The wonder that was India

 Once upon a time, philosophers-- men and women alike-- observed systems of interacting elements, and noted that the system as a whole, can be in different "states of being." They also noted that some states of being are more "stable" and "sustain" against perturbations. It is in these sustainable states, we can nurture life. The entire ecosystem of our planet, they noted, is just a sustainable state of being.

They called this phenomenon of sustainability against perturbations, as "dharma".

Sustainability is not a binary. Some states are more sustainable than others. They also noted that regardless of how sustainable was a state of being, every physical system eventually collapsed. Nothing in this physical world, they noted, is in a state of eternal dharma.

This prompted them to embark on a quest for "eternal sustainability" which is called "Sanatana dharma".

Physical systems are trivially not eternally sustainable. They hence called physical reality as "Maya." Eternal sustainability, if it exists, needs to be in the realm of prajna or consciousness, they noted. Even here, they saw that not every element of data, information and knowledge, represented eternally sustainable assertions. For example, an assertion that "summer is hotter than winters" is mostly true, except when there have been exceptions.

They then noted that, as long as assertions connected with physical reality, they can't be eternally sustainable. But then they saw that no matter how much they tried to go meta, some connection to physical reality remained. But some of them managed to get into a state of consciousness, that was completely unconstrained by physical reality.

They called this, the universal consciousness or Reality or Brahman.

They then went on to create a vibrant civilization that was based on this quest for experiencing the state of eternal sustainability. They saw that, when the core inquiry of the population is on eternal sustainability, we can derive notions of ethics, fairness, harmony, freedom, and other elements of humanities, fairly easily.

This in a nutshell, was the wonder that was India. Not the drivel meted out by Indology experts in high citadels today.

Delusions in Indian thought - I

 While Indian thought has profound fundamentals, like every other hermeneutic framework, there are a number of mistaken notions and delusions that continue to bring untold misery. Reform and rejuvenation is nothing new to Indian thought-- which has seen several reformers over the years including Buddha, Mahavira, Shankara, Ramanuja, Madhwa, etc. Indeed, the resilience of Indian culture is due to its ability to reflect, question and reform itself. 

In this series, I'll put forth some delusions that I've encountered, that continue to complicate our lives and brings unnecessary hardship. 

One of the most damaging delusions in Indian thought is the idea of "prarabda karma" or the "karmic baggage" (whatever that means), that we start off at the beginning of our lives, based on our actions in our "previous life".

This mistaken concept leads to a variety of cognitive fallacies like self-fulfilling prophecies, affirming the consequent, begging the question, etc. Somebody is suffering? Oh, he must have done something bad in his past life. Someone feels they have bad prarabda karma? Well then lead your entire life under a cloud of guilt and be defensive.

Firstly karma simply means action. It is not some kind of retribution, and there is no such thing called "karmic baggage". "karmaphala" means the response we get to our karma-- and it is not the same as some kind of moral retribution. Karmaphala for our actions is based on systems and their sustainable states, which I've explained in my book called the Theory of Being. It is not a simple, moral retribution of the form "As you sow, so shall you reap." It is a much more profound concept that is based on a deep understanding of systems and ergodicity.

To be sure, we are born with "prarabda guna" or some characteristics (guna) that are hardcoded into us by birth. Some of us are nervous by nature, while some are gregarious by nature, and some are hypersensitive by nature, and so on. Our birth characteristics or our emotional disposition, comes from our genes. We are pretty much stuck with our prarabda guna and it is futile to change our basic nature. What we can do however, is to become aware of our basic nature, and this awareness leads us to better strategies for managing it. We can use our basic nature to our advantage, if we are aware of it-- without which, our basic nature will be using us.

But this is not the same as "prarabda karma". Sure of course, we may get undeserved accolades or brickbats. We may be adored or hated just for being who we are. That again is not some "karmic baggage"-- it is a question of what we identify with, and the history of that object of our identification.

