The bright light tore through the thick wood-paneled grilled window, blurring the borders, like a painting with a million white rays coming out of a rectangular-shaped fissure. The chip-studded Terrazo floor underneath us was still cool from the previous night and would soon become tepid warm as the sun rays left the window and moved higher and hotter. It was hard not to appreciate the setting, the light, the ancient Egyptian mosaic floor, sitting next to Dad, both of us huddling around the rectangular lighted frame, sitting in a chokdi (the Indian way to sit on the floor, to meditate, to eat, or to study) and anticipation for Mom to finish making the aaloo paranthas, my favorite Sunday breakfast. I was 10 years old, in a perfect quantum state of absorption, to whatever my Dad was going to teach me that morning.
As he sketched in his notebook, my father would speak only after completing each element of the drawing. "The surface of a desert marks the boundary between two realms – the hot earth below and the cooler air above," he explained while his pencil moved across the page. His words flowed as he illustrated – drawing a straight line to represent the critical angle, followed by an inflection, and finally shaping it into a convex rising u shaped curve. I was seeing a convex curve for the first time. "These stark temperature contrasts give rise to a mirage, an intricate illusion of an oasis amidst the desert," he continued, unraveling the science behind this natural phenomenon and its complex architecture.
Life in Delhi as a child was beautifully simple. It took me years to appreciate how hard our parents worked through the complexity of meager resources to simplify our lives, as if in an oasis. We had no washing machine, no dishwasher, no vacuum cleaner, and no water cooler. In 44 plus degrees Celsius, the tar on the road that brought us back home back melted, and on occasions, you could see the mirage, as the road transformed into a mirror. And it was during this heat, we had the summer vacations, when we put thick blankets on every window of the house and soaked them in water. The oasis in the desert was real, a simulated flood. The fun was priceless.
I sat there with him, in my oasis, in awe of how Science had demystified the miracle of nature. Drawing was the preferred way of learning and teaching at home. We used Dad’s architectural boards and blueprints to use the blank broadsheets with thick 6B lead pencils that worked better than permanent markers. Growing up with standing canvases made it easier for me to hold a pencil.
My school was another oasis. A private school that interviewed the parents and students. I don’t remember my interview, but I remember the revered principal, who was a disciplinarian, spoke with authority and was feared. I was an average student, never up there, never down there, somewhere there. I was in the choir and drummed everyone for their morning parade in the lovely central ground. The controlled reverberations, the baton with its soft balled head when passed on to me was like the passing of a crown jewel. I had other highs at school. I loved geometry. I loved shapes. In a competitive world of 44 diligent students in class, I remember acing my 6th grade geometry test, which had a question on Isosceles triangles.
Our gifted art teacher Torit Mitra made us sketch, putting the student without a sketchbook in the middle, there was always one who forgot it. And the rest of us circumferenced him, sketching all facets of that face and body that was punished to "freeze" for the 30 - 45 mins class. I took to sketching as an innate skill and it did not take me long to realize, that it overlapped with geometry. Mom was a mathematician and always used to tell me, how I took a longer route to solve the problem, compared to the genius next door, who became a top-notch accountant, and had a knack for the fastest way to solutions. Somehow, I was always decomposing things in my head, playing with inefficiency, and imagining many solutions rather than a unique one. It bothered me for a long time, how though I was the teacher's son, I was not the best.
Tiger parenting was not a term then. When you are designed for failure, never good enough, you either can fall off the radar and nurture inferiority or you can slowly continue the grind up, dealing with your mediocrity, self-accepting, a step at a time, striving to complete an ultra marathon, just to prove yourself, you are someone. Well aware, that your first competition was with yourself. You could not blame your parents who rose from wretched poverty. Dad was the only one among 9 siblings, who ended up getting higher education. My mom’s family was not as poor as my dad's, but still, a low-income family, with five siblings, work and learn was all that they did. There was no other entertainment, the television was a box that used to open once a week. I ended up getting used to a life without Tele, an opportunity of time rare in today’s world. The time window I used creatively, to think, write, read, paint, and think again.
