Math is often called the language of science. And the beautiful thing about that language is that it says the same thing whether you are working in chemistry or biology. Peter and Daniel will learn that as they discover why vampires can’t be real!
It was a bright, sunny fall afternoon. The houses were all decorated with pumpkins, mummies, and ghosts. The sky was clear and the air was crisp with the promise of a cool, clear night just perfect for trick-or-treating. Even better, the sidewalks were piled high with leaves that Peter and Daniel ran through on their way to the school’s annual Fall Festival. The crunch of the leaves and the smell of the air promised great things to come and both of the boys were looking forward to the candy that they would collect that night. Both were in their costumes. Peter had on the cape, fangs, and slicked back hair of a vampire while Daniel had decided to go as a mad scientist, complete with labcoat, black gloves, and goggles.
“It sure is a shame that Mary couldn’t come,” Daniel said after crunching thourgh a particularly large pile of leaves. “Her costume was great! I love Doctor Who.”
“Yeah, she even had the little K-9 on a chain to tow behind her,” Peter replied. “But her dad is pretty strict; if your homework isn;t done, you don;t get to play.”
“Maybe that’s why she gets such good grades.” Daniel felt sorry for Mary; his dyslexia made studying a chore so he knew how it felt to miss a bright afternoon.
“You should talk, Mr. Brain!”
“That’s Dr. Brain to you!” The boys laughed and turned into the school grounds. There at the entrance to the gymnasium was their favorite teacher, Mr. Medes; for the holiday, he was wearing insect wings and a pair of antennas but had painted his face grey and green.
“Hi, Mr. Medes!” the boys chorused. Then Peter asked “I don’t get it. What are you supposed to be?”
“I’m a zombee,” Mr. Medes replied. As the boys groaned at the pun, he explained. “There is a fly that lays its eggs inside of bees. The larva eats the bee’s brain and takes over, creating what biologists call a zombee.”
“So there really are zombies?” Daniel said. “Cool!”
“Are there really vampires, too?” Peter asked.
“Well, there are a lot of animals that drinkt he blood of other animals. There’s the female mousquito who needs the blood to make her eggs.There’s the hagfish, which rasps a hole in other fish with its tongue and sucks their blood. And then there’s the vampire bats; all three species live off of the blood of others. But if you mean creaturees like Dracula, then the answer is no; there can’t be.”
“Why not?” Peter insisted. “If we can have real live zombies that eat brains, why can’t we have real live vampires?”
“Because there would be too many predators and not enough prey,” Mr. Medes replied. “Here, let’s go inside and we’ll do an experiment to show you what I mean.”
At that the boys perked up. They both wanted to be scientists and doing experiments was one of their favorite things. They quickly followed mr. Meddes inside the gym and over to a table.
“Have a seat while I grab some apparatus from my lab,” Mr. Medes said. “I’ll be right back!”
As the boys waited, they speculated on what the experiment would be.
“Maybe he’s got some blood for us to look at,” Peter said. “That would be cool.”
“Nah,” Daniel replied. “It has to be neater than that; I’ll bet he’s got some real, live zombees for us!”
In just a few moments, Mr. Medes returned with a piggy bank in his hands. The boys stared at him, confused.
“A piggy bank? What does that have to do with vampires?” Peter demanded.
“Patience,” Mr. Medes advised. “We’re going to be doing a model of how vampires would interact with humans. And since we can’t use real humans and real vampires in our experiment, we’ll substitute something else. The people will be pennies and the vampires will be nickles. We’re going to need about 100 pennies and 100 nickles.”
With that, he pulled the cork from the bottom of his piggy bank so that the change spilled out. Quickly the three of them sorted the coins and piled up the necessary change. Pouring the rest of the money back into the piggy bank, Mr. Medes began explaining the experiment.
“Here’s the way it works,” he began. “There are twenty vampires, represeented by our twenty nickles. And there are fifty people, represented by fifty pennies. The remaining coins will come into play later. The vampires go first. Peter, you’ll gather up the nickles and shake them in your hands, then drop them on the table. The nickles that land face up get to eat; you’ll take away one penny for every face up nickle because the vampire just killed a person. And then you’ll add a nickle for every person eaten so your vamprie population will grow.”
Peter picked up the nickles and shook them over the table before letting them drop. When they landed, he quickly sorted them into five that landed face up and fifteen that landed face down. Peter then took eight pennies from Daniel’s pile and added eight nickles to his.
“Hah!” Peter said in his best Transylvanian accent. “You people sure are tasty!”
