All the World is a Differential Equation

by | Apr 15, 2022

There is so much humbug about the idea of the mind. Religions, philosophers, psychologists, medical doctors and, of late, businesspeople, especially those in the marketing domain, offer their own constructs about how the human mind works. And, for sure, people have no clue about the origin of their temperaments, attitudes, fears, and desires. It is interesting to understand the mind from a Calculus perspective.

Calculus is the child of two fathers – the English, natural philosopher, Isaac Newton (1643-1727), and the German polymath, Gottfried Wilhelm Leibniz (1646-1716). The tendency to observe similarities and see a need for integration, and the tendency to notice dissimilarities and see a need for differentiation, is common and widespread. Labeling these two ways of looking at things as “integration” and “differentiation” from Calculus, is reasonable. 

There is variety. Some individuals are high in both, integration, and differentiation, and conversely, some people are low in both traits. For simplicity, and to emphasize their distinctness, we can call people as “lumpers” and “splitters.” A child is a great lumper, over-inclusive and its classes are generic and undifferentiated. As we grow, the development of “I-ness” makes us divide things, mostly into “what I like” and “what I dislike.” 

The “I-ness” is straightforward and should be accepted as the cornerstone of human personality. In the Shrimad Bhagavad Gita (VII. 4), it is written as having been said by God Himself:

भूमिरापोऽनलो वायुः खं मनो बुद्धिरेव च।

अहङ्कार इतीयं मे भिन्ना प्रकृतिरष्टधा।।

Earth, water, fire, air, ether, mind, intellect, and the feeling of I-ness (अहंकारः) – thus is My Nature divided eightfold (इति अष्टधा भिन्ना मे इयम् प्रकृतिः).

The Austrian doctor, Sigmund Freud (1856-1939), called “I-ness” as “Ego.” The Swiss psychiatrist and psychoanalyst, Carl Jung (1875-1961), called it the center of the “conscious mind” and placed the “unconscious mind” as its opposite. The “I-ness of me” is held in balance by “what I am, but not aware of,” thereby, making it a dynamic entity. It will keep expanding as more and more psychic energy emerges out of the unconscious and gets added into the conscious. 

The issue is, therefore, not “what I am”, but “what I can be”, and the focus must be on “my openness” to “become.” The idea of openness to experience was articulated by the British polymath, Sir Francis Galton (1822–1911), and the Five-Factor Model (FFM) of personality traits is currently the dominant theory in all of psychology today. The five factors are – Openness, Conscientiousness (careful way of working), Extroversion (outgoingness), Agreeableness, and Neuroticism (irritability). 

Self-development is all about discern, which is differentiating functions. The environment we live in offers a basket of options – some good, many bad – and there is always scope to choose one, especially not to go with that which is unwholesome. Growth demands declutter – letting go off all that and all those who have not been good. This not only includes primordial identities, dogmas, habits, and beliefs, but also faling into grooves of careers and roles in the society.    

The first differentiation, fundamental and the most difficult, is that we separate from the “parent” we have internalized. This is filled with anxiety and the most prevalent reason for young people getting into addiction or substance abuse – mostly smoking and alcohol – is to pacify this anxiety. Successful differentiation from the “parent” is like a “second birth.” Failure in differentiating ourselves from the parent effect settles us permanently in mediocrity and powerlessness. 

The second differentiation involves recognizing and changing the negative personality borrowed from our parents and other influential figures in childhood. Altering these unpleasant or toxic personality characteristics is essential. All vanity, phoniness, self-centeredness, a victimized orientation towards life, attitudes of superiority and contempt are appropriated from people around, and must be disowned. 

The third differentiation is, looking into the psychological defences we developed early in our lives to deal with pain. There is a strong, and almost automatic, tendency to defend ourselves the way we did as children. Denying, forgetting, exaggerating, projecting our fears, and outbursts are childish behaviours. Saying goodbye to our “child selves” is essential for living fully as the adults we are now.

The fourth and final step of psychological differentiation is to identify our own values, ideals, and beliefs that may be different from those of the culture in which we grew up. For example, Dr. APJ Abdul Kalam did not eat meat from age 15 onwards. This is the last barrier before we can strive to lead a life of integrity, according to our own ideals, overcoming social pressures to conform to the standards of others. 

Integration operates in two domains – internal and external. Internal integration is to allow and assimilate the unconscious into consciousness. External integration is concerned with relatedness, interpersonal communion, and intimacy. Seeing similarities and connections is beneficial. Looking at the food before start eating and appreciating the complex ways it traversed to come before you – grains from fields, salt from the sea, spices from the hills, curd from the dairy…. and so on.  All forms of meditation are essentially integration exercises. 

Finally, I come to Limits and Continuity, the central concept of Calculus. All phenomenon is a function; constant for a while, that is, in a narrow frame of time, but eventually, changing. Only within limits is a function an independent variable. Outside the limits, it is part of chaos. This is like a line that can be drawn on a paper. Once the pencil is lifted or the paper border is breached, there is no more extension of the line.  

