The Famous Rain Problem and the Importance of Mathematical Reasoning Ability

Photo by Gage Walker on Unsplash

Before starting my mathematics education, rain was a significant natural occurrence for me. Right after the rain had ended, I would run to the streets and put the paper boat my father would make for me on the side of our street where water had collected. My favorite pastime was riding my bike in the rain during university life. I learned to love birds while they were drinking the rainwater in the bucket my grandmother had set up for them. Getting wet in the rain was never a problem in my life. However, I would hide my books in my jacket now and then to not get them wet.

For a long time, rain was just a reason to be happy for me. In my first year in university, however, my mathematics professor asked me a question regarding rain. After that question, rain would become a mathematical equation for me for a while. The problem was simple; who would get more wet, the person walking in the rain or the person running in it?

I remember not approaching this question very mathematically at first. Why would it matter if the person, who had gotten soaking wet already, ran or walked? Besides, everyone on the street was running to get somewhere where the rain would not hit them, anyway. All those people could not be mistaken, and therefore, the answer had to be that the running person got less wet. When I came to this conclusion, I did not know that most people, most of the time, were mistaken and therefore made the wrong decisions. How do I know that this is true? Look at Turkey, Brazil, the United States of America, Russia, India, North Korea, and many other countries and their decisions in choosing their government leaders. You will see just how correct my conclusion is. Besides that, I have to get back to mathematics.

After that, I wanted to test the rain question myself. However, while debating if I should run or walk in the rain, my hesitation led me to get soaked.

After I dropped everything and examined the situation scientifically; however, I concluded that it was nearly impossible to come to a strict solution. There were too many variables at play in this situation. For example, the place the person has to get to while under the rain is the most crucial factor, and it determines how long this person will stay under the rain and is therefore of utmost importance to the question.

“Mathematics is not the art of finding the right answer, and it is the art of understanding why the answer is correct.” — Ali Nesin.

Ali Nesin has been awarded the Leelavati Prize 2018 in recognition of his outstanding contributions and great achievements towards increasing public awareness of mathematics in Turkey, especially because of his tireless work in creating and developing the “Mathematics Village” as an exceptional, peaceful place for education, research and the exploration of mathematics for a wide range of people. | Source

Let us say that you and your friend are at a cafe, sipping your mango-flavored tea. You are debating whether the person running in the rain or the person walking will get wetter. Neither party can convince the other of their standpoint, however. Afterward, you plan to go to the most fantastic bookstore in the world, which happens to be 100 meters away. Right as you are exiting the cafe, it starts to rain. You and your friend smile at each other and determine, through a game of rock, paper, scissors, that you will be the one walking, and they will be the one running. The two of you make your way to the bookstore, you walking and them running. In this case, you will be the one getting wetter. However, that does not mean that the person in question walking will always be the one getting wetter. This is because your friend is under the rain and the time you are under the rain are different. The place it takes you 50 seconds to go takes them only 10.

To reach a more accurate conclusion, you would have to adjust your travel distance to your travel speed. For example, if we assume your speed is 2 meters per second and your friend’s speed is 10 meters per second, you would go to the bookstore 100 meters away while they would have to go to the bookstore that is 500 meters away. This way, the time that each of you spends in the rain is the same. It is incredibly likely that your friend, who is running, will get wetter. The question is, why so?

*** The reason I give the example of running into a bookstore is that most people treat bookstores as places only to go to escape the rain.

Before I move to the more logical explanation of this question, I would like to talk about some of the scientists’ experiments regarding it. In the past, the MythBusters conducted an experiment that showed that both individuals stay in the rain for the same duration, that the person running gets almost twice as wet as the one walking. The same people later conducted an experiment that gave the exact opposite results.

However, the question is, why? It is because the conditions were varied. The raindrops were different; the subjects were not running at the same speed.

In 2012 however, scientists Trevor Wallis and Thomas Peterson set out to find the answers to the question by wearing cotton-woven clothing. They traveled the same distance, Peterson running while Wallis walked. They later weighed the cotton-woven clothing, and they found that Peterson’s clothing had caught 40 percent more water.

In reality, these results do not mean much in practice. That is because when doing calculations, many variables do not get taken into account. For example, it is assumed that the raindrops fall vertically and are all the same size. In physics and mathematics, assumptions like this are made to come to conclusions. So after making such assumptions, we can set up an equation and come to a solution. In other words, there is an entirely theoretical approach to this situation.

For example, in order to come to a solution, Italian physician Franco Bocci used cuboids and cylinders in place of the human body. After his experiments, he concluded that even the shape of the raindrop changed the results, finding that if there is a strong gust of wind when it is raining, we have to find the optimal tempo to get the least amount of rain on us. You can find Bocci’s article concerning this matter here.

For me, even though this question does not mean much in practice, it is an excellent question to hone one’s mathematical thinking skills. That is because before dealing with the numbers, one has to do intense brainstorming regarding the variables.

For instance, if a child is thinking about this question and considers that the person running will be more careless and run into more puddles than the person walking, they would be considered an excellent thinker and brainstormer.

Also, mathematical operations here are incredibly detailed and will not be useful to us. Instead of this, if one says that the person walking gets their shoulders wet because of the rain coming from above, while the person running also gets wet from the raindrops that he runs into in front of him, we can say that they have found the solution. Likewise, if one notices that the rain continuously changes the angle at which it falls due to wind conditions, we should say that they have also come to a solution. If all the values of the variables are not known, the answer cannot be found.

If a reasonable observer can find out the angle at which the rain is falling and change their route to lessen the amount of rain they get hit by, it can even be said that they have entered the territory of being considered genius.

In summary, mathematics is a way of thinking. Unlike what gets shown in terrible education systems, it does not consist of just equations and formulas. It is especially not something that people who do not care about their hair participate in.

Mathematics is completely intertwined with our lives. If you pay close attention to your surroundings, you will see countless examples of math around you. For example, mathematical terminology gets named very simply. A right angle is precisely 90° (degrees) in geometry and trigonometry, corresponding to a quarter turn. The term is a calque of Latin angulus rectus; here, rectus means “upright,” referring to the vertical perpendicular to a horizontal baseline. Nobody thinks while inventing something that has to do with math; let us make it extremely hard to understand and make people feel stupid. For example, the probability was named that way because it measures the probability of something happening in real life. Anyone can see that the sum of the probability of something happening or not happening is one if they pay enough attention to it.

While the raindrops hitting a car at a red light is sparse, when the light turns green and you start moving, you will notice that the rain feels like it has picked up. This means that you can turn even a simple car ride into an exercise of mathematical thinking and solve a complicated question with a logical solution.

The famous mathematician Hilbert said to his student, who dropped mathematics to become a poet, “You made the right decision because you lack the necessary imagination to become a mathematician.” People who have not understood the whole meaning of beauty can say that mathematics is soulless and strict. That, in turn, proves that their life is far from aesthetic and that their imagination is poor.

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