For instance, Indians and Indian thought faced and continue to face a lot of contempt in the Western and West Asian world. By calling this our "karmic baggage" the guilt is put back on Indians by saying that Indians must have done something bad in our "previous life", etc. And there is a whole ecosystem called "atrocity literature" that does just this. The contempt of course, comes from the oppressor's need to justify oppressive policies. How can one morally justify colonial occupation or plunder and loot of a vast civilization, other than by calling it the "white man's burden" to bring civilization to the primitive natives, and so on?

The saddest part of this story is the extent to which, flawed concepts like "prarabda karma" are internalized within India itself.

If we need to unshackle ourselves, it is imperative that we "smash" such delusions and understand the law of karma for the profound concept that it actually is.

Dharma and Ergodicity

In the last couple of years, I have spent a lot of time trying to interpret the notion of dharma and traditional Indian worldview using systems theory. You can check out older posts with the label "Theory of Being" and also my book on Amazon called "Theory of Being". 

In this post, I put forth some more working ideas towards building a more comprehensive theory of systems using Indian thought. The ideas presented here are work in progress-- meant to provoke thought and get feedback. Ideas presented in this blog are subject to future revisions as I get more clarity. 

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When we study systems we are first taught that a system is an ensemble of interacting parts. The interaction between the parts or the system dynamics, is what characterises a system-- without which, it would just be a collection of different parts, and not a system. 

Systems are everywhere-- in fact, a non-system is much harder to find and/or create, than a system. Even an inanimate piece of matter, like a stone, is a system of tightly interconnected molecules interacting in specific patterns that keep the solid matter intact. 

When we study systems in today's world, we are taught about two kinds of systems called as: linear and non-linear systems. The latter is also sometimes called "complex" systems. 

Linear systems are so called because their dynamics can be represented in the form of linear differential equations. In an intuitive sense, they represent an "open loop" interaction with their environment where inputs from the environment and the outputs to the environment do not confound one another. 

Almost all machines adopt a linear design model. Even with complex machinery like say an airplane, the overall flight dynamics is still linear. What this means is that the input that goes into the airplane (the air in front of the engines) is separate from the output (or the exhaust) that comes from the airplane. Airplanes in their current design would find it very hard to fly, if the exhaust and the turbulence it creates, were to somehow come back to the front of the engine. Indeed, when planes fly too close behind other large airplanes, they are known to even crash from the exhaust turbulence, also called the wake turbulence. 

But most natural systems are non-linear in nature. Human societies, ecosystems, weather, etc. all display rich forms of "closed-loop" interactions where the output of some unit in the system comes back to affect it subsequently. We see that in human societies all the time. Our output or actions have consequences that can come back to haunt us, in the (wrongly) called "law of karma".

Non-linear systems are known to be very hard to model, understand and predict. The term "butterfly effect" comes from the study of non-linear systems, representing what is called "sensitivity to initial conditions"-- which means that a small change in the initial conditions of a non-linear model, can result in vastly different ways in which its dynamics would pan out over time. Colloquially, it is said that, a butterfly flapping its wings in one part of the world, can potentially create a chain of events causing thunderstorms in some other part of the world. 

While non-linear systems are hard to model and understand, not all non-linear systems pose a hopeless case. Ludwig von Boltzmannn, who was one of the pioneers in statistical mechanics-- or the study of large number of interacting entities using statistical techniques, had this hypothesis about complex systems: large systems of interacting particles settle down to a stable state where the time average along a single trajectory equals the ensemble average.

This hypothesis was later found to be false, and not applicable universally. But it was true of a specific class of interacting, non-linear systems that has now come to be called "ergodic" systems and the above hypothesis is now called the Ergodic Hypothesis.

To understand ergodicity, let us take an example. Consider a music troupe-- my favourite is ABBA-- (I know, I am old!) who are famous and have a large fan following. They are known for their superlative performance that draws a huge audience whenever they perform. But each time they sing, their performance would not be an exact replica of previous performances. The same song sung at different times would be a little different from one another. But this difference will not be arbitrary-- most of the performances would hover around an expected set of metrics about music quality, beats, emotions, etc. that have made them famous. It would hardly ever be the case that the first time they sing a given song, it would be sublime and the next time it would be downright jarring. 

