Without Tears

When I read a book or watch a movie, I try to read its reviews first. Mind you, it is the reviews and not the summary. I don’t do it to cheat. Instead, I find it helpful in knowing what to expect of the book or the movie. I want to know if it’s worth my time and if I am going to learn new things. So, I try to search first. Unfortunately for this book, I wasn’t able to read a review. And so, I don’t really know what to expect. I don’t know the topic or if the book is great.  The only thing that I know of the book is it has a nice title and cover.

Reading the first paragraph of the introduction of Len Fisher’s Rock, Paper and Scissors, I learned that it was about game theory and its connections to everyday life. I really don’t know a lot of things about game theory.  The later paragraphs help me to understand more about Game theory, which is not only a mathematical science that studies the strategic decision making. It is also that the results of the strategies depend on the other people strategies. Also, it is specifically about mathematical models of conflict and cooperation between the makers.

  Fisher continued more with game theory and its applications in the next eight chapters. Fisher provided examples of game theory. One of these is the Prisoner’s dilemma in which he described in chapter one. I find it really cool. The prisoner’s dilemma can be applied in all areas. Like in the book, it can be with few boys having the same crush to the supermarkets and marketing. He also discussed Nash equilibrium. He said it is a logical trap. I find Fisher’s view on Nash equilibrium a negative one. In the second chapter, he told the story when he was a kid and the trouble he caused. His idea to minimize the consequence is an application of the minimax principle. Fisher also gave another example with the meat and the elder sister.  He then explored this subject more with its concepts and also he discussed fair division.

The third chapter is about the seven deadly dilemmas. They are the seven of the most interesting game theory problems. Fisher gave an interesting exploration of each seven dilemmas. In the seven, one that I like the most is the chicken. Somehow I can relate more to this. The next chapter is for me, the most exciting one. It discussed the game rock, paper and scissors. Rock, paper and scissors is more commonly known as bato, bato pick. I used to play it every day when I was a child. To know more of the game is exciting, I find out that there is no really strategy that is better or that would dominate. Random choices are better in playing this game. Also, I found out that the simple game of rock, paper and scissors can be used in other conflict situations.  The next three chapters of the book discussed more about getting together and trusting each other. In other words it is cooperation and communication. It discusses more strategies and approaches that can help in preventing the consequences of the prisoner’s dilemma.

As I read the book, I realized that game theory is everywhere. From the simple game we all have played to the conflicts and problems we have encountered in this world. It is also interrelated with biology. Game theory is used in biology. Biologists used it in understanding cooperation in the survival of the fittest. Also, he mentioned some scientific experiments used in the game theory. I really appreciate it that he included some biological experiments and examples. As biologists, it helps us understand more things and broaden our knowledge.

Now that I finished reading the book, I realized that it was good that I did not have any expectations. I wouldn't think that it would be met. The book was simply amazing. It may have some dry and slow moments, but overall it was fun to read. The author discussed things without causing us to bleeding in our nose or tears running down our face. And, he also gave us a few laughs. In other words, the book is simple and light, cheerful and humorous.  It was also a fascinating guide for math people and dummies like me.  Also I learned a lot of the given problems, dilemmas, history and science. Len Fisher is a good author. He did a good job on the book. He fascinatingly and with enlightenment explored the world of game theory. He also accomplished his goal of discussing game theory and its connection to everyday use. I would recommend this book to anyone who loves games, science and math.

Farewell to Curiosity

               Speaking of Hersh, he has yet completed another masterpiece written by his hand and inspired once again by mathematical cataclysms and foundation of ideas as he has always been. Professor Stewart’s Cabinet of Mathematical Curiosities is certainly holding true to its title. When I read this book, it doesn’t even start with an organized table of contents. It’s not even a table of contents if I’m to judge it visually and technically. It’s a list! It’s not just an ordinary list containing incomprehensive phrases.

               As I read along the pages of familiar formats and fonts as in Hersh’s other book that we first made a book review on, I was slowly beginning to understand the book. It’s not a book of characters and plots and plot twists. It does not connect or interlink previous and next chapters. So basically, it contains all that can be read in a mathematical perspective. You there, gamers and logic lovers! This book’s for you. It’s interesting, those different games. Added to that are follow-up questions on various and highly diverse topics which are significantly rooted on old and new mathematical principles and theories alike. There are a lot of games to choose from, you don’t have to start and proceed in a chronological order. Pick at random and you’ll see that anywhere in this book, you’ll be sure to get away out of boredom’s way. You’d be killing time all through summer, if you’d like to put it that way.

               Finally, I can say that this book summarizes the previous books we reviewed. It reflects all the information, points and stories of the mechanisms explained from previous books. All the teachings we got from those mathematically related books are applied in this book. It’s as if it takes you to testing your knowledge of how much you’ve learn so far besides and beyond the conventional mathematics we’re taught. Nevertheless, each game profoundly explained all its questions and answers. Yes, it holds answers which are concentrated on the last chapters of this book. Honestly, you’re going to appreciate more of all that you learn as you see them came into action by participating with the mechanics and instructions of this book. This is really fun. Some are a bit challenging and that definitely adds to the thrill of reading this. Aloha! You've got the key to every lock in this book. Enjoy and say farewell to curiosity.

