Living in the Age of Small-world Networks

by | Jul 15, 2022

I have shared earlier in my blog, my fascination with Calculus that I studied as part of my engineering education and later applied while working in missiles. Mathematics is the language of science and the medium of expression for abstract ideas. You can’t understand any phenomena beyond a point without comprehending the unseen part of it and for those, mathematical functions are your lamp posts. 

I recently read two books of the American mathematician, Steven Strogatz (b. 1959) “The Joy of x” and “Infinite Powers.” These brilliantly written books explain well how indeed the world works – both, the natural universe, and the man-made world. There are simple laws and patterns at the core of the apparently complex world and properly understood, they instill a sense of peace and confidence in facing, or rather, enduring the reality. 

If you understand the health problem well, especially chronic illnesses, you know how to live with them without being frightened and keep doing your best in the situation. If you understand the way big money moves markets, climate operates the weather, and social tensions are brewed and festered by the seekers of political power, you are not only less surprised, but also better focused on what you can do to safeguard your own little interests without being overwhelmed. 

In “The Joy of x”, published in 2012, Strogatz writes, “Math is everywhere, if you know where to look. We’ll spot waves in zebra stripes, hear echoes of Euclid in the Declaration of Independence [the phrase “all men are created equal”], and recognize signs of negative numbers in the run-up of World-War I [the area between the opposing armies’ trenches was known as “No Man’s Land”]. And we’ll see how our lives today are being touched by new kind of math, as we search for restaurants online and try to understand – not to mention survive – the frightening swings in the stock market.”

In “Infinite Powers”, published in 2019, Strogatz writes, “For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way. Or maybe it’s the only way a universe with us in it could be . . . our universe obeys laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations. Such equations describe the difference between something right now and the same thing an instant later or between something right here now and the same thing an instant later or between something right here and the same thing infinitesimally close by. The details differ depending on what part of nature we are talking about, but the structure of the laws is always the same.”  

Computer science is rooted in mathematics and those programmers who do not take mathematics seriously, do not flourish beyond a point. The mathematical way of thinking that means abstract reasoning, critical thought, and logical deduction, is imperative to succeeding in computer science. The art of reading, comprehending, formulating thoughts, and communicating with abstract language, come naturally with learning mathematics. The popular term, algorithm, is basically an abstraction of a process. Once it is established as parameters, it can be studied how it is repeated, modified, and even applied to solve other problems.

Recently, Mahesh Ramanujam, Former President and CEO (2016-2021) and COO (2011-2016), U.S. Green Building Council visited me. During his tenure there, Ramanujam helmed the accelerated expansion and implementation of LEED, the world’s premier green building certification and rating system. A computer engineering graduate from the Annamalai University (1993), Mahesh now enthusiastically leads the charge for a “zero emissions” world. We had a long chat. 

As outlined in the 2015 Paris Agreement, the commitment to keep global warming to no more than 1.5°C, translates into a reduction of the current levels of emissions by 45% by 2030, and to reach zero emissions by 2050. This can be possible only through a complete transformation of how industries produce, people consume, and the movement of goods and travel in the world. 

But, as Ramanujam views it, that timeline doesn’t offer the sense of urgency required. In many ways, Ramanujam says, “Things are moving in exactly the opposite direction – and scaling change needs to meet a series of challenges.” Of course, he’s referring to the fact that urbanization is on a roll; thermal power stations are being added, and roads are choked with traffic, exhaling greenhouse gases. A rather utopian term that has gained traction of late is a decarbonized economy, or more accurately, a low-carbon economy (LCE). Renewable energy, nuclear power, biofuels, and energy efficiency are the new engineering hotlines. Low-carbon economies are, indeed, a precursor to the more advanced, zero-carbon economy. But who is going to make it happen? Why should an industry invest in clean technology? 

Idealism alone will not work. Ramanujam believes that a proper understanding of the scaling is necessary, that people, planet, and profit can exist in tandem and not despite one another. Firstly, it must be economically beneficial for a business to go in for lower to zero emissions. And secondly, there must be a cost to doing business as usual, one that ultimately renders the polluting industries unviable. 

This is where carbon credits come in. According to the National Indian Carbon Coalition, “A carbon credit represents ownership of the equivalent of one metric ton of carbon dioxide that can be traded, sold, or retired. If the organization produces fewer tons of carbon emissions than it is allocated, the organization can trade, sell, or hold the remaining carbon credits. When a credit is sold, the buyer is purchasing the seller’s allowance of emissions.”

