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Latticework of Mental Models: Critical Mass

This article is the tenth of this weekly series called Latticework of Mental Models, which will be authored by my friend and partner in writing the Value Investing Almanack, Anshul Khare. Anshul will write on various mental models – big ideas from various disciplines – which can help you think more rationally while analyzing businesses and making your stock investment decisions.

It’s said that you can find extraordinary intelligence in nature. To unearth this brilliance, all you need is curious eyes and close observation. In that spirit, let me start today with the story of a Chinese bamboo tree.

Imagine that you were given few Chinese bamboo seeds and asked to grow them. You take the little seed, plant it, and start watering it. You add fertilizer and wait patiently for the seed to turn into a plant. You wait for a whole year, and nothing happens.

The second year you continue to water it and fertilize it, but still nothing happens. Looks like somebody is testing your patience.

The third year you water it and fertilize it, and the same story repeats i.e., no visible results. Many people would have given up on the tree by this time. But not you. At least not in my story.

The twist in the tale comes sometime during the fifth year. One fine day a tiny bamboo sprout breaks through the ground. Yay! Your happiness knows no bounds, after all you didn’t give up and your perseverance finally paid off.

While the neighbouring trees are bullying the innocent baby bamboo, you wish that the tiny sapling at least lives for few more weeks. But the bamboo tree has some other plans.

What transpires in the next few weeks is phenomenal. In a matter of six weeks that puny sapling shoots up in the sky, not stopping until it achieves a dizzying height of ninety feet. This unreal growth leaves you flabbergasted and the fellow trees in shambles.

What the heck happened?

To many readers, this story might sound familiar. But chances are that you were told this story in a different context. The anecdote is quite popular among motivational coaches and self-help gurus who use this metaphor to extol the virtues of tenacity and never-give-up attitude.

Their pep talks sound something like – “Don’t give up! Keep putting in efforts and the results will one day come like the Chinese bamboo tree!”

I don’t disagree with them, however, my intention here is not to motivate you. I want to dig deeper and try to unravel an interesting mental model depicted by this phenomenon. So let me start by putting out some obvious questions on the table.

  • What do you think was going on in the case of the Chinese bamboo tree?
  • Was there really nothing happening at all in the first five years?
  • Why did the visible growth happen so fast in such a short period of time?
  • Is it just the Chinese bamboo tree, or are there other areas where a similar pattern can be observed?

The Big idea from Physics
Before we can make an attempt to answer those questions, we need to understand the notion of Critical Mass which made its debut in nuclear physics.

I can almost hear you yawning – “Anshul, if electrons and nucleus excited me so much, do you really think I would be worried about P/Es and ROEs? C’mon, I’m here to learn about investing and you’re boring me with nuclear physics!”

Well, I know nuclear physics excites very few. So before you run away, let me just reassure you that I’ll be done with my physics lecture even before you open your eyes.

I promise it won’t hurt. Ready?

In nuclear physics, Critical Mass is the minimum amount of a given fissile material (raw material for nuclear reaction) necessary to achieve a self-sustaining fission chain reaction. The term, however, is now used as a much broader construct. In astrophysics, for example, Critical Mass is a concept used to designate any mass that when exceeded causes something to happen.

You can open your eyes now. 🙂

Jokes aside, Critical Mass can be understood by observing something as simple as a metal spring. A spring goes back to its original size and shape when you release it after stretching it a bit. However, if stretched beyond a certain limit, it merely deforms rather than returning to its original position. That limit is akin to the critical mass for the spring.

To make it more clear, I want to take Peter Bevelin’s help. So let me draw your attention to this excerpt from his book, Seeking Wisdom

At a certain scale, a system reaches a critical mass or a limit where the behavior of the system may change dramatically. It may work better, worse, cease to work or change properties.

Small interactions over time slowly accumulate into a critical state – where the degree of instability increases. A small event may then trigger a dramatic change like an earthquake.

A small change may have no effect on a system until a critical threshold is reached. For example, a drug may be ineffective up until a certain threshold and then become effective, or it may become more and more effective, but then become harmful.

Another example is from chemistry. When a system of chemicals reaches a certain level of interaction, the system undergoes a dramatic change. A small change in a factor may have an unnoticeable effect but a further change may cause a system to reach a critical threshold making the system work better or worse.

A system may also reach a threshold when its properties suddenly change from one type of order to another. For example, when a ferromagnet is heated to a critical temperature it loses its magnetization. As it is cooled back below that temperature, magnetism returns.

This mental model finds its relevance not only in physics but in scores of other areas. Let’s explore some of them.

