December 2024 – An End for A Beginning

 

Those of us who have seen the 1997 movie Batman and Robin, will know its main tie-song "The End is the Beginning is the End" written by Billy Corgan, and performed by the Smashing Pumpkins. The refrain (chorus) in the song, goes as follows:

Is it bright where you are?

Have the people changed?

Does it make you happy?

You're so strange.

You may wonder why I am referring to this song and writing about the End and the Beginning. Allow me, upfront, to let the cat out of the bag!

Thirteen years and more than 160 posts after I first started to write and publish a monthly piece on my random thoughts pertaining to leadership & entrepreneurship, self-introspection as well as feedback from a few readers (genuine well-wishers) have suggested that the time for change has probably come and that the change will actually benefit me as well as my loyal readers.

Change, they say, is the only constant; in fact, some would even argue, that it defines the infinite continuum of experiences. Most of us though, often regard change as an end to ‘normal current expectations and a beginning for uncertain future expectations.’

Conveniently, we disregard the facts about the actual desirability of either!

Leaders and Entrepreneurs are no different in this aspect. There is excitement and euphoria when new initiatives are begun and they progress as planned or as expected. There is no conscious effort to ‘end the game’ when ‘the going is good’; no strategic initiative to leverage on ‘the good showing thus far” and build entirely new initiatives that will excite everyone, and most of all, themselves!

There is a need to re-learn, reinvent, and re-write the rules of the game, if one needs to remain relevant. And for these, the first step is to be bold enough to pause and review the experiences of the achievements themselves.

The Batman and Robin song can help in such a review.

When there is ambiguity in answering the questions in the song’s refrain, or when the answers do not excite with new visions of infinite possibilities (read ideas!), it is the time for changing the storyline.

Is it bright where you are?

Have the people changed?

Does it make you happy?

You're so strange.

And so it happens, I have decided that the time has indeed come to change the storyline of the monthly articles on this blog.

This will be the last one on the theme of leadership and entrepreneurship. In that sense this is an End.

Starting with the New Year, I will endeavor to entertain you with a new series on an entirely new theme. What it is, will hopefully be a pleasant New Year Surprise to all of you. That will be the Beginning.

The End is the Beginning is the End!

November 2024 – Colour Blindness and Entrepreneurship.

 

What’s the link, you may wonder! First things first!

Healthy human eyes detect three colors: red, green and blue. Color perception is normally described in four ways:

ü    Trichromatic – Seeing all three colors (normal vision).

ü    Dichromatic – Perceiving two colors but not the third.

ü  ,Anomalous trichromatic – Perceiving three colors but with deficiencies in red, green or blue.

ü   Monochromatic – Perceiving no colors.

     It’s a bit difficult to imagine a color deficiency if you have normal vision. People who cannot see red or green might perceive things in a manner that the rest of us would think of as murky green with some blue and yellow tones. They also have difficulty making out the differences between pale shades.

Red-green color blindness is the most common variety of color deficiency in humans. It happens to people who cannot see shades of red and green the same way as people with normal color perception do.

The dichromatic color blindness conditions of Protanopia (Red-blind) and Deuternopia (Green-blind) hold some significant parallels when it comes to Entrepreneurship.

Protanopia - the propensity amongst some business promoters and leaders for ignoring ethical and governance redlines is a minefield that will inevitably lead to loss of stakeholder trust (especially that of consumer). The belief that there are no permanent redlines in business is the precursor to many a ‘shady deal’.

Deuternopia – the inability of many CEOs to see the ‘green shoots’ - the new opportunities from emerging trends and from leveraging collaborative networks - often results in business failure and sometimes even in business irrelevance. Often, the inflexibility from subscribing to illogical self-defined redlines (such as profit margin expectations or hiring policies), acts as a double whammy!

Just as there are ways to help cope with color vision deficiencies (except for inherited color blindness which is incurable), business protanopia and deuternopia can be removed if entrepreneurs seek the support of good coaches and mentors.

October 2024 – Grasping the DEI story!

Organisations these days are struggling to understand and implement the DEI (diversity, equity and inclusion) agenda.

Interesting, when all that is needed is to look closely at one’s hands. After all, our fingers are excellent examples to know how to grasp the DEI story!

Be it the thumb or the little pinkie, or the digits in-between, there cannot be a more diverse set of appendages in the human body that work so closely and harmoniously with each other to help us.

