To survive a zombie apocalypse, one will need more than instinct and short term solutions – one will need logic and, most importantly, math. A thought-out plan comprised of sophisticated calculus equations will ensure long-term safety objectives. Thankfully, Zombies and Calculus by Colin Adams colorfully illustrates the critical implementation of calculus components when going head-to-head with zombies. Adams demonstrates how a professor and his students successfully exercise calculus to survive the attacks of zombies who not only disrupt their calculus class (the horror!), but are also out for human flesh.
Here are a few need-to-knows:
Zombies travel approximately at one yard per second – a constant derivative.
A derivative of a function is its rate of change. If a function is changing quickly, its derivate will be high, while if a function is changing slowly, its derivate will be low. Adams explains that we can measure the function’s rate of change through the steepness of the tangent line.
Since speed is defined as distance divided by time, one can calculate the speed required to get from Point A to Point B in a specific time, while being able to evade any unwanted visitors (zombies). Keep in mind — speed tends to vary (not for zombies, remember, they travel in a constant derivative!), so the derivate of the function has the potential to increase or decrease. Using these simple formulas, one is able to plan out the distance, time, and speed needed to outrun these deadly predators.
It’s hard to crack a zombie’s skull. It’s easier to knock a zombie unconscious.
As detailed in Zombies and Calculus, the amount of force necessary to crack a human skull is 10,000 newtons (a newton is a measurement for force that equals 1 kilogram meter per second squared). Adams offers an example: if a baseball is going 90 miles per hour (40.2 meters/second), weighs 5 ounces (0.145 kilograms), and comes into contact with a head for .007 seconds, its force can be calculated through:So since a baseball, with said specifications, can only create approximately 800 newtons, imagine how much force is needed to produce 10,000 newtons! When attacking a zombie with force, do not try to go for the easy kill — rather play strategically by knocking the zombie unconscious with a sudden sharp blow to the head. This will create a dramatic head jerk, causing the brain to get knocked around in the cranial cavity, thus causing a short circuit. The benefit of knocking a zombie unconscious, of course, is additional planning and escape time!
Zombies pursue in a radiodrome path.
Like a dog pursues a rabbit, a zombie pursues its human prey. A zombie will follow its prey’s path at the prey’s given location at that specific instant. In a scene from Zombies and Calculus, (pause to imagine it), a Dean is running towards the safe haven of an academic building in a straight line. However, a zombie is present and begins to pursue the Dean, always having its tangent vector pointing at the Dean. The zombie is going to travel to wherever the Dean is in that current moment.
Since zombies are incapable of developing an efficient plan, the zombie does not run at a diagonal towards the academic building, which would cut-off the dean’s path. Instead of recognizing the Dean’s travel pattern or destination, the zombie is chasing the dean like a dog chasing a bunny’s tail to the rabbit hole. If only the dog knew that its radiodrome procedure was flawed, the dog would be able (with a speed higher than the rabbit) to cut-off the rabbit at its hole and claim victory. If dogs were to catch on, there would probably be fewer bunnies hopping around.
Cold-blooded creatures are unable to regulate their body heat.
Like other cold-blooded creatures, zombies hibernate. A zombie’s body temperature will decrease according to the differential equation that guides the temperature change of an object placed in a space with a different temperature (so for instance, if a zombie with a temperature of 60 degrees is placed a room of 30 degrees.) According to Newton’s Law of Cooling (remember Newton from discussing the measurement ‘newton’ for force?), the temperature of a body’s rate of change is proportional to the difference between the present temperature of that body and the ambient temperature (basically, the temperature of its surroundings). Given as a function of time, the zombie’s temperature (where Tg is the specific location):The larger the contrast of temperatures, the faster the body temperature will drop. As the characters in the book discover, if there is a zombie apocalypse, it might be time to consider a move to our friendly neighbor to the north, Canada.
To discover more lifesaving tips, fun and entertaining mathematical applications, and learn the fate of the brave calculus professor and his students, read Colin Adam’s Zombies and Calculus. Just in case the zombie apocalypse does occurs (maybe tomorrow?) it should be comforting to know there’s a mathematical guide to survival on your bookshelf.