The fundamental philosophy of Calculus is to approximate, to refine the approximation, and apply a limit process. An insight into Calculus helps us identify the “balance points” as steady states. Moving away from steady state invites reactions, which may or may not be what we expect. To predict what changes would appear – integrating one instant, differentiating the next – is the real of art of living.

Unheeded happiness is, indeed, fatal. The more you desire, the weaker you become. The more you consume, the more diluted your life gets. The Scottish philosopher, John Stuart Mill (1806-1873), described his despair of “becoming a utilitarian machine with a suicidal ghost inside.” All the world’s a differential equation, and men and women are infinitesimal variables – may be less than any finite quantity; yet, never zero. 

Know your soul as a continuous function – infinity to infinity – but live within the limits of the time and space imposed by your body. Don’t slight or belittle anyone, or overlook a change, however minute it may appear. And never allow your mind to create its own imaginary world, neglecting the people around you, and running away from difficulties. Live your life embracing both, the good and the bad that it brings. You are an infinite function, so always choose to rise over run. 

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19 Comments

  1. Your mathematical model of the world as a differential equation is outstanding, Prof Tiwariji !

    Your connection of the concepts of Calculus for the real art of living is intellectually stimulating !!

  2. Your blog always bring out serious issues, sometimes it directly connect with our own state of mind. Live your life embracing both, the good and the bad that it brings: its a nice thought to ponder on. However, embracing bad is the most difficult thing to do.

    Human mind is so complex, sometime we don’t understand why we reacted so differently to a situation at that moment, later thinking on that make us regret. I personally want to follow that – letting go off all that and all those who have not been good, but it seems out of my control.

    Will be happy if some more lights can be thrown on these aspects as to how to live peacefully in this world where not only things but humans are also changing constantly. I will be eagerly waiting for the same. Thanks for such interesting article with which the reader can connect.

  3. What a way to model our world! The interpretation is brilliant. Concepts of calculus made us understand and resolve the mind’s complexities.

    ‘What can I be’ throws upon infinite possibilities in the continuum of our soul. Limits to our body help define our actions–humility is automatic. Understanding the mind’s nature makes stride over good and bad with equanimity.

    Thanks, professor Tiwari.

  4. Dear Arun, A highly intellectual article on relating calculus with life. In essence, I understand from your blog that one should be wise enough to choose with what to integrate and with what to differentiate.

    For example, I am bit concerned when you talk about differentiating from parental teachings. It may be good for career progression (or call it career aggression) but lot of frustration associated with failure in career growth are result of differentiating from parental teachings while this down side could have been reversed with integration with parental teachings. Therefore, wisdom is needed for balancing between what to differentiate and with what to integrate.

  5. When I was studying in US at Towson University in Maryland, I was attracted to mathematics and sat through few lectures but could not dare to get into it for a lateral entry into the field without acquiring basic skills like calculus and matrix algebra you can’t even make out what is being talked in the class. This blog brought all those memories to surface and I must thank you for this beautifully written blog.

    In the US higher education system mathematics and philosophy are entwined. Whereas the natural sciences investigate entities that are in space and time, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way: by deduction from basic principles.

    The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. The way you looked at differentiation and integration is amazing philosophy.

  6. Very interesting blog about how calculus depicts life. I have learnt in my engineering that calculus measures the rate of change that occurs in almost every phenomenon in the universe. There are two branches of calculus, integrals, and derivatives. The derivative component of a mathematical function defines the rate of change at a specific point, whereas integrals show the accumulation of discrete values of a function over a range. Later I learnt how Calculus is used to determine the growth or shrinkage and number of cells of a cancerous tumor. Using an exponential function, oncologists analyze the progression or regression of a disease. But your take on Calculus to live a good life is indeed a new and interesting concept. All the world’s a differential equation, and the men and women are merely variables echoes Shakespeare’s All the world’s a stage, And all the men and women merely players.

  7. Sir your world is a differential equation blog is mind-blowing. You have weave together the unity of all knowledge. The sum of human mathematic knowledge is no more than a tiny fraction of the complete, perfect system.

    May I add here a beautiful formula given by Swiss mathematician Euler: e^iπ + 1 = 0,

    It’s almost unnerving. Taken alone, numbers like e (2.71828… going on continually, without repeating), (3.14159… going on continually, without repeating), and (the square root of -1, which is impossible), seem like the results of an imperfect human effort to understand the complexity of the world through mathematical relationships.

    Humans can hope to uncover mathematical truths, but we cannot create them.

  8. Thats really deep. never ever thought of connecting calculus to spirituality. Amazing

  9. Very rightly said Sir—“I-ness”
    It is in the swabhaav of everybody.
    This is what great all our holy persons told ‘kill your I-ness. You are nobody.’

  10. When they say where do you see Mathematical concepts in real life, I believe this blog should definitely be cited. Such a beautiful analysis of life and one’s mind based on a Mathematical model. Your writings are always thought provoking which leads one to sit back for a moment and self-realize. Meditation/integration exercises are so necessary to un-complicate things.