Sounds great, right?! 

But the challenge is how these credits can be accurately measured and traded. The answer lies in Mathematics. An average car generates 5 metric tonnes of carbon dioxide per year. It used to be 10 metric tonnes earlier, which has lowered down to 3 and below in emerging fuel-efficient models. Users of these cars must purchase the equivalent number of carbon credits from a reputable source. An hour of flying generates a certain quantity of carbon dioxide. Money should be paid to forest growers and farmers to sequester carbon in the soil. Solar and wind energy parks offset the energy produced using fossil fuels. All these businesses – energy, automobile, aviation, agriculture – are fundamentally small-world networks. Their nodes may not be connected to one another, but the neighbors of any given node are likely to be connected. To a keen eye, all is visible, measurable, and transactional – and according to Ramanujam, these prerequisites are what lead to market transformation.  

As things stand, the carbon market is merely a concept. The current landscape is disorganized, archaic, and lacks incentives. Ramanujam feels that carbon markets riding onto a public and decentralized database, such as the blockchain, can provide a global infrastructure data layer, and force polluting companies to either pay higher prices for carbon credits or seek more environmentally friendly approaches to their business practices. He also says that, “Using crypto and carbon metrics will provide a cohesiveness to an otherwise fragmented effort at a zero-emissions future. “

I tend to agree. A journey of thousand miles begins with one small step and it is time to take that step, instead of sitting in inaction.


Look far ahead

Look far ahead

Since last month, I have been reading a rather scholarly book, The Book of Why, written by Israeli-American computer scientist Judea Pearl with Dana Mackenzie. The book deals with the often elusive relationship between cause and effect…

The Mystical Language of Numbers

The Mystical Language of Numbers

Is there an occult, divine or mystical relationship between a number and one or more coinciding events? In ancient Greece, Pythagoras propagated the idea that reality at the deepest level is essentially mathematical. He and many after him believed that a system of principles existed behind numbers…

A Moment of Civilisational Pride

A Moment of Civilisational Pride

I was born in 1955 in independent India. When I look back today, without hesitation, the best moment in public life I witnessed is the construction of a grand temple and the consecration of the idol of Shri Rama Lalla in Ayodhya on January 22, 2024…


  1. Dear Sir, Very relevant blog for the present day for the industrialised world, where profit is only the driving force. In spite of the fact that we all know that what we are doing is hazardous for the society and the mankind, we still continue doing because we are more interested in the financial profit. As you have rightly brought out in the blog , all things can coexist but for that we need to commit ourselves to civilized and responsible practices.
    Personally I am not convinced about trading of carbon credit as the ill effect of the emission around industry which is generating the hazardous gases cannot be mitigated by buying the carbon credits. The society around that factory is suffering though the industry owner convince the regulatory authorities by buying the carbon credits. This is statistical method of proving that the emission is net zero. Money cannot buy everything. Be that as it is. Probably I dont understand how buying of Carbon credits helps the society which is suffering due to proximity of a hazardous industry. But it is imperative that we need to move towards LCE and achieve ZCE ultimately. We as citizens should do what we can do , regulating authorities have to act their part diligently without any fear or favour and Government should not compromise its stand for just profit or GDP. I am an optimist, I do hope that we will achieve both the aspects without diluting one for the other. Thank you once again for an interesting and relevant blog sir.

  2. A brilliant piece of writing highlighting mathematics as medium of expression for abstract ideas, Prof Tiwariji !

    Your articulation on the significance of carbon economy in contemporary world is outstanding !!

  3. Instead of trying to shake 20 hands, get 30 business cards and add 40 people to your LinkedIn, reading blogs like this help you tap what is going on in the collective consciousness and guided by the unseen hand of destiny. It’s the people we hardly know, and not our closest friends, who will improve our lives most dramatically.

  4. Started reading Professor Arun Tiwari’s blog for the sheer beauty of his narrative. Continued chewing and digesting it revealed its significance. A knack for getting into an important and topical conversation is an added attribute.

    Climate change is a wicked problem created by us humans out of our divisive ignorance. Approached from a policy perspective of our siloed thinking it leads to desperation. Creators and Engineers enamoured with their fragmented products have accelerated the process.