Suppose, in order to "quantify" ABBA's performance, we develop a set of metrics like highest musical pitch, number of frenzied fans, number of beats per minute, and so on, and we measure them painstakingly across each of their songs. Now, we can see the ergodic property that in a single long performance, the average of these metrics would likely be the same as the average of these metrics obtained from a large number of independent concerts. In other words, to get a good idea of an ABBA performance, we could either take small samples from several of their performances, or sit long enough in a single performance. In both cases, we would get a pretty good idea of an ABBA performance. 

Sometimes the troupe may try to experiment with their performance and change some fundamental stylistic elements. Most likely, such fundamental changes from their signature performances would not have gone down so well with the audience. In other words, the more the troupe changes, the more they would remain in the same neighbourhood of activities that made them what they were.

The ergodic property of systems points to a number of interesting implications. One, it indicates the presence of an "invariance" or a stable set of characteristics of the system that regulates and keeps each individual instance of the system around this stable region. It is almost as if, the system-- the music troupe in our example-- has its own characteristic sense of "self" that is expressed in its performances. Just like when we express ourselves as individuals, we display both a signature set of invariant properties that characterises us, as well as a randomised but bounded distribution of each individual expressions. If a single musician (my favourite now is M S Subbulakshmi) were to sing a given song (my favourite is Bhaja Govindam and here are two different performances of the same song: Performance 1 and Performance 2), each rendition would be somewhat different from each other-- yet all of them have the signature tune of the singer, whom we can recognise instantly. 

Consider again, our music troupe. Suppose that they hire a manager to promote their music, and the manager starts insisting on various changes to their styles according to what he thinks is the latest fad. Each new idea from the manager pulls the troupe's style in a different direction. But one day, if they grow weary of the manager and fire him, the troupe would then almost immediately revert back to their original characteristics. The "invariance" property again. Or shall we say the "elastic" nature of ergodic systems? That is, subject to minor distortions, the system reverts back to how it was, once the distorting influence is removed. 

Suppose also that the favourite troupe was once just a garage band when they started out. As they become rich and famous, they lifestyles change. They move on to bigger houses, buy cars and travel, and even invest in better, high quality instruments and audio systems. Despite all this, their signature distribution would still remain pretty much the same. The sound and video quality of their music may vastly improve, because of which, their impact may become even higher than before. But yet, the better "capability" they now have due to better instruments and money, only serves as a catalyst-- and not as a replacement or an alternative-- for their signature brand of music. 

If you have read about the Theory of Being, the above characteristics would have sounded very familiar. 

Dharmic thought that developed in India, was primarily based on observing life forms and its variegated characteristics. This is in contrast to the physics and mechanics developed in ancient Greece, that models the world in terms of inanimate matter. 

Dharmic philosophers observed living beings and were able to understand the invariance property of living beings. They could see that, despite the variegated behaviours of an animal-- these behaviours were not completely arbitrary. There was something latent and invariant behind the rich set of behaviours, which they could identify as the self. 

It was also apparent that it is our sense of self that drives us, and this is what we strive to preserve, and this is what sustains us. This characteristic of sustaining our sense of self is what is called dharma. They could also see that not every kind of interaction is conducive to dharma, which leads to the concept of adharma. We know this today as not every kind of non-linear interaction is ergodic, and there are indeed non-ergodic systems. 

Dharmic philosophers could also see that they could extend this concept of self and dharma to systems of being, like human societies, ecosystems, climate, and so on. Indeed, they could also use this method of inquiry to even understand the behaviour of metals and annealing, and in understanding several forms of systems of inanimate objects and their interactions. 

This lead to the development of a complete abstract theory of "being" which characterised Eastern thought for several thousands of years and sustained a vibrant civilisation under this thought umbrella. In Indian society, dharma is seen as an essential property for sustenance of life, since thousands of years. Life indeed is ergodic and to preserve life (and human societies and ecosystems), we need to preserve its ergodicity. 

