Wednesday, March 5, 2014

A MATHEMATICAL GUIDE ON LIFE AND ON PEOPLE



“Books are the compasses, telescopes, sextants and charts which other men have prepared to help us navigate the dangerous seas of human life.” – Jesse Lee Bennett
In this book called “Rock, Paper, Scissors”, Len Fisher talks about the applications of game theory in real life. He relates game theory to the strategies and the means that people take to interact with each other on a daily basis on different occasions. He talks about using game theory to develop strategies for cooperation and social interactions in different environments. That it helps us understand the holes in our interactions towards other people that lead to broken promises and cheating. It is a guide on what to do in situations like competitions and conflict. It is applied to different sectors from business to military.  Fisher then talks about the two different sides of game theory: the cooperation and collaboration side and the confrontation and competition side. In the field of biology, it is shown in the cooperation involving in the evolution of nature. While in the field of sociology and psychology, it is used to explain the problems of cooperation and resolution in the social relationships between people.
The book started off in a quite slower pace than I had expected. In the first chapter, Fisher gives an informative description about the Prisoner’s dilemma and a somewhat negative notion of the Nash equilibrium being a logical trap. Afterwards, he gives a lot of interesting examples and explanations. Fisher then introduces the different concepts of minimax and fair division in the second chapter. On the topic of fair division, he tells stories about how much trouble he got in when he was shooting fireworks as a kid. It was then that he arrived at an answer and now, he realized that it was an application of the minimax principle. Fisher then gives a discussion on the principle of equal division of the contested sum. Now, chapter three talks about seven of the most interesting yet challenging game theory problems, some would even call them deadly. In this chapter, a summary of these problems like the free rider issue and the game of chicken is given. The title of the book is the focus of chapter four. It talks about the “rock, paper, scissors” game and how it is being played around the world. Here, Fisher explains how this game is a means of conflict resolution; his reason being that this game has no pure strategy to speak of. No strategy that purely dominates the others. So the situations and games which look like they seem to be standing still can actually be solved through strategies and looking at them as rock-paper-scissors situations. The fifth chapter talks about the twin keys that can be used to resolve social dilemmas and these keys are communication and negotiation. It is through these keys that we can form alliances and share information and ideas though these also have their negative sides. The rest of the chapter is focused on how to make the communication between people more reliable, their negotiations fairer and their alliances more stable. Chapter six is about trust. Fisher starts this chapter by recalling a scene from the Peanuts cartoon. An unfortunate effect of both the game theory and the real world is due to the fact that people don’t trust each other. He talks about how he once did something nice for other people and how they doubted his intentions. Communities are built on trust and the lives of people would be easier and more fruitful with trust. He then uses the game theory to prove his claim and to understand how people can prove their trustworthiness. He believes that trust would lead to win-win situations. He then talks about his social training as a child in chapter seven. He talks about the book he was given when he was a child about two women whose personalities seemed to be based on the game Tit for Tat which is a payback strategy that comes into play when two people or groups are likely to meet repeatedly. There is a cycle of retaliation and counter retaliation and in order to break this cycle, one side must stop and just forgive. He then recalls more memories with his grandmother relating to this topic. Another way to break the cycle is to just apologize. Fisher then talks about the social norms and how they guide us to cooperation. Chapter eight is about how to change the game to improve the chances of cooperation. This can be done by introducing new players and using quantum mechanics to read each other’s minds. Fisher then talks about how quantum game theory and classical game theory provides us with a range of strategies to overcome social dilemmas. Then in the last chapter, he reviews these strategies and creates a top ten list of tips for strategies that can be used to promote cooperation.  
This book is a wonderful thing to read for me. While reading it, I didn’t feel like I was reading something about mathematics or the feeling you get when you read those types of academic and educational books. It was very insightful all throughout and even comical at some points. It wasn’t a book on equations or algebraic problems; it was more of a book about life for me and about how people are in general. It was such an eye-opener; it made me see the problems that society has and how the simple mathematics of game theory can be used to explain it and even solve it. This book speaks about life so the reader can really find a way to relate to it and therefore find reading it more pleasurable. I learned a lot from this book about how to interact and deal with people and how to develop a deeper relationship with others. It has a lot of life lessons along with personal stories that made it easier to understand and read. I would recommend this book to other people because its approach isn’t too technical and doesn’t come across as too strong. It also comes with some mind-boggling realizations and tips on how to achieve a better social relationship with other people.

