If you knew everything
in the present, exactly, and you also knew the “laws of nature” could you
predict the future? We live in a dynamic
system that we can measure, and we know all of the rules we can measure, so
like predicting the eclipse of the sun, can’t we predict more complicated
things as well?

A
conventional dynamic system (CDS) is defined as a system where all the parts
(every part) are described precisely as to position, and motion, (and by
implication; the rules that govern their interaction - what they can do). The rules are that we don’t make up outside influences;
they are all defined in our complete and precisely defined system.

The Rule
takes the system one step from its current state to the next (possible, ergo
defined state) step. If we’ve done
everything right, this will be predicable.

If we work
with a planetary solar system, (this means all the planets, their sizes and
densities, distances, velocities, moons, gravitational constant, etc), it’s pretty
complicated. But we can, and do, predict
eclipses and the position of our planets and moons millions of years into the
future with excellent accuracy. Even the
Mayans did this 1,400 years ago for eclipses, (hold that thought*). So this means we can predict at least some
parts of the future; we live among predetermined systems, right?

Consider a
far simpler CDS, it has only four or five defined parts and only three
rules. The parts are a graph paper like
grid (two parts?) and a locator of the starting
point, the initial state. The rules are:

Rule 1). Each step in this CDS takes the locator one square forward.

Rule 2). At
a white square, turn 90° right, flip the color of the square, move forward one
unit

Rule 3). At
a black square, turn 90° left, flip the color of the square, move forward one
unit

This called
“Langton’s Ant*. The ant is the locator
that moves one step at a time, following the “rules”. This can be run on a very simple computer
program (OK, the computer is complicated but it is doing a very simple step by
step process).

This is much
simpler than planets, moons, velocities, orbits, distances and all their
interactions as they whizz around our sun.

So when you run it, it
should be very predictable, right? Info
in, info out; always the same result…
Nope. Try, unpredictable for the
first few hundred moves then a strange locked in pattern to infinity.

This simple
CDA leads to complex behavior. Three distinct modes of behavior are apparent.

Simplicity. During
the first few hundred moves it creates very simple patterns which are often
symmetric.

Chaos. After a few
hundred moves, a big, irregular pattern of black and white squares appears. The
ant traces a pseudo-random path until around 10,000 steps.

Emergent order. Finally
the ant starts building a recurrent "highway" pattern of 104 steps
that repeats indefinitely.

All finite initial
configurations tested eventually converge to the same repetitive pattern. No one has been able to prove why this is
true for all such initial configurations. It is only known that the ant's
trajectory is always unbounded regardless of the initial configuration.

Here is a
super simple CDS that results in a pattern that no one could predict, and even
now that we know what happens, we can’t explain why, we had to run it to see it
happen.

So the
debate about the future being determinable from the present is over. Now do a CDS with 200,000 atoms in three dimensional
space…. You know, like a virus.

*The Mayans could predict the eclipses with great accuracy
(at the same time that most Europeans believed the earth to be flat and the
center of the Universe). But before you
get too laudatory of the Mayans’ scientific abilities, at the same time that
they could do this, they still had religious mythology about jaguars eating the
sun. Their CDS still had outside
influences, Gods.

If you’d like to see this
in action, go to: https://en.wikipedia.org/wiki/Langton%27s_ant

## No comments:

## Post a Comment