Critical Mass as Tipping Point
Malcolm Gladwell has done a brilliant job of refining this concept further to explain the phenomenon of epidemics, like social trends or contagion of ideas, in his book The Tipping Point.

The advent and popularity of fax machines is an interesting case study he explained in his book –

Sharp introduced the first low-priced fax machine in 1984, and sold about 80,000 of those machines in the United States in that first year. For the next three years, business slowly and steadily bought more and more faxes, until, in 1987, enough people had faxes that it made sense for everyone to get a fax. Nineteen eighty-seven was the fax machine Tipping Point. A million machines were sold that year, and by 1989 two million new machines had gone into operation.

It’s very interesting to note that, using the concept of Critical Mass, a lot of social behavior can be decoded like how rumors spread, voting, mob behaviour (leading to strikes or riots), adoption of new technology, consumer behaviour, education, and host of other things.

Farnam Street has put together some great insights and relevant examples describing the above situations in the light of Critical Mass mental model.

Coming back to the Chinese bamboo tree puzzle, now we have some clues to explain the explosive growth. Although, outwardly nothing significant seemed to have occurred for the first five years but the bamboo roots, underneath the ground, were slowly taking shape and growing steadily. In effect, the foundation was getting built to support the upcoming rapid growth.

The moment a critical mass, in terms of amount of roots required for external growth, was achieved the bamboo sampling broke free and grew with a nonlinear speed. You could say that the day, when bamboo sapling saw the sunlight for the first time, was the tipping point.

Checkout the non-linearity as shown in the graph above. In any system prone to critical mass effect, the tipping point is where the non-linearity kicks in.

For that matter, the boiling point and the freezing point for water are kind of tipping points where the state transition happens for the water.

Another great example around us is the city traffic. On any given day the traffic affects our commute time. If you increase the traffic by twice, our commute time may also increase by a factor of two. However, at a certain point, addition of few more cars chokes the road completely and the vehicles movement comes to a grinding halt. The number of cars on the road at that inflection point can be dubbed as the Critical Mass for the commute system.

Critical Mass and Lollapalooza
When it comes to multidisciplinary learning, one leg of the latticework of mental models is hinged on the idea of Critical Mass. Take a look at the definition of Lollapalooza as defined in Poor Charlie’s Almanack

Lollapalooza is, as personified by Charles Munger, the critical mass obtained via a combination of concentration, curiosity, perseverance, and self-criticism, applied through a prism of multidisciplinary mental models.

If you could look at the world from Charlie’s eyes, who according to Warren Buffett has the world’s best 30-second brain, majority of the worldly problems would be no-brainers. Simply put, when you learn the most important mental models and start applying them for problem solving, you will realize that multiple models seem to converge in one direction and together they form the dynamic critical mass for a cascading of positive effects – a lollapalooza. It simplifies your decision making tremendously.

Critical Mass in Business and Investing
Warren Buffett suggests that for finding great businesses, one should look for strong moats. And one of the underlying forces for a moat is economies of scale.

A company may reach a certain critical size, writes Peter Bevelin in Seeking Wisdom

…and get advantages of scale in experience purchasing, marketing, manufacturing, administration, research, logistics, distribution, etc. For example, expenses can be spread out over larger amounts of volume, lowering average costs. These advantages often permit greater specialization, making people better at what they do.

That’s the positive side of Critical Mass. How about it’s role in understanding the financial disasters?

Think about the 2008 economic crisis. One of the factors contributing to the fiasco was poor quality debt issued by financial institutions. Now, in a healthy economy, few bad practices and bad loans can be absorbed without much news. However, when certain factors related to environment and regulations promote the misaligned incentives, they end up triggering positive feedback loops feeding the bad. Remember Gresham’s Law?

Unfortunately, before a Critical Mass (of bad debt) could be achieved, no dramatic changes were visible for a long time. And one fine day in 2008, people were caught off guard when the whole financial system tipped.

Reminds me of the saying – “It is the last straw that breaks the camel’s back.”

Perhaps, the first bad loan (packaged as mortgage backed security) which defaulted and the first buyer in the stock market who couldn’t find another buyer became the last pieces of the Critical Mass puzzle.

For eons, people have been searching for the magic recipe for wealth and happiness. In this search, they often look up to the uber-successful or ultra-wealthy individuals in contemporary society, hoping that they would divulge the secret.

We are lucky to be alive in an era where people like Charlie Munger, world’s leading authority on multidisciplinary thinking, have literally been shouting the secret from the rooftops since decades.

Superior performance in life and in investing, according to Mr. Munger, doesn’t come from a magic formula. It comes from what he calls “constant search for better methods of thought,” a willingness to prepay through rigorous preparation, and from the extraordinary outcomes of multidisciplinary research model.