Yet, if we see current day public rhetoric and self-help "motivational" books, many times they fail to recognise this important characteristic. 

"Travel and discover yourself" they say, and keep urging people to spend their money on "experiences" rather than "things". Travelling all the time helps us discover something alright-- we discover that we have spent most of our money, have no place we can call home, have no sense of belongingness anywhere, and so on. Travelling indeed does help us discover new things about the world and about ourselves-- provided we can do this in a sustainable fashion. If our passion for travel uproots us from our homes and our sense of identity and belongingness to somewhere, we have indeed paid a very high price. 

Indian wisdom on the other hand, always advised us to invest our money on building strong relationships and develop new ideas, rather than the dichotomy between experience and things. The underlying reason was of course, dharma. 

Similarly, "live outside your comfort zone" they say. And I'm tempted by Sheldon's quote in the Big Bang Theory: "It is called comfort zone, for a reason". Our best performance may indeed be outside of our comfort zone. But if our life motto is about living outside our comfort zone, we are most likely neglecting an important part of what sustains us. The fact that we feel comfortable in some settings says something about ourselves. It is one thing to just enjoy the comfort of our comfort zones, and yet another thing altogether to discover what does our comfort zone say about ourselves and how can we use it for self actualisation. 

Indian wisdom does not compel us to either be comfortable or uncomfortable. It instead urges us to meditate and observe ourselves, understanding what drives us, what is it that we seek, and by what do we feel disspirited. Our best performance comes not from being comfortable or otherwise, but from a deep sense of self awareness.

Let me stop at this note for now. There are several more interesting characteristics of ergodicity, and the dharmic way of life. More on them in some future posts.

The importance of identity

During the recent election for the next US president, there were a lot of expert opinions, debates and analyses by WhatsApp experts going around. 

In one of these recent debates, I witnessed a debate that went something like this. One member of the group criticised one of the candidates in the US election fray, saying that even though the candidate had her roots in India and was wooing Indian-American voters, she would be bad for Indian interests, given her stance on several issues bothering India at the moment. To this, one of the others answered that, the candidate's misadventures with India would be of no interest to them, and that there are several American issues that she would address well, which is enough to get her elected. 

The above opinion would have been nothing out of the ordinary, had this been said by an American. But this was said by someone who grew up in India, went to the US a couple of decades ago and became a naturalised US citizen, and who still has a large extended family back in India and keeps visiting India often to be with family. And she just said that what her former country is concerned about, is of no consequence to her. 

It was surreal to see this. It reminded me of another instance several years ago when a professional acquaintance, had referred to "Jana gana mana.." when speaking to her children, as "India's national anthem," and not "our national anthem" as parents usually refer it to their children. 

I'm not judging either of these people for their choices-- just that, the experience was so surreal. It was as if, some core element in our conversational semantics has suddenly been replaced with something else. Something that was so deep and fundamental, that we had considered axiomatic, was suddenly no longer so. 

What is that deep rooted element that has changed? It is our sense of Identity. Something that most of us don't even understand what it is and its impact on our lives, and give it up for short-term material benefits. 

Identity is the set of external entities-- including physical entities, ideas and concepts that we associate our sense of "self" with. In other words, the set of things we identify with-- psychologically we feel that they are part of us, or make us who we are. 

Psychologically, we are also hardwired for sustainability or upholding our sva-dharma. All our biological and psychological actions are fundamentally driven by the need for sustaining our sense of self for as long as possible. So what exactly are we striving to sustain? It is simply the set of all entities that we identify with. 

Our sense of self is something internal to us-- not an external entity. When we attach our sense of self to something external, we treat that external entity as something internal to us. Our caring for our sense of self is not driven by "rational" considerations like returns on investment, or utility. Our sense of self is the driver of our decisions-- and is not an external rational choice. We work for the interests of whatever we identify with, regardless of what it gives back to us. We don't stay with family only because they provide for us-- we stay with them through joy and sorrow, through sickness and health, and so on. Because at some level, they are part of our sense of self. This is also the reason why we grieve more when we lose a family member, versus when we lose some stranger. In the former case, it is as if we have lost some part of ourself, because they were part of our identity. 

