“Moore’s law” is the observation that, over the history of computing hardware, the number of transistors in a dense integrated circuit doubles approximately every two years. The observation is named after Gordon E. Moore, co-founder of the Intel Corporation, who described the trend in a 1965 paper.
The math behind this statement is so profound. Profound enough that the only way to truly understand the implications of this on the future is to use an anecdote like this one, on the invention of chess:
When the creator of the game of chess showed his invention to the ruler of the country, the ruler was so pleased that he gave the inventor the right to name his prize for the invention. The man, who was very clever, asked the king this: that for the first square of the chess board, he would receive one grain of wheat, two for the second one, four on the third one, and so forth, doubling the amount each time. The ruler, arithmetically unaware, quickly accepted the inventor’s offer, even getting offended by his perceived notion that the inventor was asking for such a low price, and ordered the treasurer to count and hand over the wheat to the inventor. However, when the treasurer took more than a week to calculate the amount of wheat, the ruler asked him for a reason for his tardiness. The treasurer then gave him the result of the calculation, and explained that it would take more than all the assets of the kingdom to give the inventor the reward. The story ends with the inventor being beheaded.
2 to the 64th power = 9.223372e+18 or approximately 10 quintillion! More than a billion times the population of the planet.
There are similar stories that use compounding pennies – you get the gist of it. In all these stories, the power of compound effect is severely underestimated or overlooked entirely. In fact, a great quote describes this human affliction:
“The greatest shortcoming of the human race is our inability to understand the exponential function.” —Albert A. Bartlett
If Gordon Moore’s law stands true for the foreseeable future, which it has so far, then it is safe to assume that in the very near future we’ll begin to see some mind blowing technological advancements as we move to the second half of the chessboard. This is the zone in which our capacity to mentally compute the compounding effect absolutely fails. It also renders current predictions of future technology deficient.
You should check out “The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies“ by Erik Brynjolfsson, Andrew McAfee.