Writing forced me to read, reading forced me to think, geometry and patterns everywhere made it easy to make a vocation in stock markets, which was a pattern manufacturing machine, every piece of information had numerous facets, that saw a swarm of investors, betting on every facet of how that information will enter the ring, deliver a knockout or be knocked out. A noisy celebration. A deluge of information that is not for the meek. You could not lose just your shirt, your house, but your sanity. The lesson of the mirage I learnt, kept me detached as I kept my head above my shoulders, like Odysseus, I kept going through the siren valley with wax in my ears, seeking Science in the madness of wealth. The wealth which caused people to jump from the stock exchange floor, the wealth that became addictive, a wealth that turned out to be a mirage, sucking in time like a black hole, with nothing to show in the end. Knowing the Mirage gave me a purpose, to continue learning, without getting stuck in the allure, as if the reward was the end of the game called understanding the architecture of complexity. The aim was still to be an architect.
From the school in Delhi to the business school in Mumbai needed adapting. The scales changed. I remember one of my business school colleagues Patrick during a conversation told me how the Don Bosco school next to our Business School at the Khalsa College premises had a "humungous" park. The excitement about green patches or large green patches was a common theme between us but I could not measure his excitement till the time I stepped with him on the other side of the road to enter the Don Bosco premises to see that the size which excited him was a modest size for me coming from Delhi. Nodding at him with bright eyes, I concurred, not to dampen his spirit, but it drove home a point about how context made us look at things differently. The context formulated in time, with culture, with experiences, changes everything about human responses, the degree of excitement for each of us was so different.
Human behavior, as unpredictable as a mirage, results from the complex interplay of convex (u shaped) and concave (n shaped) patterns in our actions. Like a mirage bending light, our behaviors shift unpredictably. Convexity in human actions can lead to rapid escalations, as seen in intense emotional responses or swift trend adoption. Conversely, concavity reflects diminishing reactions over time, like the principle of diminishing returns. These patterns intricately intertwine, creating a complex dance of increasing and decreasing responses, echoing the formation of a mirage. This dynamic blend of behaviors complicates the understanding and prediction of human actions, presenting a challenge as intriguing as unraveling a mirage's mystery.
Detachment is a researcher’s gift, especially if it is about interpreting mass psychology. Another incident in 1996, the first day at Business School in Mumbai, after a gruelling fight of group discussions and interviews, when it all seemed that the world of finance was going to unravel and when a rookie felt he was going to conquer the world. The dean announced that to open the batch of 1996-98 they had planned some ice breakers for us. One was a role-play of the trading floor where groups were made to interact on incoming news. I had never seen a trading floor and felt so much in awe of my colleagues, who grew up with their families and friends in the "stock exchange culture". It did not take much time to simulate a maddening floor, trading frantically, a real theatre, while I stood there lost, as a villager, first time in a big city. My convexity from the Don Bosco field incident suddenly transformed into a concave flagging moment. I was still that child decomposing the moment, frozen in my tracks, listening, re-reading, overcoming my lack of experience, picking myself up, observing, and starting again. I had no idea then about the world where the skill to read this noise was with less than 1% of the elite minds. I did not know how the simplicity of indexed investment would become a trend. I was clueless about my future as a man who would challenge the market design, less than two decades later. The mirage and the science in it kept me glued to my path.
Just like human behavior, the information created by mankind bends to the will of the curvature. Just like light had no will, Information was spineless and converged and diverged on the whims of an undiscovered mechanism. What society saw was the mirage of wealth, while the reality was fleeting. Information was just another object with no life of its own, but a proxy at the capriciousness of a phenomenon.
Researchers came and went, a few earning Nobel for seeing its relevance and a few for discovering its irrelevance, but a few in the search of the engine that drove the mirage. Equipped by my lack of knowledge, I jumped into the world of stock markets in June 2000, unaware of the mistakes I would make, and the highs and lows that would happen as my life will go through its mirages, but then the Science kept me on track.
Allow an underdog and give him a data machine called a stock market to churn out something, he will weave the wool into a crochet. Markets need imagination more than mathematics because mathematics is one tool, a multi-dimensional object needs more than a toolbox, it needs creativity. That’s what happened to me as I pulled the data into his machine and started creating pictures of butterflies with wings, understanding how and when they flap their wings, and how they flit, and create tornadoes. The deterministic disorder was a name given by mathematicians to chaos, a theory touted as the biggest scientific breakthrough of the twenty-first century because the scientific advances were limited to the level of seeing a pattern not understanding what formed those patterns. Chaos was the mirage of the Scientific world, which did not understand why Chaos was magically connected to three, what drove nature to create fractal geometry, and where the demons came from.