Monday, March 3, 2014

Individual Report (Geometry)

ge·om·e·try noun \jē-ˈä-mə-trē\
: a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids; broadly :  the study of properties of given elements that remain invariant under specified transformations
-  Merriam-Webster Incorporated

Having geometry as a topic can be strength and at the same time weakness of our group. For me, its approach to the public is not that dreary unlike the other math topics. Geometry deals with shapes which mean a lot of illustrations to look at. It can be considered as our strength because almost all people wanted to look on pictures rather than texts. Geometry could easily get a man’s sympathy in its own simple ways. But I was just talking about the approach, the first impression upon recognition. Now, the said weakness comes in. In my own opinion, geometry is difficult to teach. Luckily, we do not need to demonstrate every single piece of geom to the class. Hence, we ended up on making a video. One of my group mates have looked for some geometry topics that we could discuss to the class, those topics that our classmates could surely relate. Fortunately, “The Story of Maths” documentation was also filled with geometry stuffs which Ma’am Cielo keeps on showing to the class. These documentations now served as our guide in completing our video. The funny thing was instead of understanding what we are talking in the video, our classmates ended up laughing at us while watching it. At the least, I know they are enjoying what they are seeing and that is the most important.

About the games we let them play, I observed that they really had a hard time with it. Our first game was like a puzzle. We first made a heart and have broken it to pieces. These pieces were scattered inside the room and they need to find it in order to form the said shape. The second game was concerned with some sort of decision-making. They were given a number of toothpicks which they will be using to form the shape instructed by the game master. Although these games have shaken their brains, I can tell that they loved what they have experienced.

Being able to handle a class just for two meetings is really a fun experience. I totally loved the feeling of giving a difficult task to others and seeing them struggle to do it. Sounds harsh but I just found it amusing. J I know you (the one reading this) too have the same feeling as mine.


Deadly Dilemmas


A Book Review to Rock, Paper, Scissors: Game Theory in Everyday Life
Written by Len Fisher

     This book entitled with Rock, Paper, Scissors: Game Theory in Everyday Life and was written by written by Len Fisher, introduces the different applications and examples of game theory in our daily lives. Game theory is a theory of social situations often correlated with parlor games and the likes, but this focuses on how a group of people interact and cooperate.
This book had shown how the modern science of game theory has helped to understanding of the evolution of cooperation in nature, and probes how to apply those lessons to our own society. In a series of conducted experiments, that takes him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics. It gave a solid connection of game theory to our everyday situations and suggests several strategies for achieving cooperation.
At the beginning of the book, it described the Prisoner’s dilemma and provided the negative connotation that the Nash equilibrium is a logical trap. It then introduced the concepts of minimax and fair division. Fisher illuminates fair division with anecdotes and gave applications to the principle of minimax. The seven deadly dilemmas that Fisher mentioned were the seven of the most interesting game theory problems, in which he have given a summary to the game of chicken. Also it tackled the rock, paper, scissor game. It amused me of how this simple game we use to play when we were young can resolve conflicts. The reason of using this game according to Fisher is that the game has no pure strategy that dominates the others.
            This fun game theory guide reveals the pervasiveness of game theory in everyday life, in an entertaining, enlightening and practical guide to the abstruse discipline of game theory. Fisher engages intensely in mathematical subject without heavy reliance on equations or jargons. His treatment of the subject makes game theory appears only slightly more complicated rather than childish play. It then explains that it further illustrates the role of game theory in our daily life.
            This book reveals that through this fun game theory guide, though there are problems of cooperation to everyone, it has endowed lessons that will both teaches and give delight to everyone interested in solutions and strategies to take enable to get people to work together in unity.


Skeleton on his Cabinet


A Book Review to Cabinet of Mathematical Curiosities


        Cabinet of Mathematical Curiosities written by Ian Stewart is a delightful book featuring cornucopia of mathematical idiosyncrasy such as games, paradoxes,  puzzles, facts, numbers and math-based nibbles that could fill up ones curios mind. Stewart had collected books that were entertaining for he believed that the exuberant and merriment of mathematics are not taught in school but rather can be known elsewhere. Those were placed in his cabinet and were certainly called as curiosities. Veiled and hidden gems of logic, geometry and probability were some of those. He spent years for filling his cabinet with all those mathematical factoids and anecdotes premeditated for the adventurous mind of the intriguing mathematics.
        Stewart had succeeded on bringing out the exciting and fascinating part of mathematics.  He called this kind of approach as the recreational mathematics in which less of those requires numbers and arithmetic but is greatly associated with logic and the study of patterns that occupies higher mathematics.  He included non puzzle materials, such as taking back the readers to the history of the mathematical development which includes some biographies of idiosyncratic great mathematicians and allows giving details to the different discovered theories just like Poincare Conjecture, Fermat's last Theorem and Riemann Hypothesis that comes in a very outstanding ability of bringing no dullness to his explanations. He had opened doors to enticing perspective of understanding geometry in accordance to Euclid’s Theorems and in riveting themselves by calculating just how the genius Archimedes had moved the earth with his famed fulcrum. The beauty of logarithmic spirals and the dynamics of Chaos Theory was Stewart’s way to beget and lead us to be induced in mathematics’ magical mysteries.
        Pulling out the 179 drawers of Professor’s cabinet would be an enigma to the rest of the curios mind. No one will ever know what interesting, challenging and funny quirks of number patterns, witty mathematical games, puzzles stories and jokes could be found in the legendary mathematical cabinet.
                This book reveals the most invigorating oddities from Professor Stewart's mathematical cabinet. Inside, are mystifying trinkets of mathematics just like how to extract a cherry from a cocktail glass, a pop-up dodecahedron, and the real reason why anything cannot be divided by zero. Scattered among these are keys to Fermat's Last Theorem, the Poincare Conjecture, Chaos Theory, and the P=NP problems.
This amusing book will take you to a roller coaster ride of thrills and fun through discovering mathematics is really not that hard at all. The different curiosities were tough enough to give anyone a battle grounds for mathematical wits and conquest. Anyone who has read this book would really be damned great he did.