All economic arguments and considerations can be thrown into the dustbin when our sense of identity is involved. 

Soldiers are indoctrinated with an intense and passionate sense of identity with their country-- which makes them even sacrifice their own lives to protect their country. Similarly, parents see their children as an extension of their own sense of self, and hence strongly identify with them, leading them to sacrifice their own comfort and economic well-being, for the well-being of their children. 

We literally surrender our lives to whatever it is we identify with. It is our sense of identity that brings us all the travails of our lives. Attaching our sense of self to something, without putting enough thought into it, may result in our lives becoming a psychological roller-coaster, and may result in identity crises leading to different forms of dissonance and disorders. 

The archetypal question "Who am I?" is precisely us questioning our identity-- or the set of all things that are driving us. Most of us go through this phase some time or the other in our lives, when we can't understand what is driving us-- prompting us to ask: Who am I?

Our sense of identity is the cause of all joy and misery in our lives. It is the reason why existential philosophers often advocate identifying our sense of self (Atman) with the entirety of the universe including its physical and conceptual realms (Brahman). Working on associating the entire universe with our sense of self, helps keep our equanimity. Nothing that happens in our lives will ever threaten the sustainability or dharma of the entire universe-- which is now our sense of self. 

But associating our sense of self with the entire universe, is easier said than done. It needs enormous practice, determination and focus, which very few of us manage to achieve. 

We can then safely assume that for most of us, our sense of self does not transcend too much beyond our worldly affairs. Some of the things we commonly identify with include: our houses, our cars, our children, our family, our religion, our language, our ethnicity, our country, and so on. These objects of identity are not as eternal as the universe. Sure, they may outlive us, but they still face existential crises. Religions get wiped out, countries get dismantled, cultural groups get diluted (which is why some cultural groups, deluded with a sense of "purity" lead very insular lives-- even inter-marrying within their cultural group, to prevent it from getting diluted). 

By attaching our sense of identity to some worldly entity, it is as if we have tightly attached ourselves to some large creature, like an elephant. We are affected by what happens to the elephant, but we may have little or no control over the elephant itself-- its preferences and actions. 

It is hence, very important to think deeply before identifying with some worldly entity. Do we understand the values and principles with which the entity functions? Do we know the entity's history well enough to understand what kinds of challenges it is going to face? Do we have enough clout over the entity to influence its actions? Are we prepared to remain attached with the entity through all its crises? Do we know how its crises would affect us? And worse, if we have strong links back to the elephant from which we thought we uprooted ourselves from, to attach ourselves to the other elephant, do we know how these two elephants interact? Where do we wish to be if these to elephants start moving in different directions or start fighting with one another? 

Bhajagovindam English Translation

 Bhaja Govindam (Think of Govinda-- Krishna) was a great composition of Adi Shankara, written in the 9th century CE. This composition was immortalised into music by the famous M S Subbulakshmi, and her renditions are widely played today. 

Here is an English translation of the composition by Ramesh Krishnakumar, which I encountered today and thought of sharing through my channels. The translation written in red is my translation from my understanding.

Bhajagovindam bhajagovindam .. O, Worship Govinda, O worship Govinda..... Govindam bhaja muudhamadhe ...Let Govinda be the object of your worship... O ignorant one.... Bhajagovindam bhajagovindam O, Worship Govinda, Worship Govinda ... govindam bhajamuudhamate . ...Let Govinda be the object of your worship... O ignorant one....

sampraapte sannihite kaale

..when the time of death comes..
... regain real happiness at least at the end of your time (death)....

