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. 

Beware the stories we tell ourselves

Some days ago, I was reading a post on Quora about emigrating to Canada. The person who had posted an answer was saying that she shifted to Canada a few months ago "in order to give a better life for her 2 year old son" and went on to describe the immigration procedures and protocols. 

What caught my attention is the underlying justification behind her decision, which formed the basis for effecting an irreversible change in her life and that of her son. 

Of course, it is quite possible that the author and her son were subject to oppression, persecution and unspeakable horrors from her family and society back in India, and emigration was the only option. But then, it is also quite unlikely that someone who has fled persecution would be writing so openly, and make no references to their trauma as part of their decision. 

The more plausible explanation is that, it was her choice and preference to emigrate to another country in search of a better life. But something was pricking within her mind, and to silence this voice, she has been repeating to herself that she is doing it for the benefit of her son. 

That is the fatal mistake most of us do. When conscience pricks, we prefer to renarrate our decisions and silence it, rather than listen to what it is saying and be led by it. 

The son in this story is too young to have consciously preferred Canada over India. And even if she genuinely believed that she is emigrating for the best interests of her son, there is no guarantee that this decision is in fact in his best interests. 

As the saying goes: the road to hell is paved with good intentions. 

How then do we realistically estimate what would be "good" for our children? Is it a nihilistic question and do we just take on a fatalistic belief that no matter what we do for them, they will always blame us; or no matter whether we care for them or not, they will be happy on their own? 

Of course, we cannot predict the future or others' preferences-- even if it is of our own kin. But we can provide them the necessary foundations that are reasonably stable, on top of which , they can build their lives. 

In order to understand these dimensions, we need to take a longish look into the future. Surely, Canada was a better place to live in (in terms of material wealth and comfort) than India, at the time of her writing. But will it still be the same, after 20 years, when her son is ready to go into the world on his own? Similarly, is a better material wealth able to compensate for questions like "Who am I?" "Why was I born? "What is the purpose of my life?" and so on, that her son might ask when he is able to think on his own? 

In dharmic philosophy, there are at least four dimensions that characterize the well being of a person's life. These are called the Purusharthas, and the four Purusharthas as dharma (sustainability), artha (wealth), kama (pleasure), and moksha (spiritual liberation).  

If we notice, these are pretty much what drives our decision-making throughout our lives. We may be driven by sustainability considerations, worrying about how we will survive over time. We may be lured to faraway lands by wealth and the promise of power. We may be lured by its promise of pleasure and living out our fantasies. Or finally we may make decisions to move away from our existing lives, out of a sense of disillusionment with material life and its shallow pursuits. 

It is important for us to be aware of what is driving our decisions. There is per se, nothing "wrong" in moving away to some other place in pursuit of wealth or pleasure. The only thing that would be better than this, would be to pursue wealth and pleasure not just for us as individuals, but for the larger system that we are part of, and for the entire world. But then, not everyone thinks of things bigger than themselves-- and that is perfectly fine too. 

But if we keep telling ourselves that our decision to uproot ourselves is a "sacrifice" we are doing for the sake of our children, we will end up bringing them up with a sense of guilt or burden-- as though, we have endured unavoidable hardships just so that they can get a better life. They will not even be able to ask what is so much better in this life as compared to where we were born. Disdain and contempt for their roots will become a part of their identity and deeply embedded into their sense of self. And this can cause deep rooted trauma in the children, that the parents may not even be aware of. 

The road to hell is indeed paved with good intentions-- or rather, with the comforting stories that we tell ourselves. 

Communities and Stability

It is common to see people lashing out against "communal" cultures, and at the same time swear by clubs, communities, farming collectives, open source, (un-)conferences, etc. Not realising, they are one and the same thing.

Indian society has predominantly been "communal" in nature. Not casteist. Caste is a feudal construct, and the Indian "caste system" that is considered characteristic of Indian culture is largely a European import.

Indian society had different kinds of communities that went with different names-- jati, mata, pangada, kula, gotra, varna, samuha, samaja, balaga, okkuta, sampradaya, etc. Of these, only kula and gotra pertained to blood lineage (dynasty and blood ancestry, respectively), while the rest were based on several other factors.

A community is different from a formal organization, or an amorphous crowd. An organization has formal, contractual association of its members to the collective, that comes with a legal binding. A crowd on the other extreme is completely disorganized and there need not be anything in common among all members of the crowd. Indeed, crowds are most effective, as in, they display the "wisdom of the crowd" when the members have very little in common. If not, they can reduce to herds or mobs or gangs, each of which are far less "wise" than crowds.