Together with the phalanges or the extensive bone framework beneath the fingers, the fingers work in perfect conjunction, complementing each other and helping in vital human endeavors.

The Thumb

Also known as the pollex or digitus primus manus, the thumb is anatomically different from the hand’s other four digits. Many consider it is not a finger. These differences allow the thumb to move and function differently from the rest of the fingers. The thumb’s primary function is to either work with or against the other fingers to manipulate objects and perform actions such as pinching or grasping.

The little finger

Also known as the digiti minimi, the little finger is the tiniest and usually considered the weakest. It  plays a vital role in hand dexterity, which is the ability to move the fingers with precision and accuracy. It helps to stabilize the hand and provide a secure base from which the other fingers can move. Some medical experts opine that you’d lose 50 percent of your hand strength if you lose your pinkie; while the index and middle fingers function with the thumb in pinching and grabbing (think of zipping zippers or buttoning buttons), the pinkie teams up with the ring finger to provide power.

The Index Finger

The index finger or the digitus Secundus (also referred to as forefinger, index finger, pointer finger, trigger finger) is usually the most dexterous and sensitive finger of the hand. The index finger’s importance comes because of its its ability to abduct, and its closeness to the thumb. It has a major role in precision pinch and directional grip.

The middle finger

The middle finger or digitus medius is located between the index finger and the ring finger. It is usually the longest finger. It is a source of strength for grabbing and holding on. The middle finger is the longest and strongest finger in the human hand. It plays an important role in many hand activities, such as Power grip used to stably lift and move heavy objects, Pinching used (in conjunction with the thumb) to hold small objects, and in several Fine motor skills such as writing, typing, and playing musical instruments. The middle finger helps to provide precision and dexterity for these tasks.

The Ring Finger

The ring finger is called digitus medicinalis, the fourth digit, digitus annularis, digitus quartus. Often thought to have only an ornamentation purpose, as its name suggests, the ring finger supported by the little finger provides power grip prehension and power to the hand.

 

What better illustration can we get for understanding how DEI is beneficial!

September 2024 – Insights from the Indian festival season

 

It may seem to be punctuated by discrete celebrations, but the Indian festival season is more likely to be a never-ending relay race of joyous events that are typically characterized with tradition, culture, and religious fervor. Not just individual families, but entire communities are involved in a seamless manner.

Such festivities certainly offer several useful insights for entrepreneurs and business leaders.

Let’s look at a few of these.

Family Bonding: Festivals in India such as Holi, Raksha Bandhan and Eid often involve family reunions, where people come together from far and wide to celebrate. The emphasis on family and community values often acts as a reinforcing glue.

The use of corporate events such as foundation day or project milestones and work anniversaries need to place emphasis on the core values of the business. These can also be a reinforcing glue for the team.

Resilience and New Beginnings: The festival of Navratri, for instance, is celebrated with great enthusiasm, and represents the triumph of good over evil. It emphasizes the need for resilience in the face of adversity and encourages embracing new beginnings with an open mind.

Success in business ventures is also dependent on these two traits in entrepreneurs. While good forward planning helps, an adverse environment cannot always be accurately predicted. Setbacks – be they small hurdles or debilitating ones – can only be overcome with focused action that is energized by a resilient mindset.

Embracing new ideas is another trait in business leaders, that is a precursor for success.

Mindfulness: Participating in religious and cultural festivals such as Navratri and Durga Puja, often requires a sense of cultivated mindfulness. It involves being fully present in the moment, immersing oneself in the rituals, and appreciating the beauty of the celebration. This practice of mindfulness, as many Indians will assert, is essential for stress reduction and overall well-being during the intense period of the festival celebrations.

Effective business leaders and entrepreneurs need to master the art of mindfulness. This will ensure that the “pulls” and the “pushes” from various stakeholders do not jeopardize the operations and there is an overall appreciation and satisfaction of the progress being made towards the visionary objectives.

Time Management: Indian festivals often follow specific schedules and rituals, emphasizing the importance of time management. The punctuality and precision required for festival preparations – for instance the preparations and the performance of Midnight Mass during Christmas where the service involves carols, a short sermon and the celebration of the Holy Communion (the blessing and sharing of bread and wine) – illustrate the need for, and the benefits of, effective time management.

