Ah, November.
A time of changing weather, falling leaves, and cozy sweaters. To the few of you reading this (especially you seniors out there!), it’s also application season! Unfortunately, like someone who teeters on the brink of insanity, I have completed all sixteen of my college applications. To be fair, most of these applications are pretty cut and dry; it’s just completing the parts that haven’t been filled in by the Common App yet. It’s quite simple, but of course, nothing can ever be too easy. As many of us are aware, some of these colleges ask for writing prompts. While some colleges ask relatively simple questions. Why do you want to attend [Insert College Name]? What can you bring to [Insert College Name]? Who are you as a person? We expect you to sum up your entire life up until now in a maximum of 300 words and a college application! I think it’s a tad strange to have our entire future at stake, being defined by a document that’s only a few pages long. But what do I know? I’m the one answering questions as stupid as this so I can get an education in a society that has ridiculous standards for jobs!
Besides the point, I’d like to highlight an outlier of the prompts in my application processes. The University of Chicago. Wow. Just. Wow. I mean who comes up with these? Well, we know who. The strange students of UChicago who thought up the most ridiculous prompts they could create. If you haven’t seen them, I highly recommend checking them out. They’re kind of fun! Of the six different essay options, I chose option five: Create your own Fermi Estimation problem. I preferred this prompt to the others as I was already familiar with the physicist Enrico Fermi, after whom the Fermi Estimation is obviously named. Fermi, for lack of a sufficient descriptor, was the freaking GOAT of physics. He was proficient in both experimental physics and theoretical physics. This guy created the first artificial nuclear reactor, received a Nobel Prize for both his work on induced radioactivity (the process of making a once stable material radioactive using radiation) and discovering the element Fermium in the same year that Einstein discovered the element Einsteinium, each being Transuranium elements, chemical elements with an atomic number greater than 92 and are highly unstable/radioactive. He was also a member of the Manhattan Project… yikes. There are plenty of other insanely brilliant (and possibly ethically questionable) things he accomplished but I’m getting off task. I was already well versed with his Fermi Paradox, something I had stumbled upon during the space-crazed phase of my life in which I wanted to study the stars. Or something like that. If you’re unaware of the Fermi Paradox, I highly recommend watching a video or two and researching it. It’s quite fascinating. But that’s not what this article is about.
Fermi Estimation Problems are open-ended questions created to estimate (Buzzword of the week here guys!) something or another. To be honest, it’s a process of making educated guesses and many assumptions. The hardest part about the entire thing was just trying to figure out how to make an Estimation Problem. Of course, UChicago has oh so graciously provided us with some examples, such as “How many piano tuners are in Chicago?” or “What is the total length of chalk used by UChicago professors a year?” You’d be surprised how hard it is to make a question that can be quantified, calculated, and is interesting to read about. I went through a couple of iterations, either too boring or too difficult to calculate. I also didn’t write them down, so I guess you’ll never know. And neither will I because I don’t remember them. Whoops.
Then I found it. I can’t remember why I thought of airplanes, but it just happened. Is this what destiny is? Probably not. But once I got on the topic of airplanes, I couldn’t stop. Airplanes are a relatively new invention, and statistics are easily available with a simple Google search. There’s a plethora of information on airplanes, so naturally, I settled on the topic.
We’ve come a long way in the aviation industry since the first sketches of Da Vinci’s flying machine, known as the ornithopter, was theorized to generate lift by flapping wings, akin to a bird. Then, about 400 years later, the first airplane was built and flown by the Wright brothers. Although the flight lasted merely twelve seconds and covered a meager 180 feet, this began an era of human exploration and aviation, which continues to grow and flourish. Today, airplanes are one of the most important modes of transportation throughout the world. They’ve become so normalized in our society that the most important thing you’ve got to consider during a flight is how you’ll occupy the time spent. This might seem strange, but it represents human ingenuity and feats. To have gone so far as to reach the skies as nothing else has done before, but to be able to do something as mundane as reading, watching movies, or sneezing without an afterthought? I can guarantee without a doubt, the Wright brothers most certainly held in their sneezes on the first flight. So this brings me to my Fermi Estimation: What is the total amount of sneezes that have occurred above 40,000 feet in the air? I understand that out of all things, it seems strange. But that’s the point of these kinds of prompts, to bring out the creativity in students applying.