nahi nahi rakshati dukrijnkarane ....your knowledge of grammar (worldly wisdom) will not save you.... mudha jahiihi dhana agama trishhnaam ...O foolish one, give up your craving to amass wealth.... kuru sadbuddhim manasi vi trishhnaam. ... Be desirous in your mind to act with good sense ..... yallabhase nija karmo paattam ... whatever you obtain by your duty ("nija karma" honest actions) .... vittam tena vinodaya chittam ... be content with that earning. .... yaavad vitto paar jana saktah ... as long as one is earning and is healthy..... staavan nija parivaaro raktah ... he will be supported the family..... Pashcha ajjiivati jarjara dehe ... but later when one is without earnings and old in the body ..... vaartaam koapi na prichchhati gehe ... there may be none to even enquire in the house..... bhagavad giitaa kijnchid adhiitaa ... study a portion from the Bhagavad Gita as a least ..... gangaa jalalava kanikaa piitaa ... drink a drop of the ganga water ..... sakridapi yena muraari samarchaa ... worship Lord Krishna (Murari) even once ..... kriyate tasya yamena na charchaa ... then the Lord of death will not have an argument about you ..... punarapi jananam punarapi maranam ... there is, birth again and again, there is, death again and again ..... punarapi jananii jathare shayanam ... one has to lay in a mother's womb, again and again ..... iha samsaare bahudu staare ... one has to struggle in this ocean of life ..... Kripayaa apaare paahi muraare ... Protect me with boundless compassion, O Krishna,..... artham anartham bhaavaya nityam ... Remember that wealth seeking is always purposeless..... naastitatah sukha leshah satyam ... the truth is that one cannot derive sustained happiness from it..... putraadapi dhana bhaajaam bhiitih ... ones who are after money even fear their sons..... sarvatra ishhaa vihiaa riitih ... that is the way of wealth always.....

Snippets from Bharatiya mathematics

In school, one of our first introductions to theorem-proving came from geometry. Sometime in high school, we learnt about Euclid's axioms and several geometric theorems that were proved from the axioms. 

One of the main techniques for proving geometric theorems was by the use of a compass and a (uncalibrated) ruler. For instance, we learnt how to bisect a line segment using a compass and marking intersecting arcs from either ends and connecting the arcs together to cross the line. 

Every method of inquiry has its own advantages and limitations, and embeds within it some deep assumptions about the underlying worldview. So too it is with the way in which Euclid's methods developed. Geometry literally means "earth measurements"-- and Euclid's geometry is deeply rooted in this application area. 

One of the vexing problems with the compass and ruler approach is to make arbitrary divisions of geometric elements. For instance, we used to be challenged by "Maths Olympiad" problems that asked us to trifurcate a line segment into three equal length segments using a compass and a ruler. I vaguely remember having learned the technique from some form of a "brain vita" tutor, but have forgotten it since. 

Recently, I came across Jonathan J. Crabtree-- a mathematics researcher and historian from Australia, who has dedicated himself to the study and popularization of Bharatiya maths dating back to the time of Aryabhata and Brahmagupta. He runs a website called Podometic.in to popularize Bharatiya maths. Crabtree also clarifies that this is not the same as "Vedic Maths". Vedic period preceded advancements in Bharatiya mathematics by a couple of millennia. While there are references to very large and very small numbers in Vedic literature especially based on powers of 10 (resulting in some theories that the notion of zero and infinity was known at that time), there is hardly any literature on formal theorems and mathematical results from that time. Crabtree has even offered a reward of INR 5,00,000/- for anyone unearthing the 16 Sutras in the book ‘Vedic Maths’ in Vedic literature. 

Bharatiya Maths in written form, as we know today, dates back to about 2000 years ago. One of the earliest mathematical treatises is the Brahmasputasiddhanta by Brahmagupta, which is a compilation of several mathematical techniques (thus suggesting that actual mathematics and its application, predated this date). 

Predating the Brahmasputasiddhanta by about 1500 years are the "Shulba Sutras" that provide proofs for several theorems of arithmetic, number theory and geometry. 

The Shulba Sutras around geometry, do not use a ruler and a compass-- but instead, uses a ruler and ropes. And we can see that, just by changing our underlying tools, we can easily address a number of problems that were challenging when tried to be solved using a ruler and a compass. 

For example, Crabtree has a cartoon that shows how to square a circle with rope the Shulba Sutra way, which is impossible the Western way with a compass. 

