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  • The Long History of Free Will: From Greece to India to China

    The Long History of Free Will: From Greece to India to China

    Introduction

    Since the beginning of human history, one question has always troubled human cognition and, in turn, human philosophy: Does free will exist? For millennia, scholars, thinkers, philosophers, and theologians have sought to answer the question in their own way, considering their time and place. In this blog, we discuss various theories regarding free will from twenty ancient philosophy schools across Greece, India, and China. We also discuss their basic ethics, metaphysics, and epistemology, which helped determine their stance on free will.

    Chapter 1: Platonism

    Platonism was the ancient Greek school, based on Plato’s teachings. They believed that moral goodness comes from aligning the soul with the good. They considered the soul to be eternal and indestructible, while the material world was considered to be continuously changing.  For them, the ultimate virtue was knowledge, while the real evil was ignorance. According to them, free will depended on recollection of knowledge. The more the soul makes a decision based on knowledge and reason, the more freedom it has over its will. In short, free will increases with rational thinking. Although officially, the school ended, their idea of free will shaped early Christian theology, creating an amalgamation of idealism and moral realism.

    Chapter 2: Aristotelianism

    Aristotelians gave more priority to practical knowledge over reason and induction. For them, the substances were composites of form and matter, and causes explained changes. Thus, they believed that humans have complete free will, as they could make informed choices, assisted by rational thinking. Aristotelianism gave the foundation to modern Western ethics as well as many concepts within psychology and psychoanalysis.

    Chapter 3: Stoicism

    Stoicism was an hellenistic school, which considered living according to reason and nature as the highest virtue. According to them, everything unfolded necessarily, as the cosmos was governed by Logos (a kind of divine universal reason). The external events were already determined, but the inner ascent based on knowledge gained was free, thus giving assurance to a limited free will.  Stoicism, centuries later, strongly influenced modern CBT and psychology.

    Chapter 4: Epicureanism

    The Epicureans were the descendants of the ancient Greek Atomist school. They considered that the world is made of atoms, roaming freely in space, thus denying an overlooking God. They believed pleasure (absence of pain) to be the highest virtue and the sensory experience to be the foundation of knowledge as free will. Since the Epicureans defined the world to be independent of any external forces, they advocated for complete free will, breaking strict determinism. Epicurean thoughts can be found within modern secular ethics and materialism, particularly in the Western world.

    Chapter 5: Skepticism

    The Skeptics were rationalists with no claim about either an ultimate reality or an overlooking power. They considered knowledge to be always contestable and preached living life pragmatically. The skeptic school believed in free will and avoided any theory regarding predestination. Skepticism shaped scientific reason and critical thinking, even centuries after the school formally ceased to exist.

    Chapter 6: Cynicism

    The Cynic school had a radical virtue that rejected any type of convention and promoted living according to nature in a minimalistic and anti-speculative way. They believed that truth is lived, not theorized, and intellectual systems corrupt authenticity. When it comes to free will, they avoided answering that directly and considered true freedom came from detachment from social and psychological constraints. Cynic values are today found in some form within anti-consumerism and moral minimalism.

    Chapter 7: Neoplatonism

    It was a school that rose at the end of the Hellenistic period and influenced the Roman Empire after Greece became a colony of Rome. They were the believer of a hierarchical world. The highest of the realities was the One, an ultimate reality beyond thought, followed by the Intellect or Nous, where thoughts and ideas thrived. The third level was that of the Soul or Psyche, which animated the world and acted as a bridge between the higher and the lower levels. The final bottommost level was the material world, a gross world filled with imperfections changing continuously. The school gave intuition priority over reasoning, and believed that the soul is free to turn inward or outward to the material or the intelligible realms. Neoplatonism greatly affected Western mysticism as well as medieval and early-modern philosophy.

    Chapter 8: Sāṁkhya-Yoga

    Sāṁkhya and Yoga were two of the oldest Indian philosophy schools. The twin schools were dualistic in nature, believing the world is made of Puruṣa (consciousness) and Prakṛti (nature). They considered liberation as a result of acquiring discrimination between consciousness and matter. To them, although psychological processes were determined, they believed in limited free will through the process of non-identification and detachment. The schools gave birth to meditation techniques for various Eastern traditions and also contributed to the modern mind-body dualism debates.

    Chapter 9: Nyāya-Vaiśeṣika

    They were the proponents of ancient realist pluralism. The Nyāya school used highly developed logic with great emphasis on inference and debate, while Vaiśeṣika believed the world is made up of smaller indivisible particles called Anu, thus both school rejecting a creator God. They believed that humans are moral agents capable of choice, and their karma (action) determines the karmaphala (outcomes). The schools, although nearly extinct today, became the foundation of logic and epistemology for the Indian religions.

    Chapter 10: Mīmāṁsā

    It was a non-theistic school that emphasizes dharma (righteous conduct) and rituals over everything else. The followers gave importance to language and testimony (Vedas) as the authoritative sources of knowledge. They believed in limited free will, as they debated that will is mostly determined by the moral and righteous act, thus limiting free will to a lower importance. Mīmāṁsā influenced the later Hindu rituals as well as the rule-based ethics system.

    Chapter 11: Advaita Vedānta

    The Indian non-dual philosophy school and tradition, Advaita Vedānta, believes that only Brahman (collective consciousness) is real, while the entire universe is merely a reflected/limited projection of it because of Māyā (cosmic illusion). For the Advaitins, avidyā (ignorance) causes bondage, resulting in the debate of whether free will exists or not. But acquiring self-knowledge (jñāna) makes one realise that everything is Brahman, so the question of free will becomes somewhat meaningless. The Advaita Vedantā school still exists today and strongly influences consciousness studies and non-dual philosophies all over the world.

    Chapter 12: Theistic Vedānta 

    All the other Vedānta schools (Vedānta means that which ends or completes the Vedas, i.e., the Upaniṣads, which all the Vedantins follow) except Advaita Vedanta are theistic in nature, i.e., they believe in a personal God with qualities or attributes. Important schools like Viśiṣṭādvaita Vedanta and Dvaita Vedanta believed in a creator God, independent consciousness, and a very real world. Although the schools ranged from qualified non-dualism to complete dualism, all of them believe that real and moral free will exists within divine governance, and thus emphasize bhakti (devotion to God) over jñāna (self-knowledge). They are some of the dominant philosophical schools in India today and have heavily impacted Hindu cultural ethics and devotional theology.

    Chapter 13: Theravāda Buddhism

    They are the oldest branch of Buddhist philosophy, which emphasizes that reality is impermanent and conditioned. They believe that no enduring self exists, and true insight can be gained through mindfulness and direct experiential observation. They believe in a conditioned free will, which can be transformed through rigorous disciplinary practices. Theravāda is most famous today in Sri Lanka and Southeast Asia, and has greatly impacted mindfulness-based therapies, meditation, and cognitive psychology.

    Chapter 14: Mahāyana Buddhism

    Mahāyana or the Greater Vehicle Buddhists believe that emptiness (śūnyatā) denies the fundamental nature of all phenomena, and everything is relative. They emphasize interdependence and compassion as some of the highest virtues. Regarding free will, they believe that the freedom of someone increases as they get to understand the relativity of everything around, and also the importance of relational causality and interdependence. Mahāyana today exists and dominates the Himalayan regions as well as the East Asian countries, and contributes heavily to the ethics of care and interdependence.

    Chapter 15: Jainism

    Jains are the proponents of absolute non-violence. They believe in pluralistic realism, as souls are distinct and eternal. According to their epistemology, truth can have multiple interpretations, suggesting that different people perceive it in various ways. This principle is called anekāntavāda. Regarding free will, they have a strong emphasis on individual responsibility and self-control over complete freedom. Jainism today exists mostly in western India and is a true leader when it comes to ethics, environmentalism, and agency debates. 

    Chapter 16: Cārvāka

    It was the Indian materialistic school that believed neither in any consciousness nor in any afterlife. They were the ultimate anti-ascetic, pleasure-oriented, pragmatists, who saw only perception as a valid knowledge. They believed in complete free will, which is unconstrained by any God, karma, responsibility, or anything. As they believed nothing exists after death, they advocated living life to the fullest. Although the original atheistic school went extinct, it gave rise to early secularism and rational critique of any kind of metaphysics.

    Chapter 17: Confucianism

    Confucianism is an Ancient Chinese school which gives emphasize or moral cultivation through roles, rituals, and virtue. It advocates deep respect for tradition and self-cultivation. According to the school, true freedom lies in self-discipline, and not in individual autonomy. Confucianism is completely absorbed within most of the East Asian cultures and acts as a guide for social ethics, proper education, and political philosophy.

    Chapter 18: Daoism

    The Daoists believe in effortless action (wu-wei) and harmony with nature. They consider Dao as the ultimate source or principle of the universe, which also maintains the natural order over everything. They emphasize intuition over analytical reasoning and believe that free will emerges from non-resistance to natural flow. Presently, Daoism is greatly present in China, Korea, Taiwan, and Vietnam as it continues teaching systematic thinking along with considering the ecological consequences.

    Chapter 19: Legalism

    Legalism was a Chinese philosophy that considered law and order as more ethically important than virtue. They had a pragmatic worldview and considered knowledge as a tool for power. Regarding free will, they had the belief that human nature should be shaped externally with law and punishment. Legalism significantly influenced the political realist and authoritarian governance model in China over the centuries.

    Chapter 20: Mohism

    Mohism was an important school in ancient China based on universal concern and social utility. It was naturalistic and anti-ritualistic. The Mohists considered that humans have a considerable amount of free will, as they can make decisions based on logical argument and reason. The school strongly impacted the scientific and logical development in the Sinosphere throughout the millennia.

    Conclusion

    Thus, we see that the question of free will was answered by different ancient philosophical schools differently. While the Epicureans and the Cārvākas believed in complete freedom, the Cynics and the Legalists advocated nearly no free will. Most schools tried answering not whether free will exists, but whether free will should be exercised in their own way. From Neoplatonists to Advaitins, from Daoists to Jains, all had their own conclusion. Hope you followed the individual perspectives of these schools regarding free will clearly. 

    That is all for today. Hope you enjoyed it. Please like, share, and subscribe to keep me motivated. And finally, thank you for reading the blog.

  • From Shadows to Smartwatches: The Fascinating Evolution of Clocks Through History

    From Shadows to Smartwatches: The Fascinating Evolution of Clocks Through History

    Introduction

    Human beings have been fascinated with time for tens of thousands of years. Early Homo sapiens used time to know when to hunt, rest, cultivate, etc. For measuring time accurately, Neolithic humans began to construct timekeeping devices, which later came to be known as clocks. These clocks added punctuality to the human mainframe and accelerated efficiency to a great extent. In this blog, we discuss nine such clock models that revolutionized the field of Horology (the field of measuring time and making timekeeping devices). We discuss their construction, working, and their impact on timekeeping. So, let’s explore the evolution of clockmaking technology through the sands of time.

    Chapter 1: Sundial (~3500 BCE – 1600 CE)

    Sundials are the earliest known clocks or timekeeping devices, created by human beings. They consisted mainly of a platform with indicator markings and a rod-shaped figure above it, also known as a gnomon. During the day, the gnomon cast a shadow over the platform, whose length and angle were measured and calculated to find the exact hour. The device depended on human observation and calculation, and only worked when sunlight was available. Sundials were soon replaced by more efficient clocks in the future, especially the mechanical clock. They are still on display in various regions for decorative and educational purposes.

    Chapter 2: Water Clock / Clepsydra (~1500 BCE – 1600 CE)

    Water clocks (or Clepsydras) were one of the earliest known clocks made by man, which were independent of any external cause, like sunlight. They were famous in ancient Egypt, Greece, and China. They were built with various designs, especially the Chinese and Arabs devised many complicated mechanisms. In simple terms, the device consisted of two containers connected through a simple pipe or a hole. Water was poured into one of the containers and allowed to drip into the other at a controlled and measured rate. The empty container had markings that could indicate the time passed based on the volume of water filled. In some models, markings were instead on the container filled with water, and time was calculated on the basis of the decrease in water levels of the container. In both models, the water clocks proved superior to sundials and were used mostly at night. Their use declined after the invention of the mechanical clock during the 15th-16th centuries.

