Maths, Mechanics & Eureka

When we study the history of science, specifically physics, we find that a good idea simultaneously existed in various places. This suggests it may be better not to overemphasize a person for the origin of an idea. If we focus on the context, utility, and exchange of ideas, we get a broader picture of scientific ideas.
This approach creates a spatio-temporal network, an interesting way to view the historical evolution of ideas across the humanities, space, and time. People, ideas, and technologies collectively progress the frontiers of science in various places at different times. In that sense, science, including physics, is a global human endeavor.
This is evident when we look into the history of mechanics from ancient times until now. Mechanics is a fundamental sub-discipline of physics and has a strong connection to mathematics and engineering. It has evolved with logical reasoning and understanding of natural phenomena.

Engineering structures, which humanity has long been interested in, have played a significant role. Mechanics has been the playground of philosophers, scientists, and engineers. The questions it raised led to new thinking and new technologies.
Mechanics offers a way to understand and engineer the universe. In this episode, we explore its links to mathematics, engineering, and key thinkers.

The importance of counting.

Counting has played a critical role in human life for a long time. In fact, we use fingers as a counting device, and this has been a very powerful tool for a significant period. So much so that it has been utilized to keep a tally of small numbers, which can be counted and analyzed in everyday life. Interestingly, as the numbers became larger, one had to externalize the counting process, and in ancient times, people had very creative methods to count objects. One of the fascinating aspects of counting was to use bones. Yes, bones were used as platforms on which marks were created, and these marks were utilized as the counts in a tally.

**Images of Ishango bones with periodic marks on its surface.**

One of the pieces of evidence for such behavior was found in the Congo Basin in a place called Ishango. The bones that were found are dated around 9000 BCE to 6500 BCE (although a big debate is going on regarding the dates, with some putting it beyond 20,000 BCE), on which marks have been identified that look like counts registered on the platform. Indeed, it is quite fascinating to see how people used various devices to enumerate objects.
If you ask any child what is 1 plus 1, they will be able to say that it is 2. This may sound trivial, but the concept of addition itself was not in the historical context. To consider two numbers and add them together needs a certain degree of abstraction, which has been part of the evolution of mathematics since ancient times. A variety of counting methods have been devised in different civilizations, which have added a kind of flavour to the history of mathematics.

Importantly, language has played a critical role in facilitating a vocabulary for counting. Depending upon the syntax and the order of letters, numbers have been represented in a variety of ways across space and time of human history.

In this context, let me emphasize two important aspects of numbers and their representation. The first aspect is related to the positional notation. What is it? Let me give you an example. If you take numbers 24 and 42, the position of the number 4 is different. In 24, the number 4 is in the unit’s place, and in the number 42, it is in the tens place. So, the position of the number determines its value, and this is an important concept that civilizations have thought about and utilized in their counting systems.
The second aspect is the concept of zero. Let me give an example. If you consider number 007 and compare it to 700, obviously, depending on the location of the zero, the value of the number drastically changes. But what is intriguing is that various civilizations used a variety of symbols, such as dots, circles, and empty spaces, to represent nothingness.
What is not trivial is the recognition of zero as a number by itself. This needs a leap of thought because it must be an abstraction of a concept where the nothingness has to be associated with a number, and hence the association to zero. It was Brahmagupta around the year 628 CE in his Brahma Sputa Siddhanta that we first encountered the concept of zero as a number. This is indeed one of the great achievements because, without zero as a number, one cannot build mathematical concepts. It is both fundamental and profound. It has further played a critical role in laying the foundation of mathematics as we know it today.

02 Geometry

Now, let’s look at the connection between geometry and physics. Across various civilizations, the size and shapes of objects were curiosities, and understanding them was an important necessity for everyday life. Given that objects in the natural and artificial world come in various sizes and shapes, it was necessary to understand them for further utilization.

In ancient Greece, Thales of Miletus was one of the earliest to use a mathematical way of thinking and to formulate a framework to understand nature through logical analysis and not based on faith or myths. This thinking further percolated to all the subsequent philosophers, and that included a person named Pythagoras. Pythagoras’ life and times are not as well documented as those of other Greek philosophers, but by some estimates, he was supposed to have lived around 570 BCE to 495 BCE.

