Note: If you haven't yet read the post on complexity and fractals you should start there.
It's a curious aspect of knowledge that both ends of the development spectrum, from naive beginner to well-versed expert, are marked by simplicity.
Bruce Lee once said, "Before I studied the art, a punch was just like a punch, a kick just like a kick. After I studied the art, a punch is no longer a punch, a kick is no longer a kick. Now that I understand the art, a punch is just like a punch, a kick is just like a kick."
Resist the urge to dismiss this as trite pseudo-wisdom involving single hands clapping and break it down a little bit. It entails a three-stage process of knowledge development. Simplicity to complexity back to simplicity.
When you begin an undertaking, you have no idea how much detail you don't understand. As you begin learning and exploring more, you begin to see the fractal nature of your subject as it increases in complexity with each advancement in understanding. Finally, and this doesn't happen very often, you begin to assimilate the scattered complexity into simple, unified, yet precise concepts.
Towards the end of this talk, Berlow says, "We're discovering in nature that simplicity often lies on the other side of complexity, so for any problem, the more you can zoom out and embrace complexity the better chance you have of zooming in on the simple details that matter most."
Note that an understanding of complexity is an essential and intermediary step in that process.
Earlier in the talk, he makes this point again in a slightly different way when he says, "So the more you step back and embrace complexity, the better chance you have of finding simple answers and it's often different than the simple answer that you started with."
The word elegance is used to describe an object of beauty with remarkable aspects of simplicity and effectiveness. Einstein's E=MC² formula is an example of this. It also applies to the TED speaker's distillation of U.S. military strategy in Afghanistan to a small number of easily understood points.
The inherent simplicity of elegant solutions often leads them to be misunderstood. It's common for them to be dismissed as too simple to be original or truly effective.
This is sometimes the case, for example, with John Boyd's OODA Loop, a strategic concept originally developed for military applications which is now prevalent in the business world. The OODA loop is so simple on its surface that it's easily dismissed as self-obvious, but few understand the overwhelming depth of knowledge from an incredibly diverse range of fields that was synthesized by Boyd in order to produce it.
The concept of elegant simplicity is easily applied to the fitness world, from individual movements to principles of nutrition or training. In fact, if you look past the methodological differences in most successful training and nutrition systems, you'll find quite a few seemingly simple principles at their roots.
This is not to say that anything in the fitness industry that is reduced to simple set of principles is inherently effective. As Eric Berlow said in his TED talk, the simple answers you end up with are often different than the simple answers you started with. In many cases, people who adhere to simple concepts are merely stuck in the first stage of development and haven't even realized how potentially complicated their field is.
Likewise, that a system has an in depth knowledge of a single aspect of something like nutrition is not to say that it's going to be effective either. It's quite easy to be sidetracked with informational "rabbit holes" and fixate excessively on a few particular components while disregarding many others and failing to see how they function together. This is essentially grasping at elegance without the necessary means of attaining it.
Think of how many faddish dietary trends have focused on a single concept, analyzed the crap out of it, and attempted to use it as a philosophical basis without integrating other related factors.
Things like calorie counting, volumetrics, precise macronutrient ratios, or focusing on things like cholesterol and saturated fat can all potentially have a place in effective nutrition. But to focus on one of them at the exclusion of everything else leads the end-user further away from effective long-term results. Don't mistake reductionism for elegance.
If you look at most successful physical training systems you'll see that they focus on doing simple things extremely well. Squat, run, push, hinge and pull. Simple things, but difficult to do flawlessly. Once that flawless simplicity is attained those movements are used in a countless variety of combinations to induce a desired training effect, but it all comes down to simple movements done well with gradually increased load, volume or density.
Elegant, beautiful simplicity is the end result of the knowledge development process and can't be produced without first understanding the complexity of the system in question. It's also easily confused with reductionism and distinguishing between the two is an art in itself.
When looking for a system based on an elegant solution, look for easily expressed simplicity. In order to determine the basis of that system, you'll have to work backward in the process toward fractal complexity and see how much the creators know about the myriad interrelated factors underlying the system.
As a user, you don't have to know the complexity part in order to benefit from the simple principle that it produced, but it's a good idea to make sure that the people advocating it do.