The Allegory of the Clever

There are a whole lot of things the subject mathematics can cover. As I have highlighted a few articles ago, Mathematics is the language of the universe or almost everything. Anything that studies the relationships and interactions between variables, quantities, and change is mathematics. It is a very abstract concept.  Mathematics is the expression of the logical concepts and forms more complex concepts out of these basic logic. It is a logical progression.

Out of the book I had read an interesting fact. The logic of something ‘advanced’ is clearly complicated. Intermediate facts are usually simple. However the simple or the elementary facts is actually more complicated than the advanced. It may be the reason why we say that mathematics is a very difficult subject.

                Our notion of mathematics is basically a series of unending computations and all the other boring stuff in blackboard. Every math thing being taught in school is always about the principles, the theories, the calculations, and the algebra.  Mathematics taught in school is always our perspective of mathematics. However, Professor Ian Stewart in his book ‘Cabinet of Mathematical Curiosities’ had led my math path to a different, odd way. It is absurd and intriguing as he uses mathematics in games, puzzles, stories, and facts. There I found the fun on using logic, statistics and geometry in situations I have never thought of. I had compiled all my favorites from the book and these are some:

                Extracting the cherry. Well, I think everybody already knows how it is done. It is having the cherry out of the glass figure and the thing you will do is to move two matchsticks. I sometimes play that game when were eating out just to check if I have remembered how it is done.

                Much Undo About Knotting. Knotting, for me, is a Boy Scout thing. The facts raised by Ian Stewart drag my interest in knots. A mathematician’s knot is a different kind of knot having two ends stick together. It was that simple until I found out that the Knot theory is used in the study of molecular biology. It is already used in the mysteries of the DNA and in quantum physics.

                Perpetual Calendar.  It was more like “Great idea. I’m gonna use this on my desk tonight”. I had not really solved the problem.

                Mathematical Jokes 1. It has been hard for me to understand the joke. I was looking for something in that joke to laugh about but then I saw the warning. So, I skipped.

                Why Does Minus Times Minus Make Plus? It is arithmetic. We have already mastered this in school.  The highlighted problem there is how it is applied. He explained the problems in banking and debts.

“Well, if the bank kindly writes off (takes away) two debts of £3 each, I am £6 better off – my account has changed exactly as it would if I had deposited £þ6. So in banking terms, we want (-2)x(-3) to equal +6.”

I may have not thought of that. If we are to apply and use that, we will be confusing ourselves and also complicating arithmetic. The fact is somehow clever and I realized that simple math is more complex than advanced math. Just saying.

      The Bridges of Konigsberg. Ah, the Bridges of Konigsberg. It is somehow famous for having no existing solutions. This simple puzzle works as having to cross one bridge only once. I have also tried the puzzle several times and I had an existing proof that it very impossible. However, Euler, a mathematician, made a point that the geometry is not relevant in this situation. What matters is how everything is connected. Somehow I had made a philosophy that you cannot always have to entertain all people even if it is hard for you to prove your worth. It is very important to just maintain a good connection to these people.

Magic square. It is also famous ancient mathematical problem and a coincidence. The magic square is astonishing in a way that each row and column equal to 15. The ancient Chinese really knows how to play with numbers.

All of these games and concepts are clever. Ian Stewart has brought my mathematical perspective to a different world. Aside from the puzzles, He also had highlighted the concepts and the history of pi, Fibonacci and the golden numbers, Fermat’s theory, Pythagoras and the triangles, Euler’s principles and a lot more. It is a really good read and people might have enjoyed math out of it.  

A book review on Cabinet of Mathematical Curiosities

                Math in both elementary and high school was a little bit challenging, fun and somehow easy. When I entered college I thought it will all still be the same, what I thought was wrong. Mathematics in college was ten times more challenging, boring and was never will be easy. So I wondered how do mathematicians look at math that exciting and fun? In the book of Professor Ian Stewart; "Cabinet of Mathematical Curiosities" he discussed where the real fun is. Through the years Professor Stewart has been filling his cabinet with mathematical games, puzzles, stories, and facts. Written in his book are the different answers to different questions that each person might have about how mathematics work. The author had discussed different logic behind games, puzzles by using the science of mathematics in a fun and entertaining way.