During that time, the Greeks had colonized various parts of Europe, and this included some parts of Italy. Pythagoras remained in that colonized part of Greece, where he had established a school, which was also interestingly a mythical cult. His school hardly shared any information with the outside world, and this is probably one of the reasons why there is very little known about Pythagoras’ life and times.

In fact, none of his writing has survived to date, and most of the information that we get is from indirect sources. However, the attribution of some scholars to Pythagoras’ work needs attention. Interestingly, Pythagoras did some experiments and tried to understand the production of sound.

He made an interesting connection to the strings and the pleasant sound that they produce. He hypothesized that there is a rational number of steps in strings that led to the pleasant sound. This thinking was further extrapolated to rational numbers, and that became an interesting connection. Pythagoras has also been attributed to have thought about astronomical objects.

Earth being spherical is one of the concepts that he had thought about and played a role in rationalizing the distances of objects such as the Sun, Moon, and planets. This kind of methodical thinking further influenced many Greek schools of thought, and this included the famous Plato’s Academy. Plato himself was a renowned philosopher, but he had a very strong inclination towards mathematics.

He also came up with the five solids and the four elements, which played a critical role in his interpreting of the natural world based on them. But it is in 300 BCE that we see an epoch in geometry in the form of Euclid’s Elements. Euclid of Alexandria was one of the great mathematicians whose work is still of significant relevance today.

Euclid, like many of his predecessors, had a life immersed in the ancient university system—in his case, the University of Alexandria. Again, not much is known about Euclid’s life and times, except for the fact that he wrote 13 volumes of his magnificent book titled Elements.

This book has turned out to be the foundation of mathematics and has played a critical role in creating a new worldview both for natural scientists and abstract mathematicians. Most of what we know today about Euclid is thanks to a Greek commentator, Theon of Alexandria, who lived roughly 700 years after Euclid. He played a critical role in interpreting and highlighting the works of Euclid, and going forward in time, Arabs took a keen interest in Euclid’s geometry and incorporated it into their education and research.

Euclid’s work on geometry is a masterpiece, which has 13 books in a series and contains 465 theorems. Each of them contains foundational knowledge about geometrical entities, including lines, angles, shapes, and solid geometries that past people had discussed. It is a tribute to his knowledge that Euclid’s Elements is still in print, and this shows how much the impact of Euclid has been over the centuries.

Importantly, the geometrical way of thinking has deeply influenced physics, along with the principle of counting and geometry. Physics, armed with mathematics, became an important way of looking at natural life in ancient times. This way of thinking further influenced another remarkable thinker named Archimedes of Syracuse.

If you want to think about a remarkable person who has deeply contributed to science and mathematics from ancient times, there is nobody better than Archimedes. Born in 287 BCE, Archimedes had a remarkable life because the number of things that are associated with him related to science, mathematics, and technology is probably unsurpassed compared to anybody else across the ages. Generally, when we talk about Archimedes, we associate him with the famous Eureka, where he probably ran naked in the excitement of discovering a specific concept related to buoyancy.

Of course, this might be altogether a myth, but the science that Archimedes did was indeed real and outstanding. He contributed to various areas in science, including mechanics, hydrodynamics, optics, engineering, and mathematics in both the pure and applied forms. We know about his achievements thanks to nine ancient Greek treatises, which give us a glimpse of his work.

An important aspect related to mechanics is the fact that in the ancient age, one can divide the contributions in terms of statics and dynamics. The dynamics aspect was mainly related to thinking driven by Aristotle and his school, which has turned out to be kind of incorrect from the modern viewpoint. But when it comes to statics, Archimedes had a very important role to play, and many of the discoveries he made have turned out to be correct and highly useful.

Related to statics, he wrote many interesting treatises, one of them being On the Equilibrium of Planes. In this book, he talks about the concept of the lever and utilizes the concept of the center of gravity. It is in this treatise where the concept of the center of gravity is used to understand various geometries, and he discusses the center of gravity of different geometrical objects.

Another important book related to Archimedes is On Floating Bodies. In this book, he discusses buoyancy and gives an important hypothesis to understand bodies immersed in a fluid. His discoveries were very critical in naval architecture.

