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How Not to Be Wrong: The Power of Mathematical Thinking - Jordan Ellenberg

The "reality" we live in consists of many worlds. The world of traders, the world of politicians, the world of workers, the world of scientists, etc. Out of these world, I am particularly attracted to the world of mathematicians. For some strange reason, mathematicians seem to have "explanations" for various phenomenon occurring in almost all of the other worlds. These explanations are spoken in a language that is understood among mathematicians, but alas, there are few good translations from the language of mathematicians to the language spoken in other worlds. Having studied computer science and some of it theoretical underpinnings, I am familiar and comfortable with some of the conversations among mathematicians. This book is an attempt at translating some simple aspects of mathematics into the common parlance. As expected, the translation focuses on aspects that are most common in public use.

If you really understand this book, you will not fall for some of the lazy analysis that is often passed off as "Math" in common parlance. You will have the confidence to look at the data and then make inferences of your own. There is a crash course on interpreting probability and correlation in this book, which will come in very handy whenever you read a science article. Finally, this book goes into the abstract realm of mathematics to explain the meaning of meaning. and its relation to domains such as law and public opinion. There is a final chapter on how to be right, that is very informative.

I liked this book a lot! I highly recommend this book to anyone who wants to understand the math behind most of widely reported phenomenon. The insistence of the author to not use mathematical equations, but rather convey the essence of concepts using illustrations and examples is refreshing. If the author uses a technical word, you need not wonder what does that term mean; he will tell you, in simple and lucid terms, what it means and several ways to interpret it. After teaching for 3 years, I found that restricting myself to not use mathematical jargon while explaining enriched my understanding of the concept itself. I could look at concepts that I thought I knew for a long time from a very fresh perspective. I also found the high praise of Nate Silver by the author to be very surprising, but the author justifies it very well.

I thought that the part of book on expectation was the most beautiful and ironically, the least profound to general public. Let me explain: it turns out that the mathematical universe is itself split into several worlds and there are a lot of underground connections between these worlds. In the world of mathematicians, people who expose these underground connections are held in high regard. The "beauty" that mathematicians constantly rave about are the connections between these seemingly disparate world. Unfortunately, to get a feel of this beauty, one needs to have a good amount of mathematical training. A more easy to understand example is classical music. One might find a piece of classical music somewhat repetitive and boring, while others might find it beautiful and heart warming based on their training. It is the same with some aspects of mathematics. I would say that the part on expectation is ahead of its time as it is based on more recent research. 

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