Exponential Growth


This chapter contains a bit of math but we will keep it to the basics.

Exponential Growth is one of the most powerful force of the Universe and is the underlying structure to many phenomena.

It is observed in many places in life: compounded interest of mortgages and credit card debt but also of savings, vicious and virtuous circles, feedback loops, self fulfilled prophecies, confirmation bias. Napoleon Hill named it Hypnotic Rhythm. Conventional wisdom calls it snowball effect. A more modern term is viral.

Although not exactly the same thing, it is also called geometric progression in Maths.

Exponential growth is what brings things to the tipping point fast (a.k.a. the last straw).

Growth is what happen when change occurs in one single direction. Often change occurs in several directions and basically keeps things the way they are. Earning and spending are both changes in your bank account and they each pull the balance in opposite directions and your bank account usually remains the same over time. If earning dominates, then your bank account will grow because the sum of all changes is going in one direction. We are better acquainted with the opposite, where spending dominates, and debt is growing.

There is linear growth and exponential growth. Linear growth occurs when things add up. Exponential growth occurs when things are multiplied or elevated to a power.

  • If you take 1 and add 2 several times, you get 1, 3, 5, 7, 9, 11, 13, 15 …
  • If you take 1 and multiply by 2 several times, you get 1, 2, 4, 8, 16, 32, 64, 128 …


Please note the two most important characteristics of Exponential Growth

  • It tends to grow a lot higher a lot faster.
  • It does not seem like much at the beginning and may even stay below a linear growth, then there is a tipping point, and things go out of control.

Exponential growth is at the foundation of interest loans and credit cards and of savings, so it is imperative you understand this concept to have a healthy financial life. You don’t need to necessarily get the math, but the concept of exponential growth.
Your financial survival depends on it.

The problem is that our brain is wired to understand linear patterns so we always oversimplify reality so we can grasp what is happening but this oversimplification has a real drawback. And some people who know that will try to trick us for their lucrative benefit.

This is a fictional example of linear growth: Deposit $1000 on an account and the bank pays you 10% every month. You are smart and put that money in your piggy bank. Your piggy bank will grow as follow: $100,$200, $300, $400, $500, $600, etc. after 6 months you own $1000 in the bank and $600 in the piggy for a total of $1600.

This is pure fiction.There is no such thing like a 10% return per month. Investors were lured by Bernie Madoff with 10% a year, which is a dream like return. Most saving accounts merely bring 1% a year

Now a fictional example of exponential growth: Deposit $1000 on an account and the bank pays you 10% every month. You are even smarter and put that money back in the bank account. So the bank is now paying interests on the initial deposit PLUS the interests that you kept on the account. And it grows like this:

  1. $1,000.00 yields $100.00 and balance becomes $1,100.00
  2. $1,100.00 yields $110.00 and balance becomes $1,210.00
  3. $1,210.00 yields $121.00 and balance becomes $1,331.00
  4. $1,331.00 yields $133.10 and balance becomes $1,464.10
  5. $1,464.10 yields $146.41 and balance becomes $1,610.51
  6. $1,610.51 yields $161.05 and balance becomes $1,771.56

As you can see, the same 6 months have paid an extra $171.56 for apparently no reason. That is the power of exponential growth.

The same logic happens to credit and interests on balance due. Debt gets out control because interests is built on the borrowed amount plus the previous interests. Basically the debtor is paying interest on interest. And that is where the real money is made by the lender.

Einstein once said that compounded interest is one of the most powerful force of the Universe.

Exponential growth gave birth to famous riddles like this one.
A wise man taught a king the game of chess. The king was very pleased and offered the wise man to pick his reward. The wise man asked for a grain of wheat on the first square of the chessboard, two on the second square, 4 on the third square and so on. Amused by such a modest request, the king ordered the wise to be paid at once, only to discover that there was not enough grain in the entire kingdom to fulfill that request. I highly recommend you try to do the math, (spreadsheets are great for that kind of fun). By square 24, the amount is about a metric ton. The final amount (at square 64 plus all previous 63 squares) is around 1.2 trillion metric tons. The World produced around 700 million metric tons of wheat in 2013. It would take roughly the global production of wheat since the dawn of agriculture to pay off that debt.

The opposite riddle concerns lily pads on a pond. On day one, two lily pads are on the pond. Each day they double in number; day two, four lily pads; days three, eight lily pads, and so on. The pond is completely covered with lily pads after exactly 28 days. At what point is the pond half covered by the lily pads? Jumping to conclusion would say that the lilies covered half the pond in the first two weeks and the other half during the last two weeks but we are dealing with imaginary geometrically growing lily pads here. If they double in number the next day, that means they were half as many the day before.
So they cover half the pond on day 27 and complete their pond domination scheme the next day by doubling in number overnight.

Exponential growth is tricky because our brain is wired for linear consideration and is blind to other form of progression.

Now, would you like to be paid a penny on day one, doubling every day for a month? (making 64 cents on your first week…) Or rather sign up for a solid 100K for the same month? You guessed it, the penny-a-day approach yields a cute 5 million dollars at the end of the month. (10 millions on a 31 day month)

A Penny a day Doubling every day goes a long way

Again as the chart shows, the Exponential Growth looks like a lot less for a long time
(64 cents at week 1, $82 at week 2, $10K at week 3…) then:

  • Day 24, 84K
  • Day 25, 168K
  • Day 26, 336K
  • Day 27, 672K
  • Day 28, 1.3M
  • Day 29, 2.6M
  • Day 30, 5.2M

Showing the last 5 days on the chart would stretch it 10 times higher, so it is truncated to reasonable size. You got the point of this riddle.

Exponential growth in life is present in situations like walking with a load. The load feels light at the beginning but as time goes it feels heavier and heavier. Because the load makes you tired and being tired makes the load feel heavier, which makes you more tired, which makes the load feel heavier, which makes you more tired, etc. Everyone experience it, having to change shoulder more and more often until the need to take a break comes and then taking breaks more frequently. Usually it only becomes a funny anecdote where you eventually hailed a cab unable to carry it for the last 50 yards.

But that is also what happens to hikers whose remains are found following a trail of abandoned belongings. Many inexperienced wannabe adventurers neglect to acknowledge the power of exponential fatigue and forget that half way is not half effort. Return to base is always more dangerous and takes more time. They feel good and confident and decide to turn back when fatigue begins to cast a shadow on the fun of the expedition. So they basically start a journey of the same distance but with their energy depleted. The lucky ones, again, will tell fun stories of being grounded by worried parents. The less lucky made the news.

Exponential growth is also observed when something goes viral on the internet or the news. The video or song or piece of news gets some attention from people who will in turn expose it to more people. The exposure attracts more people which increases attention which increases exposure, etc. Although there is a business segment that tries to create such momentum for lucrative purposes, this exponential growth is usually nothing but wild randomness at play.

Finally, exponential growth can be the engine of happiness or misery.

A nice person invites people to be nice to her, which in turn gives her the energy to be nicer which makes more people nicer to her and so forth. This is called the Power of Optimism or a Virtuous Circle.

Unfortunately, most people tend to work the cycle the other way, self sustaining their own misery and inviting others to be miserable. They fall into what we call Vicious Circles.

Thank you.