Behind the Magic Trick

Save the best for last! Ian Stewart yet wrote another book that is fun, enjoyable and with attempt to make the readers fall in love with math.  This time he compiled tricks, problems, puzzles, brainteasers, facts and jokes which he calls “curiosities” in a notebook he’s been keeping since he was a kid.

I would have to admit that most of the problems I did not get to solve, and some I just skipped. And that it was getting tedious going back and forth the answers page. Solving it correctly is a very rare case, in which instances I’d find myself ridiculously happy. My favourite one was the sliced fingers. It took me an awful lot of tries that when I finally got it, I didn’t want the string removed from my hands! I just understood topology a tiny bit more than I used to a few moments before I read the book.

Not everything is new. Stewart also tackled about the classics such as the Fibonacci numbers, why we can’t divide anything by zero, the sausage conjecture. All of these concepts I have heard before, but not as well explained as it was in this book.

There was also something about the way it was written that would make the reader find the enigma interesting.  Like how the Great Whodunni and Grumpelina are more palatable starting points than A and B. seems completely random and unrelated, but they sure are otherwise. Also, the entries are usually short (except for that global warming part) which captures my short attention span quite well.  Somehow because of this, the information is reduced to bite-size that makes it easier to digest.

In totality I find the book like watching a magician perform a trick and then he tells you how it’s done afterwards (something that doesn’t happen everyday, does it?). The author has that writing aura that makes the reader feel like he’s just a friend telling a story, not a professor trying to teach math. I may not have developed the love for math like the author did, but I just started to realize how interesting it could be outside the math I’ve always known, the one with often inexplicably hard structure with strings attached to grades.

Statistical Probability of Passing or Not

        Statistics make research, surveys and data analysis easier and way more understandable. Imagine research without statistics, raw data being analysed manually and piece by piece, biased judgement for the error and significance of each value and the wasted effort and time that will be spent. The importance of statistics may be neglected at times but its usefulness is evident, although sometimes, unnoticed.

            Through Math 1, I was able to appreciate statistics in a deeper sense. As the members of the group ‘Statistics’, we were able to review some statistical lessons to the class through different activities such as games, film viewing and debate. For the games, we conducted an outdoor activity in which the class was divided into their respective groups and had a race to every station to answer several questions related to statistics. As for the film-viewing, the movie was made and produced by our group in which each of us was able to participate. My part in the story was exciting since it would be my first time to act in front of a camera and that it is out from my usual character. I was Serena and I was the antagonist in the story, a killer, more specifically. The filming was really fun and even with the busy schedule of each member, we were able to finish it early although the editing part became the problem because of its long rendering time. The debate has the topic of whether the statistical poll is reliable or not. At the end, the opposition won the judgment of the audience.

            Through these series of activities, not only the importance of statistics became clear to me. But also the friendship, cooperation, understanding and patience for each and everyone became clear that it is very important and the key for the successful presentation and the possible way to pass the subject, in general.

3 C's; Cannot be Contained in a Cabinet

There are three kinds of knowledge. One is what we obtain from school, second is what we get from other people and lastly the knowledge that we ourselves unknowingly learn. Stuart was one of the peculiar guys whom I admire. And Oh, by the way I meant awesome peculiarity.

I myself have been filled with curiosities and good thing that the world can satisfy it. I like the line from Ian’s book “The math you didn't do at school is interesting”. Indeed learning without pressure on taking tests is the ultimate way to genuinely gain knowledge. Every time a gap in me brought by curiosity is filled, I feel that I’m walking on air. What I find in the author of the book similar to me is being able to see things at a different perspective and not limiting my education to what is known. The book gave me an insight to what math is outside of the box and not the creepy subject to be feared about. Math is about putting things into places in their perfect fit just like managing things inside a cabinet.

The first chapter was my favorite since it was about aliens and I am forever interested in extraterrestrial life. His hypothetical story about two men encountering aliens was impressively nerdy and I liked it. The question represents logic that is applied by twisting truth and false. I enjoyed finding whether Alfy, Betty and Gemma were Gibberish or Veracitor which are groups of the same species determined by how they tell statements based on truth. I will admit I really got puzzled.

Puzzles and games are a part of everyone’s life. His examples are entertaining and not to mention he had incorporated math together with humor. There were so many interactive games concerning patterns and puzzles that are challenging. I think school math should be more interactive, innovative showing the creativity that can be found in math. Games include probability, geometry (my favorite) and logic. For example a pop up dodecahedron, one is  how to extract a cherry from a cocktail glass which is hard as drinkers say and the true reason why you can't divide anything by zero. There were even some tips to make money just by proving the obvious; yeah I know it was hilarious. As a biology student this book presented math as something to look forward to everyday, even in our metabolism math is used.

