The Two Types of Growth: How to Navigate Yourself in Both Logarithmic & Exponential Curve

By Dean Yeong on December 4, 2017

In 1965, the co-founder of Intel, Gordon Moore, observed that the number of transistors in a dense integrated circuit doubles approximately every 18 months. It’s known as the Moore’s Law.

The extension of Moore’s Law explains that machines become smaller in size and computing power becomes more efficient over time. Simultaneously, the cost of high-power computers also decreases. In fact, the number of transistors in an integrated circuit grew from 2,300 in the year 1971 to 2.6 billion in the year 2011.

It’s easy to believe that growth happens linearly. In the purest sense, the more time you spend walking, the more steps you walk, and the further you get from point A to point B. However, we’re living in a complex world where growth is usually affected by multiple factors concurrently, with different levels of impact, happening at different rates.

While Moore’s Law is an excellent example of what is known as exponential growth, our lives are constantly influenced by two types of growth. In this article, I’m going to show you the differences between them, their impact on our work and lives, and a few solutions to overcoming the challenges they pose.

Logarithmic Growth

The first type of growth is what known as the Logarithmic Growth. Things that follow the Logarithmic Growth curve increase or improve rapidly in a short period or with only a tiny amount of effort. But up to a certain point, the growth acceleration increases where the output is proportionally smaller to the input.

The Logarithmic Growth Curve

Here are a few examples of Logarithmic Growth:

STRENGTH GAINED FROM LIFTING WEIGHTS

People who have never worked out before experience strength gains and fitness improvement in a short period. Then, the progress slows down as one becomes stronger. In my personal experience, my squat PR grew from 40 kg to 70 kg in eight weeks but from 70 kg to 100 kg in six months. Now, I reach a threshold where I can hardly break my squat PR (Personal Record) in months.

LEVEL OF HAPPINESS AS INCOME INCREASES

People say money doesn’t buy happiness but the truth is, it does. Having enough money removes many unnecessary worries and frustrations. However, a study shows that the relationship between income and happiness stops at $75,000. No matter how much more people make, they don’t report any greater degree of happiness after earning $75,000.00. (Sometimes people become miserable as the freedom increases.)

MASTERY OF A SKILL

It takes a short time for a total beginner to achieve a decent level of competency in practicing almost any craft. On the other hand, it takes years for a competent practitioner in any field—like sports, music, and fine arts—to breakthrough and become great and become the best.

Exponential Growth

The Exponential Growth curve is the direct opposite of the Logarithmic Growth curve and is the second type of growth that influences our lives.

The Exponential Growth Curve

Instead of rapid growth in the beginning, things that follow the Exponential Growth pattern make insignificant—almost zero—progress in the beginning for a very long period of time. However, as these small improvements stack up and reach a threshold, growth explodes exponentially suddenly with very little effort in a short time.

In fact, we’re experiencing this type of growth more and more today with the advancement of technology.

BUILDING A CREATIVE BRAND OR A BUSINESS

Most successful companies have existed for years without people knowing about them. Entrepreneurs hardly see progress in the early stage of their startups. But as their business grows bigger and bigger, the progress accelerates in a nonlinear manner.

INVESTING IN COMPOUND INTERESTS

A small monthly saving doesn’t seem like much in the short-term, but with compound interest, it can grow to a significant amount in the long-run. In the book Unshakeable by Tony Robbins, Theodore Johnson, who made $14,000 per year, retired with  $70 million by investing 20% of his income every month in compounding interests.

TECHNOLOGICAL ADVANCEMENT

Almost every growth in technology follows the Exponential Growth curve. It took humans 3.3 million years to progress from the prehistoric age to early civilization, 4,000+ years from early civilization to the modern era, and 400 years from the early modern era to the information age. And now we’re exploring fields like artificial intelligence, the cure of aging, and the colonization of Mars.

Challenges and Solutions

It’s hard for us to grasp the idea of these growth patterns—especially exponential growth—because our ancestors aren’t living in the environment we live in today. Back  a few hundred thousand years ago, the one:

  • Who spent more time hunting got more food that lasted longer.
  • Who could resist fatigue and walk for longer periods of time traveled further.
  • Who worked longer hours got paid more.

We as a species were mostly exposed to linear growth until recently. Today, our environment has changed while at the same time, our mental models and behaviors are still hardwired to it. That means living with the two types of growth—Logarithmic Growth and Exponential Growth—is somewhat challenging to almost everyone today.

LOGARITHMIC GROWTH: FOCUS ON THE PROGRESS AND BUILD HABITS THAT SUPPORT THE GROWTH

The primary challenge that comes with the Logarithmic Growth is stagnation at the top of the growth curve. It’s sometimes discouraging to experience rapid growth acceleration for a short period of time at the start, and then encounter how incredibly difficult it is to move forward from that.

Often, we need to put as much as ten times the amount of energy into making even a small improvement in a particular skill we’re trying to master. And sometimes this pushes us to the edge of giving up because it’s just too hard to keep going. Some fall into the trap of dabbling between multiple things due to the addictive element that instant growth brings us.

The only solution is to embrace the true nature of Logarithmic Growth. Instead of focusing on the results, shift your focus to the progress and build supporting habits to promote growth at a sustainable pace.

At the same time, acknowledge that small improvements at the top can make a huge difference. In one of my previous articles, I showcased the “Winner-Takes-All Effect” where small differences and advantages create a significant impact on how big of a pie you get (in a competitive environment).

EXPONENTIAL GROWTH: IDENTIFY THE FUNDAMENTALS THAT CREATE THE GREATEST IMPACT

On the other hand, Exponential Growth introduces another set of challenges in our work and life. It tests our patience in the pursuit of any goal. We often feel like we’re getting no results after all the hard work we’ve put in.

The solution to this challenge is likely the same as the one I’ve mentioned above: acknowledge that each tiny improvement adds up to something more than you imagine. It’s where one plus one is equal to three or more than just two. As James Clear puts it, 1% improvement every day can create a compounding effect that makes us 37 times better in a year.

The key is to not rush to the threshold of Exponential Growth because then it possesses another type of risk where we might fail to handle the sudden growth that comes with it. This is a common mistake made by many startups. They scale up too quickly without the foundation and experience needed to maintain it to the point where it eventually collapses.

If you must speed up the Exponential Growth curve, identify the critical fundamentals of what you do. Find and focus on the element that if improved, can create a cascading effect on everything connected to it.

  • Optimize your positioning and offering before thinking about what social media post to publish.
  • Focus on the principles of health and fitness instead of the brand of supplements you should take.
  • Improve the quality of your creative work first before spending the entire day thinking about what time to publish.

Setting Realistic Expectations

The very first step in overcoming the challenges that will accompany different types of growth is to acknowledge them. Figure out which type of growth you’re currently experiencing in each area of life. Then track and measure your progress to get a clear picture of the journey you’re pursuing. This alone will help you to set better expectations for the growth rate in everything you do.

Regardless of any type of growth, one strategy that guarantees help in maximizing your growth is doing the right thing. By doing the right thing, I mean tapping into the insights and wisdom of people who have achieved what you want to accomplish.

Instead of being a busy idiot running around in circles, reach out—read books, hire a coach, get mentorship. All of this will help you identify patterns. Then put them to the test to see if your growth rate improves many folds.

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