On 12/4/2016 7:59 PM, Steven Carlip wrote:
> On 12/4/16 4:05 PM, Jonathan wrote:
>
> [...]
>> The butterfly effect shows the output (effect) diverges
>> /exponentially fast/ from the input (cause).
>
> Roughly. In a chaotic system, *changes* in the final
> state diverge exponentially fast in response to *changes*
> in the initial state.
>
>> Meaning in takes but a few step from initial conditions or
>> 'cause' before a direct relationship with 'effect'
>> becomes impossible to draw.
>
> Sometimes. It depends on the actual value of the exponent.
> Planetary motion in the Solar System is chaotic, for example
> -- we can only accurately predict the locations of the planets
> for the next hundred million years or so. (You might consider
> a hundred million years "a few steps," but I think most people
> wouldn't.)
But several things, orbits are exceedingly simple
systems.
And once an orbit reaches a critical point
which is rare, it's future can no longer be
predicted.
In nature virtually every step is a critical point.
Also once a stable orbit forms, the starting point
is erased. For instance where and when did the orbit
of Earth begin??? That can't be answered once
the orbit becomes stable.
Cyclic behavior erases the initial condition.
To extrapolate an already stable orbit into
the future is not the same thing as starting
at the ultimate initial condition and
extrapolating to the present.
>
> Details matter.
>
>> That means the assumption all effects have an
>> identifiable cause is erroneous and a fools
>> assumption.
>
> Not necessarily, though it might. It depends on what you
> count as an "identifiable cause." If you mean *precisely*
> identifiable, then you're right. If you mean *approximately*
> identifiable, then it depends on the particular system.
> Learn about basins of attraction.
>
An attractor is future behavior, not initial as
the attractor shows what behavior the system
is attracted to...in the future.
It's important to keep clear where complexity science
applies, and where classical or quantum like
methods apply.
If a system has a few easily definable variables
then it can be solved in classical Newtonian
like methods. Using the deterministic equations
we all know and love.
If a system has countless variables that can't
be precisely defined, then statistical or
quantum like methods need to be applied.
Complexity science applies at the boundary...between
those two opposites.
Complexity Science applies to where there are
too few variables for a statistical method
and
too many variables for a classical method.
The 'messy middle' as the Cambridge mathematician
Neil Turok says.
That middle ground, or transition space between
classical and statistical methods is generically
called the 'complex realm' and defines the
concept of complexity.
Complexity = neither classical or quantum.
But both at the same time, entangled.
And remember this is about behavior or the
output side. Not part details, but system
behavior.
The next question is, where does the 'complex realm'
apply? The short answer is to everything that
evolves up to and including the universe itself.
The classical and quantum realms are merely
simplifications that are made so that we can
apply the math...we have.
We've been simplifying reality down to the
point it can fit existing math
That's not the same thing as finding a math
that...properly models reality.
Complexity science is the math that works
without simplifying nature, the math of the
transition /between/ classical and quantum
behavior.
As it's that transition realm that is the
/source and cause/ of all visible order
in the universe.
Not classical or quantum behavior.
Nature is the result of the /critical interaction/
between /classical and quantum behavior/.
When simplifying to either classical or quantum
you're only seeing half of he 'equation' of
reality, and as a result seeing only half
the picture.
For instance, if evolution is the result of
the critical interaction between genetics (rules)
and natural selection (random interactions)
then anyone that only looks at one or the other
will see a grossly incomplete picture
chock full of brick walls.
>> That means an equation of the form y = F (x) is useless
>> for modeling the real live non-linear world of evolving
>> systems.
>
> Why? Do you think y = F(x) is necessarily linear?
>
No, but when any deterministic equation is iterated
back into itself, as all cyclic or complex behavior
does, then it creates non-linear behavior.
Behavior which can diverge or converge exponentially fast
away from the starting point depending upon
the mere flap of a butterfly's wings.
Or an infinitely small error can cause the iterated
deterministic equation to create wholly unpredictable
future behavior.
That's why people keep saying complexity is inherently
deterministic, it is, it follows very simple deterministic
equations. But when those same equations are endlessly
iterated back into itself, the output can't be...determined.
> One of the simplest standard examples of a chaotic system is
> the logistics map,
>
> x_{n+1} = r x_n (1-x_n)
>
Right, but click here and look at the graph on the right
to see what happens when such an equation is iterated
https://en.wikipedia.org/wiki/Chaos_theory#Topological_mixing
Simple predictable equations become unpredictable when
iterated as in just about any real world complex system.
As a result to understand what the parts are doing
only the output, or emergence, is useful. Since
the /ultimate starting point/ can't be used to
extrapolate into the future and construct the
present reality.
If we see emergence, we know the ultimate
starting point is useless, as cyclic iterations
dominate. As with life, which is HIGHLY
cyclic in character
s
> Steve Carlip
>