How Are Turkeys and Extraterrestrials Related?
How many turkeys are consumed each year in the U.S. on Thanksgiving? And how many extraterrestrial civilizations might exist in the universe? Umm…wait…what?! Although these seem like unrelated questions, they’re really not. As we’ll soon find out, they’re united by math.
My family and I cooked and consumed an entire turkey this week. We certainly weren’t alone in this endeavor/achievement since turkey is—for better or worse—the big cheese on most Thanksgiving menus. In our case, the turkey was rather delicious. As, of course, was the conversation with my delightful family.
At some point early on in the meal someone began pondering aloud about just how many turkeys must have met the same misfortune as our ill-fated fowl. While sort of a morbid thought to have while eating this particular meal, it’s nonetheless a good question.
Mid-way through the meal the conversation turned to the topic of intelligent life in the universe and whether or not it exists. The joke around the table was that the existence of intelligent life is debatable since we humans do a lot of things that might exclude us from the club. But all joking aside, humans are undoubtedly one example of intelligent life in the universe. The question is: Are there any others?
Both of these are very good and seemingly very unrelated questions. But they actually aren’t entirely unrelated. Because it turns out we can use the same type of thinking to answer both. In particular, we can use a little logic and some simple math to make what physicists like to call “back-of-the-envelope” calculations and obtain approximate answers to each. Which is exactly what my family and I did this Thanksgiving. And it’s exactly what we’re going to learn how to do today.
Thanksgiving Day Turkey Math
According to statistics from the National Turkey Federation (which, by the way, is the same group that provides the president of the United States with a turkey to pardon each Thanksgiving—a particularly strange tradition given what everybody else is doing to them), around 212 million turkeys were consumed in the United States in 2015. This is, obviously, a lot of turkeys. But the question that I and my Thanksgiving companions had was how many of those 212 million birds were, shall we say, contributing to dinners around the country on this particular holiday (rather than just on any old day).
Around 212 million turkeys were consumed in the United States in 2015.
This kind of question seems tough to tackle. Of course, you could simply look up the answer (as we’ll see in a few minutes the National Turkey Federation will be happy to provide it to you)—but that’s not much fun. Instead, I and my intrepid family preferred to figure it out on our own by making a good old-fashioned back-of-the-envelope approximation! OK, I’m sure that some members of my family probably would have preferred the “look it up” approach; but they humored the rest of us and at least pretended to be amused by our quest.
Anyway, the best way to reason your way through a problem like this is to break it down into small pieces that can each be tackled easily. It’s important to not get too hung up on being overly precise along the way since high precision isn’t the goal here. In this case, we’re just interested in a ballpark estimate—say to within 30%—of the total number of turkeys consumed on Thanksgiving. After all, we don’t need to know the number down to the nearest turkey to learn about the magnitude of their contribution to the holiday.
Back-of-the-Envelope Turkey Calculation
There are a number of ways you could approach a problem like this, but here’s the one we chose. To begin with, there are nearly 300 million people in the U.S. If you wanted to be super-precise, you could check the US Census web page as I just did to find out that there are actually nearly 325 million people in the United States. But since we were enjoying our Thanksgiving dinner, we didn’t want to go check out that web page—and we really didn’t need to since we were only after an approximate number anyway—so we used the nice round number of 300 million people for our calculation.
Next we reasoned that we should estimate how many of these 300 million people ate at least part of a whole turkey cooked on Thanksgiving. Obviously we didn’t know this number. But the beauty of the back-of-the-envelope approximation is that we didn’t need to know it … a good estimate would do. As our thinking went, it seems a fairly decent bet that the number of people eating a portion of a whole turkey cooked on Thanksgiving must be somewhere between 30% and 70% of the population. So we simply took the middle of this range and assumed that half of the population—or about 150 million people—consumed at least some part of a whole turkey cooked on Thanksgiving. It’s certainly an uncertain estimate, but it seems completely reasonable … and it’s good enough for our purposes.
Sometimes Ballpark Estimates are Good Enough
At this point, the only thing left for us to do was figure out how many people on average shared each whole turkey. And that’s because the number of whole turkeys cooked on Thanksgiving (what we want to know) is given by the number of people eating portions of a whole turkey (what we just estimated) divided by the average number of people sharing each turkey (what we’re working on now). The number of people sharing a turkey is, once again, kind of hard to know with much certainty since some gatherings are large (with twenty or more people) and some are small (with just a few people). But, once again, this really doesn’t matter because we’re just after a decent ballpark estimate.
There are likely to be roughly 40 million turkeys consumed on Thanksgiving.
So we made the ballpark assumption that the average gathering on Thanksgiving includes 4 people. The real answer might be closer to 3 or 5, but it’s certainly not 1 or 10 … so we felt pretty good about our assumption. Putting this all together, we concluded that there are likely to be somewhere around 150,000,000 / 4 or roughly 40 million turkeys consumed on Thanksgiving—definitely not a good day to be a turkey.
Is this estimate close to the actual number? Well, the National Turkey Federation estimates that 46 million turkeys were consumed on Thanksgiving day in 2015. So we did pretty well and perhaps got a little lucky too since there was plenty of uncertainty in the assumptions and estimates we made. But, as noted at the outset, that’s fine here since we just wanted to know the answer to the nearest 10 or so million turkeys. We weren’t flying rockets or building skyscrapers, we were counting turkeys. And in that case, close enough is definitely good enough.
Is There Anybody Out There?
Which brings us to aliens. Although turkeys do look a little bit alien, the’re definitely of this world. But there is a mathematical connection between the two in the sense that just as we employed a back-of-the-envelope calculation to obtain a deeper understanding of the turkey population (an obviously important problem), astronomers have devised another back-of-the-envelope calculation for obtaining a deeper understanding of the population of technologically advanced alien civilizations in the universe. This calculation is summed up by something called the Drake equation, and the implications behind the mathematics of this equation are fascinating to think about.
But unfortunately, we’re all out of time for today. So we’ll have to return to the mathematical underpinnings of the Drake equation and its implications for the existence of alien life in the universe next time.
Wrap Up
For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. Also, remember to become a fan of The Math Dude on Facebook and to follow me on Twitter.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Turkey image from Shutterstock.
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About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.
