About 49 Days

The title of this blog is based on an example from Dennis Sherwood’s book ‘Seeing The Forest For The Trees‘ that helps illustrate the difference between linear and exponential growth.

“A colony of frogs is living happily on one side of a large pond.  On the other side is a lily pad.  One day a chemical pollutant flows into the pond and stimulates the growth of the lily pad – it starts to double in size every 24 hours.

Question 1: If the lily pad will cover the entire pond in 50 days, on what day is the pond half-covered?

Question 2: The frogs have a method of stopping the growth of the lily pad, but it will take 10 days to put into effect.  What proportion of the pond is covered at the latest possible time to take action and save themselves?”

Our brains think in terms of linear growth, but we are living in an exponential world, thanks to Moore’s Law. Like the frogs, we need to act before the threats are apparent in order to stop them. However, since the answer to Question 1 is 49 days, how do we even realize what’s going on in time to stop it? The answer to question 2 is 0.00098 – the frogs need to identify the problem and take action by the time the lily pad covers less than one thousandth of the pond.

Linear vs exponential growth over 50 days
Linear vs exponential growth over 50 days

We don’t need to stop every bit of exponential growth, of course, but we do need to be able to respond quickly to those that are problems. Thus, I try to send up flares about technologies and trends which seem to show exponential lilypad spread.

 

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