asymptotes

Artificial Intelligence is Love. Below is a proof in 5 simple steps.  Artificial Intelligence is AI (substitution by initials) AI is あい (substitution by hiragana) あい is 愛 (substitution by kanji) 愛 is Love (substitution by semantics) therefore, Artificial Intelligence is Love (iterative transitivity) Q.E.D. Bonus: How does an Artificial Intelligence major confess his love? He says: I do AI - ＡＩしている (AI shiteiru). This means "I do AI - I love you".  Below is the context. "I do AI" in Japanese is ＡＩをしている (read "AI wo shiteiru" )。(Apparently, Japanese also uses ＡＩ to refer to Artificial Intelligence.) To make the sentence sound casual, the particle を (wo) could be dropped, making it ＡＩしている (AI shiteiru).  Now "AI shiteru" could be interpreted as "I do AI" (ＡＩしている - AI shiteru) or "I love you" (愛 している- ai shiteiru). This is because "AI" could be read as "AI" which stands for Artificial Intell...

Tolkien and The Lord of the Rings are now household names thanks to the huge success of Jackson's film adaptation of the Trilogy.   The Hobbit will soon follow, as Jackson finishes another film trilogy adaptation for it. However The Silmarillion , the book which provides the backdrop for the stories of The Lord of the Rings and The Hobbit remains out of reach for many people, even among Tolkien fans. One of the main reasons given is that The Silmarillion is a difficult book to read. I think I agree with that claim, although I would also add that the enjoyment I got from The Silmarillion surpasses that which I got from The Lord of the Rings (LotR) . I read LotR before Silmarillion .  I almost gave up reading LotR... twice. But once I got to the Mines of Moria chapter, I couldn't let go of the book.  I am already a Tolkien fan when I started reading the Silmarillion , so perhaps that eased out a bit the effort of reading a "difficult book". But th...

I lost a turn driving to the airport today and ended up in a department store called SM.  Driving from the airport, I lost a turn again and I ended up in SM once more. Suddenly, I thought that I was in a  möbius strip. Or, you could say, I had a möbius trip. A möbius strip is a surface with only one side and one edge.  You can make a mobius strip by getting a strip of paper, giving it a half twist (180 degrees), then joining the ends together. Möbius Strip by David Benbennick The möbius strip has many curious properties. In an ordinary cylindrical strip (ends joined together without a twist),  if you start from the seam then draw a line around the strip, you end up in the same starting point, in the same surface. In a möbius strip, drawing a line from the seam, then around the strip, will bring you to the "other side" of the strip. The möbius strip is studied in the field of mathematics called topology. An ant walking along a mobius strip can cover "both ...

I’ll be celebrating my birthday in a few days time. I’ll be 17 again! Yes, I have discovered the Fountain of Youth! The  Fountain of Youth that has evaded many explorers and philosophers for ages! The thing is, they were looking for it at the wrong places! The Fountain of Youth is to be found in Math, in Number Theory, in the Base Number System! I was 17 turning  18 when I found out I could remain 17 forever by simply changing the base number system when calculating my age! The day I turned 18 (Base 10), I decided to say goodbye to the Decimal System (at least in computing for my age) and adopted the Undecimal Number System (Base 11) so that I’ll be 17 again. The following year, I adopted the Duodecimal Number System (Base 12), and thus, I was 17 again!  As  I approach another birthday, I’ll be 17 yet again. But please, don’t ask me which Base Number System I will be using then . We are most familiar with the Decimal Base Number System.  In grade s...

My chemistry teacher one time came to class with her daughter. She said, "Class I want you to meet my daughter, Chlorine." My classmates and I began to snicker. We wondered whether her other children are named Fluorine, Bromine, Iodine and Astatine, and that, in fact, their family name is actually "Halogen". In college, I found out that one physics professor named his children after atomic particles and subparticles. At least I'm sure that one of his children is named Atom. It's quite amusing how some people name their children after things related to their field of work. With this blog entry, I would like to suggest names for babies, depending on the field of interest or work of the parents. The list is not exhaustive (of course!). Feel free to give your own suggestions. Is your field not here? Well, why not make a comment and add your suggestions! ***** Like Asymptotes on Facebook : http://www.facebook.com/Asymptotes Follow Asy...

