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Writer's pictureAman Deep

The Joy Of Non-Linearity




Once there was a wise man who lived in a small village with his happy family. He had a cute son and a beautiful wife. He loved them more than himself. His wife acted as a source of strength to him in all his expeditions. She was his true soulmate. A true soulmate shows you the true picture of yourself and accepted you with all the virtues and vices. One day his cute wife requested him to make a tool made of stone that will help her in crushing the ingredients while preparing supper. He accepted her request and start searching for a big stone. Luckily, he found a big stone in the backyard. As he was about to break the big stone with a hammer, his son arrived and interrupted him. "Dad! Let's play. I am feeling boredom." My dear son! I am building a tool that will assist your mom in preparing the food. We will play together once I will finish the task. The obedient son nodded and sat on the bench placed in the backyard. The son was very inquisitive and believed in learning by observation. He was keenly looking at his father with wonder to acquire the skills needed for creating a tool. His father started hammering the stone with great force. The stone was very hard and nothing seems to happen to it in the face of heavy blows. The son started counting the heavy blows made by his father on the stone. He kept on hammering again and again but was unable to make a single dent in the stone. When the count reached ninety-nine, his impatient son burst into anger and told his Dad, "Please Stop! You are unnecessarily wasting your energy. Nothing is happening to the stone. Let's play and have some fun." His father replied, "Oh! my dear son, wait for some more time. You are going to learn a very deep lesson in a short while." When he hammered the stone for the hundredth time, the big stone was shattered into pieces. His son was amazed at it and his father started smiling. The curious son started mulling over the following questions:


  1. Does anything happen to the stone until the ninety-ninth blow?

  2. Why does the stone break at the hundredth blow?

  3. Do such patterns found in other areas of life?

Before answering these questions, Let's understand the deep lessons hidden in the story.


  1. Patience and Persistence are the virtues. One has to cultivate these qualities to become successful in life. Persist but experiment in the face of setbacks. Obstacles make us creative by forcing us to think that has never been thought before.

  2. Never judge anything based on an outcome. Follow the process over the outcome. Willpower is fragile so don't rely on it. Create a system that will move you toward the desired outcome.

  3. Sometimes circumstances make the person very hard. Keep on hammering their hard hearts with good deeds despite their bad behavior. One day the softness will ensue.

  4. The most important insight is about the non-linear system. The system in which input and output are not directly related to each other. The critical mass is the underlying idea behind non-linearity that derives its origin from nuclear physics.

Let's spend some time understanding the fundamentals of the critical mass to apply the concept of non-linearity in our day-to-day life.


The minimum amount of nuclear mass required(Critical mass) to create a reaction in which the output of one reaction acts as an input for another to create a self-perpetuating reaction known as Nuclear fission. When a system reaches the critical mass, the last input changes the state(properties) of a system known as a tipping point, which can either make a system better or worse. In a nutshell, the underlying idea behind critical mass is the minimum amount of energy that changes the state of a system. It's like a proverbial straw that breaks the camel's back. A single straw will never break the back of a camel. As the weight goes beyond a certain threshold only then it will break the back of a camel. The last straw looks impressive but the change in the state of a system happens due to the buildup that starts by putting the first straw. The final result is an outcome of the small micro-actions.


The water changes its state at a hundred degrees celsius. Until ninety-nine degrees, it is in a liquid form. The last one-degree change in temperature (acts as a critical mass) changes the state of a system from liquid to gaseous. In a similar manner, the minimum number of people required to act as a critical mass so that the group gathering feels like a party. As the people keep on coming until a person comes which crosses the threshold that tips the system into high gear to make the gathering feels like a party.


I don't have to convince everybody in the room. I just need a critical mass of the people in the room. Simon Sinek

A person's expertise is beneficial to him if he is working on an idea that is on the verge of critical mass to become a mainstream technology. Unlike a person working on an idea that will take ten more years to reach a critical mass to become a mainstream technology. The concept of critical mass is closely tied to the idea of non-linearity. In a linear system, X amount of input yields Y amount of output. Fixed deposit is an example of a linear system that yields a fixed amount of return per annum. In a non-linear system, the output is not fixed concerning an input. Investing in stocks is an example of a non-linear system. Invest in non-linear systems when it comes to intellectual and social domains.