    Chapter 3: Candle / Incense Clock / Hour Glass (~500 – 1800 CE)

    Around the middle of the first millennium CE, a new type of mechanism was created to make timekeeping portable, so it could be carried from one place to another. Thus, the candle clock and the hourglass were invented. The candle clock was nothing but a candle with markings on it that indicated the time elapsed as the candle burned over the course of time. Hourglasses, on the other hand, were an improvisation on the water clocks, where sand and glass bulbs replaced water and containers. The amount of sand passed from one bulb to another indicated the time elapsed. After the entire sand had passed to the second bulb, the clock could be easily reset by just switching the second bulb on top, so that sand could then pass to the first bulb, and the clock worked in the opposite direction. Hourglasses were mainly used in long voyages, while the candle clock was mainly used for domestic and ceremonial purposes. Their use declined around the 17th-18th century due to the invention of more advanced clocks.

    Chapter 4: Mechanical Clock (~1300 – 1800 CE)

    Mechanical Clocks were the earliest form of properly engineered clocks. They were much more accurate compared to their predecessors and slowly led to their decline in usage. A typical mechanical clock consists of 5 parts: a power source, a gear train, an escapement, a regulator, and an indicator. In the earliest mechanical clocks, a falling weight was used as the power source. The falling weight interacting with gravity created a steady pull that drove the gear train. A gear train is a system of interconnected gears arranged so that the rotation of one of the gears leads to the rotation of all the gears. These gears drive something called an escapement, a disc with two tooth-like arms called pallets, mounted on a rotating shaft, that control the movement of the gears. This escapement is guided by another object called the regulator. In the earliest clocks, a horizontal cross-bar with adjusted weights known as a foliot was used as the regulator. As the gear train moved the pallets, the escapement moved the bar back and forth. The weights on the foliot resisted sudden changes due to rotational inertia, thereby regulating the movement of the gear train. The regulated motion of the gear train was finally transferred to an indicator, in the form of hands, which displayed it in the form of passage of time on the clock’s face. These types of clocks created a revolution in horology and were in continuous use till the 1800s.

    Chapter 5: Pendulum Clock (1656 – 1930 CE)

    The mechanical clocks, although far superior to their predecessors, had a major disadvantage. Their regulators worked on rotational inertia, depending on the movement of the gear train; thus, their accuracy reduced with time and needed to be readjusted. In 1656, the Dutch mathematician and engineer Christiaan Huygens invented the pendulum clock. It had almost the same design and principle as that of the mechanical clock, except for the regulator part. Instead of the dependent foilot, a pendulum was used as the regulator. Unlike the foliot, the pendulum works on the principle of simple harmonic motion under gravity. The pendulum thus swings in a uniform motion independent of any external object. Thus, the pendulum clock worked as a far better-regulated and, in turn, more efficient clock than the mechanical clock. Another innovation was that the power source was changed from a falling weight to a spring whose potential energy provided the power. The pendulum clocks were in common use till the late 1930s.

    Chapter 6: Marine Chronometer (1735 – 1970 CE)

    The Pendulum Clock, although very efficient and requiring very little calibration, had a major drawback. It was inefficient in sea voyages, as the motion of the pendulum was interfered with by the constant rocking and rolling of the waves. In 1735, the English engineer John Harrison invented the marine chronometer, suitable for sea voyages. The marine chronometer had a balance wheel and a spring in place of a pendulum as the regulator. The wheel oscillated in a uniform harmonic oscillation, and the spring attached to it provided the elasticity, thereby maintaining a uniform regulation independent of both gear train motion and motions from sea waves. The marine chronometer proved to be very efficient in naval expeditions and warfare, and continued to be used till the 1970s, when they were replaced by atomic clocks.

    Chapter 7: Quartz Clock (1927 – present)

    The Quartz Clocks are the first electrical clocks. Here, the power sources are batteries, in place of springs or weights. But the most important innovation is in the regulators. Quartz is a crystal that possesses a unique property called piezoelectricity, the ability to generate electrical pulses when under mechanical stress. Thus, in quartz clocks, tuning forks made of quartz crystal are installed in vibrated conditions, thus creating electrical pulses which act as the regulator. Electrical clocks are far superior in accuracy and efficiency compared to mechanical clocks, and thus, the former completely replaced the latter within decades. Also, quartz being extremely abundant on earth, made quartz clocks extremely cheap, and thus they are still in use in nearly every household.

    Chapter 8: Atomic Clock (1949 – present)

    Atomic Clocks are the champions of accuracy. In an atomic clock, the quartz crystal vibrates and sends electrical signals at a fixed frequency. These electrical signals are then converted to microwave signals. These microwave signals are sent to certain atoms: either Cesium-133, Rubidium-87, or Hydrogen (maser). The microwave signals excite the atoms. These atoms pass through a detector. Any change in the frequency of the electrical signal will change the level of excitation of the atom. The detector will detect the change and send a feedback signal to the quartz, thereby maintaining the regulating frequency. These clocks are so accurate that time has been defined by them. Before the atomic clocks, time was defined by the Earth’s rotation and revolution, whose measurements were affected by tides, earthquakes, and other causes. But after the invention of the Atomic clocks, one second is defined as 9,192,632,770 oscillations of radiation corresponding to a specific energy in the Cesium-133 atom. So, with the invention of atomic clocks, the calculation of time became finally independent of the Earth’s surface. Atomic clocks are now used in global navigation systems like GPS, telecommunication and internet facilities, stock markets, astronomical observations, and many more.

    Chapter 9: Smart Watch (2000 – present)

    Smart watches are direct descendants of Quartz clocks. The main body is the same except that the electrical signals are passed through a digital logical counter, which counts the oscillations. The software associated with it compares the oscillation with an external timeframe (GPS, phone, satellite, etc.) and sends feedback signals to the quartz crystal. Another thing that changed is that smart watches have a digital display frame with no clock hands as an indicator. Except for the regulator, almost all the mechanisms are the same for a smart watch and a quartz watch with a digital frame. They are today used both as timekeeping devices and for external features like measuring heart rate, weather reports, etc.

    Conclusion

    Clocks have evolved along with human civilizations over time. From calculating time to defining time, they have come a long way. The evolution can be classified into three different stages: pre-mechanical, mechanical, and electrical clocks. A proper electronic age for a clock is yet to come (if we don’t count mobile phones and personal computers as electronic clocks).

    That is all for this blog. Hope you enjoyed it. Finally wrote my first “technology” blog after 36 blogs. So, kindly forgive the technical jargon. I will try to minimize them in the future. Will be bringing more blogs on the history of science and technology like this. Please like, share, and subscribe if you want to get updates for my blogs. And thank you for reading the piece.

  • The Evolution of Brain Games: How Culture Shapes Strategy Through Chess, Go, and Beyond

    The Evolution of Brain Games: How Culture Shapes Strategy Through Chess, Go, and Beyond

    Introduction

    A game is a form of human interaction where one or more individuals compete to accomplish a specific task under certain conditions or to outperform other participants in that task, within a casual environment with no serious consequences. A game is generally played for entertainment during leisure time, but many individuals who excel in certain games often pursue the art of playing those games as a professional career. Games can be of various types: played by individuals or teams, requiring a toned physique or a sharpened mind, and completed in minutes or taking days to complete. Games that require more organized skill or training are known as sports. 

    In this blog, we are going to discuss some specific types of games and sports. Those that are played mostly through the mind, memory, and intellect. Most of them are played on a board. We are going to discuss the origins and evolution of seven such “brain games” that got embedded in the history and culture of those civilizations, if not the whole world. This blog won’t discuss the nitty-gritty of the gameplay, but will just discuss the relationships between the basic gameplay and the cultures it influenced, or was influenced by. So, let’s begin.

    Chapter 1: Oware / Mancala

    Mancala is one of the earliest known game families in human history. It originated in Sub-Saharan Africa around 3000 BCE, but slowly travelled to the Middle East and Caribbean during the medieval and colonial periods. The original gameplay consisted of a turn-based game which involved sowing of seeds in pits. The objective was to capture the seeds from the opponent’s pit. The seeds had no hierarchy, and thus, the one with more seeds won. The game slowly evolved with additions of multi-row boards, involvement of abstract game strategy, and formation of local variations, which grew into individual games. One such popular game is Oware, which is played mainly in Western African nations like Ghana. Oware is one of the most popular games within the Mancala family, with a fixed set of rules for gameplay and outcome. Mancala, in early African cultures, acted as a reference for resource distribution. The game influenced the culture by establishing virtues like communal balance, resource redistribution over domination, long-term strategy, and presenting a non-zero-sum worldview.  Manchala games are still very popular in Africa and are embedded in its culture.

    Chapter 2: Backgammon

    The earliest history of a game related to Backgammon can be found in Mesopotamia from 2600 BCE, in the form of the Royal Game of Ur. Originally, it was a dice-based game, which slowly spread to the Roman Empire, and later to the Islamic and Western worlds, via the Byzantine Empire. Both the Royal Game of Ur and Backgammon are types of racing games that depend on luck and probability for outcome. The objective is to remove all the pieces from the board faster than the opponent, depending on dice rolls. Backgammon, over time, gave rise to a basic understanding of probability, especially in the Middle Ages. The game shows how those cultures considered fate and luck as important conditions in determining outcomes, which is still present in many modern societies. This game also popularized the “dice” to the world, which in turn influenced different games across different cultures.

    Chapter 3: Chess

    Chess is perhaps the most popular board game. It is a two-player turn-based game whose objective is to capture or “Checkmate” the opponent’s king. The pieces are hierarchical, and each piece category has its own power and value. The game actually developed during the 5th-6th century CE in India, originally called “Chaturanga”. The original pieces were representatives of four types of armies: Infantry, Cavalry, Elephants, and Chariots. After the Islamic invasions in India, the game passed to Persia, where it got the name “Shatranj.” In Islamic Persia, the pieces became aniconic, as Islam forbids idols. The game soon went to Europe through both the Iberian Peninsula  (via Cordoba Sultanate) and the Kyivan Rus (via Byzantine Empire). In Europe, the Queen and the Bishops’ power increased due to the political and theological influences. The game continued to grow in Mediterranean Europe and the Russian Empire, with various evolutions like world-class tournaments (1850s), time controls (1860s-80s), tactical & positional plays, world chess championship(1886), chess engines (1980s), AI engines (2020s), etc. The game of chess reflects the warfare abstractions, the hierarchical chain of command, rational planning, intellectual prestige, and strategic thinking models, which were core to different environments through which it evolved: whether it’s India, Persia, Russia, or Western Europe. Today, chess is a professional sport played all over the world, with countries like Russia, India, China, and the USA dominating the top spots.

    Chapter 4: Pachisi / Ludo

    Pachisi was another Ancient Indian game from the 6th century CE, which slowly evolved into what is now called Ludo. While Chaturanga was mostly popular with the elite or intellectual class in Ancient India, Pachisi was more popular with the common households. The gameplay consisted of a cross-shaped board with around six cowrie shells as dice. The objective was to bring all the pieces off the board as fast as possible with respect to the outcome of the cowrie shells rolled. The gameplay also involved capturing opponent pieces, which resulted in the pieces restarting their journey from home. With the passage of time, the cross-shaped board became a square-shaped one, the multiple shells became a singular die, and Pachisi evolved into Ludo, with the influence of the West. The game clearly depicts the Indian acceptance of fate on outcomes, and also the use of strategy and tactics when encountering unfavourable circumstances. Ludo, today, is a highly popular casual game, played among the families of the Indian subcontinent, and is now going through a high digital emergence with a huge number of apps.

    Chapter 5: Go

    Go is an East Asian board game that dates back to around 3000 BCE. Although the origin is so old, the actual game was formalized around the early Tang period (7th century CE). The game also spread to Japan and Korea, with a huge influence on the latter’s culture. The objective of the game is to control a larger portion of the board than the opponent, through black and white stones across the grid. It is a turn-based game where stones can only be placed on a grid if there is at least one adjacent empty grid. If a stone or a group of stones is surrounded by enemy stones from all sides, that group is considered captured and is removed from the board. The game has undergone several changes over the course of time, including tactical evolution, some innovation in set rules, and even the involvement of AI through AlphaGo. The game upholds the Chinese philosophy of positional strategies combined with disciplined rigor. Go also visualizes the art of controlling a territory with brains instead of brawn. Today, the game is very popular in China, Taiwan, and Korea, with strong professional circuits.

    Chapter 6: Shogi

    Shogi is a Japanese strategy board game that evolved from the Indian Chaturanga in the 10th-11th century CE. The pieces are the same shape and color, with their ownership indicated by the direction they point, i.e., towards the opponent. One major difference from regular chess is that the captured pieces can be used by the opponent as their own piece under certain conditions. This game emphasizes recycling pieces. The game saw tactical evolution during the Edo period with many minor rule changes. The game requires players to be flexible without sacrificing discipline, which symbolizes Japanese flexibility. Presently, the game is very popular in Japan and has a professional ranking system.