Gratitude: Many Indian festivals, revolve around the concept of gratitude. For example, the harvest festivals such as Pongal, Lohri, Makar Sankranti, are events where farmers express their gratitude to nature. It is a celebratory reminder to everybody, to appreciate the abundance in their lives and find contentment in what they have achieved.

Good entrepreneurs always demonstrate their deep appreciation of the support that they receive from their customers, partners, suppliers and employees. They periodically showcase their gratitude through appreciatory letters, gifts and rewards.

Discipline and Purity: Festivals like Paryushana and Ramadan are occasions where people observe strict fasting perform various purifying acts. These practices require discipline and self-control.

Entrepreneurs and Business Leaders need to realize the value of delayed gratification and patience - these are essential for sustainable growth. Also important is the concept of purity – in a business these are relatable to quality, ethics and compliance.

Philanthropy: On the auspicious day of Gurupurab or Guru Nanak Jayanthi, the Sikhs offer prayer to their first Guru, cook food and offer it to all those who are needy. Guru ka Langar is another tradition where gurudwaras serve food to all regardless of social status, gender of faith.

Corporate philanthropy is a means by which entrepreneurs can earn the long-lasting goodwill of the social communities in which they operate. CSR initiatives are increasingly contributing to solving intractable social challenges.

August 2024 – Paris Olympics – A natural home for Entrepreneurs!

 

The 2024 Paris Olympics has begun and there is palpable excitement amongst sports fans the world over for a bonanza of excellence as over 10500 athletes will compete across 329 events.

As exciting as this spectacle is, it should be noted that the Paris Olympics is also actually a shining example that showcases the best of entrepreneurship. Three aspects can drive home this point:

1.   Firstly, the choice of the mascot – the Olympic Phryge – is based on a traditional small hat that was symbolically used during the French Revolution. It represents freedom – an aspiration that drives people to plan for and achieve change in their lives. Good entrepreneurs are also driven by an aspiration to change customer experience for the better! 

2.  Next, the focus on creativity while innovating – let’s start with the opening ceremony; it wasn’t on a vast expanse of a stadium, but on the lovely river Seine, with eye-catching performance on electric boats. There could never have been a better example of creative disruption of a tradition! And then what to say of the Olympic medals being made using iron, amongst other traditional materials; the iron was removed from the Eiffel tower during its renovation. There are many other instances of creative innovation that supports circular economy –coffee tables made out of recycled shuttlecocks, and beanbags from recycled parachute fibre. As good entrepreneurs will vouch for, the challenges for embracing change can be overcome with great design thinking and innovation!

3.  Lastly, the 12 core qualities of Olympians can be seen on display – confidence, the ability to cope with and control anxiety, the ability to focus and block out distractions, competitiveness, intensiveness, work ethics, plan for success, mental toughness, hopefulness, optimism, perfectionism and open-mindedness to be coached – isn’t it so easy to see that these are the same qualities that good entrepreneurs continuously hone!

 And that’s the reason, why entrepreneurs will feel themselves at home as they see their favourite sportsperson perform in front of a global spectator base!

July 2024 – The virtue of Minimalism in Entrepreneurship

 

Minimalism in entrepreneurship is a non-conformist approach that advocates greatness (rather than bigness) in business as a value-enhancer.

But what exactly is minimalism?

The concept has its genesis in the world of art.

Minimalism in art is an idea (extremely non-conformist and abstract one to say the least!) that art (such as paintings, sculpture, lighting) should have its own reality and not be an imitation of something else.

Minimalist Art uses hard or clear edges, repeating shapes and contours, repeating blocks of limited color choices.

What you see is what you see - The minimalist artists wanted to create art that referred only to itself, allowing the viewer an immediate, purely visual response. The personal, gestural elements were stripped away with the aim to reveal the objective, visual elements of art.

In the world of business and commerce, there are virtues that the minimalist approach offers. Let’s consider a few parallels from minimalist art

Ø  Clear, hard edges – enterprises that define in simplistic (unambiguous) terms to their stakeholders – be they customers, investors, or regulators - the dimensions of their operations and offerings stand to benefit long-term from stakeholder confidence.

Ø  Repetitive contours and colors – often business partners and employees need periodic reassurances that standard operating practices and policies continue to govern in transacting value.

Ø  What you see is what you see – for entrepreneurs this translates into a core value proposition. What is promised in a value-exchange or transaction is what will actually be delivered! All superfluous and ambiguous elements are continuously stripped off.

