Elegance, Sophistication, and Complexity

October 26, 2017

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Elegance, Sophistication, and Complexity

The saying, “Everything should be made as simple as possible, but no simpler,” is widely attributed to Albert Einstein, yet there is no evidence that he actually said this, or at least that he used those specific words. Scholars hypothesize that this misquotation stemmed from a lecture Einstein delivered at Oxford where he actually said, “It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” Apparently, Einstein’s fans took his words’ meaning to heart, if not the words themselves.

Lexical minutiae aside, one cannot deny the twin perils of unnecessary complexity and oversimplification. The world is teeming with people who either obscure bad reasoning behind a veil of complexity or arrive at skewed conclusions via a grossly oversimplified view of reality. Like most things, information complexity nicely obeys the Aristotelian concept of the golden mean - any deficiency and any excess in the delivery of the truth is tantamount to a lie.

Scientists and mathematicians alike share this pursuit of simplicity without oversimplification. The word elegant is generally synonymous with style and grace but its usage in mathematics is more specific: an elegant solution is one that is pleasingly ingenious in its simplicity.

A prime example of mathematical elegance is Euler’s identity:

\[e^{i\pi} + 1 = 0\]

The five constants are zero, one, pi, Euler’s number, and the imaginary unit. These are all numbers that feature in countless other formulas that underpin entire fields of science and mathematics, and combining all five in such a short and simple equation reveals deep relationships between seemingly disparate fields. Euler’s identity demonstrates that an idea doesn’t have to be complicated to be meaningful, and yet to arrive at such a powerful insight requires sophisticated knowledge of mathematics spanning across several disciplines. It is through this sophistication we glean simplicity from complexity.

The intrinsic value of solutions extends beyond hypothetical discourse into practical business applications. Too often, people are attracted to solutions that are intimidating in their complexity - as if each additional complication were a safeguard against failure.

In the analytics space, this manifests itself in the creation of complex yet crude metrics that obscure the KPI. All of this leads to reports chock full of pretty numbers that mean absolutely nothing to the client. This is in stark contrast with the intended role of analytics: to derive actionable insights from data to drive the growth for the company’s bottom line.

Victor Blancada is a data scientist focused on deriving actionable insights for clients. Visit his LinkedIn page here.

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