Archimedes was not only an outstanding scientist but also an excellent engineer. He designed a water pump in which a hollow cylinder had a rotating helical shaft, which could pump water efficiently. This is usually called the Archimedes pump, and it has been used even to date.

Archimedes also contributed to the development of mathematics. He wrote On the Sphere and Cylinder and The Method, used for mechanical analysis.

One has to wonder whether he was one single person or many. Steven Strogatz’s book related to calculus, titled Infinite Powers: How Calculus Reveals the Secrets of the Universe, has a beautiful description of Archimedes’ contribution to understanding curves, including the circle and the determination of pi in an ingenious way. The logical process Archimedes used was unsurpassed for his time, and his contributions to science are among the most important from the ancient age.

There are also interesting stories related to his work, and one of them is called the Archimedes Palimpsest. A palimpsest is a technique in which one writes something, erases it, and rewrites on the same surface. In 1906, a Danish professor, Johan Heiberg, visited Constantinople to examine documents related to prayers, dated from the 13th century. To his surprise, it turned out that there was an underlying document beneath that prayer text, which was Archimedes’ writing.

It is truly outstanding that someone could discover such an important document after such a long time, and that’s another reason why one should do archival work—because you never know what kind of jewels one can discover. Archimedes contributed to various aspects of science, mathematics, and technology, but it is also vital to appreciate that he used a logical way of thinking. Such thinking had a deep influence on people who followed him, and even today, the process of his analysis stands up to scholarly scrutiny. It’s critical for us to realize that such people play a key role in spreading important ideas in science, in physics, and, in this case, mechanics.

Archimedes will surely be remembered as one of the greatest human beings who propelled human scientific thought. The legacy of Archimedes has been kept alive by introducing his figure on the Fields Medal, a major prize in mathematics. It’s considered the Nobel Prize equivalent in mathematics.

On the medal, there is an engraving with the quote: “Rise above oneself and grasp the world.” It is a great quotation to not only engrave on a medal but also to follow in letter and spirit.

With the same spirit to rise and grasp the world, we will explore the physics of mechanics going forward.

References:

GoogleTalksArchive, dir. 2012. The Archimedes Palimpsest. https://www.youtube.com/watch?v=Xe9uQVGkz9k.

Heath, T. L. 1897. The Works Of Archimedes. Cambridge University Press. http://archive.org/details/worksofarchimede029517mbp.

“Ishango Bone.” 2025. In Wikipedia. https://en.wikipedia.org/w/index.php?title=Ishango_bone&oldid=1280156982.

“Mathematics in India – Bhāvanā.” n.d. Accessed April 20, 2025. https://bhavana.org.in/mathematics-in-india-6/.

Padmanabhan, Thanu, and Vasanthi Padmanabhan. 2019. The Dawn of Science: Glimpses from History for the Curious Mind. Springer.

Stein, Sherman. 1999. Archimedes: What Did He Do Beside Cry Eureka?

Strogatz, Steven. 2019. Infinite Powers: How Calculus Reveals the Secrets of the Universe. Boston New York: Mariner Books.

Wu, Shiyue, and Francesco Perono Cacciafoco. 2024. “Understanding through the Numbers: Number Systems, Their Evolution, and Their Perception among Kula People from Alor Island, Southeastern Indonesia.” Humans 4 (1): 34–49. https://doi.org/10.3390/humans4010003.

Rene Dugas. 1955. A History Of Mechanics. http://archive.org/details/ahistoryofmechanics_201907.

April 22, 2025

Floral colours, CV Raman and illustrations

In the 1960s, C. V. Raman wrote a series of papers on floral colors and the physiology of vision. In there, he was very interested in the origin of colors from various different flowers. This was also motivated by his fascination with optics and natural colors in vegetation. Specifically, during that era, he had a large garden at his institution and he was deeply immersed in understanding the origin of the colors from these wonderful living creatures.

By using his knowledge of spectroscopy and the chemistry of pigments, he was able to explore some of the spectral features of the floral colors. The diagrams that you are seeing are illustrations from his paper published in 1963.

As you can observe, these illustrations are beautifully created. I don’t know whether Raman himself drew these pictures, but one should really appreciate the artist who has created them.