Several principles underscore a minimalist approach to entrepreneurship. Often the difficulties encountered in practicing such principles dissuade many from being minimalistic. The principles include

ü  start being a minimalist and then learn to sustain being one even as you grow;

ü  running a tight ship always; and

ü  owning the business without allowing it to own you.

June 2024 - Topology and Core Value Systems!

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 analysing 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 these branches of geometry?

In this final blog piece in the series correlating mathematics with business processes, I want to explore Topology. What can we infer from this type of geometry?

Most mathematicians associate the emergence of topology as a distinct field, with the 1895 publication of Analysis Situs by the Frenchman Henri Poincaré. There are many others though, who believe that several topological ideas had found their way into mathematics during the previous century and a half.

Topology is the part of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending. This branch of mathematics studies properties of spaces that are invariant under any continuous deformation. It is sometimes called "rubber-sheet geometry" because the objects can be stretched and contracted like rubber, but cannot be broken. As we will see later, it is this fundamental principle defined as extrinsic topological equivalence, which offers a link to the world of business.

When a continuous deformation from one object to another can be performed in a particular ambient space, the two objects are said to be isotopic with respect to that space. For example, consider two circles inside a larger circle with a point inside them. In a two-dimensional ambient space these two smaller circles cannot be continuously deformed into each other to merge the points inside them; it would require cutting the circles open to allow this possibility. However, if three-dimensional space serves as the ambient space, a continuous deformation can be performed, as in a sphere, or a doughnut! Thus, these two are isotopic with respect to three-dimensional space, but they are not isotopic with respect to two-dimensional space.

The notion of objects being isotopic with respect to a larger ambient space provides a definition of extrinsic topological equivalence, in the sense that the space in which the objects are embedded plays a role. The example above motivates some interesting and entertaining extensions. One might imagine a pebble trapped inside a spherical shell. In three-dimensional space the pebble cannot be removed without cutting a hole through the shell, but by adding an abstract fourth dimension it can be removed without any such surgery.

Now, let’s try and relate these concepts of isotopism, ambient spaces and extrinsic topological equivalence to the world of business.

Businesses operate within an ecosystem. An ecosystem is the ambient space. The boundaries of the ecosystem are defined by the nature of the business as well as its scope (or extent). As can be inferred, higher dimensions of the ecosystem will happen when the nature of the business expands or its scope widens to include new customer segments or supply chain partners.

Some core and intrinsic value systems govern the way businesses aim to deliver whatever their customers want. In a phase where the operations are stable around the current ecosystem (akin to the lower 2D in mathematics), these businesses face a dilemma about breaching some of core values (even as other core values remain intact) if they want to access some attractive opportunity. Such combinations of core values are said to be non-isotopic in the existing ecosystem. An example of non-isotopic core value dilemma may be environmental-protection and job/skills-creation for a coal mining company, which may result in a stumbling block for business growth and expansion.

However, if the ecosystem upgrades to a higher order where the technology supply chain enables improved environmental performance and the skills needed in such an ecosystem can facilitate additional jobs, then in this higher order of ecosystem, the same combination of core values can become isotopic.

Extrinsic topological equivalence, as a corollary, is all about businesses embedding themselves continuously into higher orders of ecosystems (continuous improvement), so that all their core values continue to remain un-breached, even as they pursue growth.

May 2024 - Projective Geometry and Branding!

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 analysing 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?

In my last four blogposts, I had endeavored to explore the lessons that entrepreneurs and business leaders could infer from Euclidean and Analytic Geometry. Some readers have continued to send me interesting feedback and have encouraged me to continue this adventure of correlating mathematics with business processes.

Emboldened by their comments, I want to explore Projective Geometry next. What can we infer from this type of geometry?

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.

It has its origins in the early Italian Renaissance, particularly in the architectural drawings of Filippo Brunelleschi and Leon Battista Alberti, who invented the method of perspective drawing.

The French mathematicians Girard Desargues and Blaise Pascal took the first significant steps by examining what properties of figures were preserved (or invariant) under perspective mappings. In general, by ignoring geometric measurements such as distances and angles, projective geometry enables a clearer understanding of some more generic properties of geometric objects.

Projective Geometry deals with the relationships between geometric figures and the images, or mappings, that result from projecting them onto another surface. Common examples of projections are the shadows cast by opaque objects and motion pictures displayed on a screen.