A community is neither an organization nor a crowd. It is a set of people who come together, driven by a sense of "kindred spirit". A community is a collection of people, who share some human condition across them. For instance, we can have a community of cancer survivors, a community of aviation enthusiasts, a community of data science enthusiasts, a community of sustainable farming enthusiasts, etc.

It is the common condition or common passion, that brings people together to form a community. A community does not have a collective goal like an organization. It need not offer any service or product to a "customer" outside of it. In fact, the beneficiaries of the community are the members of the community themselves.

A community also does not have formal, legally binding affiliations. If a member of a community decides no longer to be a part of the community, the community cannot legally force them to remain.

A community that has strict norms, memberships, ostracization, etc. is not a community-- it is a cult.

So if we can train our guns against feudalism or cultism-- it is fine.. But in this process, we should not throw away the importance of the community.

Communities are important elements that bring stability in a society. Over the past few centuries-- with the advent of factories and the industrial revolution, our societies have been slowly organized to become machines. Societies today are evaluated by its "productivity" rather than on life satisfaction and meaningfulness reported by its members. We are in a continuous loop of producing stuff, and tending to the health and social problems that it creates.

It is in this setup that communities become important. They bring together people that share specific conditions-- and help uphold the important social principle of kindred spirit. Communities help channelize one's passion and energies, as well as seek support from others facing similar challenges.

In a post covid world, if there is one thing that we should nurture, it is the idea of a community-- and help differentiate it from cults and feudatories. 

The problem with currency markets

Yesterday, in two different conversations, I got to speak of my misgivings about current day currency markets. In one of them I was asked, if I were able to change something, what would it be? And I responded by saying that I would abolish currency markets in their current form.

Currency, which is fundamentally supposed to be about trade, has today become a weapon of power. And at the centre of it is the current form of currency markets, which, rather than help facilitate global free trade, is actually exacerbating power dynamics across countries and civilisations.

The current form of inter-currency trade has an interesting history. We will not go into detail into this-- I've explained the history of inter-currency trade, in my 2006 book The Power Law of Information.

Currency today is predominantly tightly tied with nations and their sense of national sovereignty. There have been several exceptions to this, but with limited success.

Some countries use or accept currencies of other countries throughout their economy. Similarly, some countries (most notably, countries of the European Union) have come together, to form a common currency across them. None of these are without their complications. Nepal for instance, which used to accept Indian currency in addition to its own currency throughout the country, recently has started discouraging this practice, with its growing anti-India sentiment. Similarly, the Euro is often at the centre of the hurricane whenever there is an economic crisis in any of its member countries. Recently, it was told that the Euro was propped up solely by Germany, and it is in fact underwriting the economic costs of other countries like Greece, which were in crisis.

While currencies spanning across national borders has its problems, inter-currency trade has its own alternate set of issues.

Inter-currency trade is meant to establish a "fair" exchange rate between currency denominations. How do we know what is a good exchange rate between say the US Dollar and the Indian Rupee? The answer to this is to let the "market forces" decide.

So what are these market forces? These are the few hundreds of traders in the currency marketplace who bid to buy and sell currencies. This marketplace is hardly representative of the economy-- let alone "fair". It is largely run on trader sentiment, rather than any form of serious economic valuation of the currencies.

It is common to see the following pattern-- whenever there is a crisis in India, the Rupee falls against the Dollar; and whenever there is a crisis in the US, it is the Rupee again that falls against the Dollar. When I started learning to count as a kid, the exchange rate between the Rupee and the Dollar was about 4 Rupees to a Dollar. Since then, never once has the Rupee gained against the Dollar in a sustained or significant fashion. The latest is the Covid crisis which has hit the US more than India, and the Rupee has promptly fallen against the Dollar to almost reach 80 Rupees to a Dollar.

There is no mystery behind this. Currency markets run on sentiment. Indian traders are much more insecure and crave for the Dollar, than their US counterparts crave for the Rupee. So, whenever there is a crisis anywhere, the clamour for hoarding Dollars increases among Indian traders, while the other side has no such qualms about hoarding Rupees.

These emotional knee-jerk reactions, that are full of herding, groupthink and other fallacies, now becomes representative of the strength of the economy of 1.3 billion people!

There is an alternate notion of inter-currency valuations. This is called the Purchasing Power Parity (PPP). This model is based on a systematic study of prices for different commodities, and calibrating exchange rates based on this.

For instance, on an average, what we can buy for $1 in the US, we can buy for approximately Rs. 15 in India. So according to PPP, one Dollar should exchange to 15 Rupees. But whenever someone exchanges a Dollar, they get close to 80 Rupees! Hence for every Dollar that is exchanged, they receive about 65 Rupees extra!