Enjoy this intellectual, musical and visual treat about math and nature from a film by Cristobal Vila . Great presentation concept, nice graphics, good music, and of course, great math!    

In mathematics, an irrational number is any real number that cannot be expressed as a fraction of two whole numbers. Two of the best-known irrational numbers are pi and e (Euler's number). The decimal expansion of an irrational number is non-repeating and non-terminating. This is not the case with rational numbers (for example 1/4 can be expressed in decimal form as 0.25 - which  terminates with the digit 5; 1/3 , on the other hand, is expressed in decimal form as 0.333333... , in which the digit 3 repeats ad infinitum ). Below is a verse which relates irrational numbers with true love. Trivia Below is an interesting trivia on how pi , an irrational number, is used in the software versioning of TeX , a typesetting software popular among scientific journal-writers. TeX has an idiosyncratic version numbering system. Since version 3, updates have been indicated by adding an extra digit at the end, so that the version number asymptotical...

For a proof, you may try asking the following persons: a student trying to finish his thesis a graduate student submitting a journal article for peer review an accountant at the end of the financial fiscal year an executive preparing a report for the board of directors or, you may take a look at your own experience of trying to beat a deadline!

Fermat's Enigma by Simon Singh FAITH is reasonable, while science, to some extent, is founded on faith. These are two conclusions I made after pondering the relationship between faith and science. It was a "mathematical novel" I read recently that influenced me to undertake the exercise. The book, titled "Fermat's Enigma," was written by Simon Singh, a Ph.D. in particle physics at the University of Cambridge. It tells of the epic quest to solve Fermat's Last Theorem, regarded as the greatest mathematical problem of all times. I could say that the exercise led me to some rather startling discoveries. (Click here for a  brief explanation on Fermat's Last Theorem ) First, not everything in science has a proof. In fact, the whole of math, an abstract branch of science, is founded on statements that are so fundamental that they do not have proofs! These statements, called axioms, are either self-evidently true or else are assumed to be true. Perso...

Fermat's Last Theorem (FLT) is perhaps the most famous mathematical puzzle of all time. It was formulated as a conjecture by Pierre de Fermat in 1637 and was only proven in 1995 by Andrew Wiles. FLT states that no three positive integers  a ,  b , and  c  can satisfy the equation  a n  +  b n  =  c n    [1] for any integer value of  n  greater than 2. A very interesting fact about FLT is how Fermat introduced it to the world. He wrote the following on the margin of the book Arithmetica : I have discovered a truly marvelous proof that it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. This margin is too narrow to contain it. With this seemingly casual and yet bold statement, Fermat issued a challenge to the great mathematical minds of his time (which included Blaise Pascal) and of the three cen...

In a previous blog post, I have posed the question " Has Stephen Hawking Killed God? "  and have answered it with an emphatic  “ No! ”.  In this follow up post, I discuss the appropriateness of Hawking’s choice of title and subtitle for his book. I would like to suggest to Hawking that he change the title of his book “T he Grand Design ”  because it betrays the book’s grand claim- the irrelevance of God in creation.  If he really wanted to take God out of the creation picture, he should not have associated the word “design” with his book, because this word implies “purpose” and “intelligence”.  And an idea as big and complex as creation would call for a Great Purpose and a Great Intelligence, thus reminding many of a Great Being.  He should have, instead, called his book “ The Grand Chance ” or “ The Grand Coincidenc e” because he suggests that human life is a product of mere chance. I also suggest that he change the subtitle of his b...