As the images below can will help illustrate, some of the fundamental theorems of Euclidean geometry such as those of similarity, preservation of angles and intersection of parallel lines seem to lose sanctity when projections on to different planes of higher dimensions are made.

                                                 

 

                                                             

However, Desargues clearly showed that while some properties such as distances and angles are not preserved in projections, there will be other properties, such as collinearity (three points on a line in real plane will also be in a line on the projected plane), that will continue to be invariant irrespective of whether our focus is on the reality plane or on the projected plane.

This concept of a dichotomy between Variant and Invariant properties offers the parallels for understanding a fundamental aspect about entrepreneurial practices. This relates to Branding.

As commonly understood, a brand is a name, term, design, symbol, or any other feature that distinguishes one seller's product or service from those of others. Branding is a process of creating a distinct identity for a business in the minds of your target audience and the general population.

                                          

The process of branding is evidently one that involves projecting some fundamental truths about the value propositions that the enterprise offers to consumers of its products and services.

The overarching objective is that the consumer is able, to distinctively perceive and remain satisfied that her/his needs and wants are being met at a value-point that is a “wow”!

And, for success in such an objective, projecting and capturing the mindshare of positive perceptions of the consumer demands a clinical assessment of what “brand-truths” will remain invariant during the branding process and which ones will lose their validity.

Understanding the critical nature of the invariant-propositions and the invalid-propositions and working to managing these during the branding process is akin to what projection-painters and machinists do when converting 2-dimensional drawings into three-dimensional visual masterpieces and precision machine parts.

Understanding the laws governing “real-world” of designing and producing a product or service and knowing how they will work when projected to the “esoteric and fussy world” that exists in the consumers’ mind needs a lot of mathematical jugglery - of the projective geometry kind!

April 2024 - Analytic Geometry, Logical-Thinking and Problem-Solving!

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 analysing 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?

Analytical Geometry is a combination of algebra and geometry. In analytical geometry, we aim at presenting the geometric figures using algebraic equations in a two-dimensional coordinate system or in a three-dimensional space.

This field is often deemed as the next level of mathematics, and is often claimed to help with logical thinking and analytical thinking, both of which improve problem-solving skills – which is a fundamental requirement for successful entrepreneurs!

Let’s explore a little further.

Logical thinking focuses on drawing conclusions based on a set of rules or pre-confirmed evidence, whereas analytical thinking involves breaking down complex information and synthesizing it to arrive at conclusions. Both types of thinking are valuable and can be used in combination to enhance problem-solving skills.

More generally in analytic geometry, formulas (which are nothing more than statements), involving some variables are used. Using the convention of capital letters to designate formulas, if the truth of a formula depends on the values of, say, x, y and z, we will use notation like P(x,y,z) to denote the formula. Such formulas are either true or false when we assign particular values to each of the variables.

Example - If P(x,y) is "x²+y=12'', then P(2,8) and P(3,3) are true, while P(1,4) and P(0,6) are false. If Q(x,y,z) is "x+y<z'', then Q(1,2,4) is true and Q(2,3,4) is false.

Complicated formulas are put together from simpler ones, using a small number of logical operations. Just a handful of these operations are used.

If P is a formula, then "not P '' (written symbolically as ¬P) is another formula. Of course, ¬P is false if P is true and vice versa. Also, many derivative instances such as conjunction of formulas P and Q denoted as P∧Q, disjunction of formulas denoted by as P∨Q and conditional formulas written as P⇒Q (implying "if P then Q'' or "P implies Q'') are all almost logically derived.

We can easily see the parallels in the world of business. Three core areas of success in entrepreneurship, we all know, involve Effective Marketing, Operational Excellence and Leadership Competence. In fact, each of these three can often broken down into formula-type of statements involving variables that impact their outcomes. The following are illustrative.

Effective Marketing –

 

                                                                                             Image credit to the original creator

The well-known 4Ps can be represented by statements that correlate the dynamic linkages of variables. Product is a function of “who needs” and “why it is needed”; Price is a function of “real and perceived values”, “costs”, “special discounts”, ”margins”, “competition”; Place is a function of “location characteristics”; Promotion is a function of “visibility”, “aspirational demand”, “comfort demand” and more.

Operational Excellence –

 

                                                                         Image credit to the original creator

This is a function of “Quality” and “Acceptability”. Hiqh quality projects and processes that are low on acceptance by stakeholders will end up low on final impact excellence.

