Redefining Reality - The Intellectual Implications of Modern Science

ignoring certain elements, we can come up with approximations.
These approximations are extremely useful, but there is much
that is interesting in the gap between the approximate and the real
Such cases as three-body systems are complex, where complexity
is a technical term denoting an important aspect of the equations
taken to govern the system. Such equations stand in opposition to
state equations that are linear; these equations can be graphed so
that their solutions form a line.
A nice property of linear equations is that they are stable; a
small change in the initial conditions leads to a correspondingly
small change in the outcome.
Nonlinear equations, however, exhibit sensitivity to initial
conditions and represent unstable systems. The commonly
used phrase to describe this sensitivity to initial equations is the
effect in his work creating computer models of the weather. Lorenz
found that incredibly subtle changes in the values input into the
model yielded massive changes in the weather as it developed.
Such sensitivity to initial conditions is a problem because no matter
how sensitive the measurements, the act of collecting data itself is
accompanied by experimental error. This phrase refers to the fact
that there is always a resolution attached to any instrument that
limits how precisely something can be measured. If the system’s
our ability to distinguish between relevantly different states of the
system. The development will appear random and unpredictable,
even though it is thoroughly deterministic.
71