Complexity

I feel that the use of complexity is often misunderstood, in almost all areas and walks of life.
I've always had an interesting relationship with complex things: I have little tolerance for things 
that are complex for complexities sake, but systems that create complexity through small 
interactions of simple parts have always held my attention closely.

One of my first experiences with this was in school, learning about the Mandlebrot fractal. The
fact that such a striking and infinite piece of visual art can be encoded in a single equation
was, and still is, mind-blowing. This simplification of seemingly convoluted and infinite
recursion continues to show up in areas that I never imagined.

Studying and applying calculus and differential equations in my undergraduate degree gave me another
perspective shifting viewpoint. Our ability to model the physical world was something that I always
considered 'good enough': there always seemed to be some confounding variable or action that we
have to ignore, because it would make the calculations too difficult for whatever class I was in.
Every level deeper unlocked more questions that were answered with a hand wave, and "that's not 
important to know for this class." Then the next class would illuminate those details, but add
yet more unexplained and abstracted phenomena for the next class to explain.

A quick example is how the idea of the atom was taught: in elementary school it's the smallest 
thing, and everythingis made up of them. Then in middle school you learn about electrons and the
nucleus, and finally in high school you learn about energy levels and the octet rule, and
how electrons can move from atom to atom. Finally every thing makes sense! You can see how
molecules can come from single atoms and create huge intricate structures from such simple 
building blocks. 

Then you go to CHEM101

Every thing you've learned up to this point is such a gross oversimplification that it's 
basically useless.

Electrons don't exist, they're abstractions to easily imagine the probability fields of 
charge surrounding the nucleus. Atoms can shuffle "electons" around energy levels to 
make themselves more stable, the octet rule has almost as many violations as times that it 
holds true! There's no such thing as nicely covalent or ionic bonds like in high school chemistry;
everything exists on a spectrum. All of a sudden theres other forces that are now wreaking havoc
on your molecule, such as Van Der Waal forces, hydrogen bonding or dipole-dipole interactions.
All those things that were mentioned in passsing and hand waved away are now vitally important
parts of the calculation.

Unfortunately this is where most people stop their learning, either due to school requirements,
loss of interest, or possibly the complexity of it all. I've found that this is also the 
inflection point on the true complexity of the system. I was first exposed to the Schroedinger 
wave equation in high school, as a 'look how crazy this stuff can get' kind of example, and at
first it really does seem unfathomly complex: it's purpose is to be the mathematical representation
of all quantum interactions. I'm sure very few people truly understand what a Hamiltonion does,
or why its useful to work in k-space, until they've actually worked on the problems themselves.
But eventually something clicks; for me it was gaining a deeper understanding of the Navier-Stokes
equations and their applications in thermodynamics, along with deriving the Schroedinger equation.
Suddenly it made sense: everything is simple a balancing of forces, calling back to the most
fundamental of theorems: F=MA. There are some small differences of course, the quantified nature 
of atomic interactions deal in precise steps rather than an infinite continuum, giving rise to 
some unpredictable phenomena. Once you understand this, Schroedinger and Navier-Stokes become your
secret guides, showing up in places you never thought, or pulling you out of situations that no one
else would dare touch. So many physical phenomena are able to be reduced to these simple equations.

This is the type of complexity that draws me in: That which seems complex until it is understood,
resulting in a paradigmatic shift in viewpoint.

Complexity for its own sake is useless, I enjoy simple solutions to complex problems in a similar
way. It is easy to make a complex solution for a complex problem, it takes a true understanding and
intuition of a subject to be able to create simple solutions. This simplification and "boiling down
to the essence" allows a true glimpse into the subject, in a way that a more involved solution may
cover up or hide. 

The complexity that can arise from simple interactions is immensly satisfying, as it's incredibly
easy to understand the moving parts involved.

A quick list of examples that have truly captivated my interest for periods of time: 
	-Fractals
	-Cellular Automata
	-Generative Music (especially involving Markov chains, L-systems. and Euclidean beats),
	-LISP