Enigma – What it is, concept and differences with paradigm

We explain what an enigma is, the origin of the term and what are the mathematical enigmas. Also, differences with a paradigm.

An enigma is something with no easy solution, or even no solution.

What is an enigma?

It is understood by enigma a matter difficult to understand or elucidateThat is, it does not have an answer or an easy solution, or even does not have one at all. Riddles (or enigmatic matters) can be mysterious, but as they are not necessarily unsolvable, they can be understood more as riddles than as timeless mysteries.

The word enigma comes from Latin aenigma and this in turn from the Greek aynigma, derived from the verb ainíssomai, which could be translated as “insinuate” or “say in a veiled way.” The term was initially used for words and a certain way of speaking, but it became associated with that which, so difficult to understand, ends up being inexplicable.

In this sense, the term has been used throughout history. For example, the decoding machine used by the Allies to decipher German military codes during World War II was called an “enigma” and it represents one of the most important predecessors of today’s computers.

Other popular uses of the term have to do with the occult, with the transcendental questions (and without possible answers, for the moment) of humanity, or even with the challenges of logical and mathematical thinking.

Mathematical riddles

In the field of mathematics and calculus, the term enigma is often used as a synonym for a riddle or difficult-to-solve problem. Many of them come from ancient times and are formulated with the intention of passing time, or to reinforce a certain type of logical or mathematical reasoning, especially when the answer to the puzzle is not the one that seems most obvious.

A couple of examples of math riddles are as follows:

  • The three spirits. A pilgrim runs into three spirits on his way: that of truth, that of lies and that of chance. The first always answers your questions truthfully, the second always lies, and the third answers sometimes with a truth and sometimes with a lie. However, the three spirits are identical in appearance, and the pilgrim must guess which is which by asking three questions whose answer can only be “true” or “false.” The questions can all be asked to the same spirit or one to each, but the condition is that the second question is related to the first and the third to the previous two. How can the pilgrim deduce which spirit each one is?
  • The triangular cake. A man wishes to bring home a scalene triangle cake, and he gives the pastry chef the measurements of the three unequal sides. The pastry chef makes the cake to the letter and asks the customer to bring a box to put it in, but when he tries to put it away, he realizes that the cake and the box have the same measurements, but symmetrically. He decides then to cut the cake to redistribute its pieces and fit in the box, and he realizes that just two cuts would be enough. What are those two cuts?

Enigma and paradigm

The words “enigma” and “paradigm” have nothing to do with each other. An enigma is a mystery or a riddle without an answer, instead, a paradigm is a way of looking at things, that is, a general way of thinking and / or acting, which defines the perspectives of an era, a culture or a discipline.

For example, the great revolutions have broken the paradigms of their times, forcing us to think in a different way what until then we thought as resolved and understood.