Simplicity: The Ultimate Sophistication?

Leonardo da Vinci, famously known mostly for his painting genius but really a Renaissance polymath in the truest meaning of the word, claimed that “simplicity is the ultimate sophistication.” What I personally understood by these words when I first read them was that elegance and beauty need not be difficult to appreciate –that the highest measure of elegance should in fact be how easily it is expressed.

These words are important to think about especially today, when systems are becoming increasingly more complex and sophisticated than ever before. Therefore, new paradigms have been adopted to simplify complexity. A few centuries before da Vinci, William of Ockham had championed the principle of parsimony, which is about choosing the explanation with the fewest assumptions in the face of multiple explanations for the same phenomenon. This so-called Occam’s razor seeks to favor the simplest explanation that is at the same time the least likely to fail, and thus the most robust. In his book Antifragile: Things that Gain from Disorder, Nassim N. Taleb puts forth a general definition of the concept of via-negativa. When dealing with a complex system, it is more robust to improve it by removing elements that one is certain do not add to the system than by adding new elements. In other words, the via-negative approach seeks to simplify complexity of a system.

Now, why are “fun facts” fun? I recently saw a beautiful pattern involving non-zero digits posted on Twitter by World of Engineering (@engineers_feed), and I couldn’t help but try to uncover the full complexity of the pattern. It’s often some fundamental truth that underlies a fun fact which makes it so interesting. The truth is easily and immediately perceived and one feels the need to explore how a very simple fun fact managed to simplify such sophisticated truth.

In a more formal and general way, a calculus teacher would perhaps have asked: Prove that for all n ∈ N*

This mathematical expression is the beginning of the unravelling of the sophistication of a so-simple-to-understand-yet-elegant fun-fact!

Seeing a tweet-sized fun fact take a number of equations to explain should perhaps help one appreciate da Vinci’s idea that simplicity is the ultimate sophistication. This concept is useful not just for fun fact writers, but also for systems designers and engineers who are faced with complex and sophisticated systems on a daily basis. The ability to simplify elegance and sophistication of a system means not only being able to communicate in the simplest way with the world, but also being able to more easily manage the system without sacrificing its integrity.

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