The limit of
influence
As an example of
the
(unknown to us)
strict determinism that governs
the phenomena and connects an impressive result
with a distant invisible cause,
the hypothesis is often used that a butterfly can beat its
wings in Beijing
and as a result of this a typhoon
devastates the Caribbean.
The idea behind
this example is that
the effect of the
beating of a butterfly’s wings
weakens as we move away (in space and in time)
from the source but it never reaches level zero.
It only reaches
level zero in an infinite
distance and at
infinite time.
That is in fact
never.
So, if there exists
somewhere a very sensitive
equilibrium, like
those which shape the
weather, this tiny distant effect could be
the reason to tip the balance in favour of
creating a hurricane.
Certainly every phenomenon has
its impact on the world.
But if the cause
is weak
and the path
connecting it to the supposed
result long, which means a very large number
of collisions intervene between the cause and
the effect, then the causal relation is lost.
It disappears
under the
uncertainty that is added by each
collision.
Now that we know
that the uncertainty exists
we can understand
that it is not necessary
for the effect of the wings of the butterfly
to reach level zero.
It is sufficient
if,
weakening continuously,
it passes below the
limit of uncertainty.
Then the
specific direction of the action in space
cannot be recognized,
so that it cannot
any longer serve as a "signal".
The action will be lost forever
in the "swamp of noise" of the
uncertainty of the thermal motion.
The current state of the world was not
completely specified at its beginning
as we supposed in Chapter 6.
It was specified only in general terms.
The Natural Law
granted freedom
to the basic
particles to
follow different paths.
If the Cosmos were to be shaped from the
beginning again,
we probably wouldn’t have this actual planet, nor the specific
rain drop falling at this precise moment to this certain place
on the earth, nor our painter with his particular inspiration.