In a broader sense, it also indicates two important aspects. The first is that Raman was deeply motivated by natural phenomena. His intuition of optics helped him to understand the origins of a variety of natural optical processes. Spectroscopy was a crucial element in all the things that he did. The second aspect is that, in a deeper sense, aesthetics is interwoven with the pursuit of science and Raman’s work, especially towards the later part of his life, showcased it.

There is a fascinating video conversation with Richard Feynman where he describes the appreciation of the beauty of flowers by a scientist. Raman’s appreciation of beauty is close to what Feynman is describing in the video.

C. V. Raman was a curious person. He had a deep inclination to explore natural phenomena, using the knowledge and tools he had accumulated over several decades. In that sense, he was a scientist driven by curiosity before and after his Nobel prize.

Next time when you see a flower, remember that it is a creature of beauty and science merged together.

ps: blogpost in audio-visual format

April 9, 2025

A Global History of Physics

Welcome to essays in A Global History of Physics, where I discuss people, ideas, philosophy and technology involved in the development of physics across the world

Some aspects of the essays are published in journals and magazines, and some are written as part of my podcast. The intention is to eventually collate them into book(s). You are free to use it for educational and non-commercial purposes with attribution.

March 25, 2025

Engineering Civilizations

1. Introduction:

Welcome to essays in the global history of physics, where we discuss people, ideas and technology connected to physics in the historical context. Let me explain why the global history of physics is important. Physics, as you know, is one of the central disciplines of natural sciences from which various branches of science and technology have emanated.

Understanding the evolution of such an important output of human thought is imperative. It not only gives us a glimpse of how people over the ages have thought about ideas but also reveals how those ideas are connected to philosophical and technological questions that were of interest to people in the past. In fact, it is that dual connection of physics to philosophy and technology that makes it interesting, important and intellectually rich.

This series of essays aims to capture the historical evolution of physics by paying attention to the global evolution of the subject. In doing so, we will visit the people from the past and learn about their ideas and technologies that eventually led to the topics within physics.

Here, I need to emphasize the global aspect of history. Conventionally, the history of science as a discipline has been criticized for being Eurocentric in nature. In recent years, as highlighted by James Poskett’s excellent book Horizons (1), there has been an emerging scholarship in the history of science to reveal a decentralized evolution of science and that includes some developments in physics itself. In these essays, I will give credit to people, ideas and technology irrespective of their origin and emphasize curiosity as a basic human instinct prevalent across space and time.

This thought reinforces science, specifically physics, as a global intellectual pursuit over many ages and times. The way I will do this is to take on a particular branch of physics and discuss its evolution in chronological order. Of course, my aim is not to cover everything that is known but to highlight some interesting developments in that field with attention to some interesting people, ideas, tools and technologies at the relevant place and time.

Such an exercise cannot be done in one single essay. So, I intend to cover the chronological evolution with a series of essays spanning all the branches of physics. Yes, it will be a long journey, and I hope you will accompany me in this one endeavor.

2. How a physical phenomenon is explained.

One starts with a concrete situation of a particular problem. Associated with this situation is a general law. One applies the general law to the situation in a logical manner and utilizes mathematical descriptions where precision is needed. This logical and mathematical description leads to an explanation witha concrete prediction. Observations must test this prediction. The ability to predict a future observation is one of the remarkable traits of science in general and physics in particular (2). It is through this ability to predict that one can envisage the utility of a physical concept. That utility forms the seed of development towards technology.

As you may observe, there is a nice connection between scientific inquiry and the eventual realization of technology. This connection is what makes science and technology go hand in hand. Importantly, this is one of the outstanding features of physics and historical explanation, as we intend to do in these essays, which will justify the claim.

This connection between science and technology is not a one-way coupling. In fact, many interesting questions in physics have emerged out of technological development across various eras of human history. This recognition of jugalbandhi between science and technology is at the heart of the essay series.

Physics has played a critical role in engineering civilization over the centuries. This role has been explicit in recent times, say around the last 300 years or so. But what is interesting is that inquiries in physical sciences have implicitly influenced the growth of a civilization.