    Chapter 7: Dominoes

    Dominoes is a popular game in the West, which finds its origin in medieval China, around the 11th century CE. The gameplay involves matching tiles called dominoes by the number of dots. And arranging them in a chain until one player is out. The number of matching dominoes remaining with the opponent became their score. In this way, the person to score a set number first wins. The game has a huge factor of probability and critical thinking. The game evolved across the last millennium, with respect to scoring systems, until it reached Europe in the 18th century CE. The game gives importance to Chinese logic and pattern matching. Today, the game is very popular as a casual game and is embedded in many Western regional cultures.

    Conclusion

    Games have influenced humans as much as humans have influenced games. Games, especially these “brain games,” beautifully depict how humans gather information, process it inside their brains, and respond accordingly. Playing such games from a very early age also helps in cognitive evolution, pattern recognition, and memory development of a child. These games can also help in binding together friends, families, and other relationships, despite daily human struggles. Games and sports help us in many more ways than we actually realize.

    That is all for this blog. I know, this blog was a bit technical. I tried to write the gameplay details as little as possible.  Hope you found it helpful. If so, please like, share, and subscribe to my newsletters for updates on my future blogs. Thank you for reading this blog.


  • 5 Game Theory Models in Action: Historical Decisions That Follow Logic

    5 Game Theory Models in Action: Historical Decisions That Follow Logic

    Introduction

    Human Beings are social animals. Since the development of their cognition, humans have developed various kinds of tactics and strategies to survive and evolve at both personal and social levels. Game theory is the science related to strategy, developed in conjunction with mathematical models, to determine the best outcomes with respect to the implemented strategy.

    Although officially, game theory was developed by the Hungarian-American mathematician John von Neumann and the German-American economist Oskar Morgenstern in the 1940s, the various “Games” or strategies had been used by human civilizations throughout history. They had taken important decisions for their survival across different cultures and societies on earth, based on their Nash Equilibria. Now, a Nash Equilibrium is a situation inside a game, in which none of the players can improve their state through strategies, without changing the strategies of other players. Its name comes from its developer, the American mathematician John Nash. In the Nash Equilibrium, all players are basically in their best response state and will remain so until one or more players deviate to other strategies. Many games have been developed and studied among the economic, mathematical, business, and even philosophical circles. Each games create a certain interactive situation, with a certain Nash equilibrium, or equilibria. In this blog, we discuss the five most famous games and strategies, along with one historical example for each, showing how certain geopolitical powers acted and reacted in accordance with their specific Nash Equilibrium. So, let’s begin.

    Chapter 1: Prisoner’s Dilemma

    The Prisoner’s Dilemma is perhaps the most well-known, studied, and discussed game in game theory. It is a paradoxical situation developed, which includes two players, each deciding for their general self-interest without knowing the decision of the other. Let us imagine a situation: The police arrested two different individuals on suspicion of robbery in a building. They are kept in two separate cells such that they cannot interact with each other in any possible way. Now, the police went to the individual suspects and gave the following offer. If both of them confess to doing the robbery, both get 3 years of imprisonment. If neither confesses, they get 1 year of imprisonment. But, if one of them confesses to having robbed together while the other denies, the one who confessed is immediately released by the police, while the one who denied gets 10 years of imprisonment. Let us consider the two suspects, A and B. So, the following situation arises:-


    From the table, let us assess the choices of both A and B. As they cannot contact each other, their individual decisions should be based on assumptions about the other. So, if we consider that B confessed, the best decision A has is also to confess, as 3 years imprisonment is better than 10. Similarly, if B didn’t confess, the best decision for A is still confessing, as he would be released instead of serving 1 year of imprisonment. The situation is the same from B’s side. So, both confess and arrive at the Nash Equilibrium, which is confessing.

    Now, let us consider the Trench War Stalemate on the Western Front during the First World War in 1914. The German and Allied forces clashed in Belgium and France. But after both sides failed to achieve a decisive breakthrough, they dug continuous trenches in the ground to avoid catastrophic losses. After months of a potential stalemate, the options the armies had were to restrain, retreat, or continue bombardment. Although at first glance, restraint sounds like the best option in a stalemate, none of the armies could afford to do so without knowing the motives of the other. If one party had stopped bombarding and attacking, there could have been a possible “10-year prison” situation as mentioned before. Also, they could not run away, as this would lead to an unavoidable defeat. So, even after months and years, the two parties continued their aggression till 1918, in order to maintain the Nash Equilibrium of the Prisoner’s Dilemma game.

    Chapter 2: Game of Chicken

    The Game of Chicken is a very different model from the Prisoner’s Dilemma. In this game, there is not one but two Nash Equilibria. Let us consider a situation in which there are two drivers, A and B, driving their two cars towards each other. They had the pre-made agreement that the one who swerves will be trolled by being labelled as a chicken. Now, if none of them swerves and drives full speed toward each other, they will ultimately crash, resulting in severe injury, if not death. Let us consider the injury or death as 0 (the worst possible outcome), being called a chicken as 1 (the second worst outcome), the opponent as 3 (the highest positive outcome), and both swerve as 2 for each (as they neither won nor lost). So, the situation is as follows:-

    So, even though the safest outcome looks like both swerving, that may lead to humiliation for both. Also, neither of them swerving can lead to serious injury or death. Thus, unlike the Prisoner’s dilemma, the best possible outcome is if both players make the opposite decision from each other, i.e., only one of them swerves. This leads to two Nash Equilibria: either Driver A swerves or Driver B swerves and accepts the humiliation of being called a chicken.

    An example of this game is the Kargil War Resolution in 1999. At that time, both India and Pakistan were recent nuclear powers. In May 1999, Pakistani forces and militants illegally occupied high-altitude positions on the Indian Side of the Line of Control (LoC), which is a militarily sensitive region, in the hope of altering the status quo. Indian forces retaliated, and soon the 4th Indo-Pak war, also known as the Kargil war (Kargil being the region), began. India launched strategic, high-altitude operations while avoiding crossing the LoC. Pakistan, on the other hand, faced growing international pressure. Neither force could retreat at first, as it was a matter of pride and honor. For Indians, Kargil was legally part of their motherland, while for Pakistanis, it was their newly occupied territory. Thus, the war continued for two and a half months, until the Pakistani forces retreated. Already hammered and predicting more upcoming devastation, they had to accept defeat. The Indian forces, on the other hand, became victorious and restored the pre-conflict status quo. Thus, both parties attained the Nash Equilibrium of the Game of Chicken.

    Chapter 3: Stag Hunt

    Another interesting game, or model, is the Stag Hunt. It was devised by the French Philosopher, Jean Jacques Rousseau. As per the game, two hunters, A and B, could hunt together a stag, which is a large meal, or could hunt rabbits individually. But hunting together needs trust, as one could always betray the other. Also, hunting a stag alone is very difficult as it is a large beast. Here, we give credit to their accomplishments. If both successfully hunt the stag, we give 10 to each. If they individually hunt rabbits, each gets 2. If one goes for the stag and the other goes for the rabbit, the one hunting the stag is almost certain to fail and gets 0, while the one who goes for the rabbit gets 4, as he is the only successful hunter. Thus, the following matrix describes the situation:-

    From the matrix, we see that neither the hunter will go to hunt the stag alone, resulting in two possible Nash Equilibria: they either hunt the stag together or hunt rabbits individually. Although hunting a stag will give a better outcome, there exists a possibility of betrayal, whereas hunting rabbits gives a lesser outcome but no chance of betrayal, thus resulting in two different kinds of equilibria. The Stag Hunt model thus has two solutions: one based on more profit and the other based on more security.

    A real-life great geopolitical example for this model occurred more than two millennia ago, at the Battle of Salamis in 480 BCE. When Emperor Xerxes (Kshayarshsa in Old Persian) of the Achaemenid (Haxamanesi in Persian) Empire invaded Greece, many Greek states, of different customs and culture, allied under the Athenian general Themistocles. Thus, we see how the Greeks approached a trust-based Stag Hunt equilibrium, thus finally leading to their victory. If they hadn’t allied, it would have been nearly impossible to hunt a stag named Xerxes. 

    Chapter 4: Battle of the Sexes

    Let us suppose a couple where the man wants to watch an action movie together, while the woman wants to watch a romantic movie together. This situation gives rise to a game theory model called the Battle of the Sexes. In this situation, both want to watch the movie of their choice, but together. So, let us give ratings to their satisfaction levels. If both watch different movies, their satisfaction rating is zero, as they feel lonely, not surrounded by their loved ones. But if both watch the same movie, the person whose preferred movie is chosen is more satisfied, getting a satisfaction rating of 2, while the one who compensates for the movie to be with his or her partner gets a satisfaction rating of 1. This results in the following matrix:-

    In this game, we see that to achieve equilibrium, one of them must compensate and achieve a lower level of satisfaction. Thus, the Battle of the Sexes also has two equilibria where one achieves a lower level of satisfaction than the other.

    A classic example of this model is the imperial court arrangement of the Tokugawa Shogunate in Japan from the 17th to the 19th century. Japan, at that time, had two parallel sources of legitimacy: The Emperor in Kyoto, the sacred, ritualistic, and symbolic authority, and the Shogun in Edo (modern Tokyo), the military, administrative, and real power. In the 1600s, Tokugawa Ieyasu became the Shogun after centuries of chaos. He had 3 choices: if the Shogun dominated, a potential rebellion may arise due to moral illegitimacy; if the Emperor dominated, the chaos resumes,  and the only realistic choice was that both powers cooperate with some sort of compensation. Thus, the imperial court was designed such that the Emperor remained as the ceremonial head, while the Shogun took over the administrative, financial, and military powers. Thus, the Shoguns settled with more satisfaction, while the Emperors settled with a little less but were still satisfied. This system of equilibrium with respect to the Battle of the Sexes continued for more than 250 years till the Meiji restoration in the 1860s. 

    Chapter 5: Zero-Sum Games

    The previous games we explored above were all non-zero-sum games, i.e., when one player wins, the other player doesn’t need to lose. But in zero-sum games, when one player gains something, the other player loses the same amount, so that the total outcomes of the strategy remain zero. For example, in a coin toss, if one side picks heads and the other picks tails, only one side wins, and the other side loses. In zero-sum games, the Nash equilibrium is not about trust, fear, coordination, or compromise, like in the previously mentioned models. The only sensible thing each player can do is to assume that their opponent will try to harm them and thus choose a strategy that limits the damage, even in the worst case. In short, strategies here are individualistic.

    An example of a real-life zero-sum game is the Great Game in Central Asia. In the 19th century,  two expanding powers faced each other in Asia: the British Empire in India and the Russian Empire moving south through Central Asia. The central buffer states between them included Afghanistan, Persia, and the Central Asian Khanates. Both had the ambition of influencing these regions. Their options included a formal alliance, open war, and complete withdrawal, with each resulting in a moral or practical defeat. Thus, both empires chose a fourth option, an option of constant rivalry, with espionage, proxy influence, diplomatic pressure, and local interventions. Thus, both sides chose a zero-sum strategy, and when one got a small win, the other suffered a small loss. They interacted independently based on their individual interests and settled into balance, not through cooperation but through mutual limitation.

    Conclusion

    In this blog, we see how mathematical models dominated human interactions and decision-making, even before they were officially formalized. Game theory, however, is not limited to only human beings, but also affects plants, animals, and even algorithms and AIs. Every decision made by them can be modelled into a game of game theory. So, studying these games, which are numerous in number, can benefit those who want to understand human psychology, business interactions, and geopolitical decisions.

    That’s all for this blog. Hope you find this interesting. Please like, comment, share, and subscribe to my newsletters to be notified of future blogs and updates. Finally, thank you for reading this piece, and wish you all a Happy New Year, 2026.

  • From Spies to Metadata: A Chronological Evolution of Surveillance Practices

    From Spies to Metadata: A Chronological Evolution of Surveillance Practices

    Introduction

    Security and surveillance are an important part of human society. Without proper monitoring and surveillance, no civilization or nation-state can maintain its peace and prosperity for a long time. Thus, every country, government office, public enterprise, and even localities on earth today have their own levels of security and surveillance. This practice is not a new phenomenon in human societies but goes back to at least five millennia. In this blog, we discuss how security and surveillance have evolved along with human societies, from the cradles of civilization to the modern age of information. We mention the fourteen important events in human societies that contribute to the evolution of surveillance on a historic scale, either global or regional. So, let’s begin.