Let us take the problem of trifurcating a line segment-- or even dividing a line segment into any number of parts. We start as follows. Let us say, we want to divide a line segment into k equal length segments. Start by taking k rulers of equal length (any length). Place them horizontally in a compact sequence one after the other as shown in the figure below. Now, take the line segment that you want to subdivide, and place it in some angle to the horizontal sequence of equal length rulers. Next, take a long ruler and place it such that it connects with the other end of the horizontal line with the other end of the angular line. Now move this rigid ruler inwards and mark off segments from the angular line, whenever a segment boundary is crossed in the horizontal line. 

The following video also illustrates this principle:

 

We can use the same technique to segment a circle into any number of arcs so that their angle at the center is the same. 

For doing this, imagine the angular line in the figure above, as a rope that is stretched out tightly. This rope would have been first wrapped around the circle which we need to segment, and hence represents its circumference. Now use the same technique as earlier, to segment the tightly drawn out rope. Then, wrap this rope again on the circle and mark points on the circumference based on the segments. Connecting these points to the center of the circle, gives us an angular segmentation of the circle into any number of arcs. 

Similarly, the "Pythagoras theorem" was also well known in ancient India centuries before Pythagoras. The above diagram illustrates the proof that was normally used (with altar design being the most widely used application). If we take a square embedded within another larger square such that it segments any edge of the square into two parts: a and b, then we see that the area of the inner square is precisely (a+b)² - 2ab. 

This is illustrated further in the figure above. The right-angle triangle theorem, which may be better termed as the Baudhyana Theorem shows the inner square reorganized into two rectangular and two square regions in the lower figure, essentially dividing c² into a² and b². 

In the talk above, Crabtree also gives several other examples of how Bharatiya thought towards mathematical concepts differed from Western thought, and the implications of same. Note specifically about the concept of negative numbers. In Bharatiya Maths, negative numbers were not considered "lesser than 0" as we are taught in Western maths. They were considered to be an increasing sequence greater than 0, but with opposite semantics of the positive line. This has several implications in interpretation. For example, a wealth of  -7 does not represent a "lesser wealth" than -4, but a "greater debt" than -4. 

The definition of 0 is precisely what results when a negative number is added to a positive number of the same quantity. 

The universality of dharmic thought

Recently I came across an argument that sustainable lifestyles promoted by dharmic thought can be implemented only in "sustainable geography"-- meaning tropical regions where life forms thrives in abundance-- and cannot be implemented in "unsustainable" geography like deserts or colder regions of the earth. 

In this post, let me try to deconstruct this argument. 

There is definitely an influence pathway between "sustainable geography" and a culture of sustainability. But to say that there is an exclusive causal relationship between the two, would be a great oversimplification. 

Worse, this argument also leads to some kind of a fatalism. Other than tropical regions of the world, we cannot sustain anywhere else anyway, therefore either these cultures collapse, or they dominate and consume others (leading to a collapse of the entire world-- but much later). 

Such kinds of fatalism are typically only used to justify one's reckless acts-- for instance, a terrorist justifying his acts by saying, "What else could I have done? We are all doomed anyway!" 

If a culture of sustainability could have emerged only from sustainable geography, we can analogously argue that today's mechanistic culture could have only emerged from unsustainable geography, where medieval Europe fits the bill. But this does not mean that other cultures across the world cannot implement elements of mechanistic cultures like factories and production units. Most countries today are run on factories. 

Similarly, the core elements of dharmic culture are universal in nature-- and not relegated to only those regions where they were conceived. 

Such kinds of misunderstanding comes in because, we equate sustainable living with specific things like vegetarianism or low per-capita energy consumption. Dharmic or sustainable lifestyle does not directly imply either vegetarianism or low per-capita energy consumption. 

The essential element of dharmic lifestyle is a worldview that is not based on linear models. For instance, as long as we keep thinking in terms of food chains, world dominance, feudal hierarchies, social ladders, and so on, or we keep reducing a nation to its economy and economy to its GDP, we cannot build sustainable cultures. 

