30 doubling steps

Here’s a math problem for a ten year old – a normal human step is about 0.75 m long. How far would the average person travel when they take 30 steps? The answer, of 22.5 m comes easily to us.

Here’s another problem. Can you guess roughly how faraway a person would be if they took 30 doubling steps? What does your intuition say?

It turns out that 30 doubling steps is more than a billion steps in total! At 0.75m per step, that is enough steps to walk around the earth 20 times.

Despite being familiar with several such examples, exponents catch me by surprise each time. This is because the human brain isn’t built to think exponentially. We are wired for a simple, more linear world. And yet, the number of internet users, the processing speed of computers and the number of solar cell installed worldwide – all of these measures double after fixed intervals.

Our brains need to swim against the current to understand a doubling world. But given how entrenched doubling is in our times, it is a worthwhile exercise.