The GaMERCaT

The GaMERCaT is a cute and funny comic series written and illustrated by Samantha Whitten.

Read more at www.thegamercat.com!

The Connection Between Math and Music

Since ancient times, the Chinese, Hindus, Persians, Egyptians, Israelites, and Greeks experimented in music. The word music comes from the Latin word musica, which was derived from the Ancient Greek word mousike, meaning “the art of Muses.” Greek Mythology portrays the Muses as the Greek Goddesses of the Arts and Sciences. Gottfried Leibniz, a philosopher and mathematician, stated that “music is a secret exercise in arithmetic of the soul, unaware of its act of counting.” Greek philosophers, such as Plato and Aristotle, are credited with discovering music’s mathematical foundation, and registering music in the quadrivium of mathematical arts alongside geometry, arithmetic, and astronomy. They assigned various geometric shapes different tones, numbers, names, colors, and forms to create drawings which described the musical notes that constituted a melody. In addition to mathematical properties embedded in music theory, there are contentious implications that have already influenced many aspects of musical composition.

Pythagoras (6^th Century B.C.) was the first Greek Philosopher to take notice of the harmonic ratios between different pairs of notes to create the diatonic scale (the traditional western scale). He thought that harmonies were controlled by mathematical proportions. Pythagoras used a monochord to test frequency ratios. This instrument features a single string with adjustable bridges that allow the string to be proportionately divided.  A 2:1 ratio produced similar sounds and therefore became the interval of an octave and the basis for the other 11 pitches between each octave. By experimenting with his theories, Pythagoras deducted that music follows a series of natural laws and can be broken down into an exact science. Therefore it was widely believed by the Pythagoreans of ancient Greece that the laws of harmonic intervals could be applied to all characteristics of nature. The Pythagoreans central belief was that “all of nature consists of harmony arising out of numbers.” Many objects in nature approximate another one of Pythagoras’ discoveries: the gold ratio (1.618 or “phi”; pronounced fee). Another example is found in the progression of natural elements in science according the ascending order of their atomic weights substantiated that every eighth element possessed similar properties. In modern chemistry, this pattern is called the Law of Octaves. 

Patterns are evident throughout music. The Greek Philosopher, Plato, once said, “Mathematics was born from music.” Aside from time, rhythm, and meter, music consists of many other calculated principles that are exemplified in areas of math such as abstract algebra, set theory and number theory. The mathematical structure of a single piece of music commonly features underlying patterns. For instance, Pachelbel’s Cannon in D features a repetitive structure, rhythmic beats and looping breaks that construct the song. Composers can musically vary themes by rearranging a single melodic phrase over and over again. Studies have been conducted on the relationship between the aesthetics of harmonic ratios and the patterns in songs. The results show that some music becomes popular due to its mathematical structure. 

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A bit of Philosophy: Empiricism vs Rationalism

Empiricism - The theory that all knowledge is derived from experiences through the senses.
Rationalism - The theory that all knowledge is derived from reason rather than experience.

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After exploring several different philosophers on the two different epistemological theories, Rationalism and Empiricism, I have concluded that ideas supporting Empiricism seem a great deal more plausible than those embracing Rationalism. From reason alone, neither knowledge nor truth can be obtained about anything in the physical world. Taking away our sense of sight, smell, taste, touch, and hearing would completely sever any connection to any objects or concepts outside our minds. Therefore, knowledge of what exists must extend to something beyond the point of reason.

Empiricists, such as Locke, Berkeley, and Hume, support the theory that all knowledge is derived from sense experience; hence, there is no such thing as innate ideas. A rationalist would argue that a person’s sense of morality, the ability to determine right from wrong, is an innate principle. However, there are many examples that contradict this. A child depends on a parent to teach them what is good and what is bad. It is unfortunate, though, that some parents allow their children to grow up believing that some things (like drugs, cursing, or even fighting) is alright. There have been cases where parents have even encouraged behaviors that have been determined morally wrong in our society. These young adults, who had relied on another person to demonstrate what is socially acceptable and what is not, may commit acts of “wrong” because their experience tells them these acts are “right”.  Thus, morality is a learned concept.

