For my independent reading book, I am reading The Drunkard’s Walk: How Randomness Rules Our Lives, by Leonard Mlodinow, a nonfiction book about applied math. In this book, Mlodinow discusses theories of probability and how we, as humans, perceive a series of events. He writes with a passion about mathematics and what it reveals about human behavior and the world around us, offering humorous stories and detailed references.The book is based upon the fact that much of the math that resides behind seemingly coincidental or surprising events often indicate the exact opposite. Mlodinow also discusses how we see patterns where they don’t exist, or use strategies to solve problems that are not the best. Take, for example, trying to guess whether or not a light will appear green or red. Mlodinow asserts that, if you are given the fact that the light shines green 75% of the time, and red 25% of the time, most humans would try to match their guesses with that proportion, guessing green 75% of the time and red 25% of the time. According to the math, doing so would, on average, yield a correct guess only 60% of the time, while guessing green every time, a strategy used by rats and other animals, yields a correct guess 75% of the time, thus outperforming the average human. Another example presented, like many of them, is from the lottery. In Germany, in 1995, the exact same lottery numbers, consisting of 6 numbers from 1 to 49, were drawn in two consecutive days, the first repeat in 3016 drawings. The participants were flabbergasted by the result. What were the odds? The chances of this happening once over 3016 draws comes out to be about 28%. Not bad, huh?
The book continues on, mentioning famous problems such as the Monty Hall Problem, and mentioning famous mathematicians like Bernoulli or Cardano. Ideas such as regression toward the mean are brought up, as well as issues such as how much a CEO should be paid. There are many issues that are brought up in this book that are possible routes for research and/or an expository essay, and many more unexplored phenomena out there in the world just waiting to be found. There are just so many interesting things that happen in everyday life that we think is random or coincidental, when they should be expected on a day-to-day basis. Such as the probability of running into an old friend, or finding the parking meter that still has an hour on it. These ideas of human fallacy and misunderstanding of probability and patterns could definitely be built up into a multi-genre research paper, since they appear almost everywhere. The idea that there is so much that we are doing wrong, or going about the wrong way to do things excites me, and the mathematics that can guide us toward a better path intrigues me.
I haven't seen you in so long! So, what do you think you will research? A couple of your peers whom I will not see today and I sat down to discuss the ideas and perhaps the format of the expository essay. It might be an explanation, it might be an argument, it might be weighing two sides to something. I am wondering here if anyone would challenge Mlodinow's assertions, or if he is just stating the facts? Also, why is the title The Drunkard's Walk? Is there any more scholarship on how math could help guide us? Hope to see you soon to talk about it! If I don't see you before Monday, you might use the next blog post to test your expository essay? Kill two birds with one stone.
ReplyDeleteAs soon as I started reading your blog I knew that I was really interested in your topic and I am excited to hear your presentation. I especially loved the example about the red and green light and the situations that come up in every day that we might not realize. Going off of that, I think a cool idea for the structure of your project and your expository essay (if this is allowed) would be to follow a person throughout the course of their day, presenting a series of normal scenarios that an average person would come across that are related to the math concepts discussed in your book (such as the lottery or running in to an old friend or finding a meter with time left on it) and then you can branch off into the math behind it (and then move on to the next thing throughout their day, where they will encounter another example of hidden math). From a reader's perspective who hasn't read your book, I think that presenting your findings in a way that relates to people really shows how common and overlooked the things you are talking about are. The everyday random/coincidental aspect that you talk about really intrigues me and I think a lot of other people would be fascinated by any examples you could find and present. Another area you could explore has to do with human nature and behavior and function--why do we choose to guess green 75% and red 25% of the time, and what is different in our minds than other animals. Or, why do we choose not to pick the same lottery numbers again, or give up in trying to find a meter with time in it? I think that exploring that would also be very interesting from an outside perspective, if you think that is possible or something that you would want to discuss. I think it is cool that thinking about math more often than we might can change our everyday lives. I hope this makes sense!
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