TWI #45 Linear Vs Exponential Thinking

Aug 24, 2023

Read Time: 5 min 

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Today at a glance: 

  • A mental model is a cognitive approach individuals employ to enhance their comprehension of and streamline their interactions with the surrounding world. It serves as a perspective through which you navigate daily experiences.
  • The billion-year history of ice ages surprisingly holds insights for finance through the lens of interconnectedness. Despite predating currency, studying these ancient climate shifts reveals the potency of incremental changes.
  • This compounding pattern, seen in both natural phenomena and wealth growth, is exemplified by Warren Buffet's lifelong investment and Jim Simons' late-starting but exceptional returns. Comprehending compounding's exponential power is vital, as it defies intuition and underscores the significance of sustained, consistent growth over time.

 

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"$81.5 billion of Warren Buffet's $84.5 billion net worth came after his 65th birthday. Our minds are not built for such absurdities." 

- from The Psychology of Money by Morgan Housel 

A mental model is a cognitive framework or conceptual framework that people use to interpret and understand the world around them.

It's a simplified representation of how things work, allowing us to make sense of complex information, predict outcomes, and make decisions.

Mental models are built through experience, learning, and observation, and they serve as mental shortcuts to process information efficiently.

They help us organize knowledge, identify patterns, and solve problems by providing a structured way to approach various situations. 

There is an age old mental model that confounds many because of it’s logic defying exponential characteristics.

However, because it’s immense power, I feel a need to help clarify this way of thinking so you can use this as a mental model moving forward. 

 

Thinking Exponentially vs Linearly

When making investment decisions we are faced with two potential ways of thinking:

  • Linear Thinking: Linear thinking involves a straightforward and sequential approach to processing information and problem-solving. In this mode of thought, events and concepts are connected in a linear, cause-and-effect manner, where each step leads logically to the next.
  • Exponential Thinking: Exponential thinking is a mindset that embraces the power of growth and change that accelerates over time. Instead of following a linear path, exponential thinkers envision outcomes that compound and multiply at an increasing rate.
  • This approach acknowledges the potential for small initial changes to yield remarkable and often unexpected results. Exponential thinking is crucial in understanding technological advancements, financial investments, and the dynamics of complex systems. It challenges conventional perceptions, encouraging individuals to consider the broader implications of compounding effects and the transformative potential of rapid growth.

The power of this framing comes from understanding the role of compounding and the impact it has on our envisioned future self.


 

Nature's Paradigm Shift

Unveiling the interconnections between seemingly disparate domains, consider the billion-year history of ice ages and its unexpected relevance to finance.

While ancient ice ages predate the concept of money, delving into this history provides insights into the power of incremental changes.

Our comprehension of Earth's mechanisms is relatively young.

Only in the 19th century did scientists concur that the planet had experienced multiple extensive ice coverages.

Five occurrences were identified, each necessitating colossal energy shifts. The force behind this remained a puzzle.

Early theories proposed mountain ranges' impact on winds and volcanic activity as drivers of climate shifts.

However, these failed to explain cyclical ice ages.

In the early 1900s, Milutin Milankovic proposed that gravitational forces from celestial bodies influenced Earth's tilt and, over millennia, altered solar radiation exposure to create intense winters and subsequent ice ages.

Meteorologist Wladimir Koppen later revealed a different aspect. Cyclical ice ages stemmed from insufficiently warm summers, causing persistent snow accumulation.

The snow that remains after winter makes it easier for snow to accumulate the following winter. This increases the likelihood that the snow will not melt during the subsequent summer, which in turn attracts even more snow accumulation the following winter.

Reflected sunlight perpetuated the cooling cycle, gradually transforming the landscape into massive ice sheets.

The same thing also happens in reverse: an orbital tilt allows more solar rays to enter, which melts more of the snow, allowing for less accumulation, and so on. This is the cycle.

The amazing thing is how a small change in conditions can give rise to such an enormous continental event. It all starts with a small layer of snow and ice left over from a cool summer, and before you know it, a continental ice sheet miles deep has formed.

The lesson from a billion years of history is that you don't always need a massive force to create tremendous results.


 


 

Linear Vs Exponential - A Mental Model for Investing and Life 

This pattern, known as compounding, showcases substantial results arising from minimal initial changes.

The parallel with financial success is evident.

Warren Buffet's story exemplifies this principle.

There have been hundreds of books written about Warren Buffet's success, but few highlight the simple fact that his fortune is not just due to his extraordinary investing skills, but also because he has possessed those skills since the age of 10.

Currently, Buffet's net worth is around $84.5 billion, of which $81.5 billion was earned in his mid-60s.

Consider this: Buffet began his investing career at the age of 10. By the time he was 30, he was already worth $1 million ($9.3 million adjusted for inflation).

Now, imagine if he had spent his teens and twenties exploring the world and finding his passion instead of investing. What if, by age 30, he was only worth $25,000?

Even if Buffet had gone on to earn an amazing 22% annual return until he retired at the age of 60, his net worth would have been far less than $84.5 billion. In fact, it would have been only $11.9 million, which is 99% less than Buffet's actual net worth.

The key isn't just his investing acumen, but the time span that enabled compounding.

Jim Simons, renowned for his superior investment returns, emphasizes the importance of time. Despite a 66% annual return since 1988, his net worth falls far short of Buffet's due to starting later.

No one comes close to Simons’ return. Warren Buffet's average annual return is nearly 1/3 at just 22%.

However, Simons' net worth is about $21B, which is still 75% less than Warren Buffet's.

Why the difference if Simons is such a superior investor? The answer is time. Simons didn't hit his investing stride until he was 50 years old.

What if Simons had started when Warren started? The number defies logic.

$63,900,781,780,748,160,000,000,000,000,000.

Most people think in a linear fashion but if you want to understand compounding then you have to think exponentially.

Even as small as a 1% difference every day can be extremely impactful.


 


 

If you were asked to calculated 8+8+8+8+8+8+8+8+8, you would say that’s easy 72. But If I asked you to calculate 8x8x8x8x8x8x8x8x8, you would have a lot of trouble. Its 134,217,728.

Thinking linearly versus exponentially is a crucial distinction. Compounding defies intuition, illustrated by the computer storage evolution, from Bill Gates' disbelief in needing 1 GB to today's terabyte drives. Similar oversights occur when examining phenomena like ice ages or wealth accumulation.

Comprehending compounding is pivotal. Many divert energy towards one-off endeavors seeking exceptional returns, missing the sustained power of steady growth. True success lies in nurturing sustainable, consistent gains over extended periods.

Find Balance Between Logical and Illogical

The Linear vs. Exponential thinking mental model is one that I find myself coming back to over and over again in my own life.

When I am faced with a key investment decision, I ask myself two questions:

Am I thinking linearly or exponentially?

What would an exponential thinker do?

My goal is to have a high ratio of exponential vs linear thinking.

Note that the goal is not to be so broad with your thinking all the time. Sometimes the step we can take is the one in front of us.

Lesson: Success in investing and in life lies in understanding the power of sustaining and compounding net positive results.


 

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