                The author created an atmosphere where he as the author can interact with his readers through asking them to solve and perform puzzles and problems. I like the connection he makes with his readers however, since I am not a fan of mathematics I eventually got tired solving his problems and instead I skipped some of it. The book was not arranged in a chronological order, each chapter is not directly connected from the previous one which makes it less boring because each chapter opens a new topic.

                In the book my most favorite part was on the chapter of Curious Calculations. During elementary and high school I find it fun calculating lengthy mathematical problems but when Professor Stewart showed an easy and even more fun way to solve problems I realized how different mathematical problems in college could also be solved that way. It's like solving puzzles and the answer itself is the prize.

                His book was indeed a cabinet of mathematical curiosity. I myself was not that curious about mathematics but when I read his book I realized that my mind has a cabinet of curiosity that was yet to be filled with answers.

A written report

                All groups were assigned to create a debate, game and movie about the topic assigned to us. Our group, being the last one to perform and entertain our classmates was assigned to discuss about the broad world of computers. I thought it would be easy to discuss about computers since we are currently living in a computer generation, where there would be various topics to choose from to suffice the necessary topics needed for our debate, game and movie. However, I never thought of the idea that our group was assigned during the hell month of the semester. I even thought that we would not perform anymore since we have no time left. Unfortunately or let's just say it was a blessing in disguise that we were still able to perform, entertain and add some information about the world of computers.

                First we started with our game. Just like every group we decided to have the theme of amazing race however, due to the bad weather we played inside two different classrooms. It could be more fun if the game was outdoor, to avenge from all of the running that the other group had done and to feel the spirit of the race. Our second event was our debate; the stand was "This house believes that illegal "downloaders" should be punished". In the government side was Omid Siamard, Kissel Cablayda and Klimpol Maganaka. Under the opposition side was Ruth Nasibog, Claire Jacinto and Me, Ivy Gail Doringuez. The point of the opposition side was basically about having an easier access to different entertainment material at the most convenient and safer way. It would also be very impossible to put into bars all the people who are illegally downloading. Majority of the class voted for the opposition side since almost all of them are illegal downloaders and the practicality of downloading illegally.

                Lastly we had our movie with no title at all. The movie was basically about a teacher who got killed by a mysterious killer. On the crime scene there were bloods seen all over her body however, there were no lacerations. Her students, Gregory (Edwin) and Omid decided to test the blood using the Blast Software, only finding out that the blood contains the DNA of a cat. I was the killer in the movie being a cat lover and a person who loves her job who envied the other teacher (Klimpol) because she got the promotion I thought I should rightfully have.

                It amazing how math had evolved through time from simple numbers to gigantic computers. The innovations around the world are mostly because of computers. Indeed computers makes our life easier, it open doors to new discoveries and learning.  

Curiouser and Curiouser

Finally, the last book review is here. Actually, I have already read this book last January because I thought this was the book assigned to be reviewed at that time and I’ve also made an unfinished book review for it but when I learned that a different book was assigned, I stopped making the report. But at least now, I can continue what I’ve started.

The book entitled A Cabinet of Mathematical Curiosities, unlike the four others that were given before, was not a book with a definite storyline. It was filled with enjoyable games and puzzles that surely readers would have fun with. It is very pleasing and challenging at the same time which would surely improve and develop the thinking skills of its readers. Stewart was great in giving out elaborate discussions on the topics involved in the book where even ordinary readers are bound to be fascinated with. He was a very good mathematician because he managed to explain and discuss the book in the simplest of terms. This book is definitely my personal favourite because it was such a brain teaser.

The book opened up where Stewart mentioned that he had a notebook filled with problems in math when he was a kid. With this, it can be inferred that even at a young age, he was already a big fan of Mathematics (something rare in children nowadays). He then looked at Math in a new perspective, a more fun and enjoyable paradigm. He viewed it in a fun way so that he wouldn’t be pushing or forcing himself to learn such overwhelming topics because if you’re having fun with something, you won’t have a hard time in learning that something.  This then allows you to clear your mind and answer the problems immediately.