Leadership Competence –

                                        

                                                                         Image credit to the original creator

The competence will be an outcome of the dynamics of functional convergence of the “potential”, “motivation” and “development” of individuals in the organisation.

The successful enterprise is a result of an efficient problem-solving capability. This is often  be facilitated by the logical and analytical thinking across multiple paradigms that govern the truth (or otherwise) of the markets, as well as the possibilities from conjunction and disjunction of the functional elements of the enterprise ecosystems.

Yes, analytical geometry and the world of business are indeed linked by the skillsets of logical and analytical thinking!

Mar 2024 - Analytic Geometry and Why Business Connections matter!

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?

Analytic geometry was initiated by the French mathematician René Descartes (1596–1650), who introduced rectangular coordinates to locate points and to enable lines and curves to be represented with algebraic equations. It is that branch of Algebra in which the position of the point on the plane can be located using an ordered pair of numbers called as Coordinates. For this reason, it is also called Coordinate geometry or the Cartesian geometry.                      

The increased interest in curves that resulted in part from the recovery and Latin translation of the classical treatises of Apollonius, Archimedes, and Pappus was an important trend that contributed to the development of analytic geometry. The earlier works of other German and Italian mathematicians was also consolidated by another mathematician Viète into the development of the algebraic tools and practices.

The work of Pappus and Viète in the development of analytic geometry have a great relevance to some effective practices (nay tools!) employed by all successful entrepreneurs.

The use of business connections – networks – have been researched well and is acknowledged as a powerful tool that can catalyze the entrepreneurial journey. That journey seeks to build a bridge from known customer needs to unknown profitability scenarios. Equating these with the help of production and distribution factors is certainly augmented by use of the “connections”.

Successful businessmen intrinsically seek to answer the unknown beginning variable (profitability) by using well-understood parameters (market demand, production and distribution factor efficiencies), proceeding to link them all in multiple ways that will help them derive the desired value for the unknown.

Analytic geometry has parallels to what the entrepreneur does!

Pappus had employed an analytic method for the discovery of theorems and the construction of problems; in analysis, by contrast to synthesis, he postulated that one can proceed from what is sought until one arrives at something known.

By laying down an equation among known and unknown magnitudes in an arithmetic problem, and then solving for the unknown, one was, Viète reasoned, following an “analytic” procedure. Viète innovated by introducing the concept of algebraic variable, as well as the concept of parameter. This innovation, considered by historians of mathematics to be a major conceptual advance in algebra, facilitated the study of the symbolic solution of algebraic equations and led to the creation of the first conscious theory of equations.

Unknowns, Parameters and Equations - the basis of much of analytic geometry - have seamlessly infiltrated much of the toolkits of today's entrepreneurs!

Feb 2024 - Euclidean Geometry and Innovation!

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 analysing 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?

Euclidean Geometry which greatly influenced the domination of axiomatic-deductive methods in analytical processes for many centuries has some interesting insights that can help entrepreneurs mainstream innovation across all aspects of their ventures. How? 

                                  

There has always been innovation even without the aid of current methodologies and theories.  A century ago, Henri Ford was able to identify a need outside of the physical context of horses, and innovate a new means of affordable transportation, the Ford Model-T.

The allure of the innovation process lies in its transformative power, turning a mere idea into a tangible and successful reality! The process is all about exploring new market applications, introducing ground breaking methods and diverse sources of supply, as well as reshaping the organizational structures to creating and delivering innovative goods and services.

The axiomatic-deductive process of Euclidean geometry greatly enhances the application of the above-mentioned distinctively central aspects to the process of innovation.

Successful entrepreneurship demands constant innovative efforts across four domains:

customer – what are the current and emerging customer needs;

function -   what functions to be met;

physical – how can these be achieved vis-à-vis the constraints - what are the design parameters;

process – how to build for and deliver to the customer.

It is evident that a logical deductive approach from some core elementary propositions offers a strong building block for success in such efforts.

Three core elementary propositions - the axioms – are the foundational precursors for initiating and maintaining any robust innovation process.

(a) the independence of core functional requirements and the bare-minimization of functional information needs,

(b) the structures, domains and hierarchical framework in which the innovative solutions can develop and

(c) a process for decomposing the solutions from abstract ideas to detailed features that can be integrated into deliverable components of a product or service.

Building on these three elements, entrepreneurs can deduce pathways across each of the four domains and build innovative products and services.

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.