This growth is not only materialistic but also intellectual in nature. Therefore, understanding the evolution of physics gives us a glimpse of the evolution of humankind. Of course, it may not be the complete picture, but at least we learn about people, ideas and technology that gave rise to the world that we identify as a physical, real entity.

3. Engineering Civilizations

Let us start with some ancient civilizations. The oldest tools used by humans were stones. In fact, the ‘Stone Age’ gets its name from this. According to archeological explorations, the earliest stone tools found in Lomekwi, Kenya, date back to 3.3 million years ago (3). This is the Paleolithic age, in which hunting and gathering were the main occupations of human beings. The stone tools found within India at Attirampakkam, a village close to Chennai in Tamil Nadu, date back to around 300 thousand years ago (4). From such archeological evidence, humans were acquainted with toolmaking long ago. Towards the Neolithic age, we also have evidence of pottery in civilizations, indicating a gradual change to farming and agricultural occupations that were assisted by toolmaking based on clay and fire. I need to emphasize that knowledge of these tools was handed over from one generation to another without a formal writing process. The oldest written record dates to around 3500 BCE in the form of a cuneiform script from Mesopotamian civilization, which is somewhere around present-day Iraq (2). Such writing itself needs small tools, such as a stylus and a platform, such as clay, to imprint the written text. Well before any form of writing became part of any civilization, tools and structures had to be invented.

An interesting element of the Indus Valley Civilization was that they used measurement scales (5). In the Harappan museum, one can find a linear scale made of a shell that has nine divisions with a small circle engraved on it. A periodically divided scale indicates a quantitative measure of length and indicates the sophistication of thought, both from device and utility viewpoints.

A remarkable aspect of this scale is the utility of the shell as the material. Given that shells are robust and can sustain large temperature fluctuations, they make for an excellent choice as a material for scale. One must really marvel at how humans came to the point where such a design was implemented without modern tools, scientific knowledge or a written script.

To emphasize this fact, one of the earliest texts from the Indus Valley civilization dates to around 3000 BCE. Of course, in this case, the script is yet to be deciphered completely. What is interesting is that ancient civilizations achieved remarkable engineering feats even before any formalization of scientific disciplines, including physics, came into the picture.

This is because for civilization to survive, grow and sustain, they had to manage their natural resources and construct structures. These tasks would not have been feasible without an intricate understanding of how things work and how they can be used to construct physical structures. This can be achieved only through certain tools and techniques.

The civilizations would not have evolved without this engineering and, therefore, deserve credit as a human achievement. These tools and techniques have implicit physics in them. Of course, there was no formal discipline called physics until around 300 BCE, but the empirical knowledge about tools and techniques for construction was already present long before physics became a formal discipline of science.

4. The role of philosophy

As human beings cultivated crops, their mobility was confined to a smaller region compared to the hunter-gatherer era. This settlement at a place gave humans leisure to think and wonder about nature. As a consequence of this thinking, philosophical thoughts emerged (6).

Questions pertaining to philosophy, such as what life is and how humans live and interact with nature, occupied human minds. This exploratory era also gave rise to the need to understand the world, explore nature and harness it. Inquiries pertaining to the motion of celestial objects and that of common living and non-living things captured the attention.

To understand the intellectual foundations of physics, one needs to understand its connection to philosophy in general and philosophy of science in particular. The connection between reality and physical law is through an abstract formulation (2). Reality has its own complications, and a physical law retains only a small set of the complications that are evident in reality.

Although this connection between reality and a physical law looks to be straightforward, historically, there has been a large intellectual struggle to come to this point. It has not been an obvious task to connect reality to physical laws. And by studying the history of physics, it is evident that the route has been anything but smooth.

Another important aspect I need to emphasize is how reality becomes a raw material for scientific investigation. In essence, reality provides a kind of formless raw material on which physical laws can be formulated. These physical laws are drawn from a simplified structure of reality, and there is a process of encoding reality in a language that is amenable to scientific investigation.

This process of going from a multi-faceted reality to a slightly more precise physical law is done through assumptions, and these assumptions play a critical role. The pathway from reality to general laws has been through inductive methods, at least in the historical context. In the inductive method, there is an extrapolation from the finite to the general principles.