This disparity between market and PPP exchange rates leads to an enormously skewed economy that has no bearing on economic fundamentals of demand and supply.

In the last century, this difference in exchange rates didn't matter much. Not many people inside the country cared for or were affected by the exchange rate with another currency. But with information technology, and its new line of businesses like IT, software and allied services, this disparity in exchange rates now touches every corner of the economy.

For a fresh graduate in India today, it is much more attractive to serve some other market and earn in Dollars, rather than understand and solve local problems to only earn in Rupees. The professional who has earned 1 Dollar, would have put in the same amount of expertise and labour as someone who has earned say 15 Rupees. But the former will have a much higher buying power within India than the latter.

This economic skew is not some academic curiosity. Its impact goes deep. It rips apart not just the economy, but also families and individual relationships. The 1987 movie "Wall Street" hits close to home for many of us in India, because we face the same kind of social and family strife that is seen in the movie.

With the current system of inter-currency trade, we now have just one definition of wealth, one definition of poverty, and one goal of life. Earlier, when economies were largely independent of each other, national and cultural sovereignty meant something. Cultures and nations had a lot of leeway in deciding what is important for them. But today, there is a homogeneity in wants and ambitions, that are orchestrated by a small set of multi-national corporations.

If I had my way then, I would abolish currency markets in their current form. Currency valuations would be computed year on year, based on PPP, and currency trade would be restricted to keep exchange rates within a maybe 20% error margin of the PPP exchange rate. Hence, if a Dollar exchanges for 15 Rupees, then currency marketplaces would not be allowed to exchange Dollar and Rupee only within the range of 12-18 Rupees to a Dollar.

Once we bring back exchange rates to relative purchasing power, currencies will start becoming meaningful as an economic instrument once again. 

Life after Corona

Disclaimer: The opinions expressed in this post are just speculative-- meant to initiate objective and dispassionate discussion. It is not a fatalistic rant, meant to appeal to emotions. 

What we are seeing today, it goes without saying, is unprecedented in recent times. Nowhere in living memory was the entire world in a state of lockdown, with no end in sight as to when and how things will come back to how they were.

What we are seeing today, is a state of saturation of our existing crisis responses. All our existing responses and strategies to handle epidemics have proven to be inadequate in stopping the Corona, which continues on its rampage worldwide.

What we are seeing today is a very imminent discontinuity in the nature of our lives. No longer will our lives be a linear projection of our past, and no amount of past successes of businesses, organisations and even of countries, can guarantee future sustainability.

What we are seeing today, as Nassim Taleb would put it-- a black swan event. What we need to adjust is not just our actions or strategies-- but our very beliefs and hermeneutics.

We are also mostly like the goat in Bertrand Russel's analogy about inductive understanding of our world. A goat that is well fed and taken care of by its owner, grows up believing that its owner is its saviour and protector-- until one day when it is Bakrid. By then it is too late.

We have all built our lives based on our beliefs. We have bet our careers, finances, and emotional well-being on institutions, economies and cultures that we believed were our saviours and protectors. For some of us, this belief was so intense, that we left behind our country, our culture and severed connections with our entire past, to start new lives in lands that promised us wealth and fortunes.

None of them foresaw or were prepared for this discontinuity.

And this is what "disruption" really means. These days, every new mobile app or website imagined itself to be an example of "disruptive innovation". None of the "disruptive innovations" of yesteryears-- be it Google or Facebook or 4G or whatever else, could stall the global onslaught of the virus. Sure, without them, we may have already seen huge casualties like that of the 1918 Spanish flu (which has nothing to do with Spain, incidentally) that killed millions. Yet, we are in a state of lockdown today and pretty much stopped everything around which we built our daily lives.

As companies and nations strive to get back on track in the aftermath of the Corona, life will not be easy. It is imperative then, to ask ourselves-- as individuals, what should our strategy be? So, here are some heuristics that I could garner, in no particular order:

1. Come "home": Given the uncertainty that is looming in front of us, it is important for us to be in a place where we feel we are at "home". It need not be the place of our birth or the culture we grew up in-- although, that would make it much more easier. It is important to be in a place where we feel a sense of emotional and spiritual attachment, ownership and belongingness. We should be willing to face whatever challenges it throws at us, and work for its sustainability. One way to ask what is "home" is to ask yourself the question, where would you prefer to die?

Conventional "rational choice" decisions based on what technology has a lot of "scope" or which currency is stronger, is not likely to help us survive the discontinuity.