I believe that luck plays a significant role in defining the direction of our lives and for me it was a wonderful stroke of luck that I stumbled upon the teachings of Charlie Munger. I must confess that, after discovering him, I lost my right to blame luck for my failures.

This is as far as luck could have taken me – to the doorsteps of school of worldly wisdom. Now it’s up to me.

I hope you agree with me. And I hope you take the responsibility of acquiring worldly wisdom seriously.

When I compile these posts, I imagine myself sitting in front of you and having this conversation face to face. That creates a subtle fear in my mind that I might not be able to answer your doubts and questions. This subconscious fear makes me think hard before writing. Can you guess who benefits the most from this process? Yours truly i.e., me. 🙂

Before I close, let me rehash an important insight about learning. I’ll quote Benjamin Franklin who said –

Tell me and I forget, teach me and I may remember, involve me and I learn.

So don’t just read, get involved. Don’t just learn, go out and teach.

Take care and keep learning.

Disclosure: Safal Niveshak participates in the Amazon Associates Program, which simply means that if you purchase a book on Amazon from a link on this page, we receive a small commission. The book does not cost you any extra. We give away 100% of the commission for the betterment of the under-privileged.

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About the Author

Anshul Khare worked for 12+ years as a Software Architect. He is an avid learner in various disciplines like psychology, philosophy, and spirituality with special interests in human behaviour and value investing. You can connect with Anshul on Twitter.


  1. Prashant says:

    Dear Ansul,

    Great explanation. I have a question, Can we consider Compounding as a Critical mass? As what i have observed that if you have invested Rs.100 in a year one, and if it is compounding at 15% a year, After 15 years you will see it is growing more that what you have invested in a year one. so can we consider this point as a tipping point? like Chinese bamboo, once it has crossed this tipping point you will see how fast your principal amount grow in an absolute return. same thing for even companies which are having right strategies, when they are putting their blocks to gather their growth would be little slower or say unvisible to the market but once every thing is in place, their growth will high and visible to market.

    Correct me if i am wrong.


    • Hi Prashant, before Anshul answers, let me do the honours. 🙂

      Yeah, compounding passes through the critical mass stage, and that’s why it’s such a wonderful model. Things don’t seem to compound for the first few years, and then it just shoots up. For instance, if you were to multiply your money 100x in 25 years, the first 20 years produce 40x…but the remaining 60x comes in just the last 5 years.

      Hope this helps.


  2. Prashant says:

    Thanks Vishal



  3. Ankit Kanodia says:

    Dear Anshul and Vishal,
    As always a wonderful post.
    As I promised you yesterday, I will try to be a devil’s advocate here. . Pardon me if I fail to raise a concrete point. ..

    Critical mass in terms of a company’s performance would be something like where a company goes through the initial years or maybe be a decade or two before they really start bearing the fruits of all the struggles it has gone through. But as an investor we often fail to differentiate between the ones which are about to achieve critical mass and the ones which are poor. .While it really is important to wait for the bamboos to grow sky high but that is only one part of the story. . The other important part is to keep checking whether it’s positioned well, it receives the adequate amount of sun light and water, soil content is upto the mark or not, moisture content etc. .. so, in effect the critical mass will be achieved only if all the other small parts work well enough.
    In short, for investment, while patience is important to get the critical mass in terms of compounding working for you … It is equally important to notice where you are not going to achieve that critical mass and stop. Waiting for critical mass to help you someday on an investment idea which does not qualifies to be a long term investment can put an investor in a lot of danger.

    These are my personal views, I may not be right so it would be great to hear from both of you on this aspect.

    • Anshul Khare says:

      Thanks Ankit! I appreciate your efforts for playing the devil’s advocate.

      I am in complete agreement with the points raised by you. I would like to extend your argument to all the other mental models. Every theoretical construct, irrespective of how rigorously it has been tested and validated, has certain assumptions inherent into it. Mental models, being no exception, too assume certain pre-conditions to render themselves useful.

      Just like it’s important to know ‘what you don’t know’, it’s absolutely essential to know the boundaries of every idea, every mental model, and every structure of knowledge. Else we become the proverbial ‘man-with-hammer’ who swings his solitary tool (critical mass in this case) every time.

      As you pointed out, it’s important to be aware of the context in which we are operating, so that we can pull out the right tool (mental model) at the right time.

      Let me end my monologue with a quote from Mahatma Gandhi. He said “Be the change you want to see in the world!”. So I urge you and the other tribe members to “Be the devil’s advocate for an idea you want to learn”.

