May 2015 | Mining University

Calculus Finally Pays Off

Well I did it. I finally used calculus for something in my life after college. It wasn't work related and I basically had to re-learn how to do an integral but it has finally served a purpose.

The question I wanted to solve was: How far would someone fall in a tenth of a second? It sounds like a silly question, but it came from one of my most serious pass times: science fiction.

Recently I have been reading (actually listening to) a fun little book called 'Off to be the Wizard' by Scott Meyer (read by Luke Daniels). The basis of the book is a classic Sci-Fi topic: what if the world were a computer program and people were just sub-routines? The hero of the story finds out this is true and writes a program to make himself 'hover.' The program just increases his elevation by three feet and then refreshes ten times a second with him in free fall in between. Meyer describes this as being a jarring and uncomfortable way to 'hover' but I wondered how far would a person really fall in that tenth of a second interval. I also wondered how far the fall would be if the program refreshed 1,000 times a second like any real programmer would do?

After some serious internet research I was finally able to remember enough calculus to make sense of the non-calculus based physics equations that are posted all over the internet and convince myself that they were correct. It shouldn't matter that 0.5*9.8*t^2 looks different than the integral I remember from calculus bit it did.

Now that we had that cleared up I could calculate that in a tenth of a second a person would fall 1.92 inches. Falling almost two inches, ten times a second seems like a really rough method to use to fly. It might even be enough to injure anyone dumb enough to try it.

I don't think that any programmer I know would leave a flying refresh rate at ten times per second. Most computer things that need to be regularly updated happen at a rate of 1,000 times per second. Given this approach, a person would fall almost two ten thousandths of an inch in one thousandth of a second. This is a much more comfortable vibration to put up with when 'hovering.'

Thank you Calculus for making a totally implausible situation seem more realistic.