Another example a rationalist may bring up is that no one needs to teach a person how to walk or how to use his or her fingers and so this concept in innate. While it is true that no one needs to teach this to a person, could he or she learn to walk or use the hands if he or she had no sense of sight or touch? Any movement of the body is constantly being analyzed and assessed by the person in order to improve his or her coordination. A person needs to have sense experience in order to respond to other objects, such as the ground to walk on or a drinking cup that requires a person to grasp the handle.

Rationalism is invalid because the knowledge and the understanding of principles require the use of the sense experience. The concept of color, for instance, demands a sense of sight. A person born blind would not be able to comprehend color, because the idea of “blue” or “red” can be understood by observation through sight.

Essentially, the majority of science is based on principles within Empiricism. Theories and laws are based on what we observe in the natural world. Empiricism is crucial to any advancement in science because observation through the senses in indispensable. According to Locke, simple ideas are external. Therefore, they must be observed in some way in order to be known. You cannot expect a scientist to reason the precise outcomes of an experiment that’s never been executed. He needs to take his experiences with certain objects, and from that he can make predictions about other ideas; but not until he conceives a pattern. Concepts are discovered when two or more simple ideas are observed together, which make up more complex ideas.

Reason uses ideas obtained through either intuition or deduction; otherwise, they are innate. How can intuition be a source of concepts or knowledge? Deduction only works when you are entirely positive that you know all the possibilities or connections, which can never be true as long as there is knowledge to be discovered. And how can you deduct from a limitless infinity of possibilities? These three concepts, on which Rationalism is rooted, render this theory of reason invalid. Therefore, only what can be perceived through the senses can be used to determine, with certainty, what is true.

Shippon: A Self-Watering Plant

Get prepared to be blown away by the most "kawaii" item ever! Shippon is a tiny self-watering system that is incredibly cute. As far as I know, they are unfortunately only available in Japan.

As shown in this picture, there are three variations; a monkey, a cat, and a dog. Three different types of plants correlate to the three different animals. The dog grows clover, while the cat grows wild strawberries. And I believe the monkey carries basil.

The picture below demonstrates how it works. Step one is to put the peat soil pellet in the small basket on the animal's back. Step two would be to place the seeds in the soil and add water to the cup. Water is carried to the basket holding the seeds through each animal's tail. Step three is to watch and wait for approximately two weeks until you have a lovely little new plant! It allows you to have a new appreciation for nature by giving you the chance to sow your own seeds and later harvest your basil, wild strawberries, or clovers, if you chose.

Adorable Paper-Star-Bead Bracelet

Making a bracelet using small hand-made paper stars as beads was an original gift idea for a friend. I also included a matching hair pin with the bracelet because my friend likes that kind of thing.

The stars are made from thin, variously colored paper (just slightly thicker than computer paper). I used about a quarter of an inch wide strips of paper and folded each star 6 times to get the perfect consistency for pushing in the sides to shape the points. (If you don't know what I'm referring to, look at this tutorial, or search "how to fold paper stars".)

In total, I used 22 stars to make a decent size bracelet. The "star-beads" were strung onto an elastic string using a needle to poke holes through the paper and pull the string through each one.

Whether you want to make a creative accessory for yourself or surprise a friend with a hand-made bracelet, this totally awesome craft is sure to impress anyone.

Compilation I

blogging, writing, reading, laughing, learning, the future, friends, hardships, pokemon, technology, running, listening, robotics, tumblr, growing, frustration, piano, socks, drawing, solving, video games, 3DS, pso, harvest moon, animal crossing, goals, dreams, pencils, summer, parks, gum, wishes, tea, obsessions, glue, books, philosophy, pillows, Chinese food, Rome, tennis, physics, tears, rhythm, paper, mornings, life, amends, thoughts, weariness, apricity, beauty, warmth, grace, singing, html, rain, trees, headphones, roads, chocolate, texts, blue, puzzles, homestuck, craziness, water, questions, answers, forks, affection, liveliness, amber, roses, coffee, memories, notes, colors,