      • Ankit Kanodia says:

        Thanks Anshul!
        Glad that my comment did make some sense…
        I am a big fan Of Vishal’s and your’s posts..
        keep writing and sharing

  4. Patient is important but at the same time contrary thinking is also equally important to get the critical mass concept work in our favor. Patient gives us success when all required parameters set in a proper manner otherwise it may ruin us also. Contrary thinking or doubts helps us to check whether all necessary parameters have been set in a right order or not.
    There were many hot stocks in 2007 which are still trading below of their price in 2007 and some of them even trading below of their 20% price level in 2007.
    To understand the critical mass concept in another way we may look at the option price in the day of its expiry. ITM becomes OTM and OTM becomes ITM within a few seconds. I have observed Nifty Index Option at the day of expiry OTM starts trading at INR 5-6 and at 3:10 pm its value reduced to 30-40 paisa and then suddenly it becomes at the ITM and closed at INR 49.15 and also observed the reverse phenomenon. So when it goes in our favor we say patient pays and when it goes against us what would we say it? Contrary thinking and a prompt exit may save us with minimum injury.
    Let us take another example of Short-strangle position. If we build a short strangle in the range of 300 points in Nifty Index Option most of the month it gives us a positive return due to the theta decay and inexperienced traders described it as “patient pays” but in one month it wash away all of their profits and turns their P&L into net Negative. Keep on patient with negative gamma becomes disastrous.
    So the conclusion is; be patient but at the same time be cautious also.

    • Anshul Khare says:

      Hey Soumen,

      Thanks for sharing your insights. Good to know that critical mass finds its relevance in trading also.

      Trading strategies fall outside of my circle of competence, hence I couldn’t really understand the analogy that you have presented.

  5. Shodhan says:

    Dear Vishal, just like finding Anshul Khare has been critical mass moment for Yet another great article from Anshul. I am learning a lot

    • Anshul Khare says:

      Thanks for your words of encouragement Shodhan.
      Even I’m learning a lot while compiling these ideas in this series.

  6. Ayush Agrawal says:

    I have a question for you if you entertain contradictory views.
    do you mean to say we may have the ability to solve most no. of question by simply learning some 30 mental model techniques.. i mean.. is’nt it quite superficial kind of learning..
    why can’t there be some other way for getting an answer..
    why learn some of the biases, when there may be thousands of them. i mean you may be able to identify biases of other people to some extent if you yourself have the habit critiquing yourself and realizing what you’re doing.

    its like knowing some of the rules.. and you see our actions tend to justify those set of rules subconsciously.. (another bias..)

    • Anshul Khare says:

      Hi Ayush,

      I am glad you asked the questions. I am not very sure if I can answer them to your satisfaction, but let me still make an attempt 🙂

      Q. “do you mean to say we may have the ability to solve most no. of question by simply learning some 30 mental model techniques.. i mean.. is’nt it quite superficial kind of learning..”

      I believe there is no guarantee that you can solve “most problems” using few mental models. A lot of real world problems are too complex to be understood, let alone solving them. These few mental models provide you a tool to gain insights about problems and makes your decision making process much simpler. They also act as sieve to filter out the problems which fall outside your circle of competence. You must have heard of this – “You can’t win if you don’t play”. Let’s invert it “You can’t lose if you don’t play!” Using mental models will leave you with a large pile on your “too hard to solve” basket, and that’s not a bad thing. Mental models will save you from getting into something which you don’t understand.

      These mental models emanate from the fundamentals of important disciplines. Once your learn the fundamentals you can always build upon them and arrive at other insights. So that’s why it becomes imperative to learn the fundamentals first. These are the distilled piece of high quality information. I wouldn’t consider them superficial.

      Q. “why can’t there be some other way for getting an answer..”

      There could be many other ways of getting the answer. However, it’s a good idea to look for the most effective tools. You could always travel from one continent to other by land or water. But flight is the cheapest, safest, quickest and perhaps most comfortable way to do that. Mental models is akin to air travel. Maximum bang for the buck.

      Q. “why learn some of the biases, when there may be thousands of them. i mean you may be able to identify biases of other people to some extent if you yourself have the habit critiquing yourself and realizing what you’re doing.”

      I guess the Pareto Principle holds some clue for this question (Aarghhh! another mental model). It says that 80 percent of your results come from top 20 percent of your efforts. Extending this to learning, 80 percent of important and relevant knowledge will come from top 20 percent of resources. So learning the very important behavioural biases will benefit you in high stake decisions. You could still go ahead and learn all the other thousands of biases but the return on invested time/effort will be minuscule. Diminishing law of marginal utility, you see!



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  2. […] website and writes on mental models (much better than I did). Read Anshul Khare’s write-up on ‘Critical Mass’ for Safal Niveshak. Another good article on Mental Models was by Farnam Street explaining few […]

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