The first factor we need to consider is the different categories of airplanes used in flight. Of course, a commercial aircraft and a private jet will have a significant disparity in the amount of people they carry, and the length of time they fly. Not to mention military airplanes, personal airplanes, crop-dusters, air balloons, and space stations. Simplifying unnecessary calculations, we can exclude most of these from our final result with simple research. Neither crop dusters, air balloons, nor most personal airplanes can fly high enough to meet our 40,000-foot requirement, thus we can eliminate those variables. There are so few personal jets that they’re statistically insignificant. Military airplanes carry few enough people and fly for times so short that the chance someone would sneeze during the flight is incredibly low, again rendering this aspect insignificant as well. Unfortunately, it seems that the International Space Station will also yield too small. While the space station has been managed around the clock at all hours of the day and night since 2000, on average only seven people live on the international space station at a time.
This brings us to our final, and objectively most important part: the commercial aircraft. Commercial use of airplanes wasn’t until the 1920s, and planes that could achieve a cruising altitude of 40,000 feet weren’t invented until the 1930s. This doesn’t even factor in the fact that in the year 1930, worldwide, there were only 6,000 passengers yearly. Of course, as time went on this number increased exponentially, four years later reaching 450,000, then another four years reaching 1.2 million, until in 2019 when the number of commercial flight passengers reached nearly 4.5 billion people. To get the most accurate estimate of the total number of passengers that have traveled by plane worldwide, I collected the yearly global aircraft passenger statistics by year. Due to some missing sets of data, either due to being omitted or unrecorded, between most of the years since 1930, I had to estimate the results using the average rate of change of the closest available points. To get my total number of global passengers, I created an equation using my data on a graph and then evaluated the integral. The equation I received, y=885,230x2-36,840,000x+286,668,000 (which will likely give underestimations) yielded a total of 1.002392354e11, or 100,239,235,400 passengers since 1930. This is an INSANE amount of people. The total number of humans to have EVER existed is about 105 billion people!
In 2010, it was estimated that the proportion of short-haul, medium-haul, and long-haul flights was 86% percent, 10%, and 4% respectively. Using this data as a base, I separated the total number of passengers into three groups. The total number of passengers who took short-haul flights is 86,205,742,440 people, medium-haul is 10,023,923,540, and long-haul is 4,009,569,416. If we assume the 12-hour day as the standard length of one’s day and that since planes spend most of their time at their cruising altitude of 40,000 feet, the short-haul flights that typically range from 0-3 hours, take up about 25% of the total day. Medium-haul flights take up 50% of the total day, spanning 3-6 hours, and long-haul flights take up nearly 100% of the total day, on average taking 8-12 hours. Over one day, the average person sneezes about 4 times and is likely not spread evenly across the day. I concluded that when you sneeze, you are more likely to sneeze twice than just once, less likely to sneeze thrice than just twice, and very unlikely to sneeze four times instead of just three. Converted into usable percentages, it’s 75% to sneeze twice, 35% to sneeze thrice, and 5% to sneeze four times.
Of all short-haul passengers, who had a 25% chance to sneeze at least once during their flight, 5,387,883,903 sneezed once, 21,012,649,720 sneezed twice, 5,374389,256 sneezed three times, 282,862,592 sneezed 4 times during their flights. After multiplying all of these by the respective amount of times that they sneezed, there were a total of 43,665,151,760 sneezes. Of all medium-haul passengers, who had a 50% chance to sneeze at least once during their flight, 1,252,990,442 sneezed once, 2,443,331,363 sneezed twice, 1,249,857,967 sneezed three times, 65,781,998 sneezed four times, bringing a total of 10,152,355,060 sneezes after each respective amount of sneezes was multiplited. Of all long-haul passengers, who had a 100% chance to sneeze at least once during their flight, 1,002,392,354 sneezed once, 1,955,665,090 sneezed twice, 999,886,373 sneezed three times, 52,625,599 sneezed four times. After again multiplying by their respective number of sneezes, there were a total of 8,121,884,049 sneezes over long-haul flights.
The summation of all the different types of flights, over many decades, the total number of sneezes that have occurred at 40,000 feet and above, is 61,929,390,870. To put this in perspective, if you stacked 62 billion commercial planes from tail to nose, you would reach the sun 20 times over. It’s certainly a nod to innovation that so many people can utilize this technology, but I’m also glad innovation brought us masks and hand sanitizer.
