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.

Πλαίσιο κειμένου: This example is not correct.

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

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.

Πλαίσιο κειμένου: This line which we drew, from the current state of the 
world back to its beginning (which led us to such 
strange conclusions that we began to doubt the absolute power of the Natural Law) is not possible.

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.

Πλαίσιο κειμένου: Nothing is absolutely predetermined.

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.

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