  11. In this joyous season of hope, this came as a timely read. Rightly said, the Easter egg symbolizes our ability to break out of the hardened, protective shell we’ve surrounded ourselves with. The “I-ness” can be well balanced with the humanity around us if we expand our thoughts beyond walls that surround us.

    Yes, let everything we do be done in love, expecting nothing in return. Just as a seed sprouts and grows with the help of the soil, water, and the all-powerful sun, may we live up to the purpose of our creation and flourish in such selfless acts as a labour of love, worship, and union with the Divine.

    Remember, THE SUN doesn’t dwell on how powerful it is but continues to rise and shine.

  12. Dear Sir, Thanks for presenting the art of living through CALCULUS. You have the unique knack of putting very difficult concepts in a simple way. For me the important take aways are:

    *Unheeded happiness is, indeed, fatal. The more you desire, the weaker you become. The more you consume, the more diluted your life gets.

    *Know your soul as a continuous function – infinity to infinity – but live within the limits of the time and space imposed by your body. Don’t slight or belittle anyone, or overlook a change, however minute it may appear

    *And never allow your mind to create its own imaginary world, neglecting the people around you, and running away from difficulties. Live your life embracing both, the good and the bad that it brings. You are an infinite function, so always choose to rise over run.

    I could never imagine that CALCULUS concepts can be applied so nicely to understand the philosophy of life.
    Thank you so much sir.

  13. If one can understand the human mind, the constant integration and the differentiation which keeps on continuously churning in the top most human storey… believe me you are the winner in a jiffy.

    Many a battle is won by understanding the human mind. Be it the mind battle on a cricket field – the batsman able to read the bowlers mind as to what type of ball he is going to ball next, the Chess player able to read the next move sprouting in his opponents mind, the boxer reading the mind game of his challenger or the General in the battle field reading the strategic mind of his rival….. it is all in the mind. And when rightly squeezed, the Calculus juices – assimilate and integrate to arrive at the final result – you score and score high.

    Your presenting Calculus for us to assimilate indeed has made a wonderful read… though confess had to read it twice to understand the maze and wriggle out of it successfully.

    Very much agree, one surely needs a de-cluttered mind. Keeping it simple probably blank, for as stated the more you desire, the weaker you become, the more you consume, the more diluted your life gets. So keep it simple… do live happily by integrating and differentiating and thereby balancing life as it unfolds.
    Assimilate the goodness and stay happy.

  14. Mathematical model for analyzing traits of mind and life as a whole is so interesting. While studying these topics, never ever imagined how concepts of integrations & differentiation can be related so well to stages & phases we go through in life. Child beginning with Integral approach to life and slowly the world pushing the child to differential model as she grows up is very visible.

    Finally loved the summarization of the modern lifestlye with these beautiful words – “Unheeded happiness is, indeed, fatal. The more you desire, the weaker you become. The more you consume, the more diluted your life gets.”

    Also this article reminded me of the book “Integral Humanism” by Pt Deendayal Upadhyay.

  15. Great piece on the human mind as approached from the calculus perspective.

    Didn’t our Creator make each one of us special (differentiated) and integrated into society while living a life in continuity? I like the way Prof Tiwari has put it to us.

  16. Refreshing with unique insights, an amalgamated thought syrup. Great read!

  17. Arun Tiwari ji, I admire your thoughts on a difficult subject. It’s very difficult to understand human mind, which is intimately connected to a personality. Psychologists like Freud and Jung attempted to interpret the behaviour of a person when he gets older. No theory till date could predict or deduce the behaviour of a person as he moves on in Life What you have professed is really thought provoking but one thing is clear that human desires and Love/Hate relationship are most important determinant of actions.

    These Days I am myself stressed to find Vladimir Putin of Russia and Volodymyr Zelenskyy of Ukraine clashing over something which they don’t know where it would lead to. Ashoka after Kalinga War looked around and got into a state of depression and adapted to Buddhism which needs to be explained in the light of your Thoughts. I really enjoyed reading your profound thoughts and wish more keep flowing from your pen. God bless you with Good Health.

  18. How we are made up of? It is a question often confuses us. The matter of concern is about the individual functions and the rate of change and the relation in between them. According to Stephen Covey there are three constraints in life that are change, choice and principles. So that our psychological wellbeing depends on the factors like Autonomy, positive relation with others, environmental mastery, personal growth, purpose in life and self acceptance. If these factors get worsened with the individual functions and the rate of change then an individual become agitated and is unsuitable to the immediate enviornment and the world outside of his accommodation. That is why it is said that the integrated development of an individual depends on physical development, mental development, intellectual development and spiritual development. Anyway there are many ways to reason out this matter of complicated concern of individual traits like self realization and self actualisation.

  19. Thank you. Nice take aways Arun ji. Do not run run away from difficulties. Embracing good and bad. I liked the message not to neglect people around you.

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