    Chapter 1: Birth of Bureaucratic Surveillance (Mesopotamia, c. 3000 – 500 BCE)

    Around 3000 BCE, the first large settled states appeared around the Fertile Crescent and Mesopotamia. This required control over people and resources. Thus, clay tablets were invented to record population, taxes, land ownership, etc. Temples and palaces acted as data centers, with surveillance being administrative, and not a secret. Everything was conducted openly with complete state visibility. Thus, Surveillance evolved as record-keeping and state memory in human history for the first time.

    Chapter 2: Surveillance as Divine Administration (Ancient Egypt, c. 2600 – 1000 BCE)

    The Egyptian civilization under the Pharaohs evolved as a highly centralized state. Scribes were employed to monitor grain production, labor force, taxes, temple resources, etc. Since the civilization thrived along the Nile River Valley, regular floods affected the region, which were also recorded by the scribes for economic forecasting in the future. Proper records were also maintained for labor gangs for pyramid and temple construction. Very soon, the surveillance policy began to be linked with divinity, with the Pharaoh seen as the divine maintainer of the cosmic order (Ma’at), through complete obedience. Surveillance was justified as maintaining harmony, not control. Thus, the Egyptians were the first to promote the idea of surveillance as a sacred duty for the first time, which was later employed by various governments.

    Chapter 3: Birth of Organized Intelligence and Espionage (Maurya Empire, c. 4th – 2nd century BCE)

    The Maurya Empire was the first recorded empire to unify the Indian Subcontinent under a single government. Being a large empire with a diverse culture, internal stability was crucial. The kingmaker of the empire, Chanakya (also called Kautilya), formalized surveillance in his text of statecraft, the Arthashastra. As per the text, the empire employed ascetics, merchants, householders, entertainers, etc., as spies to observe government officials, armed forces, and public opinion. Surveillance became a secret occupation, rather than being public. Informants were always cross-checked with several spies employed against the same person or organization to avoid misinformation. The Arthashastra became one of the earliest texts to treat surveillance as a proper study and science, in great detail.

    Chapter 4: Surveillance Through Population Legibility (Han Dynasty, c. 2nd century BCE – 2nd century CE)

    The Han Dynasty was the first dynasty to unite more than half of modern China in history. It was a large agrarian empire that needed predictable taxes and soldiers. To counter this, the state created household registers containing names, family members, occupations, and land holdings of individual families. Every member of a family was collectively responsible and accountable for other members of the family. Surveillance was continuous, routine, and non-secret, with local officials reporting to the central state. The Registrations were primarily tied to taxation, but also to conscription and social order. All non-registered people were suspected of being criminals. The Han Dynasty created the idea of surveillance as population mapping and social control.

    Chapter 5: Surveillance for Imperial Governance (Roman Empire, 1st century CE – 4th century CE)

    When the Roman Republic evolved into the Roman Empire, due to the conquests of  Julius Caesar, the Empire was vast and covered most of the Mediterranean regions. The empire, being massive, needed a fast information flow. Regular censuses were conducted across the provinces for tax collection and military recruitment. Networks of informants were deployed over the empire, who reported efficiently.  Highly developed roads and communication networks enabled fast reporting over large distances. Thus, under the Roman Empire, surveillance became an important tool for imperial coordination and control.

    Chapter 6: Surveillance Moves Inside the Mind (Medieval European Church, c. 5th – 15th century)

    In medieval Europe, the church held moral authority over daily life, with priests acting as moral observers. Confession was institutionalized, where individuals disclosed their thoughts and actions. Slowly, sin tracking replaced crime tracking with social pressure encouraging self-reporting. The church promoted fear of divine judgment, reinforcing compliance, with belief acting as the surveilant itself. The Middle Ages also created habits of self-censorship, with surveillance evolving as something of a psychological self-monitoring.

    Chapter 7: Surveillance Through Identity and Community (Ottoman Empire, c. 14th – 19th century)

    The Ottoman Empire was a multi-religious empire that needed stability. The population was classified by religious community (millet), with each community self-administering taxes, marriage, law, etc. The registration of the people was tied to their religion, and not ethnicity. The leaders of each community helped the state in monitoring their respective communities. The self-administration reduced the need for constant state spying and ensured loyalty indirectly.

    Chapter 8: Surveillance Through Administration and Numbers (Mughal Empire, c. 16th – 18th century)

    The Mughal Empire conquered most of the Indian Subcontinent, which was very large and consisted of diverse communities. The Mughals employed a Mansabdari system, which ranked officials numerically. Detailed records of villages were collected by the Mansabdars, based on land measurement, agricultural output, revenue collection, etc. The officials were regularly audited and transferred to prevent gaining influence over a certain region. They monitored the commoners while the state monitored the Mansabdars, thereby creating a division of labor. Surveillance was based purely on an economic basis while helping in maintaining stability through predictable data.

    Chapter 9: Surveillance Becomes Scientific and Classificatory (British India, c. 18th – 19th century)

    The British Colonial Empire needed control over a vast population. The British introduced an all-India census where people were classified based on caste, religion, and occupation. Later, fingerprinting was also developed for identification. They also used maps, gazettes, and surveys to monitor the colonized lands with scientific precision. They also developed the knowledge gathered from the survey to divide and rule over the large Indian subcontinent with ease. Thus, the British Empire employed surveillance as a scientific classification of humans to accomplish its colonial ambitions.

    Chapter 10: Surveillance Becomes Architectural (Industrial Europe, c. 18th – 19th century)

    The Industrial Revolution in Europe accelerated the industrial techniques across the continent. Industrialization concentrated workers in one place, with factory owners monitoring time, productivity, and discipline with ease. The prisons were redesigned for constant visibility. The English philosopher Jeremy Bentham designed the Panopticon, a prison model that enabled one watcher to watch any inmates, as well as the uncertainty of being watched, forcing the prisoners to be self-disciplined. Thus, surveillance became embedded in buildings with power working through the possibility of being watched. Thus, the Panopticon upgraded surveillance as a mode of built-in self-discipline.

    Chapter 11: Surveillance Goes Global and Technological (Cold War, c. 1940s – 1990s)

    At the end of the 2nd World War, after the Axis army was defeated, a new type of tension appeared in the world order in the form of two superpowers, the United States of America and the Union of Soviet Socialist Republics. Also known as the Cold War, the tension developed into an ideological rivalry that demanded constant vigilance. The Signals Intelligence (SIGINT) expanded with phone calls, radio, and satellites being monitored. Also, various intelligence agencies began to grow all over the world, with surveillance focusing on states, scientists, and political groups. Espionage became normalized, and information began to be seen as a strategic weapon. The Cold War rocketed Surveillance as continuous global intelligence.

    Chapter 12: Everyone Becomes a Data Source (Digital Internet Age, c. 1990s – 2010)

    During the 1990s, the internet entered the personal lives of people for the first time, slowly connecting billions. Daily activity generated digital traces with surveillance shifting from content to metadata. The corporation began collecting behavioural data, which in turn later began to be accessed by the Governments. Based on the data, the algorithm detected patterns enabling more engagement with the internet and more data collection. Surveillance slowly transformed into passive and continuous. The Digital Internet Age rewrote surveillance as data extraction from everyday life.

    Chapter 13: Surveillance Becomes Behavioral Scoring (China’s Social Credit System, c. 2010s – present)

    The social credit system, primarily in China, began to assign scores to individuals and companies based on data sources, including financial behaviors, legal records, and online activity. Based on the scores, rewards and penalties are assigned.  Rewards include easier loans and faster approvals, while penalties include travel restrictions and public blacklists. The system resulted in surveillance becoming non-event-based while encouraging self-correction of behaviour. Thus, surveillance in the 21st century became based on quantified morality and behavioral control.

    Chapter 14: Surveillance Becomes Total and Automated (Global, 2000s – present)

    By the middle of the 2000s, internet traffic was being monitored on a global scale. Programs like PRISM collect emails, chats, and cloud data, while focusing on bulk collection and not just suspects. Slowly, surveillance crossed national borders and algorithms flagged threats automatically. Thus, surveillance slowly evolved into something that is automated and borderless observation of humanity.

    Conclusion and Reflection

    Surveillance first started as something done in daylight, slowly evolved into a work done in secret, and finally transformed into something automatic, passive, and global. The practice that took root due to necessity today rules as a luxurious product that determines both soft and hard power between nations. This blog was a quick survey of the history of surveillance itself. Hope you all find it interesting, and if so, do like, comment, and share. Also, subscribe to my newsletter to be notified of future blogs. Also, wish you all a Merry Christmas and a Happy New Year in advance. Finally, thank you for reading this piece.

    Suggested Readings

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  • Understanding God in Indian Thought: An Introductory Overview of Hindu, Buddhist, Jain, and Sikh Perspectives

    Understanding God in Indian Thought: An Introductory Overview of Hindu, Buddhist, Jain, and Sikh Perspectives

    Introduction

    Since the time of cognitive evolution, humans have continually sought reasons for our existence and our surroundings. As a result, our ancestors developed their own metaphysics, cosmology, and the concept of God based on their cultural surroundings. In Indian civilization, the people slowly developed a unique way of understanding the divine creation, which is very different from the Abrahamic traditions more popular in the West. A verse from the Ṛgveda, the earliest known scripture of India, beautifully captures the Indian way of thought and the freedom of thought. It quotes, “ekam sat viprā bahudā vadanti,” which translates to “Truth is one, but the wise call it by various names.” All the traditions of India that emerged later, fully or partially, were inspired by this very verse, which led to a diverse understanding of the truth and the path for finding the truth. In this blog, we discuss the most important 20 philosophical thoughts and traditions that emerged in the Indian civilization through the lens of how they view the concept of God and the universe. This blog doesn’t intend to give any judgment on which path is superior, as ultimately all path ultimately leads to the same truth, with the right intention. This blog can be considered an introductory article for understanding the Indian philosophical school, without going deeper into any, as it’s nearly impossible to give detailed information on every school in a single blog. Most schools are arranged in a chronological order, except for a few exceptions for better comparative understanding. So let’s begin.

    1. Cārvāka (Lokāyata)

    The Cārvāka school is one of the earliest philosophical schools in India. They are the ultimate materialists. According to them, there is no God, and no individual or collective consciousness (ātman & brahman), and no transcendental principle. According to them, only matter exists, and reality is composed of four elements (earth, water, fire, air). They reject any form of scripture and give priority to only perception (pratyakṣa) as valid knowledge. They don’t believe in any form of karma, rebirth, heaven, or liberation. They are radical atheist who believe ethics is pragmatic, and not cosmic.

    2. Sāṃkhya-Yoga

    The Sāṃkhya and Yoga were separate philosophical traditions with a lot of similarities and shared doctrines. They slowly merged such that in today’s world, it’s impossible to study or follow one without studying the other. Both schools are dualistic, and according to their metaphysics, reality is composed of Puruṣa (pure, passive, multiple, eternal consciousness) & Prakṛti (primordial, active, unconscious matter). Sāṃkhya believes in no God, while Yoga believes in Īśvara (personal God – who is not a creator God but a special Puruṣa, unaffected by karma and suffering, who is an idle object for meditation). Both schools believe liberation comes from discriminative knowledge between Puruṣa & Prakṛti. According to them, reality is made up of 25 tattvas (elements) like intellect, ego, senses, and natural elements. Thus, both schools describe reality without a creator God, treating liberation as a psychological-metaphysical separation.

    3. Nyāya-Vaiśeṣika

    They are twin schools, which originally started as separate schools during the Axial Age, but were merged millennia later around the 10th-13th century CE. Both schools are pluralistic and believe in many consciousnesses (ātman) and many substances. They accept a personal God (Īśvara) as an intelligent ordering principle. They believe God is not the material cause but the efficient cause of the universe. The  Nyāya school is the school of logic, which believes in four means of knowledge: perception, inference, comparison, and testimony. They believe God’s existence is established through inference and not through revelation alone. They also believe rational argument is central and more important than faith. According to Vaiśeṣika ontology, the universe is composed of eternal atoms (earth, water, fire, air), which are arranged by Īśvara according to karma, and suffering comes from karma alone, not any divine will. Both the schools present a rational theism where God is an architect and moral governor, who is discovered through logic rather than mystical insight.

    4. Mīmāṃsā (Pūrva Mīmāṃsā)

    The Mīmāṃsā scholars believe that no creator God is required to explain the universe, and reality is governed by dharma or righteous duty. They believe the Vedas are authorless and eternal. The Gods mentioned in the Vedas are considered by them as functional entities, invoked through ritual, not supreme creators. According to their cosmology, the universe is beginningless, and ritual action itself produces results through an unseen potency (apūrva), not divine intervention. They give more preference to the verbal testimony (śabda) of the Vedas over perception and inference. Mīmāṃsā presents a ritual-centered, non-theistic worldview, where cosmic order functions without a supreme God.