2. Get rid of debts: All of them. As quickly as possible. Including non-performing assets like land or real estate that is just bleeding us. Debts are modern-day shackles that prevent us from responding adequately to challenges. Facing an uncertain future while burdened with debt, is like trying to fight a raging bull with our hands tied behind our back.

Getting rid of debts is easier said than done, of course-- and I'd like to have some pointers how to perform this step as well. But it is important to be done.

3. Build your new joint family: One of the primary things that saw India survive its cultural trauma of colonisation and resultant poverty is its cultural emphasis on large, joint families. Emotional support networks-- which is what true families are supposed to be about-- are highly underrated. In fact, in today's "modern" schooling, joint families or large family networks are ridiculed and mocked. And families themselves have become a case of "healthy competition" among its members getting into a cancerous stage. In families today, younger generation are under tremendous pressure to "prove" themselves with all kinds of achievements, when all that is required for emotional support networks is the age-old wisdom of acceptance and celebration of our diversity.

Joint families are not necessarily made of blood relatives. It is made of people who can resonate with us at a spiritual and emotional level. It does not have any rules or norms. It just is a network, where its members look out for one another. Joint families need not have to live in the same place and need not adhere to a single ideology. They need not have to be in the same profession-- nor do they need to have common finances. All they need is a common sentiment that helps them look out for one another-- and just call up or message one another to just ask "how are you?"

4. Seek intrinsic, not extrinsic rewards: In the coming years, the surest way to ruin our lives is to respond to external stimuli and build our sense of self-worth around them. Given the disruption, there are going to be a large number of no-holds barred greed and insecurity that will be practiced by organisations and nations alike. They will create all kinds of "incentives" to get young people to do what they want them to do-- which need not necessarily be in the interests of the people who are doing things. It is hence important, for the younger generation to deeply introspect and ask what gives them a sense of meaning and purpose for their lives. It is important to not fall into peer pressure and getting into a trap of excessive consumerism, debt and an endless effort to keep status quo.

None of these will of course, guarantee our sustainability. By definition, a discontinuity means that we are entering into the realm of the unknown-- where we don't even know what we don't know. The speed with which, some things have entered our lives just like that, we have no idea where it is going to take us. For instance, we have argued and debated for years and years on things like individual liberty, privacy, ethical AI, etc. But all that have been brushed aside and state-of-the-art surveillance and control technologies have been deployed in most countries across the world, in a matter of days. Sure, they may be needed now. But will they ever be removed?

We are now staring in the face of a possible "perfect" power singularity in the future. Where the powerless are almost absolutely powerless and the powerful are almost absolutely powerful.

So stay safe.. from the Corona, and what is likely to come after Corona!

Network paradoxes galore!

The nCovid-19 saga really scares me. Yes, the virus and its highly contagious nature, is one part of the scare. The other part of the scare is our response to it.

Yes, we need aggressive measures to "flatten the curve" and enforce social distancing, hand washing, etc. But the way we are going about implementing it, has the potential to make the problem worse, with long term collateral damage.

Let me explain.

One of my primary areas of research is in complex social networks and its emergent properties. What we are seeing today is almost a textbook case of all kinds of network paradoxes in action-- Braess' paradox, Cobra effects, Streisand effects, Prisoners' dilemma, bull-whip effect, etc. Just about all of these, refer to situations where a given policy or norm is adopted towards achieving a particular goal, but the end result would be exactly the opposite.

It is somewhat like the popular saying that, "The road to hell is paved with good intentions."

One of the good things India did was to act early and put in screening procedures in place, as early as mid Jan, when even the WHO recommendation said the following:

WHO does not recommend any specific health measures for travellers. It is generally considered that entry screening offers little benefit, while requiring considerable resources. In case of symptoms suggestive to respiratory illness before, during or after travel, the travellers are encouraged to seek medical attention and share travel history with their health care provider. WHO advises against the application of any travel or trade restrictions on China based on the information currently available on this event.

For a long time, India, despite sharing a border of more than 3000 kms with China, and large extents of business interactions, had one of the lowest incidences of Corona infections.

Yet, in the last week or so, we have seen increasing rates of Corona positive cases, and increasing rates of panic responses to the crisis.

For instance, the Prime Minister announced a "Janata curfew" yesterday so that people stayed home and practiced social distancing. He also implored the citizens of the country to applaud the people in the frontline at 5:00pm. This was a great success in the sense that a lot of people came out to applaud and the sense of national commune was palpable. But what also happened was that yesterday at 5:00pm, there was a celebration of sorts in several places, with people gathering in large groups to applaud and improve morale! Thus, creating a situation that was exactly the opposite of what was intended.

