ilya_prigogine_isabelle_stengers_alvin_tofflerbookfi-org

59 THE IDENTIFICATION OF THE REAL
means of its position as well as by its velocity and acceleration,
that is, by the first and second derivatives of the position.
At each instant, a set of forces, which is a function of the
distance between the points in the system (a function of r),
gives a precise acceleration to each point; the accelerations
then bring about changes in the distances separating these
points and therefore in the set of forces acting at the following
instant.
While the differential equations set up the dynamics problem,
their "integration" represents the solution of this problem.
It leads to the calculation of the trajectories, r(t). These
trajectories contain all the information acknowledged as relevant
by dynamics; it provides a complete description of the
dynamic system.
The description therefore implies two elements: the positions
and velocities of each of the points at one instant, often
called the "initial instant," and the equations of motion that
relate the dynamic forces to the accelerations. The integration
of the dynamic equations starting from the "initial state" unfold
the succession of states, that is, the set of trajectories of
its constitutive bodies.
The triumph of Newtonian science is the discovery that a
single force, gravity, determines both the motion of planets
and comets in the sky and the motions of bodies falling toward
the earth. Whatever pair of material bodies is considered, the
Newtonian system implies that they are linked by the same
force of attraction. Newtonian dynamics thus appears to be
doubly universal. The definition of the law of gravity that describes
how masses tend to approach one another contains no
reference to any scale of phenomena. It can be applied equally
well to the motion of atoms, of planets, or of the stars in a
galaxy. Every body, whatever its size, has a mass and acts as a
source of the Newtonian forces of interaction.
Since gravitational forces connect any two bodies (for two
bodies of mass m and m ' and separated by a distance r, the
gravitational force is kmm'fr2, where k is the Newtonian force
of attraction equal to 6. 67cm3g-1sec-2), the only true dynamic
system is the universe as a whole. Any local dynamic
system, such as our planetary system, can only be defined
approximately, by neglecting forces that are small in comparison
to those whose effect is being considered.