    5. Advaita Vedānta

    According to Advaita Vedānta, only Brahman (infinite, changeless, non-dual consciousness) is real, while the world is mithyā, i.e, dependent and provisional. According to them, the individual soul (ātman) is the same as the eternal soul (brahman). They believe in Īśvara (personal God), who exists at the empirical level, and is actually Brahman reflected through māyā (cosmic illusion or ignorance). They believe the universe appears through māyā and is not a real creation but a mere manifestation, as the only truth, i.e., Brahman itself does not change or act. Epistemologically, they believe liberation comes through direct, non-dual insight or knowledge (jñāna) that removes ignorance, rather than through any ritual or belief. They give importance to the teachings of the Upaniṣads (the fourth and the last section of the Vedas) that help in attaining jñāna. In short, Advaita Vedānta presents God as ultimately impersonal and non-dual, with the personal God serving as a pedagogical reality within ignorance.

    6. Viśiṣṭādvaita Vedānta

    According to Viśiṣṭādvaita Vedānta, Brahman is personal and identified with Viṣṇu/Nārāyaṇa. God is considered as one, and consciousness (cit) and matter (acit) are real and dependent attributes of God. For them, the world is real, and not illusory. Their God, unlike that of Advaitins, possesses infinite auspicious qualities, and ātmans are modes (prakāra) of Brahman, not identical to him. Their cosmology shows the universe existing as God’s body, and creation as a real transformation of God’s power. For Viśiṣṭādvaitins, knowledge is important, but devotion (bhakti) and grace are central. Complete surrender (prapatti) leads to liberation. Viśiṣṭādvaita presents God as a personal, all-compassing reality, where unity and difference coexist without illusion.

    7. Dvaita Vedānta

    This is a dualistic school and tradition that considers reality as irreducibly dualistic. In Dvaita Vedānta, the God (Viṣṇu), individual consciousnesses, and matter are eternally distinct. The difference (bheda) is real, and neither provisional nor illusory, like the previously mentioned two schools. To them, God is supreme, independent (svatantra), and personal. Consciousnesses and matter are dependent realities (paratantra). They consider five real distinctions or pañcabheda. They are: God-consciousness, God-matter, consciousness-consciousness, consciousness-matter, matter-matter. These differences persist even after liberation. Dvaitins also believe liberation leads to eternal proximity to God, and not union. Dvaita presents God as a supreme, personal ruler, eternally distinct from anything else, rejecting all forms of non-dual identity.

    8. Dvaitādvaita Vedānta

    According to them, reality is characterized by both difference and non-difference. To them, Brahman (Kṛṣṇa/Rādhā) is the supreme reality, and consciousness and the world are distinct yet inseparable from God. God is seen as personal, loving, and relational, and is considered the cause, sustainer, and inner controller of the universe. Both knowledge and devotion together are seen as the means of liberation, with special importance given to bhakti for Kṛṣṇa. Dvaitādvaita portrays God as a unity that naturally includes differences, avoiding both absolute identity and absolute separation.

    9. Śuddhādvaita Vedānta

    According to Śuddhādvaita Vedānta, Brahman alone exists, but unlike Advaita, the world is fully real. Brahman manifests the universe without losing perfection. God is seen as Śrī Kṛṣṇa, the complete and joyful Brahman, and the world is a real expression of divine play (līlā). According to them, liberation is achieved through Bhakti and loving participation in God’s līlā. This school presents God as pure, joyful reality, where the world is not a problem to escape, but a divine expression to be embraced.

    10. Acintya Bhedābheda

    The last of the Vedānta schools, Acintya Bhedābheda, believes reality is simultaneously one and different, in a way that is acintya (inconceivable to logic). They consider Kṛṣṇa as the supreme personal manifestation. God is personal, relational, and supreme, with all his energy (śaktis) manifesting both the world and the individual consciousnesses. They consider creation as purposeful and not illusory. According to this school, pure bhakti is the highest means to reach liberation. Acintya Bhedābheda presents God as a personal absolute, whose unity with the world and various consciousnesses transcends human logic rather than denying it.

    11. Pāśupata Śaivism

    It is a school or tradition where Śiva, in the form of Paśupati, is seen as the supreme, eternal God. He is completely distinct from consciousnesses (paśu) and the world. Pāśupata Śaivism defines reality as fundamentally theistic and dualistic. God is omnipotent, independent, and the giver of liberation. It is grace, not knowledge, which leads to complete freedom. According to them, the consciousnesses are bound by impurities (pāśa). Mokṣa or liberation here is seen as release from bondage, and not identity with God. Consciousnesses remain eternally distinct, but free and blissful. Pāśupata Śaivism presents God as a sovereign Lord, where liberation depends on divine grace rather than metaphysical identity.

    12. Śaiva Siddhānta

    This is another śaiva school whose metaphysics is structured around three categories- Pati (Lord Śiva), Paśu (individual consciousness), and Pāśa (impurities like karma, māyā, and other impurities), and all three are real and distinct. Śiva is seen as the supreme personal God, both transcendental and immanent. He is the effective cause, not the material substance of the universe. Emphasis is given on ritual devotion (kriyā), ethics (caryā), and spiritual knowledge (jñāna). Mokṣa or liberation in this school refers to union without identity, where souls attain  Śiva-like bliss but do not become Śiva themselves. Śaiva Siddhānta, in short, envisions God as a personal, liberating Lord, balancing devotion, ritual, and metaphysical realism.

    13. Kashmir Śaivism (Trika)

    This is a non-dual śaiva school, which considers Śiva to be the only consciousness, and the reality is dynamic, not static. God is considered to be Śiva-Śakti, the inseparable consciousness and power. According to their metaphysics, the universe consists of 36 tattvas (elements or levels of reality). Māyā is not considered an illusion but rather the self-limitation of consciousness. According to them, knowledge arises through direct recognition (pratyabhijñā), and Mokṣa or liberation occurs by recognizing oneself as Śiva. Kashmir Śaivism presents God as living consciousness, where realizing God means recognizing the divine nature of one’s own awareness.

    14. Śākta Tantra

    In this school, the ultimate reality is seen as Śakti, the Divine Mother, the dynamic power of existence. Śiva without Śakti is considered inert, while Śakti without Śiva is considered inconceivable. The reality is seen as non-dual, experiential, and embodied. The Divine Mother is worshiped in various forms:  Kālī, Tārā, Tripurasundarī, etc. According to Tantra cosmology, the universe emerges from Śakti’s vibration, the creation is cyclical, sacred, and alive, and matter is not considered inferior to spirit. Śākta Tantra epistemology considers knowledge as something that comes from direct experience, and not the denial of life. Their practices include mantras (sacred sounds), yantras (sacred diagrams), ritual, and inner discipline. One attains mokṣa or liberation after recognizing oneself with Śakti. Śākta Tantra sees the Goddess as the immanent power, where divinity is encountered through experience, embodiment, and disciplined awareness.

    15. Jainism

    Jainism is a non-theistic school and tradition, which is nowhere near materialism. According to them, reality consists ofjīva (conscious souls) and ajīva (non-conscious matter, time, space, motion, rest), and there is no creator God. By “God”, they refer to liberated souls known as Tīrthankaras, and not a creator. They are perfected souls possessing infinite knowledge, perception, bliss, and energy. The universe is considered beginningless and eternal. It operates through natural laws and karma, with no divine intervention. Jains emphasizeahiṃsā (non-violence), ascetism, knowledge, and right conduct. According to Jainism,mokṣa is the complete isolation of the soul from matter, after which the liberated soul attains a higher plane called Siddha-loka and is beyond rebirth. Jainism replaces God with moral law and self-effort, making liberation a consequence of discipline rather than grace.

    16. Theravāda Buddhism

    It is the earliest known Buddhist school. The school rejects a creator God. Gods (devas) may exist, but they are impermanent and non-liberating. According to Theravadins, reality is impermanent with no permanent self (anātman), and existence is structured through dependent origination (pratītyasamupāda). Theravāda Buddhism considers the universe as cyclic and is governed by karma and causality,  with multiple realms of existence and no cosmic designer. They emphasize knowledge gained through direct insight into impermanence, suffering, and non-self. Liberation or Nirvāṇa is discovered through attaining knowledge, accompanied by monastic discipline, meditation, and ethical conduct. Theravāda removes God entirely from metaphysics, placing causality and insight at the center of liberation.

    17. Madhyamaka

    Madhyamaka is a Buddhist school that emphasizes emptiness. According to them, all phenomena are empty (śūnya) of inherent existence. Emptiness does not mean nothingness, but dependence itself, rejecting all metaphysical absolutes. They don’t believe in any creator God or metaphysical ground, and even nirvāṇa is empty of inherent essence. They use radical dialectical reasoning to dissolve views, thereby following the middle way, avoiding both eternalism and nihilism. They consider liberation as the state of attaining freedom from all fixed views. Madhyamaka dismantles the very idea of God as an ultimate entity, replacing it with relational emptiness.

    18. Yogācāra (Vijñānavāda / Cittamātra)

    Yogācāra is the Buddhist school that suggests reality is mind-only (citta-mātra), with external objects having no independent existence apart from consciousness, and experience arises from layered mental processes. They don’t believe in a creator God or a supreme being, and the ultimate reality is purified consciousness, not a deity. According to Yogācāra, the world arises from storehouse consciousness (ālaya-vijñāna), with karma as preserved mental seeds. Cosmos is psychological rather than material. According to this school, liberation occurs through transforming consciousness with meditation and ethical cultivation. Yogācāra replaces God with mind itself, making consciousness the source of the world and liberation.

    19. Vajrayāna Buddhism

    Mostly followed in Northern India, Nepal, Bhutan, Tibet, and Mongolia, Vajrāyana Buddhism states that the ultimate reality is non-dual awarteness, inseparable from emptiness. According to the school, Buddhahood is inherent but obscured, and Samsāra (existence) and Nirvāṇa (liberation) share the same ground or plane. They believe in no creator God, while deities (yidams) are symbolic manifestations of the awakened mind. They view the universe as the sacred geography, mirroring inner mental structures. Practitioners of Vajrāyana use mantra (sacred sounds), mudrā (hand signs), and various tantric methods, with the direct aim of rapid realization. In this school, the Guru (teacher) is considered very essential as a living transmission. Through tantric practices, including proper usage of body, speech, and mind, enlightenment is possible within a single lifetime. Vajrāyana treats deities as skillful means, turning symbolism into a direct path of awakening.

    20. Sikhism

    One of the two youngest philosophies of the list (the other being Acintya Bhedābheda), Sikhism believes the ultimate reality is Ik Oṅkār, i.e., one, singular, all-pervading reality. They believe God is transcendent and immanent, the reality is non-dual, but creation is real. They consider God as both nirguṇ (without form or attributes) and saguṇ (with attributes), although God does not incarnate in human form. According to their custom, personal devotion to God is central, but God is beyond anthropomorphism. According to their cosmology, the universe is created and sustained by divine will (hukam), and creation is meaningful and structured with no illusionism. Ethical practice includes emphasis on nāma simaraṇ (remembrance of God), honest work, and service (seva). The tradition rejects ritualism and ascetism, and liberation or mukti is considered as freedom from ego and separation, not escape from the world. Sikhism presents God as one universal reality, accessible through devotion, ethics, and grace rather than metaphysical speculation.

    Conclusion

    This blog is written with the intention of giving a short introduction to the metaphysics, cosmology, ethics, and epistemology of nearly all core Indian philosophical and spiritual schools. I have tried to make the blog as unbiased and respectful as humanly possible. As per the Ṛgvedic verse mentioned in the intro, they are all interpreting the same truth in their very own way, so any form of negative comparison is ethically unjust. This blog was also written to show the spiritual diversity in India, which is mostly unknown not only to foreigners, but also to many Indians themselves. That is all for this blog. I know the blog was a bit long, in fact, my longest blog till now. Sorry for that, but I couldn’t make it shorter without avoiding any important school or principle. I feel they are all equally important with no hierarchy of importance. Hope you enjoyed the read. Do like, comment, and share if you feel so; this will encourage me to study and write more such blogs on philosophy, science, and other ideas. And also subscribe to my newsletter via email if you want to get notified for future blogs and updates. Thank you.


