Redefining Reality - The Intellectual Implications of Modern Science

Quantum mechanics has thrown doubt on the deterministic and
predictability aspects, but recent work on chaos theory has led us to
believe that even if there are aspects that are deterministic, this does
not necessarily mean that the results are steady-state solutions that
are stable and predictable. Perhaps the most famous example of this
is the .
Newton became famous when his theories of motion and gravitation
were combined to explain the elliptical orbits of the planets as
shown by Kepler. Kepler crunched the numbers and came up
with the shape (an ellipse with the Sun at one focus), but no one
knew why the planets moved elliptically. Newton gave us his three
mechanical laws and his law stating that the attraction between any
two masses is inversely proportional to the square of the distance
between the masses.
Applying these rules to two bodies in space, we ask the question:
How does the gravitational attraction between these two bodies
make them move? We can set up the equation, plug in the initial
each other in such a way that if one were thought to be nailed down,
the other would move around it in an ellipse.
But we don’t live in a universe of only two things. Suppose we
enlarge our scope to look not just at the Earth and Sun but at the
Earth, Sun, and Moon. As we know, the Moon orbits the Earth,
and the Earth orbits the Sun. The Moon’s pull on the Earth is tiny
compared to the Sun’s because the Sun is so much bigger. As a result,
the Earth’s orbit is not perfectly elliptical but perturbed in some way.
The problem is that when we use Newton’s laws the way we did
for the two-body case, the equations are no longer solvable. There
is not a class of steady-state solutions—repeating trajectories—
that is the general solution to the equations. There is no way in our
mathematical language to set out a description of the path in space.
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