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"The greatest shortcoming of the human race is our inability to understand the exponential function." - Albert Allen Bartlett
That is absolutely true.
How?
I am also figuring out 😃
However, I can tell you a famous story commonly known as wheat and chessboard problem. In some settings, this story is also called the rice and chessboard problem.
This is one of the best analogies to explain the power of Exponential I read on the Internet.
Wheat and Chessboard Problem
Once upon a time, in ancient India, the inventor of chess presented his game to the King.
King loved the game and offered a reward to the inventor by asking:
"What would you prefer as a prize? You can have anything you want in my kingdom if you name it."
Chess inventor humbly requested:
"Dear Majesty, I require my reward in the following manner: Place one grain of wheat in the first square, two in the second, four in the third, and so forth, doubling the number of rice grains on each succeeding square."
King did not understand the intention of the inventor and accepted the offer since in that era nobody knew the power of exponential growth except some highly intellectual mathematicians.
Although such a petty request did not convince him, he ordered his treasury to provide accordingly.
Today, everyone knows that the chess board has 64 squares.
So, you can imagine what would happen when the King ordered his servants to put the grain of wheat on the chessboard as per the pattern suggested by the inventor.
The King's men had placed 128 grains of wheat (a handful) on the 8th square when they reached of the eighth square of the first row. (This is the exponential growth's misleading phase.)
But at 32 squares, the number of grains of wheat had reached a frightening 2.1 billion grains of rice (equivalent to 10,000 kilograms) which they were unable to retain on the board or anywhere else.
By the 64th doubling, the amount of rice had become immeasurable, reaching 461 billion tons of rice, a mountain same as the size of Mount Everest.
Yes
That is the power of exponential growth.
It was said that King ordered to kill the inventor since he was not happy to find this out.
Of course, at that time we did not have a calculator or computers that could do astronomical calculations.
How humans solved this problem in modern life.
"The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 2^64−1 or 18,446,744,073,709,551,615"
Refer to Wikipedia to know technically.
The impact of exponential is a tricky thing for humans to fully absorb since we always think of our world in a linear fashion.
We all are programmed to forecast linearly; if you go 10 meters in a straight line, you will be across the room.
We can all anticipate where you will be in 20 or 30 linear steps with amazing accuracy.
However, predicting exponential growth is not logical and frequently surprises and disrupts us.
If you take 30 "exponential steps," which are simply doubling patterns (1, 2, 4, 8, 16, 32), rather than 30 linear steps, you won't arrive at your destination of 30 meters. Instead, you will travel the globe 26 times and find yourself a billion meters away.
In simple terms,
If you double something 10 times will make it 1,000 times bigger.
If you double something 20 times will make it 1,000,000 times bigger.
If you double something 30 times will make it 1,000,000,000 times bigger.
Three Top Examples of Exponentials:
CHATGPT, a type of Generative AI is the best example of an exponential technology. It takes Linear Input as Prompt from Humans, but Processing is Exponential.
Quantum computers have the potential to solve complex problems exponentially faster than classical computers, impacting cryptography, material science, and more.
Compound Interest is the most common form of exponential function working in the finance industry where in a bank account money you earn or owe grows at a fixed percentage rate over time, leading to rapid growth or decay.
CONCLUSION
The biggest challenge is to train our minds to think exponentially, which is still difficult for me to understand and practice.
If you observe, today’s society is both global and exponential.
Global because if something happens on the other side of the world, we come to know in seconds
Exponential because the rate of computational change doubles in performance every 18 to 24 months.
Closing on the best quote from Bill Gates how computers perform exponentially.
"If General Motors had kept up with the technology like the computer industry has, we would all be driving $25.00 cars that got 1,000 miles to the gallon." - Bill Gates
Understanding the exponentials for you will make a difference:
between success and failure,
between leading disruptive change or being the victim of it.