The idea of critical mass is ubiquitous and used in a variety of domains. In astrophysics, critical mass is defined as the minimum amount of mass required to change the state of a system. In epidemiology, critical mass can be defined as the minimum number of populations that must be vaccinated to prevent the spread of a contagious disease. In the business world, critical mass is reached when the business is generating enough revenue so that it has no longer dependent on outside investments for proper functioning. In social trends, when a certain number of people start believing in an idea that upon moving a certain threshold becomes an acceptable idea and is implemented as a policy. Ideas move in progression from Unthinkable -----> Radical -----> Acceptable -----> Sensible -----> Popular -----> Policy.


After gathering a few facts about critical mass, it's time to answer the kid's questions. (Otherwise, his patience will soon turn into a wave of uncontrollable anger.)


Does anything happen to the stone until the ninety-ninth blow?


Of course, the bonds between the atoms of a stone are weakened by the repeated blows of a hammer by his Dad. The results are not apparent but an effort(foundation) to break the stone is piling up.


Why does the stone break at the hundredth blow?


The critical mass is reached at the hundredth blow. The bonds can no longer be glued together. Hence, breaking the stone. In other words, it changes from one state to another.


Do such patterns found in other areas of life?


In any system where nodes are interacting with each other either in the form of currency or sharing of information, the potential for critical mass or non-linear growth is possible. Consider a network of Uranium-235 atoms (atoms are acting as nodes), if enough atoms are present in a system where the decay in one atom releases neutrons causing the decay in adjacent atoms creating a self-sustaining chain reaction known as an atomic explosion.


The idea of critical mass is very important for entrepreneurs to understand the lifecycle of new technology. Everett Rogers, a well-known sociologist gave the diffusion of innovation theory which demonstrates that people belong to one of the five groups before adopting new technology. The five groups are as follows:


  1. Innovators: They are those who think differently and execute new ideas. They work very hard and take the maximum risk. A very small number of the population fall into this category. They are audacious and have no fear of traversing the unknown path. They figure out the optimal strategies as they move along the path. The emergence of a product is the result of excessive hit and trial methods.

  2. Early Adopters: They believe in new technologies and growth. They have inoculated themselves from the force of social proof. They have internalized the idea that there is always a scope for improvement in products. They adopt the minimal viable product and try to make it better by giving rapid feedback to innovators.

  3. Early Majority: As new features are incorporated into the product from the feedback of early adopters, it becomes more and more valuable. More people are attracted, start utilizing the product, and help it to reach the tipping point.

  4. Late Majority: These people are under the influence of social proof. They follow herd thinking and are not interested in wasting their time and money on new technologies. The product has got immense value proposition when they adopt the product.

  5. Laggards: These people adopt the product when it becomes impossible for them to live without it. It becomes their primary need. These people are highly risk averse. If they don't use the product they will feel left behind. The widespread usage of products in mainstream society forced people to adopt them.

The rate of diffusion of a product varies on the awareness level of society, its familiarity, ease of use, and the impact it will create on people who adopt them. Let's understand the concept of diffusion of innovation through a real-life example.


Facebook is initially used by students and professionals in educational institutions. Mark Zuckerberg is an innovator who developed it. Students and professionals are early adopters and the early majority that propelled Facebook to reach critical mass. When its usage moves beyond educational institutions, it is adopted by the late majority to share valuable information with their friends. Laggards finally adopted it otherwise they will be left behind among their friends.


A Telephone is another example to get a good grasp on the concept of diffusion of technology. Graham Bell is an innovator who invented the telephone. Doctors are early adopters as it helps them to do their job quickly. They are willing to pay high prices for it. When new use cases like text messages emerged, it is adopted by the early majority and pushed the product to reach a critical mass. The late majority adopted them because it helps them to connect with their family members easily. The newly launched product has gained momentum in society. Laggards are forced to use them otherwise, it becomes difficult for them to connect to their family members.