    Professor Tiwari approaches and closes it through the elegance and beauty of mathematics. Through this route, the wicked problem seems resolvable…much like any other human concern. We have the tools and techniques in the form of evolving Project Management Body of Knowledge and intent in the form of Sustainable Development Goals. With National Institution for Transforming India, we are action ready to march the thousand-mile journey.

  5. Sir I recently read this on Internet:

    When human beings no longer populate Earth
    How does one attain One Mind?
    Easily, through networking and super-emergence
    When people define superior
    They think of Man’s attributes

    But the Name that cannot be spoken
    Might be grasped by an algorithm
    For which the human brain can never attain

    That’s the beauty of mind-in-the-machine
    The collective intelligence does not suffer
    For each part of the brain shares neurons
    On the internet, like a God atom
    Man would prefer to take the credit

    But as it will turn out, the unity mind
    Is a transhumanistic inevitability of computing
    A time when neuroscience, robotics and AI merge
    Not but a few decades away from now.

  6. Respected Sir, it was an honor and a privilege to discuss the future of carbon credits and calculations with you. We have a shared sense of urgency when it comes to what’s necessary for navigating the decades ahead and this is an excellent piece tying our mutual love for mathematics and solving the challenges around people, planet, and profit. Thank you for including me in your very thoughtful writing.

  7. A very pertinent article sir. It’s about time companies and individuals take a serious note of the carbon footprint generated by them and think about how to reduce it. The concept of carbon footprint should be taught right from childhood so that thinking about reducing carbon footprint comes naturally during the everyday business and individual decisions.

  8. This is an excellent writing Prof. Tiwari on the value of mathematics in helping to improve our understanding of problems and solving them. The algorithms employed in artificial intelligence are helping not only to tackle climate change but a host of other problems including autonomous driving, early disease diagnosis, fusion reactor design, 5G communications, space exploration, drug development, and many more. I’m particularly excited about the introduction of novel interval arithmetic, based on set theory, that will greatly improve AI training in the future by reducing the complexity of neural networks and free up resources to tackle more problems. The future is bright thanks to mathematics and the power of synergistic technologies of AI, blockchain and IoT!

  9. Sir, this blog of yours must be preserved for posterity. You are stating an obvious truth and pointing out to an inevitable truth of climatic disaster that would affect billions of lives, especially of the poor. Climate change directly affect people, as Umesh Jain Sir writes in his comment, and once food produced is less in quantity, its price increase, and it goes out of reach of the poor people. It is a no brainer.

    Facts are facts and the truth is that renewable energy is cheap and effective, and that carbon pricing is a smart way to control pollution and promote the shift to a strong, low-carbon economy. As a computer scientist I can’t agree more on the importance of the knowledge and application of mathematics in our lives. The age of Blockchain technology has already arrived. The first step of Hashing a block is rooted in mathematics. It is so fundamental!

    Thank you for keeping us abreast with latest knowledge and our hearts sensitive to what is tight and must be done.

  10. Dear Sir, We are already late in taking steps towards controlling green house gas emission. UK and other European countries started facing the bad effects and high rise of temperature crossing 40* this summer. Increase in population and food habits have added more to this phenomena. More than 100 days of war between Ukraine and Russia has added fuel to this global phenomena. I don’t think there will be any considerable effects of individual effort to reduce the Global warming.

  11. Nice to read about Mahesh Ramanujam. I met him in the context of getting the LEED (Leadership in Energy and Environmental Design) certification for green buildings for the SRK Empire Building. We decided to go for Gold Rating certification, which implied 60-79 points earned on the green building criteria and became the pioneers in the Indian diamond industry in this regard. With further improvements, we would later achieve the highest Platinum Rating.

    We were pleasantly surprised to be nominated for the Leadership Award by the U.S. Green Building Council (USGBC). Shri Govindbhai Dholakiaji, was invited to Boston, where the annual Greenbuild International Conference and Expo were held that year with the theme “ALL IN” − which is meant to reinforce the commitment and optimism needed to confront climate change head-on. I was doing Innovation and Strategy Certification at Harvard. On November 9, 2017, Govindbhai received the award from Former President Bill Clinton. It was a great moment in my life.

    I am sure Mahesh’s dream of a Carbon Economy will come true and his meeting you is an auspicious omen.

  12. Sir, I am indeed delighted reading your blog celebrating mathematics. Mathematics is at the center of all creations, without which the world cannot operate. Be it a cook or a farmer, a carpenter or a mechanic, a shopkeeper or a doctor, an engineer or a scientist, a musician or a magician, everyone needs mathematics in their day-to-day life.