Admittedly, I didn’t get to answer all problems because it got kind of tiring but still, they were fun. If I’d have more time, I think I’d also have more patience to deal with them. However, I could say that this book can definitely improve one’s interest in Math because then people would be viewing Math in a fun way and the common notion that Math is like hell or very hard to deal with would be erased.

In this book, Stewart manages to deliver to his readers about his very long relationship with Math which started out when he was a kid. Through this book, the readers were able to follow through how a simple perspective or paradigm shift could change one’s attitude towards something. A Cabinet of Mathematical Curiosities, a great read indeed.

Mathematics Who? What? Where? When? Why? How?

“One of the virtues of knowing a bit of math is that you can impress the hell out of your friends.”

This quote is probably the coolest that I have ever heard from a mathematical author. Again, Ian Stewart has proved that not all of the curiosities lie beneath the universe: they are just suspended in numbers.

The book A Cabinet of Curiosities has given me a lot of insights about the puzzles that evolve around math: certain mysteries that has not been taught or learned, just analyzed and thought.  Not just the classic puzzles, but the new ones that can really boggle up minds. I am not quite the “thinking” type, but by just reading the book, it will present math’s other side of the coin.

Can you make a pop-up dodecahedron? How can you alternately fill a glass of water? Who tells the truth and lie? How can you extract a cherry from a glass? These are just some of the questions Stewart asked that he presented in the book. And the answers? One word: fascinating.

As the author mention in his introduction, you can skip at any page you like, but it’s more fun to follow the table of contents, for earlier problems are easy to solve than the on the proceeding pages, which as he said, challenging. But I think solving the first problem was quite tricky for me. I am referring to the problem Alien Encounter in which we have to identify the species of the aliens, one being always tells the truth and the other that tells a lie. I first encountered this problem in a math quiz bowl we have attended, but I was wrong about it. Seeing it again another time made me really think. Now I really kind of contemplated and when I flipped on the answer key guide, then again I was wrong. This problem may be not math-related but I assume, and is a fact that logical deductions are indeed of a necessity in the mathematical field.

Another problem presented in this book that I have already encountered is the River Crossing which involves a wolf, a goat and a cabbage. The player is the boatman and needs to carry only one to pass cross the river without the wolf eating the goat or the goat eating the cabbage. This is quite simpler since the wolf does not eat cabbage so the goat will be the first transported followed by either the wolf or cabbage. If one of the two were transported, the goat is carried back to the starting point, and the one being left will be carried back. The boatman returns to get the goat and voila, you solved a problem.

What’s unique about this book? I can say its uniqueness lies on the table of contents. As I skimmed through it, there were many chapters included but when you look at their pages, they are really short. The longest may be two pages at maximum. There are no morale, no story, no love, and no horror. Just mind-boggling g math puzzles, math anecdotes, and the one which I am not quite fond of, math jokes.

There are anecdotes in this book as well as jokes which generally, I don’t get at all. Either that they are so deep or I’m the one shallow individual. Either way, it was a nice thing that the author has mixed it up with this to avoid his readers being bored or tired of solving his golden puzzles. But having them, a kind of say “corny” jokes is a big no-no for me.

Reading the book, I can say that Stewart has offered small bits of math problems which are really a great exercise for the mind instead of serving a full course of x’es and y’s and complicated terminologies, graphs and figures, which I think is a “hooker” for an average, non-mathematician (like me… sssssshhhh….) reader.

This book has given me an idea that not all math problems are a bunch of boring stuffs you can pin a wall and shoot with a shotgun, but enigmas that can be synthesized not by just following a bunch of long, difficult formulae and can be solved in some little ordinary ways. What it needs are three things: interest, willingness and determination. After all, “There are three kinds of people in the world: those who can count, and those who can’t.”