A time of changing weather, falling leaves, and cozy sweaters. To the few of you reading this (especially you seniors out there!), it’s also application season! Unfortunately, like someone who teeters on the brink of insanity, I have completed all sixteen of my college applications. To be fair, most of these applications are pretty cut and dry; it’s just completing the parts that haven’t been filled in by the Common App yet. It’s quite simple, but of course, nothing can ever be too easy. As many of us are aware, some of these colleges ask for writing prompts. While some colleges ask relatively simple questions. Why do you want to attend [Insert College Name]? What can you bring to [Insert College Name]? Who are you as a person? We expect you to sum up your entire life up until now in a maximum of 300 words and a college application! I think it’s a tad strange to have our entire future at stake, being defined by a document that’s only a few pages long. But what do I know? I’m the one answering questions as stupid as this so I can get an education in a society that has ridiculous standards for jobs!
Besides the point, I’d like to highlight an outlier of the prompts in my application processes. The University of Chicago. Wow. Just. Wow. I mean who comes up with these? Well, we know who. The strange students of UChicago who thought up the most ridiculous prompts they could create. If you haven’t seen them, I highly recommend checking them out. They’re kind of fun! Of the six different essay options, I chose option five: Create your own Fermi Estimation problem. I preferred this prompt to the others as I was already familiar with the physicist Enrico Fermi, after whom the Fermi Estimation is obviously named. Fermi, for lack of a sufficient descriptor, was the freaking GOAT of physics. He was proficient in both experimental physics and theoretical physics. This guy created the first artificial nuclear reactor, received a Nobel Prize for both his work on induced radioactivity (the process of making a once stable material radioactive using radiation) and discovering the element Fermium in the same year that Einstein discovered the element Einsteinium, each being Transuranium elements, chemical elements with an atomic number greater than 92 and are highly unstable/radioactive. He was also a member of the Manhattan Project… yikes. There are plenty of other insanely brilliant (and possibly ethically questionable) things he accomplished but I’m getting off task. I was already well versed with his Fermi Paradox, something I had stumbled upon during the space-crazed phase of my life in which I wanted to study the stars. Or something like that. If you’re unaware of the Fermi Paradox, I highly recommend watching a video or two and researching it. It’s quite fascinating. But that’s not what this article is about.
Fermi Estimation Problems are open-ended questions created to estimate (Buzzword of the week here guys!) something or another. To be honest, it’s a process of making educated guesses and many assumptions. The hardest part about the entire thing was just trying to figure out how to make an Estimation Problem. Of course, UChicago has oh so graciously provided us with some examples, such as “How many piano tuners are in Chicago?” or “What is the total length of chalk used by UChicago professors a year?” You’d be surprised how hard it is to make a question that can be quantified, calculated, and is interesting to read about. I went through a couple of iterations, either too boring or too difficult to calculate. I also didn’t write them down, so I guess you’ll never know. And neither will I because I don’t remember them. Whoops.
Then I found it. I can’t remember why I thought of airplanes, but it just happened. Is this what destiny is? Probably not. But once I got on the topic of airplanes, I couldn’t stop. Airplanes are a relatively new invention, and statistics are easily available with a simple Google search. There’s a plethora of information on airplanes, so naturally, I settled on the topic.
We’ve come a long way in the aviation industry since the first sketches of Da Vinci’s flying machine, known as the ornithopter, was theorized to generate lift by flapping wings, akin to a bird. Then, about 400 years later, the first airplane was built and flown by the Wright brothers. Although the flight lasted merely twelve seconds and covered a meager 180 feet, this began an era of human exploration and aviation, which continues to grow and flourish. Today, airplanes are one of the most important modes of transportation throughout the world. They’ve become so normalized in our society that the most important thing you’ve got to consider during a flight is how you’ll occupy the time spent. This might seem strange, but it represents human ingenuity and feats. To have gone so far as to reach the skies as nothing else has done before, but to be able to do something as mundane as reading, watching movies, or sneezing without an afterthought? I can guarantee without a doubt, the Wright brothers most certainly held in their sneezes on the first flight. So this brings me to my Fermi Estimation: What is the total amount of sneezes that have occurred above 40,000 feet in the air? I understand that out of all things, it seems strange. But that’s the point of these kinds of prompts, to bring out the creativity in students applying.