Critical Mass is an important idea to get deep insights from the social system. In the social system, it implies that when an idea is endorsed by enough people its growth can sustain itself. People's minds don't change drastically in a day. It is usually the accumulation of small actions that yield big results. Overton window is an idea that demonstrates when an idea is accepted by a sufficient number of people to propose it as a policy. Fringe ideas become mainstream and mainstream ideas become fringe over the decades. It means ideas or opinions are not static. They kept on evolving with time. Change is the only constant.


A huge amount of effort is required to overcome the inertia and to create a new change. When the system moves beyond a certain threshold, the last input has a disproportionate impact on the system and tips into a new state. A similar thing happened in New Zealand during the Women's Suffrage movement. In 1893, New Zealand became the first self-governing country that gave the right to women to participate in Parliamentary elections. It seems as if higher authorities suddenly changed their minds and gave women the right to participate in elections. The change doesn't happen overnight. The gradual movements from time to time nudge the people to change their minds. Some of the factors are:


  1. The population of New Zealand is very small. The majority of them came from European countries. They wanted to create a fairer society than the one they had left behind. The male population supported them at the beginning and helped them to gain a foothold in the parliament to protect their voting rights in the elections.

  2. The higher officials of New Zealand wanted to educate their females also. The first girl's school was opened in New Zealand in 1871. In 1893, the ratio of boys vs girls became 1:1. Better education paved the way for more employment opportunities other than customary domestic duties. Females started influencing the domains like teaching, journalism, medicine, art, etc. Upon facing the worst working conditions, they started to unionize which kept them together.

  3. The temperance movement also bought them closer to each other. The aim of the temperance movement is to prohibit the consumption of alcohol in New Zealand. The men drank away their weekly wages leaving their wives and children bereft. However, alcohol was not banned in New Zealand but still it helped them to raise their voice against brutality and violence. They became more aware of their basic rights and the temperance movement gave them thurst to forge the skills like administration, collaboration, and organization. Now they knew if they work collaboratively towards a common goal, they will create a fairer society in the near future.

Kate Sheppard filed several petitions and presented them to parliament in 1890. Despite initial failures, she kept on trying. In 1893, she amassed 32,000 signatures that ultimately passed the law. Now women have the right to actively participate in elections. The women's suffrage movement acts as a tipping point and after the second world war, many countries gave their women the right to vote to participate in elections. It implies when any system reaches a tipping point, the state of the system changes which can either make the system better or worse.


The network effect is the root cause behind the critical mass that tipped the system into a new state. Robert Metcalf who invented the ethernet gave the idea of the Network effect. According to the network effect, if there are N nodes present in a network then the value of the network is equal to the square of the number of nodes present in a network. It is also known as Metcalf's law. Let's understand this idea through the example of a telephone. The value of some products or services is proportional to the number of users who use them. If you have a telephone in your home and no one among your relatives uses it then the value of your telephone network is zero. When the number of users increases then the value of a network increases non-linearly.




Wherever the network effect applies, the addition of each user increases the value of a network. The rate of growth of a network is greater than the growth of users in the network. The network effect has a variety of applications in our lives.


Reading is a foundational skill to learn anything in life. Reading a good book gives the maturity of at least forty to fifty years because the author has lodged his life experience in writing a book. Let's assume reading a book gives ten ideas to a reader. When the reader reads the second book, he got ten more new ideas. When the ten ideas from the previous book are connected with the ten ideas of the second book then the total number of connections becomes a hundred. By the time, he will complete his tenth book the number of connections between ideas increases to 100000000000000000000. That's why reading makes people creative and smart. Read as much as possible to create a better life for yourself and for your loved ones.


