relativistic equations of motion are more complex than
Newtonian ones. However, as a whole, the fact that all interactions are local
means that all the processes can be described by differential equations--
and for differential equations, known feasible algorithms can provide
moment-by-moment predictions of the future states (at least for some time).

Quantum physics, in its turn, concluded that, crudely speaking, everything is
discrete and consists of quanta: light consists of photons; normal matter
consists of protons, neutrons, and electrons; and seemingly
action-at-a-distance interaction is indeed an exchange of the corresponding
quanta (photons for electromagnetic interactions, gravitons for gravity, and so on).
From this viewpoint, modern physics came back to a mechanistic model (see
chapters 4 through 6)--of course, on a different level: interaction between quantum
relativistic particles is described by much more complex formulas than in the
traditional mechanics. Such a particle representation underlies Feynman
diagram techniques--one of the main algorithmic schemes for making
predictions about quantum systems.

Similar mechanistic physics-type models are successfully used beyond physics, for example, in biology (chapter 7), in economics (econophysics, chapter 10), and so on. This
does not mean that, for example, economic processes, for some mysterious reason,
exactly follow Schrödinger’s equations of quantum mechanics: the
physics-type models are usually approximate. The beyond-physics success of
mechanistic models can be naturally explained by the fact that, according to
theoretical computer science, all complex (NP-hard) classes of problems are
reducible to each other. So, one way to solve a practical problem from a
difficult-to-solve class is to use one of such reductions, and reduce this
problem to a problem from a class for which many good algorithms are known.
From this viewpoint, physics, with its centuries of solving many practical
problems, provides a perfect class of such problems to which to reduce.

Warning to the reader: the book has several computation-related chapters and
sections (most of this material is in chapters 9 and 11), but overall most
of its ideas are on a more philosophical level and not yet on the level of
actual computations. These ideas may be raw, but they are also very interesting and
thought provoking, so I strongly encourage everyone interested to read this
book.