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  • The Evolution of Basic Mathematics: From Counting to Calculus

    The Evolution of Basic Mathematics: From Counting to Calculus

    Introduction

    Mathematics is the branch of science dealing with numbers, quantities, shapes, and measurements. It’s an abstract science that primarily consists of abstract concepts, which can also be applied in our day-to-day life for understanding and developing other branches of science. It is also the oldest branch of science practiced by human beings for 20,000 to 30,000 years. As human societies developed, mathematics evolved alongside them, branching into hundreds of specialized fields over the centuries. In this blog, we talk about the history and evolution of the nine main branches of mathematics across the millennia. We discuss how they evolved as separate branches in ancient civilizations and gradually developed in classical, medieval, and modern times. These nine branches are those that are taught in nearly every school around the globe. Branches like topology, game theory, discrete mathematics, and computational mathematics are intentionally omitted as they are usually taught at higher institutes like colleges and universities. So, in order to keep this blog accessible and understandable to everyone, only nine of them have been selected.

    1. Arithmetic

    The oldest proof of arithmetic was found in Central Africa, the Ishango Bone,  dating to around 20,000 BCE. In that bone, deliberate notches were marked that may represent doubling sequence, lunar counts, or early tallying. Later,  tally marks emerged independently across different prehistoric societies. They were generally used to record items and for other trading purposes.

    Around 3000 BCE, the Sumerians developed a base-60 system that became the backbone of Mesopotamian mathematics, which they used for trade, astronomy, and land measurements. This system, millennia later, gave rise to 60-second minute, 60-minute hour, and 360-degree circle. Around the same time, the Egyptians developed a decimal system with separate symbols for 1, 10, 100, and so on. While lacking place value, this system supported large-scale administration, taxation, construction, and record-keeping among the bureaucrats.

    At the beginning of the Iron Age, China developed counting rods arranged on a board to represent numbers using place value, centuries before their appearance in the West. Rod numerals allowed both decimal representation and efficient computation with addition, subtraction, and even multiplication techniques. In Vedic India, on the other hand, the Sulba Sutras used numerical methods embedded with geometry for structuring fire altars. Although not a fully developed number system, they developed ratios, square approximations, and applied arithmetic for ritualistic purposes. The Greeks also developed an alternative acrophonic numerical system where 5, 10, 100, and others were based on initial letters of number words.

    In the first half of the first millennium CE, the Indians introduced a number system with positional notations and zero as a number, and the Chinese developed counting boards under the Han Dynasty. The counting boards used rods arranged in vertical columns for place value, and were used for multiplication, division, square roots, and even systems of equations.

    After the invasion of the subcontinent by the Arabs, they adopted Indian numerals and promoted them across Eurasia, thus known to the world today as Hindu-Arabic numerals.

    Later, in 1202, Leonardo of Pisa, better known as Fibonacci, introduced Hindu-Arabic numerals to Europe through his book Liber Abaci. Thus, these numerals slowly replaced Greco-Roman numerals and became the dominant numeral system in the modern world.

    2. Geometry

    The earliest example of geometry can be found in Ancient Egypt from 3000 BCE. They used knotted cords to survey fields, maintain boundaries, and construct canals around the Nile River. They developed simple mensuration formulas that laid the foundations of geometry later.

    Babylonian clay tablets, especially Plimpton 322 (~1800 BCE), recorded sophisticated lists of right-angle triples like 4-3-5 and 12-5-13. Their works show that the Mesopotamian scribes understood the Pythagorean principles, at least a millennium before Pythagoras was born.

    During the start of the Iron Age, the Sulba Sutras of Vedic India developed geometric diagrams for constructing fire altars. They also contain an approximated value of √2, transformations between shapes of equal area, and methods of creating right angles.

    In Greece, Thales introduced abstract reasoning in Geometry through propositions such as the equality of angles in a semicircle and basic similarity principles. The Pythagoreans, on the other hand, developed theorems related to polygons, ratios, and right triangles. Euclid, in his work Elements, systematized geometry through axioms, definitions, and proofs. Archimedes developed formulae to compute surface areas and volumes of solid figures like spheres and cylinders. He also approximated the value of π

    In the classical age, China’s Nine Chapters on the Mathematical Art created the areas and volumes of various geometric figures independently, thereby influencing future East Asian mathematics. In India, Aryabhata also independently introduced the areas and volumes of different shapes and approximated the value ofπ. He also introduced sine tables, which later became crucial for developing trigonometry.

    In the medieval period, Ibn al-Haytham, of modern-day Iraq, integrated geometric applications to physics, especially optics, in his work, also named Optics.

    3. Algebra

    The Babylonian tablet mentioned in the Geometry section is also very important to Algebra, as the tablet contains quadratic equations solved with geometric reasoning and completing the square methods, thereby acting as one of the earliest examples of algebra known to mankind.

    The Rhind papyrus from Egypt, from around 1500 BCE,  shows linear equations for practical problem solving regarding sharing, proportions, and rates. The Egyptian algebra later influenced the algebra around the entire eastern Mediterranean coast.

    In the 3rd century CE, Diophantus of Alexandra composed Arithmetica, introducing symbolic shorthands for unknowns and methods to solve determinate and indeterminate solutions. In India, Brahmagupta, in his work Brahmasphutasiddhanta, established rules for zero, negative numbers, and algebraic operations, forming a major milestone in global mathematics.

    In the Middle Ages, al-Khwarizmi, in his work Al-Jabr, organized algebra as a discipline focused on solving linear and quadratic equations through reduction and balancing. His work gave us the word “algebra” itself. Another Islamic mathematician, Omar Khayyam, classified cubic equations into geometric types and solved them using intersections of conic sections. Although not symbolic, his work represented the most advanced treatment of cubics before the Renaissance.

    Fibonacci, in his Liber Abaci, introduced methods of solving algebraic problems in Europe. His works included linear and quadratic equations, commercial arithmetic, and recreational problems like the famous rabbit sequence. By combining Mediterranean techniques with Islamic and Indian knowledge, particularly al-Khwarizmi’s and Brahmagupta’s, Fibonacci catalyzed Europe’s transition toward symbolic algebra.

    Later during the Renaissance, Tartaglia discovered methods for solving certain cubic equations, later published by Cardano in Ars Magna, along with Ferrari’s solution to quartics. Much later, Francois Viete introduced systematic symbolic notation using letters for known and unknown quantities, transforming algebra from a rhetorical prose to an abstract language.

    Finally, René Descartes unified algebra and geometry through coordinate methods in La Géométrie, introducing modern exponent notation and the convention of x and y for variables.

    4. Trigonometry

    The earliest example of proto-trigonometric tables can be seen in the Babylonian astronomical cycles working with base-60. Their cuneiform records include lists of reciprocal pairs and angle relations useful for predicting planetary positions.

    In Hellenistic Greece, Hipparchus developed the first known trigonometric table by measuring chords in circles, enabling astronomers to convert geometric angles with numerical values. His Table of Chords effectively established trigonometry as a mathematical discipline in the Hellenistic world.

    In India, Aryabhata introduced a sine table based on half-chords, shifting trigonometry away from Greek chord geometry toward the modern sine function. His systematic values of sine differences helped Indian astronomers compute planetary motions with remarkable accuracy. Bhaskara I and II further expanded Indian trigonometry with interpolation formulas, sine approximations, and early versions of trigonometric identities.

    Islamic scholars like Al-Battani and Al-Tusi formalized trigonometry by introducing functions like tangent and cotangent, developing spherical trigonometry, and creating rigorous tables for astronomical use.

    During the Renaissance, Regiomontanus wrote De Triangulis, the first major European text devoted entirely to trigonometry, establishing it as an important tool for navigation and astronomy.

    Later, John Napier, the Scottish mathematician, in the 16th century, invented logarithms, thereby revolutionizing trigonometric computation. Logarithmic sine and tangent tables dramatically reduced calculation time and errors, enabling efficient handling of spherical spheres.

    5. Probability

    The earliest examples of probability come from the Far East in China. Texts like the I Ching explored probability-like patterns through hexagram combinations. In India, epics like the Mahabharata mention weighted dice and gaming odds, and scholars analyzed outcome frequencies, which can be seen as an early form of probability. In the Arabic World, scholars examined risk in trade, inheritance disputes, and legal judgments. Their writings used combinatorial reasoning for dividing wealth or calculating fair shares in uncertain situations. Though not yet a formal theory, these analyses introduced structured thinking about likelihood, expected value, and equitable outcomes in real-world contexts.

    In the 16th century, Gerolamo Cardano, an Italian mathematician, became the first one to systematically attempt to quantify dice and card games in his work Liber de Ludo Aleae. He used sample spaces and frequency-based arguments to estimate chances, laying the groundwork for mathematical probability. 

    Later Pascal-Fermat letters created the foundation of modern probability theory. Their analysis of the problem of points introduced expected value, combinatorial reasoning, and consistent methods for evaluating uncertain outcomes.

    In the 17th century, the Swiss mathematician Jacob Bernoulli established the Law of Large Numbers, proving that long-run frequencies converge to true probabilities. His work gave probability a firm theoretical basis applicable to statistics, insurance, and scientific inference. Later, Thomas Bayes, the 18th-century English mathematician, introduced the idea of updating probabilities using new evidence, providing the conceptual foundation for Bayesian inference. His theorem formalized reasoning under uncertainty and linked probability to belief revision.

    6. Statistics

    The earliest examples of statistical data collection can be found in the censuses conducted in Ancient Egypt, Mesopotamia, and China about 3,000 years ago.

    Imperial China later maintained the traditional registers for detailed accounts of its demographics, occupations, and agricultural output. Governments used large-scale datasets for taxation, labor allocation, and social policy.

    In India, the Arthashastra described sophisticated data-gathering methods, including crop surveys, population counts, market price tracking, and crime tables. These records supported economic planning and state management.

    Millennia later, the seventeenth-century English thinkers like John Graunt and William Petty pioneered “political arithmetic,” using data on births, deaths, and trade to analyze state power. Later, the German mathematician and astronomer Carl  Friedrich Gauss introduced the normal distribution while studying astronomical measurement errors. His bell curve model revealed how random variations cluster around a mean, becoming a cornerstone of inferential statistics. In the latter half of the 19th century, Karl Pearson, the British statistician, formalized modern statistics by creating correlation coefficients, chi-square tests, and regression methods. His work transformed statistics into a mathematical discipline rooted in probability theory. Later, another British mathematician, Ronald Fisher, advanced statistical theory through concepts like maximum likelihood estimation, analysis of variance (ANOVA), and experimental design principles. Fisher’s framework became the basis of modern statistical science and still shapes research methodology across disciplines.

    7. Logic

    Many of the early civilizations developed their own schools of logic. In India, the Nyaya school developed a rigorous system of reasoning centered on perception, inference, comparison, and testimony. It represented one of the earliest and most detailed logical traditions in the ancient world. In Greece, the Aristotelians organized reasoning into structures based on universal and particular propositions. Aristotle’s Organon shaped Western logic for nearly two millennia, defining rules for deduction, classification, and scientific argument. The Stoics later developed propositional logic, focusing on whole statements rather than terms. They introduced logical connectives, inference rules, and truth value analysis far ahead of their time. Later in India, Buddhist thinkers like Dignaga and Dharmakirti created a sophisticated epistemological framework emphasizing perception and inference. They introduced theories of exclusion, fallacies, and valid cognition, shaping logic across India and Tibet. In the Islamic World, Avicenna extended Aristotelian logic by refining modal reasoning, distinguishing between necessity and contingency, and developing new types of syllogisms. His reworked logical framework deeply influenced Islamic and later European scholasticism. Medieval European scholars later integrated Aristotelian and Islamic logic into a unified teaching tradition.

    Much later, in the 19th century, George Boole, a British mathematician, revolutionized logic by expressing reasoning through algebraic symbols, turning logical statements into mathematical equations. Boolean algebra introduced operations like AND, OR, and NOT, enabling precise analysis of logical relations.

    Gottlob Frege, of Germany, developed predicate logic and argued that mathematics derives from pure logic. His formal system introduced quantifiers and variables, vastly expanding the expressive power of logic. Finally, Bertrand Russell and Alfred North Whitehead attempted to ground mathematics in logic through their Principia Mathematica. Their monumental work formalized set theory, arithmetic, and logic in one system, responding to the foundational crisis. Although incomplete, it shaped twentieth-century logic and influenced computer science and mathematical philosophy.

    8. Set Theory

    Before the formalization of Set Theory, the early mathematicians of Greece, India, and the Islamic world used set-like concepts when grouping numbers, classifying geometric objects, or distinguishing categories of quantities.