A Book Review on Cabinet of Mathematical Curiosities by Ian Stewart

       The book was a not a novel or a story to read, but a valuable one made for us to enjoy in our leisure time. As people who are not Mathematicians, the book presents a lot of facts about the most popular facts, games and puzzles with the solutions purposely placed by the author for readers to understand them and be able to solve them. I was really in such awe when I tried to look at the solutions on the latter pages of the book. There are a lot of practicalities presented in each that I never get bored and made me crave to solve for more. It was also a great reference for me if I would like to impress some friends by knowing something really good about Mathematics. However, I would just like to highlight a few sections I just thought were really good: First, in our past learnings in elementary and high school we have calculated basic arithmetic in its standard form. However, the section on Curious Calculations amazed me on how one could calculate lengthy arithmetic in just seconds. Second, I have also discovered more from Pythagoras and his theorem commonly encountered in Trigonometry. Stories about Leonhard Euler, The Witch of Aghasi and Pierre de Fermat’s last theorem brought a lot of things new for us. Lastly, the geometrical figures such as the Greek Cross, The Sphinx of the Reptile and the Knots involving Topology brings one of us to recall one fond moment in a Molecular Biology class as true enough, topology and the mechanism of knots are evident in DNA since they are considered supercoiled most of the time.

Areas of Mathematics such as Algebra, Statistics, Arithmetic, Trigonometry, and Geometry are in the book and each are well-represented by problems. The book is good for everyone to learn while having fun at the same time. Had it not been for these Mathematicians who labored and have devoted their lives to Mathematics, this practical world would probably remain as one that is not understood by everyone. Indeed, they are amazing for making complicated things simple. 

Computers: A Written Report

I was a little bit worried when the group assignments were given during the first few meetings of Math1 since the computers group will be the very last one to initiate games, debate and a special presentation. I was thinking that our group’s presentation might fall during the hell week and that would be very unfortunate since a bunch of requirements, exams, papers, and etc. must be complied during that week. Luckily, my groupmates and I were able to manage our time despite the fact that we have to present seven days before hellweek comes.

The first thing we did was to play a game. It was supposed to be an outdoor one but the weather did not suit us well since it rained heavily so we have no choice. We utilized two rooms and three pairs from our group stationed in one room while the two remaining pairs used the other room. There were five stations having its own unique amusement and point system. The games played were all related to computers and these were the following: a.) typing speed which is a test for agility—how fast they could input characters on the computer; b.) icon/logo game in which each group was tasked to identify certain icons for two minutes; c.) unblock me which is a logical game; d.) computer history; and e.) computer trivia. The last two were mainly to test their knowledge about computers and it also aimed to reiterate information concerning computers. It was indeed a fun activity after all.

Our group had also initiated a debate pertaining to the topic “Illegal downloaders should be punished”. Majority of our classmates had reacted to this since almost all of them, “us” maybe are continuously doing piracy of movies and music. I was the whip of the government side and our main points on this matter are: illegal downloaders should be punished because they are breaking the law. Also, piracy is a form of stealing and it deprives the financial rewards that artists deserve to receive. Another thing is that it will threaten the economic growth because it is a fact that entertainment industry contributes greatly to the national revenue. However, the opposition side emphasized that illegal downloader should not be punished because of practicality reasons. Almost all people are doing this so there would be no enough prisons to punish these people. Another point is that it will encourage popularity of artists and it is also cheaper. Still, during the first and last tally of votes, nobody was in favor for the punishment of illegal downloaders. After the debate, our group had shown to the class a 15-minute movie presentation. It was all about a murder case of a school teacher. And the antidote was the utilization of computer softwares such as BLAST and DNA Analysis software in order to trace the serial killer. In the making, our group experienced a lot of fun because of some bloopers and we did some weird acts that we were not used to do in our normal lives.

In totality, it was a great experience being in the computers group and a part of Math1 class as a whole. Although I am the only upperclassman majoring in biology, I was still able to relate and mingle with my classmates especially to my groupmates. I was also very happy that this group activity was a success. Thanks to everyone! J