The main problem with economies today is that while economies are powered by factories and manufacturing units, the entire economy and the country itself is seen no more as a factory or a production unit itself. The metrics that are used to measure a nation's worth, and to provide rewards and incentives to its people, are all based on this paradigm. The second problem with economies today is to see everything outside of human societies as "resources" for our growth. 

Sure, we do need natural elements for our survival. A village in Siberia for example, cannot survive its winters if it does not consume natural "resources" to keep itself warm and consume its animal "resources" to feed its people. But advancements in technology-- like using solar or wind technology, and development of artificial meat substitutes, can greatly reduce the burden we are putting on nature. 

Sustainability is not a binary game, and sustainability is not eternal. The lesser burden we pose on nature, the longer we can hope to sustain. 

There are indeed specific elements of sustainability that are universally applicable. Here I try to list out a few I can think of, on the fly: 

1. Stable environments are conducive to sustainability: When building any business or our own individual lives, it is important to interact with an environment that is by and large, stable. Even if the environment is changing, its changes need to be bounded and largely predictable. Finding sustainable configurations requires reflection, search, and evolution. This cannot happen if the environment is too unpredictable. 
2. Innovate and change through diffusion, not disruption: When entering a foreign market these days, companies look for "disrupting" and "taking over" the market-- and not "blending into" and becoming a part of the target market's culture and social life. "Disruption" has become a virtue these days-- it never was and will never be. To give an example of diffusive versus disruptive innovation, consider how retail chains entered any market, and how say mobile phones and digital payments entered. Retail chains are known to be a "disruptor" of the market, that makes several small businesses bankrupt. For a long time, retail giants were barred entry into India for the same reason. But mobile phones and applications like Whatsapp or PhonePe diffused through the country without "disrupting" anything-- in fact, they made traditional interactions stronger by empowering them. There was much less resistance to these innovations from the society. 
3. Small is beautiful: It is much more easier to sustain societies and their expression, as a network of small communities, than a large conglomeration. Urban centres were traditionally (in the mechanistic world) seen as drivers of the economy, while in Indian thought small was always considered better than large unwieldy agglomerations. One of the reasons why large urban agglomerations developed was because factories of the past, required high amounts of manual labour. That is fast becoming a thing of the past. Manufacturing today is getting increasingly automated, requiring far lesser people to manage a large factory. It is important to note that the greatest contribution of factories is not job creation, but empowerment of the economy through mass produced, affordable artefacts. Automated factories would not only require lesser people, it would also empower small businesses in the ecosystem around, by making available affordable phones, affordable vehicles, affordable furniture, etc. 
4. The "footprint" method: In the erstwhile Mysore state, the 20th century saw several great feats of engineering. One of which was the building of the KRS dam on the Cauvery river, which enabled irrigation of vast tracts of land, making Mysore and Mandya districts into leading producers of rice and sugarcane. Another major feat of engineering was the Cauvery pipeline to Bangalore, which pumped up the Cauvery water to the city up a height of about 600 feet, over a distance of about 90 kilometers. But what this also did was to create an unsustainable solution to a problem. Bangalore grew by leaps and bounds without having a major source of natural water-- with an unsustainable assurance of Cauvery water. Today, the daily electricity bill of pumping water to the city is about 1 crore rupees! Similarly, emphasis on rice and sugarcane, which are water-intensive crops-- and creation of an ecosystem of factories and businesses dependent on them-- created an unsustainable solution. They not only eradicated earlier forms of food based on millets, they also became vulnerable to the vagaries of rain and water content in the river. To see why these are unsustainable, we need to look at any interventions from the "footprints" of their source and destination. The water needs of Bangalore was limited to the city of Bangalore-- but the solution to it, impacted the water needs of some population 90 kilometers away! Solutions tend to be sustainable when the footprint of the target is a superset of the footprint of the source from where resources are obtained from.

Sustainability is not an option-- it is mandatory. It is hence important to do whatever it takes to inculcate sustainable lifestyles around the world.