Stephen Hawking argues that God is not needed for creation in his new book, “ The Grand Design ” (co-authored with Lleonard Mlodinow). He writes, “Because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going.” Has Hawking killed God? No, I certainly do not think so. Hawking explains that “because there is a law such as gravity, the universe can and will create itself from nothing,” but he does not explain why there is gravity in the first place. He argues that “spontaneous creation is the reason there is something rather than nothing” but he does not give a reason why spontaneous creation should necessarily happen. His axiomatic acceptance of the law of gravity and spontaneous creation seems to me as dogmatic as a theist’s acceptance of the...

I began my graduate studies in computer science in 2003. After 3 years of part time study, I started groping for a thesis topic in Artificial Intelligence (AI). The experience was fun (and torturing- I had to change topics 3 times, but it was still fun… and torturing). I learned a couple of things along the way. I outline these things in this article. 1.Error feedback leads to perfection Neural Networks (NN) is an AI technique that mimics how a brain learns through billions of neurons and their interactions with each other. One of the most popular training (or learning) method for Neural Networks rely on informing other (digital) neurons about the error levels of the current output of the network. This is called the Back Propagation Algorithm. Lesson Many times we dread facing our faults, whether we discover them ourselves or others inform us about them. But come to think of it, knowing about our faults is one of the best ways to improve. I...

People tend to think that exams would be much easier if they're in multiple-choice format. But does having more choices really make them easier? Consider the test item below: Who among the following scientists contributed to the atomic theory? A.) John Dalton B.) Charles Darwin C.) J.J.Thompson D.) Albert Einstein ... ... ... S.) All of the above T.) All letters above that are valid Roman Numerals U.) All letters above that correspond to a Fibonacci number V.) All letters above which are valid symbols of an element in the periodic table W.) All letters above which are elements of the union of the sets in U and V X.) All letters above which are elements of the intersect of the sets in V and W Y.) None of the above Z.) Sirit (Filipino word for ¨I give up¨)   Post Script A few lessons we can gather from the above post: * Having a lot of choices may not be good all the time. * No matter how many choices you have, you always have to choose the right one. * ...

The poem that follows is a tribute to Euler's magnificent observation that : Euler's Irrational Imagining i to the i you equal, do you not, one over the square root of e to the pi ? What is interesting about the above equation is the fact that it involves 3 of the most important numbers in Math: the imaginary number i , and the irrational numbers e (Euler's number) and pi . Morover, it shows that an imaginary number raised to an imaginary number could actually result in a real number! Contemplating this equation, one could not but appreciate the inherent beauty that exists in math. Sidelight   I consulted a professor one time.  We discussed the graph output of the results of my experiments.  After staring at the graph for a couple of seconds, he suddenly smiled and said "It's beautiful, isn't it?" Of course, I could not disagree, lest he gives me a failing mark. So I just parrot him and said "Uhmm..ah...yes... it...

Note: You need to know Tagalog/Filipino to appreciate this proof.  Problem: Prove the following: log 2   = z   n Proof Expanding the Left Hand Side of the equation: log two = z n Substituting phonetically log tu = z n Expanding the Right Hand Side of the equation... log tu = zzzzzzz.... Using the commutative property: tu log = zzzzzzz.... Q.E.D.

It's been more than ten years since I took up differential and integral calculus (more familiarly known as Math 54) during my college days in UP Diliman. I've long forgotten most of the formulas and techniques I learned then, but the memory of the person who taught them to me remains vivid. She was Ma’am K. The first thing that struck me about Ma'am K was her mastery of the subject she was teaching. She would explain things with conviction and authority, even reciting long theorems from memory. She also remained focused on the exposition of the lesson. Once, while teaching, the chalk fell off her hand, but she continued with the discussion even as she was picking it up from the floor. Later on, it became obvious to me that she possessed an extraordinary intelligence. But Ma’am K was not just an intelligent instructor, she was also a competent one. I've met some very intelligent professors in U.P., but many of them, sad to say, do not know how to teach. They s...