I touch on chaos theory, fractals, randomized sorting and searching, rearranging infinite series for "the sum of the parts is greater than the whole", and emergence. If you understand those concepts, then you probably understand directedchaos, and this video would probably waste 5 minutes of your life.
It is a mathematical and scientific philosophy that provides a neat package for understanding and improving the universe. It is not new, in the sense that ideas analyzing the cooperative conflict between order and chaos have been around for a long time. What's more, it is not fleshed out as a rigorous viewpoint; however, I'll try to explain in more detail of directedchaos's specifications and implications.
Let's begin with a quick discussion of chaos, particularly chaos theory, which relates the idea of extreme sensitivity of initial conditions to the degree that the system appears unpredictable, regardless of whether it is deterministic. There are mathematical equations which exhibit this behavior, such as the Lorentz attractor, and really any kind of fractal. In them, knowing something about the path or inclusion of a particle tells you nothing about its infinitesimally close neighbors that you can't learn from the larger system.
Notice, however, that the paths still have features in common -- particularly, they are attracted to the two points. Indeed no system is totally chaotic -- it is bounded; the chaotic forced are channeled or DIRECTED to pockets of uncertainty. This is why the butterfly effect doesn't ruin all predictability.
These sorts of systems are not bound to unrealistic, abstract, concocted mathematical functions. All of life exhibits fractal behavior, and undoubtedly uses directedchaos.
Chaos in the form of randomization is a vital piece of advanced algorithms. Most sort functions rely on random input to guarantee their average running times, otherwise the input could be the exact opposite (for example, a least-to-greatest sort on a greatest-to-least input).
Search algorithms use randomization even more heavily, particularly in "good-enough" constraint satisfaction problems like scheduling. A common approach is "hill-climbing" where you pretend your options move you around on a 2D or 1D arena, and they result in an increase or decrease in some evaluating function. The idea, then, is to look at the gradient and move up (where the increase is greatest -- up the hill). Naturally, you can reach local maximums and get stuck, which is why "random restart" is often used.
But there are more common uses of directedchaos. Your oven is a clear example: heat is a prime incarnation of chaos, and we wield it to kill off a bunch of germs, make the food rise, taste better, etc.; however, we use it in short doses within a confined area. Chaos is a force which we direct for a greater good.
Infinite series simply encapsulate the idea of summing a common function across all integers. Conditionally convergent series such as the alternating harmonic series have the interesting property that they can converge to anything with proper rearrangement of the terms. For example, the initial formulation converges to the natural log of 2, but if we rearrange to add two negatives at a time for every positive (which we can do since there are an infinite number of terms to draw from), then we have the sum one half the log of 2.
"The sum of the parts is greater than the whole."
And this is where it may bridge on the spiritual. The universe itself may "wield" chaos to form order spontaneously, without any clear preset boundaries. This is a crude rewording of the idea of emergence, where many simple atomic interactions can build up in a large and complicated manner to create a totally unpredicted outcome.
The stock market is one example, built on simple economic exchanges which can have large, unpredictable results in the aggregate. Indeed economies in general are susceptible to strategies at the local level which can lead to undesirable global situations -- a dichotomy of scope which is foundational in the idea of emergence. A clear example is a monopoly.
Life uses emergence all the time. Reynold's famous boids mimics flocking patterns of birds with just three simple rules. Ants seem to combine pheromone trail guides and random walking to create a sophisticated quick search and optimization system. Most structures are emergent (including plants). Life's very development is emergent, with simple self-replication rules activated in turn through hormones.
There are innumerable other examples, but perhaps most importantly, our brains are emergent. All of our consciousness arises mysteriously from simple electrochemical interactions, particularly the firing patterns of our neurons.
We owe our very thoughts to directedchaos.
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0:56Chaos Theoryby AngeLeonheart37,071 views
Very good video. It appears that we may have similar educational backgrounds...
generaleskimo 2 years ago
Cool. :)
I'm fond of emergence atm -- it reminds us that we can't always extrapolate. Some systems are so complex we just have to see what they do, and try to react accordingly.
Many fundamentalists don't understand this basic mathematical idea, but I think it's necessary for the universe to make sense.
directedchaos 2 years ago