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"The greatest shortcoming of the human race is our inability to understand the exponential function." - Albert Allen Bartlett
That is true.
How?
I am also figuring out 😃
I can tell you a famous story called the "Rice and Chessboard Problem." Some people also call it the "Wheat and Chessboard Problem."
This is one of the best analogies to explain the power of Exponential I read on the Internet.
Rice 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."
The person who invented chess made a simple request:
"Dear Majesty, I need my reward in the following manner: Place one grain of rice 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."
The king did not understand what the inventor was planning. In those days, only a few brilliant people knew about exponential growth.
Even though the request seemed small, the king was not very impressed. Still, he ordered his treasury to give the rice as asked.
Today, everyone knows that the chess board has 64 squares.
The King’s servants placed grains of rice on a chessboard square by square as per the inventor's idea.
When they reached the 8th square, they had already placed 128 grains of rice —a small handful! But they didn’t realize how quick the number of grains would grow. (This is the exponential growth's misleading phase.)
By the 32nd square, there were so many grains—2.1 billion(equals to 10,000 kilograms) ! It was too much to fit on the board.
By the 64th square, there was more rice than anyone could count—enough to make a mountain as big as Everest!
Yes
That is the power of exponential growth.
As per historians, King ordered to kill the inventor since he was not happy to find this out.
Back then, people didn’t have calculators or computers to do big number calculations.
How humans solved this problem in modern life.
"Simple addition can solve the problem. 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 presented as 2^64−1 or 18,446,744,073,709,551,615"
Refer to Wikipedia for technical.
To understand number growth in this manner is tricky because we think of numbers in a straight line.
We all think linear; if you go 10 meters in a straight line, you will be across the room.
We can all imagine where you will be in 20 or 30 linear steps with amazing accuracy.
But, predicting exponential growth is not logical and generally surprises and disrupts us.
If you take 30 big steps by doubling each time (1, 2, 4, 8, 16, 32), you won’t go 30 meters. Instead, you will go around the world 26 times and end up 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 can solve hard problems faster than regular computers due to exponentials. They can help in many areas, like keeping information safe and making new materials.
In banks, money grows over time because of something called compound interest. An example of the exponential function. This means the money you save or owe increases faster and faster!
CONCLUSION
The hardest part is teaching our minds to think in big growing numbers. Even I still find it tricky!
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 means computers get twice as fast every 18 to 24 months!
Closing on the quote from Bill Gates giving example of computers what is exponential.
"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.
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