    In the 19th century, George Cantor transformed mathematics by showing that different sizes of infinity exist. He introduced one-to-one correspondence to compare infinite sets and demonstrated that real numbers form a larger infinity than natural numbers. This breakthrough challenged long-held assumptions and opened an entirely new domain in mathematical thought. He also defined sets, cardinality, ordered pairs, and transfinite numbers. He built a coherent theory explaining both finite and infinite collections, establishing the basis of modern set theory.

    Later, Ernst Zermelo, the German logician, improved set theory by introducing a formal axiomatic system in 1908, which was later strengthened by Abraham Fraenkel and others, creating the Zermelo-Fraenkel axioms with the axiom of choice(ZFC). This became the standard foundation of mathematics, defining how sets behave, how infinite collections operate, and how structure emerges from simple axioms. ZFC remains the dominant formal model today.

    9. Calculus

    The most ancient form of proto-calculus can be found in Ancient Egypt, where the scribes used practical methods to approximate areas and volumes for fields, granaries, and pyramids. Texts like the Rhind Papyrus show rules for computing slopes and circle areas with near-calculus intuition. The Babylonian tablets also show sophisticated numerical tablets for squares, reciprocals, and compound growth, enabling calculations related to interest, motion, and geometry. Their systematic use of sequences and iterative procedures hints at proto-calculus thinking.

    Later, Greek mathematicians like Eudoxus and Euclid used the method of exhaustion to compute areas and volumes by inscribing ever-finer polygons. It laid the foundational groundwork for integration centuries before calculus was formalized. Archimedes advanced the exhaustion method by summing infinitely many slices to find areas, volumes, and centers of mass. His work on spirals, parabolas, and spheres essentially performed an experimental form of integral calculus.

    In India, around the late 14th century CE, Madhava, the Kerala mathematician, discovered infinite series expansions of trigonometric functions, including a power series form of π. His results anticipated the Taylor series by several centuries, using iterative corrections and convergence analysis. The Kerala School of Mathematics created a remarkably advanced pre-calculus framework rooted in precise infinite summations.

    In the Islamic world, scholars like Ibn al-Haytham and Sharaf al-Din al-Tusi examined the instantaneous rate of change, volumes generated by rotation, and early limit-like arguments.

    Finally, in the 17th century, Isaac Newton and Gottfried Wilhelm Leibniz formalized calculus in a structured form. Newton focused on fluxions and instantaneous motion, while Leibniz introduced differentials and integral notation. Together, they unified ideas of change and accumulation, providing rules of derivatives, integrals, and infinite series that became the foundation of modern analysis.

    Later, Leonhard Euler transformed calculus into a powerful symbolic discipline by systematizing functions, derivatives, and infinite series. He introduced standardized notation and solved a vast range of differential equations. Euler’s clarity and depth turned calculus from a discovery into a mature mathematical language used across science and engineering.

    Conclusion

    Mathematics has slowly evolved over the last three millennia. Whether it is arithmetic or trigonometry, statistics or calculus, mathematics now plays an important part in each of our lives – from professional to personal. Thus, knowing the origin of each branch can be very crucial in understanding how the ideas inside the human mind have evolved. Sorry for making such a large blog. For convenience, no formulae or equations have been used. Hope you will not mind the length. So, if you find this blog interesting, please like, share, and subscribe. Also, feel free to comment- whether any criticism, any inquiry, or anything you like. Finally, thank you for reading this blog.

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  • 7 Intellectual Rivalries: How Great Idea Battles Shaped Human History

    7 Intellectual Rivalries: How Great Idea Battles Shaped Human History

    Introduction

    Homo sapiens is considered an intellectual species. For over 60,000 years, human beings have slowly evolved through time with the help of cognitive, agricultural, and scientific revolutions. Through logic, reason, trial and error, the primitive humans have evolved to their modern selves. During the course of this intellectual evolution, although agreement by the general public played an important role, disagreement and even rivalries played an important role in enquiry and further evolution. In this blog, we talk about seven such famous rivalries that shaped the course of human history to a certain degree. From classical Greece to modern science, these rivalries played an important role in how human beings began to understand the universe.

    1. Platonism vs Aristotelianism

    The school of Platonism believed that the world around us is a shadow of a higher one. Plato argued that true knowledge comes from pure reason and turning inward. He suggested not to trust our imperfect senses. For the Platonists, the real world was abstract and eternal, which cannot be perceived or understood by our five senses.

    Then came the Aristotelians. They suggest that the real world can only be seen by studying everything around us through our senses, including various substances, causes, and observable patterns. According to Aristotle, true knowledge can be achieved through practical experiences, and not from theories and inner contemplations.

    This rivalry became the foundation of modern Western thought, specifically between idealism and empirical realism.

    2. Nyaya vs Buddhism

    The Nyaya Philosophers of ancient India believed in a realistic world that can be known through perception, inference, comparison, and testimony. They gave importance to logic above all else. They believed in a permanent self (atman) and an objective world that works alone on pure logic and reasoning.

    Buddhists, on the other hand, believed everything is temporary, including the self, which is just a collection of experiences. They were skeptical of Nyaya’s claim of objectivity and propagated relativism.

    This rivalry shaped India’s intellectual debate over objective vs subjective truth for centuries.

    3. Confucianism vs Legalism

    Confucius and his followers saw society as something that flourishes through virtue, morals, and proper relationships. They believed humans could evolve through proper guidance, education, and ethics. They proposed an ethical world that would be ruled by virtuous rulers for inspiration.

    Legalism argued the opposite – a society could function properly only through strict laws and firm punishments. They believed the world could be in perfect order through proper law enforcement, and not through morals and virtues.

    Both the schools influenced China in different periods (Legalism during the Qin Dynasty and Confucianism during the Han Dynasty), before finally merging with the societies of the Chinese Civilization forever.

    4. Advaita vs Dvaita

    Adi Shankara and his school of Advaita Vedanta taught that reality is ultimately the nondual Brahman. They claimed that liberation from illusion occurs when the self realizes that God, the self, and the universe are all one.

    Dvaita Vedanta, founded by Madhva, debated that God, the self, and the universe are distinct forever. The world is fully real and not an illusion. According to them, liberation will occur not through any realization, but through complete devotion to God (Vishnu).

    This debate shaped Indian Philosophy and continues to thrive in Hindu philosophical discussions.

    5. Rationalism vs Empiricism

    Rationalists like René Descartes and Baruch Spinoza believed that the mind contains innate ideas, and reason is the strongest path to truth. Mathematics and Logic come from proper reasoning and critical thinking, and are independent of the senses.

    Empiricists like John Locke, David Hume, and George Berkeley argued the reverse: the mind begins as a blank slate, and is filled by knowledge from experience. According to them, sense organs are the ultimate tools of understanding, and even complex ideas evolve from simpler impressions.

    This debate laid the foundation of modern science and shaped the Enlightenment Period.

    6. Lamarckism vs Darwinism

    Jean-Baptiste Lamarck proposed that species evolve because organisms adapt during their lifetimes and pass these traits to their offspring. Giraffes stretch their neck to eat leaves from tall trees, and their children inherit longer necks. According to him, evolution was driven by need and effort.

    Charles Robert Darwin showed that evolution works through natural selection – random mutation occurs, and those better suited for their surroundings survive and reproduce. Traits don’t arise because they are needed; they remain because they work.

    Darwin’s model replaced Lamarck’s theory, completely changing the direction of the study of genetics and evolution.

    7. Relativity vs Quantum Mechanics

    Albert Einstein’s Relativity described the universe as smooth, continuous, and governed by precise laws. According to his theory, space and time curve around mass, resulting in deterministic patterns. It works beautifully on celestial objects like galaxies, stars, and planets.

    Quantum Mechanics, led by the likes of Max Planck and Niels Bohr, challenged the picture. At the smallest scales, reality becomes probabilistic, discontinuous, and uncertain. Particles behave like waves, and both position and momentum cannot be determined simultaneously.

    Both the theories still work – but they don’t agree with each other, leading to Physics’ greatest rivalry.

    Conclusion and Reflection

    These seven rivalries showed that contradicting ideas can survive in the same world and often lead to some kinds of revolutions. Debates, discussions, and disagreements are some of the strongest tools that humans possess and should always be encouraged, cherished, and promoted. If everyone agreed to the same idea, humans would still be hunters and gatherers in the 21st century CE.

    That’s all for this blog. Please like, comment, and share if you find this interesting. Thank you for reading this blog.

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  • From Greece to India to China: 30 Ancient Philosophy Schools Explained Simply

    From Greece to India to China: 30 Ancient Philosophy Schools Explained Simply

    Introduction

    Long before modern science and psychology, people across the ancient world were already asking the same questions we still struggle with today – what is real? What is good? What is the purpose of life? From the coasts of Greece to the forests of India and the courts of China, early thinkers tried to make sense of existence through reason, observation, and introspection.

    These pioneers built the first schools of philosophy – communities of debate, meditation, and inquiry – each offering its own map of reality.

    This post takes a quick journey through 30 ancient schools of thought – from the Stoics and Pythagoreans to the Buddhists and Confucians – to see how humanity’s oldest ideas about truth and meaning still shape our world today.

    Chapter 1: Greek Schools

    1. Milesian School – The Milesians- Thales, Anaximander, and Anaximenes – were the first to seek natural rather than divine explanation of the world. Living in the Ionian city of Miletus, they asked what the universe was fundamentally made of: water, air, or an undefined, boundless substance called apeiron. In doing so, they transformed myth into reason and laid the groundwork for science itself.
    2. Pythagorean School – Founded by Pythagoras, the school saw numbers as the hidden structure of reality. To them, harmony, proportion, and mathematical order governed both music and the cosmos. They mixed mysticism with mathematics, teaching that the soul was immortal and the universe was a grand symphony of numerical relationships.
    3. Heraclitean School – Heraclitus of Ephesus saw the universe as constant change – “you cannot step into the same river twice.” Fire, for him, symbolized the ever-living process of transformation. Beneath this flux, however, was logos – a rational order guiding the chaos. His vision inspired later thinkers who sought unity within motion.
    4. Eleatic School – The Eleatics, led by Parmenides and Zeno, turned Heraclitus upside down. They argued that change and plurality were illusions – that reality is one, eternal, and unchanging. Zeno’s paradoxes, like Achilles and the tortoise, challenged the very logic of motion, forcing philosophers to rethink how we perceive truth and illusion.
    5. Pluralistic school – Thinkers like Empedocles and Anaxigoras tried to reconcile change and permanence. Empedocles proposed that all things were made from four roots – earth, air, fire, and water – combined by love and strife. Anaxigoras added the mind as the cosmic force organizing matter. They bridged mythic unity and scientific multiplicity.
    6. Atomist School – Leucippus and Democritus imagined the universe as composed of indivisible particles – atoms – moving in the void. They rejected divine causes, suggesting that natural laws and random motion explained everything. Their vision of a mechanical universe later echoed in modern physics, centuries before it was discovered.
    7. Platonic School – Plato saw the visible world as a shadow of a higher reality – the world of forms or ideas. True knowledge, he said, comes not from the senses but from remembering these eternal truths. His dialogues blended reason, myth, and moral idealism, shaping thought for over two millennia.
    8. Aristotelian School – Aristotle, Plato’s greatest student and critic, brought philosophy down to earth. He emphasized observation, classification, and logic, believing that form and matter coexisted in everything. His Golden Mean defined virtue as balance, and his systematic works on ethics, politics, and science built the foundation of rational inquiry.
    9. Epicurean School – Epicurus taught that happiness lies in simple pleasures, friendship, and the absence of fear- especially fear of the Gods and death. He saw the world as atoms in motion, not a divine design, and encouraged moderation over indulgence. His quiet garden school was a sanctuary of calm reason against superstition.
    10. Stoic School – The Stoics – from Zeno of Citium to Marcus Aurelius – believed that virtue alone leads to happiness. They taught self-mastery, duty, and acceptance of fate, viewing reasons as the divine fire within all. Their strength lay in serenity: aligning one’s will with nature’s law brings true freedom.
    11. Cynic School – Founded by Antisthenes and made famous by Diogenes, the Cynics rejected luxury and convention, living in radical simplicity. They believed virtue was the only true good, and social norms were mere illusions. Their defiance of comfort and hypocrisy inspired later philosophies of freedom and authenticity.
    12. Skeptic School – The Skeptics, led by Pyrrho and later Sextus Empiricus, doubted the possibility of certain knowledge. They advised suspending judgment and living according to appearances rather than dogma. Paradoxically, their doubt brought peace, for when one stops insisting on the truth, the mind rests in quiet balance.
    13. Neoplatonic School – In the 3rd Century CE, Plotinus revived Plato’s vision through mysticism. He taught that all reality flows through the One, a transcendent source beyond being and thought. The soul, through contemplation, can ascend back to the divine unity. Neoplatonism bridged Greek reason and Eastern spirituality, influencing early Christian and Islamic thought alike.

