I have heard of the exponential growth of technology, whereby the technology advancement for the next 100 years, is not the same as the previous 100 years, but 20,000 years of progress in 100 years.
I haven’t truly realized this potential until the novelist, Liu Cixin put it the following way in the novel. In the novel, The Three-Body Problem, a technologically advanced alien race (trisolarist, named so because their sun system consists of three suns) aims for the earth for colonization, they will reach earth in 450 years time. However, they made the following reasoning:
“I do,” said the science consul. “We’ve all studied the first messages from Earth carefully. The section most worthy of attention is their history. Let’s observe the facts: Humans took more than a hundred thousand Earth years to progress from the Hunter-Gatherer Age to the Agricultural Age. To get from the Agricultural Age to the Industrial Age took a few thousand Earth years. But to go from the Industrial Age to the Atomic Age took only two hundred Earth years. Thereafter, in only a few Earth decades, they entered the Information Age. This civilization possesses the terrifying ability to accelerate their progress.
“On Trisolaris, of the more than two hundred civilizations, including our own, none has ever experienced such accelerating development. The progress of science and technology in all Trisolaran civilizations has been at a constant or decelerating pace. In our world, each technology age requires approximately the same amount of time for steady, slow development.”
The princeps nodded. “The fact is that four million and five hundred thousand hours from now, when the Trisolaran Fleet has reached the Earth, that civilization’s technology level will have long surpassed ours, due to their accelerating development. The journey of the Trisolaran Fleet is long and arduous, and the fleet must pass through two interstellar dust belts. It’s very likely that only half of the ships will reach the Earth’s solar system, while the rest perish along the way. And then, the Trisolaran Fleet will be at the mercy of a much more powerful Earth civilization. This is not an expedition, but a funeral procession!”