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8 The Universe Observed and Unobserved
is an astonishing fact, and it begs for an explanation. Why aren’t the phenomena
of nature far more tangled and complex than they are? Trying to explain why
nature is simple is the aim of this section.
The dynamics of moving bodies, for example planetary systems, was rigorously explained by Isaac Newton in the 1600s. The basic idea is that any two
bodies in space are attracted to one another by a force which is proportional
to the product of their masses, divided by the distance between them squared.
This particular detail doesn’t concern us here: What is important, instead, is
that the pattern of motion of the myriad bodies coursing through the universe is completely determined by a law which applies to just two bodies at a
time. Thus, to explain the dynamics of moving bodies in space, it is sufficient
to know the dynamics between two bodies. The law governing each pair of
bodies is repeated innumerable times—on every pair of objects in the universe.
Every body in space influences every other body by Newton’s law, and the
combined motion of this numberless swarm of heavenly objects is completely
accounted for by the dynamics of two bodies, repeated over and over on every
pair of them. A law involving just two—or a small number—of separate objects
is said to be simple. And when a simple law acts on every pair of objects in a
swarm, resulting in a complex global pattern of the whole throng, the overall
pattern is caused by what is called an addition of simples.
It is similar when objects are stationary: If you have a structure with many
forces acting on each component, for example a Gothic cathedral, you consider
every force vector individually, then add the forces by vector addition to get the
resultant force. In fact, vector addition is the archetypal example of addition of
simples. In a situation in which there seem to be infinitely many forces—such
as the pressure of water at every point of a ship’s hull—we integrate the force
vectors, which is a fancy way of adding infinitely many of them.
A force field such as that of gravitation is spread out in space. The field
gives rise to a force vector at every point at which a mass is present. In order to
find the total gravitational force on a solid object, the separate vectors at all the
points of the object are added together, or integrated. Physics would not exist if
it were not possible to analyze phenomena of the world by decomposing them
in this manner into elementary interactions. We are able to do this because
nature itself is constituted that way. It appears that all of the physical world is
an addition of simples.
It may not be outrageous to argue that the rise of science in the 16th Century
was less due to the discovery of rigorous reasoning than to the revelation that
nature is simple, and that this simplicity can be exploited to find elementary
laws which account for phenomena.
8 The Universe Observed and Unobserved
is an astonishing fact, and it begs for an explanation. Why aren’t the phenomena
of nature far more tangled and complex than they are? Trying to explain why
nature is simple is the aim of this section.
The dynamics of moving bodies, for example planetary systems, was rigorously explained by Isaac Newton in the 1600s. The basic idea is that any two
bodies in space are attracted to one another by a force which is proportional
to the product of their masses, divided by the distance between them squared.
This particular detail doesn’t concern us here: What is important, instead, is
that the pattern of motion of the myriad bodies coursing through the universe is completely determined by a law which applies to just two bodies at a
time. Thus, to explain the dynamics of moving bodies in space, it is sufficient
to know the dynamics between two bodies. The law governing each pair of
bodies is repeated innumerable times—on every pair of objects in the universe.
Every body in space influences every other body by Newton’s law, and the
combined motion of this numberless swarm of heavenly objects is completely
accounted for by the dynamics of two bodies, repeated over and over on every
pair of them. A law involving just two—or a small number—of separate objects
is said to be simple. And when a simple law acts on every pair of objects in a
swarm, resulting in a complex global pattern of the whole throng, the overall
pattern is caused by what is called an addition of simples.
It is similar when objects are stationary: If you have a structure with many
forces acting on each component, for example a Gothic cathedral, you consider
every force vector individually, then add the forces by vector addition to get the
resultant force. In fact, vector addition is the archetypal example of addition of
simples. In a situation in which there seem to be infinitely many forces—such
as the pressure of water at every point of a ship’s hull—we integrate the force
vectors, which is a fancy way of adding infinitely many of them.
A force field such as that of gravitation is spread out in space. The field
gives rise to a force vector at every point at which a mass is present. In order to
find the total gravitational force on a solid object, the separate vectors at all the
points of the object are added together, or integrated. Physics would not exist if
it were not possible to analyze phenomena of the world by decomposing them
in this manner into elementary interactions. We are able to do this because
nature itself is constituted that way. It appears that all of the physical world is
an addition of simples.
It may not be outrageous to argue that the rise of science in the 16th Century
was less due to the discovery of rigorous reasoning than to the revelation that
nature is simple, and that this simplicity can be exploited to find elementary
laws which account for phenomena.