Sunday, July 7, 2013

Week 8 - 2nd Book Review (Communication)

The Math Book - by Clifford Pickover

This book was a very enjoyable read, and I like how it didn’t use chapters. Each page is a new topic, and it is more like reading a comprehensive timeline rather than a book itself. I would compare to study/looking down a massive wall at a museum, in that it starts with concepts from thousands of years ago, and adds more to the history of math as it becomes closer to the present. By the halfway point of the book, you are already in the 19th century, so the book really focuses on the modern aspect of mathematics. I like how it does so since what we learn through grade school is more about the developments in mathematics that have come in more recent time. 

Another enjoyable aspect is that along with each page being a new topic, there is some sort of image that relates to each topic. It makes it a lighter, and more fun read and allows the reader to think further into each subject by giving them an image to start with. 

This is the Koch Snowflake, and is one of the topics discussed in the book. 

Many of the pages have other objectives to them, whether it’s thinking about a paradox, solving a problem, or discussing an abstract physical relation to a subject. It’s a very interactive book.

An interesting subject is the Infinite Monkey Theorem that was first thought of by Emile Borel in 1913. The idea is that if a monkey is typing random keys on a typewriter, then it would have a 1/(93^56) chance of typing a 56 character phrase. (The book uses “In the beginning, God created the heavens and the earth”). If the monkey is typing at a rate of one key/character a second, then it was calculated to take 10^100 seconds to eventually type the phrase. He states, in the original article where this is discussed, that if you have a room of monkeys that type for 10 hours a day, that the monkeys could write entire museums-worth of books by randomization. 

Another interesting paradox in the book is the discussion of Hilbert’s Grand Hotel, where there are an infinite number of rooms. Even though the hotel has no vacancy, it is possible to give any number of people a room. This is possible by constantly moving people down a room whenever a room is needed. The hotel is always full, but is always open for more people. 

A fascinating topic is the Perfect Magic Tesseract, which involves playing Magic Squares on a four-dimensional cube. The numbers that are used are from 1 to N^4. The magic square involves having an equal sum for all rows, columns, pillars, files, quadragonals, diagonals, and triagonals (“space diagonals of the cubes of the tesseract). John Hendricks  that the tesseract cannot be solved in orders below 16, and found that the numbers of order 16 go from 1 to 65,536, and has a magic sum of 534,296. I could not imagine trying to compute that in a rational amount of time. 

The Math Book is a fantastic read for anyone who wants to know about mathematics. Compared to the first book I read, The Book of Modern Math, I saw a similarity in how the books were presented in that they both focus on progressing topics individually. The books ascend through subjects in math by going into detail on each. There is so much to comprehend, but so much to enjoy and have fun with. 

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