The Ubiquity of Trilemmas

Trilemmas can be found across many disiplines throughout history. One of the definition is that out of three favourable options only two can be chosen at the same time. Normally it is visualized as a triangle where the available options are represented by vertices and choices represented by edges. For example, the famous impossible trinity in the world of international economics, as illustrated below, states that among three possible policy positions: “free capical flow”, “fixed exchange rate” and “sovereign monetary policy”, a country can only take two at the same time.

impossible trinity

Trilemmas are everywhere. In economics, other than the impossible trinity, pinker social trilemma says that a society can not be “free”, “fair” and “equal” simultaneously. In business, project management trillema argues that given the options of “fast”, “cheap” and “good” one can only pick two when a project is executed. In computing, CAP thereom suggests that for a distributed data store, “consistency”, “availability” and “partition tolerance” can not be achieved at the same time. In religion, problem of evil logically challenges the existence of an omnipotent and omnibenevelent god. The ubiquity of these trilemmas begs the question: is there anything fundamental about them?

First of all, three is a magic number in many cultures. It is a number that offers a sense of balance and completeness but is still brief enough to be memorized. Three creates patterns that can be found in many speeches, slogans and concepts. From Trinity, Trilogy, and Trias Politica to Yes We Can, Faster, Higher, Stronger, and Government of the people, by the people, for the people. In fact rule of three is a pretty well researched and documented principle in writing, which explains why when people attempt to capture and delivery the intricacies of a complicated matter, they usually come up with three items to strike the balance between completeness of the subject and effectiveness of the communication.

Three is also a number where things start to get more nuanced due to the growing complexity of the internal interactions. In physics, general solution exists for two-body problem where the goal is to predict the subsequent motions of two massive objects given their initial positions. Interestingly, after an additional object is added into the system, the interactions of gravitational forces among the objects become so complicated that the general solution cease to exist. This is called the three-body problem. Likewise, favorable options in many trilemmas are usually not independent of each other. The desire to be perceived as complete and balanced means that overlapping is inevitable, analogous to the “gravitational pull” exhibited by the physical objects. It is very difficult to achieve all three of them simultaneously since the fulfillment of any option is always at the some expense of others.

project triangle

Three also represents a sense of stableness. In fact, triangle is the strongest and most rigid shape in the 2D world. Another way of looking at trilemmas is that in a problem domain, if there exists a solution that can satisfy all three options simultaneously, it will be the perfect and stable solution that can be applied in any circumstances all the time. Obviously this is unrealistic since it ignores the fact that reality evolves constantly and good solutions need to adapt to new changes. The triangular representation of a solution should be constructed with an edge that represents the implicit reality, together with two edges from the triangle of trilemma that represents the right amount of tradeoffs for this version of the reality. Take CAP thereom as an example, there is no universal solution when it comes to choosing databases. The reality that Amazon faces is vastly different from a medium sized company, therefore the options that Amazon picks when building their distributed data store might make very little sense to others.

To summarize, trilemma is ubiquitous because it’s a concise, relatively balanced and complete way of capturing a concept. No progress can be made without also taking into account the the implicit reality.


Written on December 26, 2019