Geometry is probably one of the most undervalued aspects of Mathematics. So much so, that people consider it something that is relevant mainly for those pursuing that particular discipline, as in their minds geometry is divorced from other, more practical fields, such as data analytics. However, geometry has always been an applied discipline, intertwined with engineering. As data science and data analytics in general is closely linked to engineering, at least in certain principles, it makes sense to at least consider the relationship between geometry and data analytics. Geometry involves the study and use of visual mathematical concepts, such as the line, the circle, and other curves, to solve various problems or prove relationships that may be used to solve other, more complex problems. The latter are referred to as theorems and are the core of the scientific literature of geometry. So, unlike other more theoretical parts of mathematics, geometry is practical at its core since it endeavors to solve realworld problems. Although the latter have become increasingly sophisticated since geometry was in its glory days (antiquity), many problems todays still rely on geometry for their solution (e.g. the field of optics, the calculation of trajectories of rockets, and more). Besides, since the times of Descartes, the famous philosophermathematician, geometry has become more quantifiable, particularly with his invention of analytical geometry. Data analytics is in essence a field of applied mathematics, with an emphasis on numeric data, the kind that features heavily in geometry. Although direct connections between the shapes and the proportions of geometry with the data analytics concepts are few and far in between, the mindset is very similar. After all, both disciplines require the practitioner to find out some unknown quantity using some known data, in a methodical and logical manner. In geometry, these correspond to a particular point, shape, or mathematical relationship. In data analytics, these are variables that take the form of features (through refinement, selection, and processing in general) and target variables. Of course, data analytics (esp. data science), has a variety of tools available that facilitate all these, while in geometry it’s just the practitioner’s imagination, a pencil, some paper, and a couple of utensils. However, the mental discipline behind both fields is of the same caliber, while creativity plays an important role in both. I’m not saying that geometry alone will make someone a good data analytics professional, or that you should give up your data science courses to take up geometry. However, if you have the time and you can also see something elegant in geometry problems, then it can be a very useful pasttime, much more useful than other, strictly analytical endeavors. After all, imagination hasn't gone out of fashion, at least not in the applied sciences, so anything that can foster this faculty, while at the same time encourage mental discipline, is bound to be helpful. As a bonus, spending time with geometry is bound to help your visualization skills and enable you to view certain data analytics problems from a different angle (no pun intended). Besides, the same mindset that helped people build pyramids and accomplish several other architectural feats, is what forged many modern algorithms in machine learning, for example, turning some abstract idea or question into something concrete and measurable, be it a design or a process. Isn't that one of the key attributes of a data analytics project?
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Zacharias Voulgaris, PhDPassionate data scientist with a foxy approach to technology, particularly related to A.I. Archives
March 2021
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