Math with its Real Magic

*book review: Ian Stewart’s Cabinet of Mathematical Curiosities

Do you consider yourself as math enthusiast, passionate on it? Then try reading this brilliant piece of Stewart.

Ian Stewart was not a new name to me. I’ve read some of his reviews and I admire him. I can say that most of his works are not for the layman specially this book (Cabinet of mathematical Curiosities). It’s not the kind of book that anybody can easily read through from start to finish. It mainly circles on the famous and ignoble mathematical problems, math jokes and history, brain benders and mind boggling puzzles.

The humor of Stewart is somewhat odd, maybe because he’s a deep mathematician. The book is like a manual, a lot of problems/ exercises are partially left for the readers to answer (assuming they’ll answer). I tried answering some and checked for the correct answers at the back part of the book. One thing I’d like about the book is that it doesn't follow a chronological story, it was divided into a lot of sections of different topics wherein anyone could go only or read into a topic he/she is interested in.

Compiling those mathematical concepts, jokes, etc., in just a book was not an easy thing. And I more admire Stewart for that. Then the title cabinet then now makes sense. This book reminds me of the Riemann hypothesis and the million dollar prize.

With this book, you’ll encounter math problems which are really new to you, never had encountered in school or books. By this, math, I must say, is absolutely magic, you’ll really get amazed with it.

These problems were personally came from the cabinet of Stewart, personally collected by him over the years. Then it was published to the public, the private collection of him is bared and it’s a pleasure for me being one of the people who were able to read it.

Definitely not a waste of time.

I've seen the magic. Try reading it, trust me, you’ll gonna see it too!

Game Theory, Really?

*book review: Rock Paper Scissors: Game Theory in Everyday Life by Len Fisher

First hear on the title, sounds great. I must say the movie is light on math, heavy on fuzz. Game theory can be define as a mathematical science, dealing with this is not a relaxing affair. But mark an exception to the work of Len Fisher, which is truly for the general audience, and that includes myself.

The book was really a good piece in acquainting its readers to the 7 dilemmas and the matrix: prisoner’s dilemma, tragedy of the commons, the free rider problem, and chicken, volunteer’s dilemma, battle of the sexes, and stag hunt. From these dilemma, he connects game theory to everyday circumstances and presents answers to these problems come from 3 main approaches: changing attitude, benevolent authority and self-enforcing strategies.
           
       Fisher imparts many instances, examples of games, several of those based from his personal experiences. If somebody will ask me, “What makes the book a good read?” I’ll simply say, “It caught my attention.”  And it means something big. The book was a quite pleasingly casual on its attack of its discerning accounts of strategic notions. Fisher brought us on a cynical and enthralling circuit of one of the most earth-shattering sciences of our era.
          
        The 4th chapter of the book tickles me. It regards the game “rock paper, and scissors”, which I myself, considered it a mainstream game. Fisher was able to relate the game in real life conflict resolution, a brilliant association. The most critical part for me (I guess?) was the chapters 5-8. It circles about the picture of cooperation.
        
         If someone will ask me of which part I will recommend the most, I’ll probably answer the 50-pages long end notes. Sounds odd since the book is 250 pages long, it takes up 20% of the book’s content but it’s really informative.

Since I am at high of praising Fisher’s work, then let me mention some of my frustrations on the book. Take note, “MY FRUSTRATIONS”, if you’ll disagree with these then its fine, we have our own different disappointments.
         
          The book started so slow, it slightly discouraged me to continue. As I have mentioned earlier, Fisher cited a lot of his experiences which he relate on game theory but some of these examples were intuitive and far from being scientific (for me). I spotted a little logical thoughts on crucial matters where we can clearly relate game theory. The book fails to provide a substantial launch on game theory and still badly need acceptable elucidations on its accounts.  He was more of having the idea of game theory trivialize rather than explicating it. Well, Fisher is not a game theorist anyway but rather a chemist.

If you’ll searching for a book which will seriously make you think scientifically then this is not the book you will admiringly wanted to read. Just a friendly reminder.  ^_^