The first factor we need to consider is the different categories of airplanes used in flight. Of course, a commercial aircraft and a private jet will have a significant disparity in the amount of people they carry, and the length of time they fly. Not to mention military airplanes, personal airplanes, crop-dusters, air balloons, and space stations. Simplifying unnecessary calculations, we can exclude most of these from our final result with simple research. Neither crop dusters, air balloons, nor most personal airplanes can fly high enough to meet our 40,000-foot requirement, thus we can eliminate those variables. There are so few personal jets that they’re statistically insignificant. Military airplanes carry few enough people and fly for times so short that the chance someone would sneeze during the flight is incredibly low, again rendering this aspect insignificant as well. Unfortunately, it seems that the International Space Station will also yield too small. While the space station has been managed around the clock at all hours of the day and night since 2000, on average only seven people live on the international space station at a time.
This brings us to our final, and objectively most important part: the commercial aircraft. Commercial use of airplanes wasn’t until the 1920s, and planes that could achieve a cruising altitude of 40,000 feet weren’t invented until the 1930s. This doesn’t even factor in the fact that in the year 1930, worldwide, there were only 6,000 passengers yearly. Of course, as time went on this number increased exponentially, four years later reaching 450,000, then another four years reaching 1.2 million, until in 2019 when the number of commercial flight passengers reached nearly 4.5 billion people. To get the most accurate estimate of the total number of passengers that have traveled by plane worldwide, I collected the yearly global aircraft passenger statistics by year. Due to some missing sets of data, either due to being omitted or unrecorded, between most of the years since 1930, I had to estimate the results using the average rate of change of the closest available points. To get my total number of global passengers, I created an equation using my data on a graph and then evaluated the integral. The equation I received, y=885,230x2-36,840,000x+286,668,000 (which will likely give underestimations) yielded a total of 1.002392354e11, or 100,239,235,400 passengers since 1930. This is an INSANE amount of people. The total number of humans to have EVER existed is about 105 billion people!
In 2010, it was estimated that the proportion of short-haul, medium-haul, and long-haul flights was 86% percent, 10%, and 4% respectively. Using this data as a base, I separated the total number of passengers into three groups. The total number of passengers who took short-haul flights is 86,205,742,440 people, medium-haul is 10,023,923,540, and long-haul is 4,009,569,416. If we assume the 12-hour day as the standard length of one’s day and that since planes spend most of their time at their cruising altitude of 40,000 feet, the short-haul flights that typically range from 0-3 hours, take up about 25% of the total day. Medium-haul flights take up 50% of the total day, spanning 3-6 hours, and long-haul flights take up nearly 100% of the total day, on average taking 8-12 hours. Over one day, the average person sneezes about 4 times and is likely not spread evenly across the day. I concluded that when you sneeze, you are more likely to sneeze twice than just once, less likely to sneeze thrice than just twice, and very unlikely to sneeze four times instead of just three. Converted into usable percentages, it’s 75% to sneeze twice, 35% to sneeze thrice, and 5% to sneeze four times.
Of all short-haul passengers, who had a 25% chance to sneeze at least once during their flight, 5,387,883,903 sneezed once, 21,012,649,720 sneezed twice, 5,374389,256 sneezed three times, 282,862,592 sneezed 4 times during their flights. After multiplying all of these by the respective amount of times that they sneezed, there were a total of 43,665,151,760 sneezes. Of all medium-haul passengers, who had a 50% chance to sneeze at least once during their flight, 1,252,990,442 sneezed once, 2,443,331,363 sneezed twice, 1,249,857,967 sneezed three times, 65,781,998 sneezed four times, bringing a total of 10,152,355,060 sneezes after each respective amount of sneezes was multiplited. Of all long-haul passengers, who had a 100% chance to sneeze at least once during their flight, 1,002,392,354 sneezed once, 1,955,665,090 sneezed twice, 999,886,373 sneezed three times, 52,625,599 sneezed four times. After again multiplying by their respective number of sneezes, there were a total of 8,121,884,049 sneezes over long-haul flights.
The summation of all the different types of flights, over many decades, the total number of sneezes that have occurred at 40,000 feet and above, is 61,929,390,870. To put this in perspective, if you stacked 62 billion commercial planes from tail to nose, you would reach the sun 20 times over. It’s certainly a nod to innovation that so many people can utilize this technology, but I’m also glad innovation brought us masks and hand sanitizer.
|
Y-Axis: Number of Passengers X-Axis: Years Since 1930 |