Based on certain observations in a concrete situation, one derives a general law. Now, the question is, how does one derive such a general law? This generalization is based on a logical process, and one of the best tools to implement logical analysis is mathematics. This is where the role of mathematics becomes so important in physics. If one needs to go from a concrete, realistic situation to an abstract principle, one will have to utilize mathematical tools such as geometry to convert the reality into an abstract formulation. An important aspect of physics and science, in general, is that once this abstract formulation has been postulated, the physical law can be tested going forward. The results can be checked by performing observations, and these observations can confirm or reject the induced hypothesis.

When it comes to the observation, there are two elements. The first is the observed object, and the second is the observer themselves. The demarcation between the observer and the observed object seems trivial; historically, it has not been the case. Because the observed object can interact with the observer, the physical laws that are derived from such observations must ensure that the observers themselves are not perturbing the physical reality.

Also, the judgment of objectivity itself is a complex process because the criteria of truth have a social connection. This means what we call a factor of truth is closely connected to the social realities in which the observation is performed. This social connection brings in another layer of complication, and one must understand the philosophy behind these processes.

As you can see, formulating science and, in our case, physics has not been a trivial task, given that these philosophical questions must be addressed to get a satisfactory answer. Understanding and discriminating science from other forms of human activity has not been a trivial exercise either, but it is with the help of philosophy that progress has been made.

This also highlights the intricate connection between philosophy, physics, experimental observation and technological developments as a network of events that interact with each other. Each part of this network plays a critical role and, many times, feeds back important information in the process. Therefore, to understand physics, we need to not only appreciate the philosophical questions but also be aware of technological developments.

Because many of the developments in the realm of scientific philosophy were motivated by technology and vice versa, this is also the reason why the history of physics is so interesting. It brings together all these epistemological components into one single platform and creates an intellectual magic that has played a critical role in understanding nature and the universe, that which can be observed and, in some cases, that which cannot be observed.

So, how did ancient people think about a subject called physics? What were the initiating thoughts of philosophers that led to physics? If we want to address these questions, we need to pay attention to some of the philosophers who thought and wrote about science. Among them, one of the earliest to do so was Aristotle. In the next essay, we will discuss his physics.

References:

[1] J. Poskett, Horizons: A Global History of Science. Penguin UK, 2022.

[2] K. Simonyi, A Cultural History of Physics, 1st edition. Boca Raton, Fla: A K Peters/CRC Press, 2012.

[3] “Lomekwi Stone Tools: the oldest artifact in the world.” Accessed: Mar. 24, 2025. [Online]. Available: https://www.thearchaeologist.org/blog/lomekwi-stone-tools-the-oldest-artifact-in-the-world

[4] S. Pappu, Y. Gunnell, M. Taieb, J. Brugal, and Y. Touchard, “Excavations at the Palaeolithic Site of Attirampakkam, South India: Preliminary Findings,” Curr. Anthropol., vol. 44, no. 4, pp. 591–598, 2003, doi: 10.1086/377652.

[5] S. Guha, A History of India through 75 Objects. Hachette UK, 2022.

[6] P. Adamson, Classical Philosophy: A history of philosophy without any gaps, Volume 1. in A History of Philosophy. Oxford, New York: Oxford University Press, 2014.

March 25, 2025

Nobel is secondary

Many of the Nobel winners in science deserve the prize they get, but there are many deserving who do not make the list for various reasons, including sociology, geography & financial support. Using the Nobel prize as a benchmark of progress may lead to errors in the judgment of a country.

A better way to judge is to ask: how are science and technology in a country making lives better for the people of the country & the world? A better life includes both intellectual & material aspects. We, in India & the global south, can make progress if scientific thinking becomes prevalent in the everyday discourse of society, from family conversations to political debates. And prizes, by design, are exclusive. It is easier to exclude a country that is not scientific as no one cares in such a situation.

Scientific progress in a society is generally bottom-up. We have a large population of young people who should be more scientific in their worldview. If we have a large, scientifically oriented population, science and technological achievements become proportional.

If science-based intellectual & material progress is achieved, prizes will follow. But a Nobel should not be our primary goal. Better lives & better minds should be.

Everything flows from there.