Being an underdog always helped. The society does not lose money betting on you. You are not held to a higher standard. Your competition is with yourself. You move at your pace, but as you progress, you get courage. New experiences help. The learning kicks in. The confidence increases. The depth gives gravity because you remember how Science helped you all the way from the shy drummer, to a man who lived through his mirages and did not drown in them. This is when you break the ceiling. The moment for me was with Mandelbrot. The mathematician credited for the chaos theory. The man who gave us fractal mathematics. The man who was worshiped as one of the biggest mathematicians of the 21st century. Mandelbrot lived in a mirage, a mirage created by geometry, lacking a mechanism. He famously said, there is no law, and there is nothing beyond fractal geometry. I challenged him in a 2010 paper.
Fractal geometry, seen in intricate patterns in nature like snowflakes or tree branches, is shaped by the interplay of convex and concave curves, or the way surfaces bend outward or inward. These natural fractals form through processes where similar patterns repeat at different sizes – think of the way branches split off a tree, each smaller branch resembling the shape of the whole tree. This repetition of curved shapes, driven by natural growth and environmental forces like water flow or wind, creates the mesmerizing and complex patterns we see in leaves, mountains, river networks, and other natural formations. These patterns, which might look random at first glance, follow a sort of hidden order where nature uses curves and bends at various scales to build the beautiful and functional structures we see all around us. He failed to asked many questions like what was beyond power law or what kind of mechanisms drove curvature.
The only paper that I have read illustrating a mechanism of curvature in action was written by a Nobel laureate. William Sharpe, and his Co-author Andre F Perold, in the paper “Dynamic Strategies for Asset Allocation", focussed on stock market investing seen as concave and convex payoff curves. The paper highlighted how investment strategies respond differently under varying market conditions. The concave strategy, where investors buy more stocks as prices fall, tends to excel in flat but oscillating markets but offers limited protection in downtrends and underperforms in rising markets. On the other hand, the convex strategy, involving selling stocks as they decline, provides better protection in down markets and excels in upturns but struggles in stable, oscillating markets.
This emphasis on curvature over the content of information reveals a critical insight: it's not just the raw data or news that matters in investing, but rather the context in which this information is used. The market's response to various strategies can significantly affect its volatility and stability, underscoring that understanding the dynamics of market movements and investor behavior is often more crucial than the information itself. This approach indicates that successful investing relies more on understanding how different strategies interact with market conditions rather than solely on the informational content.
Even the Artificial Intelligence machines of today need an understanding of mechanisms that create curvature. Artificial Intelligence (AI), much like a traveler deceived by a desert mirage, sometimes struggles with its own illusions when navigating the complex world of data and decision-making. These AI 'mirages' occur because the underlying algorithms must traverse a landscape filled with peaks, valleys, and plateaus – metaphorically speaking. This landscape represents the various possible solutions to a problem, and the goal is to find the best one. However, just as a mirage misleads by bending light, the complex curvatures in this solution landscape can mislead AI algorithms, making it hard for them to distinguish between good and bad solutions. The 'curvatures' here represent the intricate, often nonlinear patterns and relationships within the data. For AI to become more reliable and effective, it needs to develop a foundational understanding of these mechanisms of curvature – essentially learning to see through the mirages to grasp the true nature of the data and make better decisions.
My journey to unravel the 'curved mirage' led me through a long, intensive process of conceptualizing, testing, and training machines to navigate the labyrinth of information complexity. This endeavor has led me to a stark realization: human comprehension often falters in the face of the ineffable complexities of the world. In the realm of investing, this vulnerability underscores the necessity for machine augmentation.
The era of making investment decisions based solely on newspaper insights is obsolete. We always existed in a world governed by natural mechanisms that not only thrived on chaos but also perpetuated because of it. Elements such as curvatures, statistical distributions, and probabilities are mere offshoots of these underlying mechanisms. To truly understand and interpret the mirage that confronts us, one must delve into the core - the mechanism itself - rather than getting sidetracked by the mirage of probabilities it manifests.