The Legend of Sissa Ben Dahir: A Cautionary Tale on the Power of Exponential Growth
According to an old legend, the game of chess was invented by a skilled mathematician named Sissa Ben Dahir, who served as a Grand Vizier in an ancient Mughal kingdom in India.
The King, Shirham, was so impressed with the game that he offered Sissa a reward of gold and silver. However, Sissa declined the reward and instead asked for grains of wheat. He requested that each subsequent square on the chessboard contain double the number of grains as the previous square.
At first, the King thought the reward would not cost him much, but as the counting began, the number of grains required for each square increased rapidly.
Despite bringing in more bags of wheat, it soon became clear that the King could not fulfill Sissa’s request.
In total, the number of grains required to fill all 64 squares on the chessboard was found to be 18,446,744,073,709,551,615. This amount of wheat would require 4,000 billion bushels, which is equivalent to the world’s wheat production for approximately 2,000 years.
The tale of Sissa Ben Dahir highlights the power of exponential growth and how it can quickly become overwhelming.
Our minds are not naturally attuned to perceive exponential growth as they were formed to seek food and respond to immediate dangers, but linear growth, which is familiar to us, is more common and can be observed in everyday events.
Exponential growth can be seen in the interest rate of mortgages, where a small rate of interest can quickly snowball into a massive amount of debt over time.
For example, a mortgage with an interest rate of 6% can double the amount you owe in just 12 years. To avoid falling victim to exponential growth in mortgage interest, it’s important to understand how interest compounds and to make informed decisions about how much debt to take on.
Exponential growth can also impact the efficiency of computer programs. Lines of code with exponential running time can significantly slow down a program as input size grows. For example, calculating the factorial of a number, 100 multiplications take much longer than 10 multiplications. Big O notation expresses the running time of a program, and exponential running time means operations grow at an exponential rate, leading to slower performance. Thus, it’s crucial for programmers to understand efficient coding and avoid algorithms with exponential running time.
The legend of Sissa Ben Dahir serves as a cautionary tale, reminding us of the dangers of exponential growth and the importance of understanding its impact. The next time you find yourself in a situation involving exponential growth, remember this tale and be mindful of the potential consequences.