    Chapter 2: Canaanite Schools

    1. Judaism – Emerging in ancient Canaan and later crystallized through prophets and rabbis, Judaism framed philosophy not around speculation but covenant – a moral relationship between humans and the divine. Its wisdom tradition, from Job to Ecclesiastes, wrestled with suffering, justice, and meaning. Rather than abstract metaphysics, it offered an ethical vision: one God, one moral law, and a call to live rightly in a world shaped by divine purpose. Greek thinkers sought truth through logic; the Hebrews sought it through righteousness.
    2. Samaritanism – A sister faith to Judaism, Samaritanism preserved an older version of the Israelite religion centered on Mount Gerizim rather than Jerusalem. Its philosophy lay in fidelity to divine law and sacred geography – the belief that holiness resides in obedience and place. While smaller in influence, the Samaritans represented a quiet protest against central authority, valuing purity of faith over expansion of empire. Their endurance for millennia makes them a living echo of philosophy rooted in devotion and identity.

    Chapter 3: Persian Schools

    1. Zoroastrianism – Founded by the prophet Zarathustra around the 2nd millennium BCE, Zoroastrianism framed the universe as a battleground between truth and falsehood. Its supreme god, Ahura Mazda, represents light, wisdom, and justice, eternally opposed by the spirit of chaos, Angra Mainyu. Unlike fatalistic myths, it gave humanity moral agency – each choice contributing to the victory of good. This ethical dualism influenced later religions, from  Judaism’s angels and demons to Christian and Islamic ideas of heaven and hell.
    2. Manichaeism – Emerging in the 3rd century CE through the Persian prophet Mani, Manichaeism fused Zoroastrian dualism with Christian and Gnostic mysticism. It saw the cosmos as divided between light and darkness, spirit and matter, and portrayed human life as a struggle to free the divine spark trapped in flesh. Its mix of philosophy, mythology, and ascetic discipline spread across Asia and Europe before persecution nearly erased it. Yet its influence endures in every worldview that sees existence as a moral and metaphysical tension between purity and corruption.

    Chapter 4: Indian Schools

    1. Samkhya – Samkhya, one of India’s oldest philosophical systems, teaches that reality consists of two eternal principles – Purusha (consciousness) and Prakriti (matter). Liberation arises when the self realizes it is pure awareness, separate from nature’s restless dance. Samkhya’s rational, dualistic framework became the backbone of later Hindu and yogic thought, offering one of humanity’s first psychological models of existence.
    2. Yoga – Built upon Samkhya’s metaphysics, the Yoga school, summarized by Patanjali, turned philosophy into a disciplined practice. It taught that through ethical living, breath control, concentration, and meditation, the mind can be stilled and the soul united with its pure source. Yoga was not merely an exercise, but a study of consciousness – philosophy turned inward experience.
    3. Nyaya – Nyaya was India’s school of logic, founded by Gautama. It argued that liberation requires right knowledge, and right knowledge comes through rigorous reasoning. By classifying perception, inference, comparison, and testimony as valid sources of truth, Nyaya built the foundation for India’s analytic tradition – philosophy as clarity and precision.
    4. Vaisheshika – Closely related to Nyaya, Vaisheshika, founded by Kanada, offered an atomic theory of the universe. It divided existence into categories – substance, quality, motion, and more – and proposed that all matter is made of eternal atoms. Though metaphysical, its aim was spiritual: by understanding the universe’s structure, one learns detachment from it.
    5. Mimamsa – Mimamsa, or Purva-Mimamsa, saw the Vedas not as myths but as eternal laws governing the body. Founded by Jaimini, it focused on ethical action and ritual precision, teaching that moral order sustains both society and the cosmos. It treated language, ritual, and ethics as tools of liberation through righteous living rather than mystical knowledge.
    6. Vedanta – Vedanta, or Uttara-Mimamsa, took the Upanishads as its core and declared that the individual soul and the ultimate reality are one. Thinkers like Shankara, Ramanuja, and Madhva offered different interpretations – from non-dualism to theism – but all sought union within the infinite. Vedanta became the crown of Indian philosophy, blending logic, devotion, and mystic insight.
    7. Carvaka (Lokayata) – The Carvaka school was India’s bold materialist voice. It rejected the authority of the scriptures, denied karma and the afterlife, and held that perception is the only valid source of knowledge. Life, they said, is short and sensual – enjoy it while it lasts. Though mostly lost to time, Carvaka’s skepticism proved that ancient India also made room for atheism and reasoned doubt.
    8. Jainism – Jain philosophy, founded by Mahavira, taught that all souls are bound by karma, subtle matter that clings to consciousness through violence and desire. Liberation comes through non-violence, truth, and ascetic discipline. Its vision of a living, moral universe made compassion and self-control the highest forms of wisdom.
    9. Buddhism – Born from the insights of Siddhartha Gautama, Buddhism turned philosophy into a path of liberation through mindfulness and compassion. It rejected speculation about eternal souls or Gods, focusing instead on suffering and its cessation. Through the Four Noble Truths and the Middle Way, it taught that freedom lies not in belief, but in awakening – the end of craving and illusion.

    Chapter 5: Chinese schools

    1. Taoism (Daoism) –  Rooted in the teachings of Lao Tzu and Zhuang Zhou, Taoism sought harmony with the Tao – the Way, the natural flow of all things. It taught that wisdom lies not in control but in effortless action, living gently in accord with nature’s rhythm. Through paradox and poetry, Taoism celebrated simplicity, spontaneity, and mystery beyond words – the silence that makes music possible.
    2. Confucianism – Confucius turned philosophy into a moral art of living. In a time of social chaos, he taught that virtue begins with respect – in family, in friendship, and in governance. Through ren (humaneness) and li (ritual propriety), he envisioned harmony between personal ethics and public order. His disciples built one of the most enduring systems of ethical and political philosophy in human history.
    3. Mohism – Founded by Mozi, Mohism arose as a challenge to both Confucian hierarchy and feudal warfare. It promoted universal love – the idea that all people deserve equal care, regardless of kinship or status. Rational and practical, Mohists valued merit over birth and sought social welfare through ethical governance. Though later eclipsed, their ideals foreshadowed utilitarian thought and humanitarian ethics.
    4. Legalism – Legalism, the harsh counterpart to Confucian Virtue, believed that order could only be achieved through strict laws and enforcement. Figures like Han Feizi argued that humans are driven by self-interest, not morality – so rulers must govern through reward and punishment, not virtue. It unified China under the Qin dynasty, but at the cost of freedom, reminding later thinkers that power without ethics leads to tyranny.

    Conclusion

    Across millennia and continents, these thirty schools of philosophy spoke in different tongues but asked the same questions: What is real? What is right? What is enough? The Greeks sought order through reason, the Canaanites through covenant and faith, the Persians through moral struggle, the Indians through liberation, and the Chinese through harmony. Each offered not just theories, but ways of living – paths toward wisdom in a world that has always felt uncertain.

    Through temples have crumbled and languages changed, their echoes remained. Stoic calm still guides psychology, Buddhist mindfulness shapes modern therapy, and Confucian ethics underlie our ideas of duty and family. Even the skeptics and materialists whisper in science and humanism today. To study these schools is not to look backward, but inward – to rediscover how the ancient mind still beats within us.

    That’s all for this blog. If you enjoyed this post, please like, comment, and share. Thank you a lot.

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  • The Axial Age Explained: China, India, Persia, Canaan & Greece

    The Axial Age Explained: China, India, Persia, Canaan & Greece

    Introduction

    The Axial Age refers to the time period between 800 and 200 BCE, which was coined by the German Philosopher Karl Jaspers (1883 – 1969). During that time,  philosophical and theological shifts occurred in various parts of the world, namely China, India, Persia, Canaan, and Greece. From Confucius to Socrates, and from Buddha to Zarathustra, almost all of the Ancient Philosophers were born during the same time period. This blog deals with the development in the philosophy and the theology of the above-mentioned places, and also mentions the great individuals as well as texts linked with the axial age.

    Chapter 1: China

    China, during the axial age, saw the formation and development of various philosophical schools, including Confucianism, Daoism, Mohism, and Legalism. Confucius or Kongzi was a 6th-century philosopher whose thoughts formed the basis of Confucianism – a philosophy dealing with ethics and filial piety. His work, The Analects, is still considered the backbone of Chinese society. Another famous philosophical school that sprang up was that of Taoism, the school of natural harmony and complementary behaviors. Famous philosophers of this school include Laozi and Zhuangzi, known all around the world for their masterpieces- Dao De Jing and the Book of Zhuangzi. Other famous schools that came up in the axial age in China were those of Mohism and Legalism, the former dealing with universal love and meritocracy, and the latter dealing with the rule of law and strict governance.

    Chapter 2: India

    In India, during that period, the Vedic ritualistic worship was beginning to be complemented by the philosophical richness of the texts, such as the Upanishads and the Bhagavad Gita. Upanishads deal with philosophical and metaphysical questions like why the universe was created, what life is, and how to lead a proper life honestly and dutifully. There are about 108 Upanishads, out of which 13 are considered principal ones. The Bhagavad Gita is a part of the Hindu epic, the Mahabharata, which can be considered a gist or abridged version of the Principal Upanishads. Around the 6th century BCE, two philosophical giants with the names of Vardhamana Mahabhira and Siddhartha Gautama were born, who challenged the Orthodox Hindu philosophy and cosmology, and formed their own philosophies of Jainism and Buddhism.

    Chapter 3: Persia

    Persia was the ancient name of Iran. Before the axial age, the Iranians followed a form of polytheistic proto-Indo-Iranian religion. But around the 7th century BCE, a prophet cum philosopher with the name of Zarathustra took birth (though some records show he was born much earlier, around 1500 BCE, but most agree with the 7th century BCE). He created a dualistic philosophy where the world was a battlefield of good and evil in the form of Ahura Mazda and Angra Mainyu, which later came to be known as Zoroastrianism. The Persians soon developed religious and philosophical texts like the Avesta and the Gathas. The  Avesta is the sacred Zoroastrian scripture, written in the Avestan language, which contains liturgical texts and codes of ritual laws. The Gathas are the texts that primarily deal with religious hymns, especially those by Zarathustra himself.

    Chapter 4: Canaan

    Ancient Canaan was the region consisting of the modern nations of Israel, Palestine, Jordan, Lebanon, and parts of Syria. It was the region from which the core theology, cosmology, and philosophy of the Abrahamic faiths came. During the Axial Age, the earliest forms of Judaism were developing. The idea of Yahweh being the moral, transcendent God probably came around this time. Also, the emphasis on social justice and the formation of covenant ethics came up during the period. Various prophets and thinkers like Isaiah, Jeremiah, Amos, and Ezekiel were born during the Axial age, who formed the foundations of the Abrahamic philosophies. It was also that time when the Hebrew Bible, or the Tanakh, was compiled.

    Chapter 5: Greece

    The philosophical development around the Greek Civilization during the Axial age is perhaps the most popular in the modern world in general, compared to the other ones discussed above. The Greeks developed a way of rational inquiry and logic in philosophical dialogue and questioning, which are still studied and implemented in modern arguments and debates. The three greatest philosophers who were born during that time were Socrates, Plato, and Aristotle, who, through their works, including Plato’s Republic and Aristotle’s Politics, made the Greek Civilization immortal, even millennia after their complete eradication by the Abrahamic philosophies. Even today, people following Abrahamic, Dharmic, or Chinese theologies still refer to Greek ideas and thoughts in their daily life.

    Conclusion

    Although the axial age ended around the 2nd century BCE, its impact can be seen within each and every modern civilization. The later philosophers of the common era took inspiration from the axial age to form their own school of philosophy, whether in China, India, Persia, Arabia, Canaan, Greece, Rome, or even Africa. No other age, except the age of the scientific revolution in the 16th and 17th centuries CE, has had more impact in human history than that of the Axial Age for the last 5000 years. That is all for this blog. This is perhaps the shortest blog ever written on this site. Hope you enjoyed it and learned something. Please like, comment, and share. Thank you.

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    Disclosure: This post contains affiliate links. As an Amazon Associate, I earn from qualifying purchases. I only recommend books I truly value.