In this paper (access not free outside of academia, but that’s immaterial), Andrew Kennedy claims that because speed capabilities of spacecraft will increase at an exponential rate, there exists an ideal time to depart Earth for a particular destination in order to win a literal Space-race. If r is the mean annual increase in world power production and T is the travel time at current speeds, Kennedy shows that a wait of t years would mean arrival in years from now.
So it isn’t always the early bird that gets the worm, it’s the smart bird!
This gets interesting when we use it to justifiably delay starting work on homework or a report. I’ll consider my assignment due tomorrow as an example. It’s around 3 hours long (T = 3). If I study the concerned chapter for an hour, I’ll be, let’s say, 25% faster at solving the problems. Yeah, I know studying isn’t exactly procrastinating, but that’s the most a Cornell Engineering student can feasibly allow. Plugging in the values and minimizing total time gives a waiting time of *drumroll* … -9.81 hours! Even if I had spent the last 10 hours studying and gaining a 25% boost for each hour, the effort wouldn’t have been worth it. Turns out that anything less than a 95% boost per hour would give a negative result. I wonder if that tells us something about last-minute cramming for exams, but that’s a post for a different day.
Sigh, I should get started on the assignment.