
Nonlinearities and Success - maruz
http://mariocaropreso.com/post/62811446044/nonlinearities-and-success
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jacques_chester
The traditional name for systems that are deterministic but unpredictable
because they can be radically changed by differences in starting conditions
that are below the threshold of measurement is "chaos". Or, in human affairs,
"luck". We like to draw parallels and deduce conclusions, but a lot of it is
down to survivor bias and confirmation bias. We think of some hypothesis of
success; soon we see examples everywhere.

It doesn't quite matter: inhuman complexity renders all of them intractable
for ordinary comprehension. History is, as Barzun observed, "above all
concrete and particular, not general and abstract".

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marcosdumay
All that is so obvious in restrospect that my mind keeps trying to convince me
that I always knew it. (Despite evidence to the contrary).

In a competitive environment there can not be a widely known path for success,
because the competitors will adapt untill the path changes to something
unknown. Thus, if you know about a model, it's probably not valid anymore, and
you simply can't study it for long enough to discover the non-linearities.

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dj-wonk
I like the article, but the author suggests (or at least creates the
impression) that "nonlinearity" causes "path dependence". This is not
necessarily true.

Path-independence or -dependence is more about history than the nature of
linearity or nonlinearity in variables itself.

From Wikipedia: "A nonholonomic (a path-independent) system in physics and
mathematics is a system whose state depends on the path taken to achieve it."

Here is counter-example where non-linearity does not cause path-dependence.
Fields that obey an inverse-square law (such as electromagnetism) are called
conservative (path-independent) because the work needed to move an object from
one point to the other is not dependent on the path.

But, I could be missing something. Let me know!

~~~
maruz
Your reasoning about the electromagnetic field is right. I think the element
of confusion here is the definition of nonlinear. Nonlinear in system theory
means that the superposition principle is not valid. From Wikipedia: "The
superposition principle states that the net response at a given place and time
caused by two or more stimuli is the sum of the responses which would have
been caused by each stimulus individually". The electromagnetic field in
vacuum is linear, because it obeys Maxwell's equations and it is a solution of
a set of linear equations. The output is always proportional to the input: you
put a bigger charge and you get a bigger field. A linear combination of
electromagnetic fields, with constant, real coefficients, is a new field which
obeys Maxwell's equations, thus it is still linear and the superposition
principle is still valid.

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spindritf
That is such a great title.

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avty
Lotto tickets are the greatest example!

