Mathematics is another form of communication parallel to natural language. Its main function, however, is to explore and communicate the scientific aspects of our lives. Without mathematics, this special language designed to explain our natural surroundings and phenomena, we would have no scientific knowledge of the world we inhabit. For instance, Isaac Newton would have no vocabulary available to explain gravity. Mathematics may not necessarily be used to express feelings, record history, or to give orders, but, as the great philosopher and mathematician Rene Descartes said: “In our search for the direct road to truth, we should busy ourselves with no object about which we cannot attain a certitude equal to that of the demonstration of arithmetic and geometry.” Mathematics’ greatest function is to generate the “truth” via its expression of logic. Mathematical laws and theorems give us at least a glimpse of what the world is really like. In fact, if we carry on with our belief of it being the language to explain the world, mathematics may even be the language of nature. As Galileo explained: “Philosophy [Nature] is written in that great book which ever lies before our eyes. I mean the universe, but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.”
Mathematics also encourages philosophy. By examining the world we inhabit through mathematics, we can question the reason of our existence and why nature is working the way it is. The structure of mathematics bears semblance to the natural language too. Whereas the natural language has the alphabet as its basic units, mathematics has the numbers and functional symbols (i.e. ‘=’ meaning equal; ‘+’ meaning addition; n2 meaning multiplying itself), which would form equations, unknowns, theorems and laws.
Philosophers often link mathematics and philosophy with music. Music is indeed a powerful language. Its function is to allow people to have less ambiguous comprehension and appreciation for the profound emotions of human soul and spirit. Quoting great American conductor Leonard Bernstein, “Music can name the unnamable and communicate the unknowable.” With words, it would be impossible to portray pure joy or sorrow. Such deep emotions must be described with some sort of metaphor, which may alter its original intention. However, describing pure emotions is the purpose of the musical language. As the celebrated Russian novelist and a friend of Tchaikovsky Leo Tolstoy said: “Music is the shorthand of emotions. Emotions which let themselves be describes words with such difficulty are directly conveyed to man in music, and in that is its power and significance.” The English word “sad” can be “translated” to Brahms’ Tragic Overture; and “hopeful, promising” to Beethoven’s Ode to Joy. The musical language can also be a tool, which allows men to create poetic stories and vivid imageries. Debussy’s La Mer is an example of an exquisite musical picture, painting the sea in its three contrasting moods. Chopin’s musical Ballads are crowning achievements, revealing a story as lyrical as the works of Lord Byron or Heinrich Heine, and as dramatic as Goethe’s Faust or Shakespeare’s Othello.
While to promote philosophy is a function of both mathematics and the natural language, music’s connection with the human mind and soul allows it to be part of philosophy. It is also interesting that while the majority of the musicians are not philosophers (the only major composer who was also known as a philosopher is Camille Saint-Saen), the majority of the philosophers take music very seriously. Plato considered music training as “…more potent instrument than any other, because rhythm and harmony find their way into the secret places of the soul.” Karl Marx described the power of music as “so great that in legends of all nations its invention is ascribed to the gods.” Greek scholar Aristides Quintilianus even believed that “music leads every change, for it is first in order and power before all learning.”
If we are to consider the elements of music, we shall find its construction similar to the structure of natural language and mathematics. Our basic symbols, instead of letters or numbers, are the clefs, the notes, and the rests. They will form a musical phrase or motif, consisting several bars of these notes. Motifs form themes and themes form a unified movement. The combination of several movements creates a grand, expressive musical cycle.
Mathematics, music and the natural language are languages tightly interwoven into our lives. We see similarities in both their structure and functions. We also see how each language is specifically made to communicate with certain aspects of the world. Yet we have often dismissed both mathematics and music as a language. “A mathematician will spin out a new theory or a composer create a miniature sonic universe; a poet will turn an experience into metaphor, a scene into a source of illumination.” Only via the study of not just one, but also all three languages, we can continue to identify and express the unknowns of the world. Let our educators be vigilant.
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Bibliography
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Chomsky, Noam, Knowledge of language, ©1986, Praeger, New York NY
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Forney, Kristine and Machlis, Joseph, The Enjoyment of Music, eighth edition, ©1999, W.W. Norton & Company, Inc., New York NY
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Hart, Mickey, Spirit into Sound: The Magic of Music, ©1995, Grateful Dead Books, Petaluma CA
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Rothstein, Edward, Emblems of Mind: the inner life of music and mathematics, ©1995, Random House of Canada Limited, Toronto Ontario
- Encarta Encyclopedia 2000, ©1999, Microsoft
P. 241, Emblems of Mind, Edward Rothstein, © 1995