Mathematics uses logic and philosophy as well, that’s why without a doubt it contains a lot of uncertainties. These uncertainties are also brought by curiosities where the latter brings knowledge that we use in our everyday lives. What I admired in Ian Stuart was that he shared his collection of ideas since he was 14 years old, as early as that and didn't just keep it on his own. This book was really made with passion and love by the author since it reflects his insights and journey in meeting mathematics.

In the end life is a cycle meaning it revolves in patterns. Equipped is our cabinet without any corners that will be filled by knowledge that is infinite ∞

Logical Thinking at Work

            Mathematics is logic. It is not just about the numbers, shapes and equations but can also go beyond the four-squared room and can be at every part of the society and life of each person. Without knowing it, we may already be inside the area of mathematics as we live our normal life everyday. In the book of Ian Stewart, the ‘Cabinet of Mathematical Curiosities’, he was able to share some of his views and personal entertainment that involve his creative and mathematical thinking. The characterization of logic in the field of mathematics and how numbers and analysis be equal to fun were some stuff that can be derived from this book. Generally, the book contains different puzzles and games that can give you entertainment and at the same time challenges which can measure the level of your analytical and understanding skills.

            At the start of the book, aliens were able to invade my mind and immediately went into space. How can you even know which is which with only some questions asked? Well, Capt. Quirk found a way to analyse this problem. Even with this simple puzzle, it was able to make your brain work into several analyses and do imaginative works of patterns and relation of each statement.

        As the book go further with its puzzles and games, different historical names in the world of mathematics were mentioned such as Fibonacci and Fermat. The works they were able to contribute were described and used in this book in a way that it is not technical yet understandable (thanks to the writing skills of the author). I can say that this is mainly for entertainment yet at the same time touches some bits of mathematical concepts.

             One amazing thing about this book is that, mathematics was made friendly and fun for those that are not really a fan of it. Reading some of the problems, I observed that sometimes, numbers were not even included just to achieve the answer. As for those that involve numbers, such as his explanation as to why we can’t divide a number by zero, he was able to explain the concept in a very simple and understandable way. This is one of my favorite because, personally, I am one of those that do not understand this type of rule in mathematics. Well, 0/0 was also not considered applicable since it is unpredictable and as Stewart said, causes headache.

            The mathematical concepts were made understandable by the problems and questions since the mind itself is the one doing the thinking which is apparently out of the traditional way of learning. Yes, answers were given at the end of the book but the urge to answer it and to feel the satisfaction of solving something drives an individual to think more about it.

            In his introduction, he mentioned that some of the puzzles in this book were compiled when he was still 14 years old. Relying in this statement, it can be concluded that even at a very young age, he is already fond of mathematics which, in my opinion, is very hard to find nowadays in the pool of youngsters in the community. With this book, the interest in math can be developed because of the different perspective it gives to the readers about math. It is more than just the complicated stuffs it solves involving numbers and variables but it also has its own side of fun and mind games. Without knowing it, we already start to appreciate math in its own fun way.

            Ian Stewart was able to share his cabinet of puzzles and games. Some may say that this book has no story or plot but it actually has its own story to tell. It is all about the tale of how logic and analysis affected the life of one person as it is one of the factors that molded him into someone that he is today. A lover of mathematics and a great writer.

The Fun and Amazement Simulator

By: Kissel Cablayda

Playful and witty- The Cabinet of Mathematical Curiosities is a must read book for all ages. Of the five books given to be reviewed, this is the book that finds the reader to be unexpectedly time and effort engaging, however, in a way that it lures the readers to play and play game after game. This is a collection of tricks that are perfect for those who believes that math is a magic, a collection of games for math gamers, and a collection of ice breaker for those who just want to kill the time. Ian Stewart, as a witty author as ever be, never failed the readers to engage his readers to the trickery of math curiosities.

His smart tactic to use universal emotions of human, such as curiosity, fun and humor is a wise way to subtly connect and develop the readers’ interest in math exploration and appreciation.

One of the most enjoying parts of his game collection is the “more curios calculations” part in which one doubles a three digit number divide it by 7, then 11 then 13 and then one gets the same three digit number as the answer. The wise way of those who have discovered this trick is a skill that can lead the “player” amazed and confused at the same time. This kind of mathematical generalization is just one of the many tricks that keen observer can do and re-enact to others. Such algebraic game is good for the brain. It is a good example to encourage one person to think and dig deeper about the situation behind the trickery. Thus it is safe to say that the author encourages the readers to become a detective- a detective for mathematical confusion and trickeries.

Among other games, the book also included mathematical facts that leaves the reader information that would astonish them thus even inspire them to become a math enthusiast. A very god example is Ian Stewart’s story about the German algebraist Ernst Kummer and his inability to solve mathematical equations. However Kummer is a notable genius that had contributed some of the best works on Fermat’s theorem. This short story would really make the reader realize that you don’t have to be a math genius to become a mathematician, in fact you can be famous in this field as long as there someone who you can rely on when you need basic calculations.

The book is indeed a good read, a good interest and amazement simulator. Thus, this should be a good peg and an inspiration to those who attempt to invite the audience to engage in different mathematical concepts and theories.