Jan 2024 - Euclidean Geometry and Deducing Strategies!

Entrepreneurship has many parallels with many other aspects of human endeavor and hypothesis. My blogs so far have attempted to capture and elaborate on some of these. 

During 2024, I will aim and attempt to link it with one of the most impacting branches of human knowledge - geometry - which has evolved over all of humankind’s existence. Hopefully, I will make it as interesting as it will be informative and useful. And I promise to refrain from any formulas or semantics which are usually the bane of mathematics, as far as laypersons are concerned!

Geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space, is one of the oldest branches of mathematics. It has evolved from the study of flat surfaces (plane geometry) and rigid three-dimensional objects (solid geometry) to analyzing the most abstract thoughts and images which might be represented and developed in geometric terms. The main branches of geometry are Euclidean Geometry, Analytic Geometry, Projective Geometry, Differential Geometry, Non-Euclidean Geometries, and Topology.

What can entrepreneurs learn from each of these six branches of geometry will be the focus in this series of my blogs during 2024.

I begin with Euclidean Geometry which greatly influenced the domination of axiomatic-deductive methods in analytical processes for many centuries.

In several ancient cultures there developed a form of geometry suited to the relationships between lengths, areas, and volumes of physical objects. This geometry was codified in Euclid’s Elements about 300 BCE on the basis of axioms, or postulates, from which several hundred theorems were proved by deductive logic.

The axiomatic method, in logic, is a procedure by which an entire system is generated in accordance with specified rules of logical deduction from certain basic propositions (axioms or postulates). These axioms, in turn, are constructed from a few basic terms that are taken to be primitive and “assumed” to be unassailable.

The deductive method goes from general to particular; that is, initially it starts with a wider and generally-accepted truths and gradually it narrows its focus on one particular area that needs validation.

We can already see some strong  parallels here - with how entrepreneurs formulate strategies to achieve specific goals! They start with some unassailable assumptions about the market and then proceed to validate the market value propositions that they have conceived.

The entrepreneur’s choice of strategy is often dictated both by the initial assumptions as well as the process of validation in the market place. It is not difficult to see how the challenge of ensuring that the strategy is effective depends on both the choice of those unassailable initial assumptions (axioms, postulates) as well as the creative ingenuity of working from and around them to convince the market about the validity of an exciting new proposition.

In Euclidean Geometry the choice of the axioms may be motivated by the observations in the “real world,” but once the axioms are accepted, the real world is left behind and the manipulations of the mathematical objects becomes purely a robust work of the mind to create new paradigms. Done with appropriate care, the axioms can be very potent in deducing a whole world of new mathematical properties that can be transported back into the real world for new observations. Two very important characteristics of axioms are Consistency (axioms don't contradict each other or no deduced theorems contradict each other) and Completeness (any undefined terms in the axiom or deductions of that axiom can be shown as true or false).

Entrepreneurial efforts also seem to show an uncanny resemblance to the manner in which axioms are worked upon in geometry. The unassailable assumptions are nothing more than initial observations of the current status of how the real world of the market is “coping” with products and services that are on offer. 

Successful entrepreneurs consciously and carefully follow up on (a) checking that the assumptions they have made do not contradict any other known facts of the market (consistency) and that there is no ambiguity in them which will later result in go/no-go dilemmas (completeness)’ and (b) innovating and creating prototypes of both a re-defined marketplace and alternate routes to penetrate such marketplaces.

Deducing the right strategy for entrepreneurial success dictates robustness in both of the follow up areas.

Euclidean geometry has several other interesting features. Can you think of what other areas of entrepreneurship can be correlated to it? Please do let me know and I will be most happy to include it in my next blog.