Analogies and numerics – an analogy

Analogies are rhetorical devices or stylistic devices used in dialogue or narrative to express a complex topic in a familiar context and simplify the underlying concept in its form – well, that sounds very much like the task of numerics as a field of mathematics.

Life can have different viewpoints

Numerical analysis is certainly not just a stylistic device or something that can be applied quickly. However, it is important to bear in mind the parallels here: when using analogies and numerical analysis, the task is to express a complex abstract construct in a more comprehensible or clearer form and to master interaction with the situation.

Etymology

The word analogy comes from the Latin word "analogia", which translates as "correspondence" or "relationship". An analytical abstraction of a topic in the context of semantics that can be projected onto more everyday areas of life. The prefix "ana-", also from Latin, has many meanings:

• up/on
• back/again
• according to/corresponding to

In the context of analysis and analogy, two of these three possible meanings come into play: 

• Analysis consists of "ana" and "lyein", whereby "lyein" means to solve and, with the use of "ana" in the sense of "on", analysis is the field of mathematics of solving.

• Analogy, however, consists of "ana" and "logos", with "logos" translating as "word", "relationship" or "reason" and then, in the appropriate combination, the prefix "ana" meaning "according to/corresponding to" in this context.

Well, this bold comparison (if not analogy) between numerics and the concept of analogy still needs to be justified: 

One can consider the situations in which analogy is used: those in which one wants to express complex events and processes in already familiar forms and thus offer a generalised understanding to the person with whom one is exchanging the analogy.

An analogy would not be feasible without a conceptual understanding of what one is referring to. The person creating the analogy and the person to whom it is addressed need a common consensus of knowledge on which to build and, ideally, a similar perception of what is easier or more understandable to comprehend.

Furthermore, numerics is subject to an almost identical situation: one approximates a concept whose comprehensibility, or rather applicability, is extremely complex or even impossible by means of a simpler and already familiar structure, thereby attempting to find an adequate compromise between simplicity and accuracy. 

- It is of no benefit to anyone if every detail is lost in an analogy. -

However, numerics does not involve a dialogue in which one has to explain something to someone else. Comprehensibility must be conveyed more to those who have to execute or apply it. Whether it needs to be comprehensible to the end consumer or, more importantly, not too computationally intensive for the available hardware, that is a matter of debate.

However, both analogy and numerics have a responsibility not to oversimplify the complexity while still retaining sufficient detail.

Richard Feynman once said:

Any analogy must fail. We mustn't mindlessly try for analogies in every case; occasionally we must throw in the towel and accept that a thing cannot be explained by reference to something other than itself.

This statement refers to quantum mechanics, and yes, there is probably never going to be a completely comprehensive analogy for this.