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Science Fiction - "The Man in High Castle"

This is another weird book by Philip K. Dick. It is an alternate history in which Germany and Japan won the second world war. America is a second rate country divided into several independent areas. In the South the slavery is again legal. German rockets carry passangers between continents, but TV does not seem to have been invented.

Main action of the the story takes place in San Francisco and it involves a somewhat disconnected group of characters. There is dealer of authentic American artifacts (like revolvers from the Civil War) which appear to be very desirable to the Japanese. There is a craftsman who quits his job making fake artifacts and starts a jewerly making business.

There are some Japanese diplomats and and German spies.

A thread connecting these various characters is a book, "The Grasshopper Lies Heavy", which some of them read and talk about. "The Grasshopper Lies Heavy" is an alternate history in which the Japanese and the Germans lost the war.

Part of the story involves a woman going to visit the author of this book. He lives in a fortified house somewhere in Colorado and the house is known as The High Castle.

Throughout the book many of the characters use

I, Ching hexagrams to decide what to do. "I, Ching" is their Oracle.

I found the book very confusing. There are a lot of characters to keep track of. They are only loosely connected, plus towards the end of the book the author throws in some weird scenes that make you doubt the reality of the universe he has created.

I had to read "Ubik" twice to understand it better, I think will have to read this book again.

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Non-fiction - "e: The Story of a Number"

This book, written by Eli Maor, is a history of logarithms, calculus and the discovery of the number "e". The story begins in 1614, when John Napier published a book about his invention of logarithms. Although they were not in the form we used them today, still the use Napier's idea revolutionalized computation. We tend to forget in this age of computers, that until about 30 years ago a slide rule and logarithms ruled (pun intended) all engineering and physical computations.

There is quite a lot in the book about the begining of calculus. One of the problems that calculus solves is the computation of area under a curve. Archimedes developed a method for estimating the area under a parabola, and later Fermat extended it to all functions f(x) = x^n ("x" to the power "n"), as long as "n" was not -1. Fermat in fact the formula for the area that is the usual formula obtained with integral calculus in Calculus I.

The curve that resisted until Newton and Leibnitz invented calculus was f(x)=1/x. This an equation of a hyperbola and the area under this curve needs the function logarithm to the base "e".

The constant "e" was further analyzed by Euler and he derived many interesting formulas for it's computations. One of the most famous mathematical formulas was discovered by Euler and it is this:

e^i*pi + 1 = 0Where "e" is the base on natural logarithms, "i" is sqrt(-1), and "pi" is pi.

All in all this book was a lot of fun. It included enough real mathematics to make precise and enough history and stories to be quite entertaining. I find that my understanding of certain areas of math can improve if I can see how ideas developed historically. Sometimes the presentation as it is in standard math textbook and courses gets too abstract and harder to follow. The historical stories make the math easier.