Given that the virus shows no signs of abating, today, the government issued a lockdown order all over the country, and cancelled public transport, inter-city transport and even domestic air travel starting tomorrow. What was the response from the population to this? As current news reports go, our highways leading out of the city are packed with people trying to leave the city to their home towns before everything is locked down. Busses and trains are packed with people on panic commutes. I do hope that the virus knows that the lockdown starts from tomorrow, and that it should not infect anyone today!

In addition to the above, there are other kinds of social panic reactions. Nurses who are working on the frontline and staying in rented apartments or paying guest accommodations were in some cases, asked by their landlords to vacate their premises in fear of the Corona! That doesn't really help in our struggle against the virus.

Then there were reports of racial attacks against people from the North-East of India, because they look like Chinese!

And yes, there are already Corona related suicides!

~*~*~*~*~*~*

I am completely aware that the situation is very serious and the virus is highly contagious with an R0 rate of about 3.0. The fact that we need quick, large-scale measures are also well taken. 

But the approach we are taking towards this problem may not only have the opposite consequences, it may also create a large collateral damage. 

There are already talks of imposition of emergency and draconian measures to keep people home. But "draconian measures" are no guarantee that the infection does not spread. Draconian measures are meaningless if they are not implemented properly. In order to implement draconian measures, some segment of the population should necessarily go out and implement it. The system of people implementing the draconian measures may themselves act as the carriers of the virus passing them from one isolated community to another. 

Complex networks of self-interested agents (human societies is an example) are replete with such emergent properties that are very counter-intuitive. These "network paradoxes" are not some academic curiosity to banter about when people in the frontlines are battling the disease. These are real consequences that can lead to systemic collapse that can greatly amplify the already serious crisis. 

So how do we deal with these paradoxes? What should we do to take swift action without the resultant panic reactions? 

There are no simple answers to this question. But some heuristics can definitely help. 

We know for example, human social networks are not uniformly random. A person is not equally likely to interact with just about anyone else. Social networks are known to be clustered, with a property called triadic closure. In simple terms, what this means is, if a person A interacts with two other persons B and C, then B and C are likely to interact with one another, the more the interaction strength between AB and AC. 

If we work out the math, this leads to a society of several clusters, with some connections between the clusters-- which are called the "bridges". These bridges are critical elements in diffusing something across clusters-- be they ideas or pathogens. 

Similarly, human societies are known to display a "scale free" and "small world" property. What this means is that, despite the complex and clustered nature of human social connections, human societies tend to have small degrees of separation. This means that we can connect anyone to anyone else with a small number of hops. This is where the popular notion of "six degrees of separation" comes from. 

A small world network is bad news in the face of a contagion. This is precisely why this virus that originated in a city in China has now become a global pandemic within a few weeks. 

But how does a network get its small world property, if it is also characterised by clusters due to triadic closure? Remember, we said that not everyone is equally likely to interact with everyone else. So how does the small world property arise? 

The answer to this is the existence of hubs in any social network, at any scale. Hubs are network nodes that connect to a large number of other nodes. The number of large hubs with respect to the number of nodes in the network remains more or less the same, regardless of the scale in which we are looking at a network (thus the name "scale free network"). 

Hubs are the primary connectors between disparate parts of the network. If we are to contain a contagion, the first thing we need to do is to shut down major hubs like airports, bus stations, railway stations, etc. or tightly regulate their traffic. Ironically, in many airports across the world, people were made to queue up in large lines for mandatory screening, which would have only increased the chances of more contagion within the place. A better strategy would be to first reduce the traffic in the hub, and divert airplanes to several other nearby airports and spread out the crowd and mandatory testing. 

Similarly within a city, if we mark out several localities, we can see that once WFH and an advisory lockdown is in place, most people would stay within the locality. Go to each locality regulate entry and exit on all the roads that connect it with other localities. Thoroughly check and sanitise every vehicle and person that cross these "bridges" between localities. Within each such sanitised locality, people should be able to move around freely-- subject of course, to periodic and proactive testing. 

Much of the exacerbation of the situation happens due to panic psychological reactions from people that impair their sense of sound judgment. One such reaction is psychological denial. The more we push in a sense of seriousness and urgency through all media channels, the faster this state of psychological denial is likely to set in. Once there is a sense of psychological denial or fatalism, people tend to act in bigoted, vindictive and reckless manner, like for example, the several cases of Corona-infected people in China, deliberately infecting others. 

Human free-will and psychology are central elements of social responses to crises. It is important to understand what could happen in response to a crisis response, rather than just what should happen.