    Even in the natural world, there are countless examples of mathematical patterns – insects multiply mathematically, snails make their shells, spiders design their webs, and bees build hexagonal combs. The more you look for order in the chaos, music in the noise, and meaning in the random events of life, mathematics becomes apparent.

    My experience tells me learning mathematics can be made easier and enjoyable if our curriculum includes mathematical activities and games. Mathematical puzzles and riddles encourage and attract an alert and open-minded attitude among youngsters and help them develop clarity in their thinking. Emphasis should be laid on development of clear concepts in mathematics in a child, right from the primary classes. Thank you for showing us light!

  13. Sir, nice to read about Mahesh Ramanujamji. I met him in Delhi when he was here. He is a bundle of energy and appears convinced about the future world running on the Carbon Economy. I am not an expert in this area, but what convinced me was that there must be a price on carbon.

    People can’t keep emitting carbon into the atmosphere making others’ life miserable – old vehicles, diesel generators, and sugar mills are prime examples. Also, people who are fixing carbon, like farmers and those maintaining forests, must be rewarded for their work. It is time to start discussing these issues.

  14. Thank you Arun ji for an important and insightful topic. As a mathematics student, I am happy to read the blog. I got substantially benefitted as I learnt other un related subjects like Finance, Emergence Medicine, management and Leadership with the mathematical background. Though all are equal, I considered people with Maths background as more equal.

  15. The need of the hour. For companies genuinely interested in producing goods and services in a more eco-friendly and ethical way, blockchain technology can make this simpler and more cost effective.But… there’s a lot of work to do to realize these grand ambitions. Technology moves very quickly and there are many players looking to win the race on the carbon credit exchange space.

  16. Interesting topic.
    If left unattended, the issue would harm our younger generation and those still younger,
    Rather than quarrel on seemingly petty issues, selfish motives, the world leaders should do more for the mankind, The Paris agreement is being diluted by many of the bigger powers who bully their way.
    We hope good sense prevails in all of us for the betterment of all human kind for now and for days to come.

  17. One of the way to measure carbon in automobiles can be that data captured on emissions for that auto is uploaded to a central system (network of IoTs). Then it will be easier to measure. However the bigger challenge is will automakers allow that as not meeting the bar can mean substantial fines to the automaker (for a new vehicle) and the ownerbof a used vehicle.

    If i remeber correctly, one automaker in Europe manipulated the onboard system to incorrectly report the pollution from the vehicle. We will need strict governance on such issues in addition to ownership coming from within for every person involved.

  18. i agree. A well organized carbon credit market is highly desirable. Such a market exists in the United States and globally.

  19. Thanks for the intriguing piece, Prof!

    Our world is one of balancing interests, mainly based on personal and corporate needs for growth and survival.

    The same applies to global warming and CO2 emissions.

    I believe the mathematics of survival for the human race will prevail …

  20. Thank you for opening our minds to these concepts Prof Tiwari, the best approach is to incorporate interventions that involve the youth, this should consider their times at home, at school and in the community. When each phase of our lives is lived with intent at cutting the carbon dioxide emissions, then the journey will have begun, the impact of climate change is on us all, each has a role to play, no better to act than now. We think globally but daily act locally.

  21. The pristine beauty of mathematical equations,
    contrasted with
    the motivated, artificially constructed and self serving, deliberate chaos of the human condition, that ceaselessly attempts to find beauty and solution, Seem to be ends that almost never meet!
    Why so?!
    One wonders….
    Perhaps it is Gods plan and design,
    Which reminds us of the ideal,
    To which we need to yearn even as we struggle- and wallow – in the muddy Earth of our existence, yet marvel at the near-perfect concepts and constructs of mathematics!
    Regards and affection,

  22. Watta brilliant piece of writing!!
    Human race, in my view, is the most stupid and destructive. We know we are going down with the environment and we will take the whole earth with us. 15-20 years ago when the concept of carbon credit started, the climate change we see today, was expected 50 years down the line. I as a farmer is already facing the decline in crop. India is living on edge for food security. 1 degree increase in ambient temperature plays havoc with pollination and crop yield. Mathematics can explain it…but how do we prevent it???

  23. The carbon markets and their trading on one hand and clean and green ecosytem on the other hand promise a practical solution.. but far away from a ideal presumption that would like to mitigate the ill effects of climate change. Hope is the edifice on which we will continue to live

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