If we create networks with the sole intention of getting something, we won’t succeed. We can’t pursue the benefits of networks; the benefits ensue from investments in meaningful activities and relationships. Adam Grant

When the idea of the network effect applies to technology, it tends to create a natural monopoly or oligopoly. One can't find too many social networking sites because of a few apps like Facebook, Whatsapp, and LinkedIn. They have dominated the entire market. Suppose a new social messaging app comes along and offers better features than WhatsApp. An intrepid user starts using it but he found no value in it because all his friends and relatives are on WhatsApp. To make it valuable, he has to convince all his loved ones to abandon WhatsApp and use the new one. His friend's friend should also be convinced otherwise his friend's friend would be on WhatsApp and they no longer can communicate with each other. The network effect creates a barrier for new entrants. To become dominant, the new ones have to replicate the existing network or at least come close to it. The network effect will create very high switching costs for the users.


The fax machine exemplifies the idea of the Network effect very well. It came on the market in 1840 but was not popular among people until 1970. It took the time of around one and a half centuries to gain sufficient critical mass to become a mainstream technology. Once the number goes beyond the threshold, its growth becomes non-linear. The key lesson to learn here is not to give up when the results are not apparent. Keep on putting the effort in the right direction and one day upon hitting the critical mass you will start seeing tangible results.


The success of the linked In app is also due to the strong network effects. LinkedIn has a large number of recruiters. Therefore, people who are looking for jobs sign-up on Linked In. Linked In got the maximum resume which attracts other recruiters who are looking for job applicants. It creates a positive feedback loop and thus makes Linked In a successful recruitment platform. Similar is the case with dating apps like shadi.com.


The network effect plays an important role in growth and relationships. If you are part of the right alumni network then it becomes helpful for you to get the right answers to esoteric questions and maybe you will be landed on the dream job through your contacts.


The idea of the network effect applies to the companies that gather data. The one that will make the first move will take all the advantages. Amazon is a dominant player in the e-commerce market. If a new e-commerce site will come along, it will still remain the dominant player. Convincing the buyers and sellers to use a new site is a very daunting task. If somehow they will convince them, still the new site is not effective because the buyers will not be able to take advantage of the product ratings available only at amazon.


Google is the dominant search engine. It gives the best possible result in response to any query. The best results will attract more traffic to it which means more user data will be available to Google. It provides free service to users and in turn sells the user's data to advertisers. Advertisers will be able to sell the right product to the right customers due to the availability of their data. Advertisers earn profit and thus more advertisers are attracted to google creating a positive feedback loop. Duckduckgo is another search engine that keeps the privacy of its users intact. Still, it won't be able to make any dent in the market of google. Once the network effect kicks in, it creates tremendous inertia for newcomers and the existing technology will retain its momentum for a longer period of time in the market.


The idea of network effects is very important for entrepreneurs. If they are working on a technology that has the potential for network effects then it follows an S-shaped curve.



To make it a mainstream technology, they have to ponder over the following questions.


  1. Where does my product lie on the S-curve?

  2. What is the critical mass for my product?

  3. What acts as a catalyst to achieve an early tipping point?

An important thing to keep in mind while dealing with critical mass or network effects is cascading of failure. These universal laws like critical mass, network effects, tipping points, etc. are applied to a system that consists of multiple subsystems. A failure in one part of the system causes a failure in an adjacent system that leads to catastrophic failure. A major blackout in the power grid is an example that happens when a subsystem fails, increasing the load on the nearby subsystem which also gets failed due to an overload increasing further load on other subsystems causing the entire grid to halt.


The housing crisis in 2007-2008 is another example where the failure of subprime mortgages brings down entire financial institutions. The species like Panda and Koyala feed on bamboo and eucalyptus. If somehow bamboo or eucalyptus becomes extinct so do the panda and Koyala disrupting the entire food chain. Similarly, some habits like adequate nutrients, meditation, sleep, etc. play a key role in our lives. Failure to incorporate these habits will disrupt the balance leading to a stressful and worrisome life.


These are the natural laws that can be either used for good or bad. Using these laws in the right way will help us to lead a better and more joyful life.


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