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
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.
uncertainty that is added by each
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,
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
follow different paths.
If the Cosmos were to be shaped from the
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.