Looking at It Backwards
A different way to look at exponential progress is looking at it backwards. imagine there is an exponential progression towards 100% of something. To keep it simple let's say it's doubling with every step. So at the last step you've reached your goal, you're at 100%. Where were you in the previous step? ... only halfway. And the step before that? Only at 25%.
Imagine a lake in a national park. the ranger notices that there is some very little bacteria in the water. But it's only 0.01%. Nothing to worry about. the ranger goes on two week vacation. By the time he comes back ... what has happened?
Human Genome Project logo
A real life example of how counter intuitive this is was the Human Genome Project. This ambitious project started in 1990. The project set out to map (sequence0 the human genome, all 3 billion base-pairs... and hoped to finish it in 15 years. After 7 years in the project and a lot of money spent the researchers only made 1% progress. Skeptics believed it will take 700 years to finish (7*100). The good news however was that progress during this first seven years showed doubling of sequenced data year after year and sure enough the project was completed in time (actually even faster, in 13 years).
BTW the cost of sequencing a genome is also dropping exponentially. The very first oe cost 2.7 billion dollars. Nowadays you can get your genome sequenced for less than 500$.
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