Analyst’s Pendulum (Trigonometry)
A Very Direct Concept Regarding Indirect Methodologies
Geometry and its trigonometry subset are not often related with analytics outside of a few physical sciences and GIS. But indirectly speaking, they are directly related. Wait, what?
I have used sin and cos in analytics before, for curve fitting, albeit very rarely and not without PhD level support. So this article is NOT about those functions. But trigonometry is the subset of geometry related to triangles and those feature directly in analytics… in a very indirect way. And while geometry class is most often where we recall learning proofs, they apply in trigonometry as well. Fittingly, proofs come in two major variants:
Direct and Indirect
Once again, we don’t live in a binary world or one full of absolutes (at least not in open systems). So using indirect and direct proofs from trigonometry as an example cannot be done too critically. Trig is a closed system.
But then, that really was never the lesson in developing a proof, was it? Indirect and Direct are only paths traveled along the way. Will you go at proving something to be true (highly difficult in open systems) or will you come at more circuitously? Actually, it is more about the right angles… or perhaps:
Triangulation
Trig is all about triangles and so is analysis of open systems. Don’t consider triangulation too directly either, but it is a valid and useful analogy.
In inductive reasoning, or abductive — if you prefer, triangulation is quite important. In these scenarios, data is often incomplete. We need to develop our understanding of a concept (or triangle) by utilizing different data (points), trends (lines), and methodologies (angles). See, that wasn’t much of a stretch now was it? And while no one is likely to go about trying to prove your triangulation in an open system (they are far too open ended), that doesn’t mean that it is not both possible and valid (or able to be proven invalid).
This validation can never quite prove the truth of the matter, only increase the probability that it isn’t wrong. There are always caveats, assumptions, and other delimiters that seek to “close” the system — allow for higher certainty. It is a somewhat sloppy process. Most open systems are. And indirect processes — doubly so.
The most critical concept in successful analytic triangulation is understanding the proper mapping. Two distinct triangles can have identical angles. You need at least one line to prove equivalence, let only identity.
Triangles teach us that “similar” is not equivalent or identical (nor congruent, but I digress). As an example, using three separate survey results with either differing populations, methodologies, or time frames is not enough to validate a finding… only prove the results to be similar. Again, no one (that I have found) is formalizing this. Open systems make the application of such a concept too hard and that is additional to the difficulty in “proving” it.
In the end, the triangle is a nice framework for our pendulum to swing. This is especially true for open systems and abductive reasoning. So take a lesson from Trigonometry and thanks for reading!
For more on triangulation consider:
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