“OK, now it is Daniel’s turn,” Mr. Medes said. “Shake your pennies and then drop them just like Peter did with his nickles. When they land, set the face up ones in groups of four; for every group, you get a new penny.”
Daniel quickly shook up the pennies and let them fall. Sorting them, he found that he had twenty-four face up pennies, so he added six pennies to his pile.
“Hah right back!” Daniel said. “We added more people than you ate!”
“So you both know how to play, right?” At the boys’ nods, Mr. Medes continued. “Then here’s the question: can vampires exist if they eat people?”
“Sure,” came Peter’s response. “My vampires ate eight people but they added thirteen. So we can eat forever and there is no reason that we can’t exist.”
“I dont know,” Daniel said. “You added almost as many vampires as we did people. If you grow too fast or we don’t grow fast enough, we might all get eaten.”
“Well, there is only one way to find out for sure,” Mr. Medes said. “Let’s do the experiment!”
What do you think will happen? Do the experiment!
The boys eagerly nodded and started flipping coins. In Peter’s next round, he had eight face up nickles, so his vampires had eaten eight people and gained eight new members. Daniel did well that round and again had twenty-four face up pennies, so he had six more people added.
“Hey! Not so hungry!” Daniel said.
“We’ll see about that!” Peter crowed. His face fell when just three nickles landed face up but he quickly brightened when Daniel could only muster five face up pennies. “You people sure are slow; you just added one new one!”
As the game continued, the boys started to add sound effects and other silliness. Peter began to chuckle like a B-movie Dracula each time his vampires ate a person. And Daniel cried out “My baby! My baby!” each time he gained a new penny.
Peter gained fourteen vampires in the next round while Daniel only added nine people. And the following round was even more disastrous; sixteen new vampires were created but only four new people. For the first time, the vampires outnumbered the people. The end came swiftly. In each of the next three rounds, far more people were eaten than were born and the vampire population exploded. In the final round, there were nearly a hundred vampires and just thirteen people.
“Wow!” Peter said. “I didn’t think that would happen!”
“Yeah,” agreed Daniel. “For awhile it looked like the people could stay alive but then, BOOM!”
“What you two have just seen is what is known as a population collapse,” Mr. Medes said. “Biologists like to study this because it can tell us things such as how long a disease outbreak will last or how many fish we can take from an area. And, as you’ve seen, it shows that vampires simply cannot exist.”
“How can this one experiment show so much?” Daniel asked.
“Well, the experiment looks pretty specific but when you express it in math, it becomes general. The math doesn’t care whether you are talking about the number of people who catch a disease like vampirism or the number of fish that get caught or the amount of chemicals left in a reaction; it works equally well in all situations,” Mr. Medes explained. “That’s why we say that math is the language of science. It helps us take what we learn in one area and apply it in another.”
“Wow,” Daniel said. “That’s cool.”
“It sure is,” Peter said. “But how did we discover that we could use math to talk about vampires?”
Mr. Medes chuckled. “Actually, Lotka was trying to describe a chemical reaction when he came across this idea. He used math to describe how the reaction happened and discovered that sometimes the solutions led to never-ending chemical reactions. He then applied the idea to biology and created what we call the predator-prey relationship. In our experiment, the vampires are the predators and the humans are the prey. Because the vampires always grow in population, they will always end up eating all of the prey and the humans will always be wiped out.”
“Cool!” Peter said. “So that’s why you said that vampires couldn’t exist. We still have people -”
“Which means that vampires haven’t eaten us all and the only way that they wouldn’t do that is if they don’t exist!” Daniel finished.
“The neat thing is that we do have something very like a vampire,” Mr. Medes said. “Every year, it attacks the human population and tries to convert as many people as possible into its slaves. This model helps groups like the CDC predict just how bad this year’s attack will be.”
“Really? What is it?” Peter asked.
“The flu! Simple diseases like the flu behave a lot like vampires,” Mr. Medes explained. “The only differences are that you are only turned into a flu monster until your body can get better and that we have a vaccine that works against it much better than garlic works on vampires. But it still builds up every year about this time, infects a lot of people, and then has a population collapse when it runs out of victims. And speaking of victims, I think I see a new one over there!”
Peter and Daniel turned to look where Mr. Medes was pointing. In the doorway was Mary, complete with a long scarf, floppy hat, and long coat. Peeking out from behind her was a model of K-9.
“Mary!” the boys chorused. Eagerly, they ran over to bring her into the party and tell her about their new experiment.