March 20, 2025

All Episodes

Pratidhvani – Humanizing Science

(also on YouTube, Spotify, Apple podcast)

Namaste, Hola, & Welcome from G.V. Pavan Kumar.

Pratidhvani (ಪ್ರತಿಧ್ವನಿ/प्रतिध्वनि) means reflection or resonance (of sound). Here, the aim of the podcast is to resonate with knowledge & humanize science.
The podcast has two themes:
1) History & Philosophy of Physical Sciences & Technology,
2) Conversations with people related to their intellectual journey & themes mentioned in 1)
Below is the link to all the episodes. Italicized ones are solo episodes

March 12, 2025

FOLLOW THE MONEY – A useful model

Our world is a place with complex ideas superimposed on people with ever-changing attention. Complex ideas are complex because they depend on multiple parameters. If something changes in the world, then that change can occur due to multiple reasons.

Unlike a carefully designed physics experiment, there are too many ‘hidden variables’ in human life and behavior, especially when they act collectively. In such a situation, it is pertinent to search for models to understand the complex world. Models, by definition, capture the essence of a problem and do not represent the complete system. They are like maps, zoomed out, but very useful if you know their limitations. I keep searching for mental models that will help me understand the complex world in which I live, interact, and comprehend.

Among many models, one of them that I use extensively is the follow-the-money model. This model explains some complex processes in a world where one does not have complete information about a problem.

Take, for example, the incentives to choose a research project. This is a task that as scientists, we need to do very often. In the process of choosing a project to work on, researchers have to factor in the possibility of that research being funded prior to the start of the project. This is critical for scientific research that is dependent on infrastructure, such as experimental sciences, including physics, chemistry, and biology. Inherently, as researchers, we tend to pick a topic that is at the interface of personal interest, competence, relevance, and financial viability.

The viability is an important element because sustained funding plays a critical role in our ability to address all the contours of a research project. Thus, as scientists, we need to follow the money and ask ourselves how our research can be adapted to the financial incentives that a society creates. A case in point is research areas such as AI, where many people are aware of its potential and, hence, support from society and an opportunity to utilize the available incentive.

It is important for the public to be aware of this aspect of research where the financial incentive to execute a project plays a role in the choice of the project itself. The downstream of this incentive is the opportunity to employ more people. This means large funding projects and programs attract more researchers. More people in the research area generate more data, and more data, hopefully, will result in more knowledge in the chosen research area. This shows how financial incentives play a critical role in propelling a research area. In that sense, the ‘follow the money’ model has a direct correlation with more researchers flocking towards a research area.

The downside of this way of functioning is that it skews people towards certain areas of research at the cost of another research area which may not find financial support from the society. This is a topic that is generally not discussed in science classes, especially at the undergraduate and research level but I think we should discuss with students about this asymmetry as their futures are dependent on financial support that they can garner.

Broadening the scope further, the ‘follow the money’ model is useful to understand why a certain global trend rises or falls. A contemporary global upheaval is the situation of war in Ukraine and Gaza. At first sight, it looks like these wars are based on ideologies, but a closer look reveals that these wars cannot be fought without financial support. Such underpinning of the money running the war reveals patterns in geopolitics that are otherwise not easy to grasp.

Ideologies have the power to act as vehicles of human change, but these vehicles cannot be propelled without the metaphorical fuel – that is, money. The ‘follow-the-money’ model can show some implicit motivation and showcase how ideologies can be used as trojan horses to gain financial superiority either through captured resources or through showcasing the ability to capture that resource. Following money is also a very powerful and useful model for understanding many cultural, sociological and political evolution, even in a complex country like India and other South Asian countries. I leave it as an intellectual assignment for people who want to explore it 😊. You will be surprised how effective it can be in explaining many complex issues, provided we know the limitations of the model.

As I mentioned earlier, a model is like a map. It is limited by resolution, the dimension and the viewpoint. But they are useful for navigating a complex world.

December 8, 2024

Conversation with Ayan Banerjee

Ayan is an experimental optical physicist and a Professor at IISER Kolkata: https://www.iiserkol.ac.in/~ayan/group_leader.html.

He is also a playwriter, theatre actor and a mentor to many science and arts enthusiasts.

What drives him to do all these things? We discuss this and many other things in this episode.

References:

“Group Leader | Light-Matter Lab.” Accessed December 2, 2024. https://www.iiserkol.ac.in/~ayan/group_leader.html.
“IISER Kolkata – Ayan.” Accessed December 2, 2024. https://www.iiserkol.ac.in/web/en/people/faculty/dps/ayan/.
“Ayan Banerjee – Professor – Indian Institute of Science Education & Research (IISER), Kolkata | LinkedIn.” Accessed December 2, 2024. https://in.linkedin.com/in/ayan-banerjee-3034208.
Department of Physical Sciences (DPS), IISER Kolkata, 2022. https://www.youtube.com/watch?v=vgv7iODxYTY.
“Department of Physical Sciences : Home.” Accessed December 2, 2024. https://physics.iiserkol.ac.in/.
Ayan Banerjee. Accessed December 2, 2024. https://www.facebook.com/ayan.banerjee.5895.
“‪Ayan Banerjee – ‪Google Scholar.” Accessed December 2, 2024. https://scholar.google.co.in/citations?user=GQo7yG4AAAAJ&hl=en.
Gupta, Subhasish Dutta, Nirmalya Ghosh, and Ayan Banerjee. Wave Optics: Basic Concepts and Contemporary Trends. CRC Press, 2015.
Haldar, Arijit, Sambit Bikas Pal, Basudev Roy, S. Dutta Gupta, and Ayan Banerjee. “Self-Assembly of Microparticles in Stable Ring Structures in an Optical Trap.” Physical Review A 85, no. 3 (March 27, 2012): 033832. https://doi.org/10.1103/PhysRevA.85.033832.
“Indian Institute of Science.” Accessed December 2, 2024. https://iisc.ac.in/events/remembering-prof-vasant-natarajan-1965-2021/.
“LML.” Accessed December 2, 2024. https://sites.google.com/iiserkol.ac.in/light-matter-lab-iiserk/.
“LML – Physics of Micro-Bubbles.” Accessed December 2, 2024. https://sites.google.com/iiserkol.ac.in/light-matter-lab-iiserk/research/physics-of-micro-bubbles.
Network, N. F. N. “Theatre At IISER-K Against Misinterpretation of Science And Superstition,” January 17, 2019. https://newsfromnadia.in/theatre-at-iiser-k-against-misinterpretation-of-science-and-superstition/.
“Self-Assembly of Mesoscopic Materials To Form Controlled and Continuous Patterns by Thermo-Optically Manipulated Laser Induced Microbubbles | Langmuir.” Accessed December 2, 2024. https://pubs.acs.org/doi/full/10.1021/la402777e.
X (formerly Twitter). “Ayan Banerjee (@ayanban7) / X,” November 26, 2024. https://x.com/ayanban7.

December 4, 2024

Conversation with Bhaskaran Muralidharan

Bhaskaran is an Electrical Engineer & a Professor at the Indian Institute of Technology Bombay: https://cnqt-group.org/?page_id=25

He is a quantum transport theorist, musician and long-distance runner.

We explore his intellectual, musical and running journey.

Also, don’t miss a segment on Bhaskaran playing the piano.

References:

“Bhaskaran Muralidharan [Department of Electrical Engineering IIT Bombay].” Accessed November 26, 2024. https://www.ee.iitb.ac.in/wiki/faculty/bm.
“‪Bhaskaran Muralidharan – ‪Google Scholar.” Accessed November 26, 2024. https://scholar.google.co.in/citations?user=PWFVEKIAAAAJ&hl=en.
“Group Members – CNQT @ IIT Bombay.” Accessed November 26, 2024. https://cnqt-group.org/?page_id=25.
Muralidharan, B., A. W. Ghosh, and S. Datta. “Probing Electronic Excitations in Molecular Conduction.” Physical Review B 73, no. 15 (April 10, 2006): 155410. https://doi.org/10.1103/PhysRevB.73.155410.
Prof. Bhaskaran Muralidharan || Electrical Engineering || EESA IIT Bombay, 2021. https://www.youtube.com/watch?v=O8fFdb3-NRQ.