Dear gcse,
Music and mathematics are indeed languages. To see why this is so,
consider the uses to which we commonly put a conventional language such
as English. We use language to: (a) make announcements and greetings;
(b) exchange and record ideas; (c) tell stories; (d) decorate and
amuse. These attributes are surely necessary in any language, and they
are also sufficient to qualify a medium as a language. Furthermore, they
do not constitute an excessively loose definition. It is impossible to
say on the basis of these criteria that football is a language, for it
is not a means of recording ideas, and food does not qualify because
it is not amenable to telling a story. We show below that music and
mathematics possess all four attributes of language.
Let us begin with music, the more accessible if not the more important
language of the two. In the earliest days of humanity, music took on an
annunciatory function that has persisted into civilized times. Consider
the bugle call issued at the beginning of a hunting expedition to
summon all participants to the chase. Although primitive man used an
instrument no more sophisticated than a hand cupped to his lips, he,
too, must have instinctively used a simple tune to announce that the hunt
was on. Musical greetings were prevalent in the ancient civilization of
Rome. The more important the subject, the more elaborate the melodies
and instrumentation. To greet a simple gladiator striding into the
arena to face death, a trumpet fanfare sufficed. But when a victorious
general returned from quelling the natives in some border province,
twenty flutists and forty singers would accompany his march into
the city. Music becomes especially important as a means of greeting
or announcement when visual means of communication are hindered
by environmental circumstances. The singing style known as yodeling
developed in the Swiss Alps as a musical way of defeating the distances
and echoing acoustics of the mountainside. When a heavy fog lies on the
water, a tugboat will sound its piercing steam whistle to announce itself
to captains who want their ships towed into harbor.
To announce oneself or to greet another is a fairly simple affair,
accomplished in English with only a word or two. Yet music is capable
of expressing thoughts of greater subtlety and complexity. Most of the
ideas expressed in Western music are emotional instead of rational, but
they are ideas nonetheless. The notion of peace, for instance, is given
full expression in Debussy's La Mer. The contrary one of war is imparted
by Tchaikovsky's 1812 Overture. Mozart's Requiem encapsulates the idea
of mourning, and Handel's Messiah conveys that of joy. Music is so well
suited to communicating one's state of mind that we often use it in the
midst of everyday conversation in lieu of words. There is a simple melody
we can whistle to show surprise, and another to express admiration. To
say that we are happy, it suffices to sing la-la-la in high tones;
to manifest indecision, we hum a pair of low tones. Indeed, the powers
of melodic communication give a serenade its allure and permit us to
understand an operatic aria or a foreign pop song without comprehending
its words. Let us not forget that in addition to melody, music has
rhythm. This, too, serves well for communication. In jungle societies,
ideas were transmitted over great distances through drumming. A rhythmic
passage served to tell a neighboring tribe of an imminent wedding,
to inform them of the results of a hunt, or to bring tidings of war.
When we have several ideas that we string together in a fashion that is
revelatory rather than discursive, we end up with a story. Music does at
least as well as mere words in fulfilling the narrative function. This
is why an opera production is equipped with an orchestra, a movie with a
soundtrack, a traveling storyteller with a guitar. There are universally
understood musical conventions for making transitions from scene to scene,
but the action of a scene can be carried by music alone. It is possible
to follow the narrative of a wordless Tom and Jerry cartoon with one's
eyes closed. Indeed, it can be said that the classic American cartoons
are accompaniments to their music rather than the other way around. When
we think of stories told by pieces of classical music without the use
of any words, the most prominent examples are those by Rimsky-Korsakov
and by his student, Prokofiev. Rimsky-Korsakov is most famous today for
the Flight of the Bumblebee, which is but one passage from his Tale of
Tsar Saltan. Prokofiev is well known for Peter and the Wolf, in which
each character is represented by a particular instrument and the story
is told by blending their voices.
The most important use of music is ornamental. Music is a wordless poetry
that decorates and beautifies and generally distracts us from the grim
duties of quotidian living. This is also an essential function of spoken
language, but one that suits music as well if not better. Music is to
words as watercolors are to ink. It is difficult to conceive of a wedding
without music. A funeral is best accompanied by a dirge. It is important
here to make a distinction between the announcement or the idea of death
-- these being expressed by the convened mourners' black garb and by the
mere presence of a choir or a lone bagpiper -- and its ornamentation by
the hymn that is sung or the tune that is played. A rhythmic tune helps
along a column of soldiers on the march, while a peasant in the field
keeps time with repetitive whistling or humming. The aseptic aisles
of a supermarket and the confines of a dentist's waiting room are made
tolerable by music piped in through loudspeakers. Birthdays, graduation
ceremonies, celebrations of every kind are accompanied by music. And who
can deny that the attractions of one's childhood home include not only
warmth and light but mother and father's favorite melodies drifting from
the phonograph in the living room through the doors and down the hallways?
Let us turn our attention now to mathematics, that most severe of
languages. Of the four criteria, it is most difficult to make a case
for the annunciatory function of math. It appears that no one but the
pathologically scholarly would attempt a greeting in the language of
math. Yet mathematics is the means by which we as a civilization propose
to announce ourselves to extraterrestrial life forms. When the unmanned
spacecraft Voyager 1 and 2 were launched into space in 1972, they each
bore an externally mounted plaque on which are inscribed symbols with
which Man declares his intelligence to any aliens who may chance upon
it. The eminent scientists Carl Sagan and Frank Drake designed this plaque
so that, in addition to pictorial representations of our world and our
species, it would make an announcement using the universal language of
math as both medium and message. The mathematical portion of the Voyager
greeting, shown below, proves that where words and pictures may fail,
math prevails.
NASA: Jet Propulsion Laboratory: Scenes From Earth: Mathematical Definitions
http://voyager.jpl.nasa.gov/spacecraft/images/image003.gif
The foremost use of math is the expression of ideas. Indeed, it is by
definition the most precise language for stating facts in geometry,
algebra, number theory, calculus, computational theory, combinatorics,
topology, and further and higher branches of knowledge. Not only the
strictly mathematical is expressed in the symbology and grammar of
math. Engineers use it to make observations on the properties of bridges,
buildings, and electric circuits. Computer programmers use mathematical
language to express directives that are subsequently translated into
machine code and executed at lightning speed.
But math can also carry a narrative. In the early days of philosophy,
the ancient Greeks used mathematical syllogisms to trace the path of
an argument from premises through to conclusion. Just as a comedic or
tragic story is made to hang together with turns of plot, syllogisms are
the connective tissue of a sound piece of apologetics. In commerce, too,
numbers tell a story. The financial report issued quarterly or annually
by a corporation to its stockholders is a mathematical narrative of the
company's doings. The paper tape emitted by a cash register at day's
end tells the story of the day's sales, transcribing the ebb and flow of
customers through a list of decimal numbers. The stories most frequently
told in mathematical terms are those that concern math itself. It is one
thing to make a statement, but quite another to prove it. When someone has
told a credible story in mathematical language about the provenance of a
mathematical statement, then and only then is it accepted as fact. Such
a story is known as a proof.
Finally, math is used to decorative effect in two-dimensional and
three-dimensional form. The Islamic art of medieval times is characterized
by its geometric effects in which polygons and harmonic curves are used
rather than figurative shapes. Cubic sections and regular prisms are
used to ornament Christmas trees, wedding cakes, conical wizards' hats,
civic buildings, and school hallways. Formulae themselves are objects
of beauty. The impenetrably intricate equations of calculus work well
as wallpaper.
In conclusion, music and mathematics are languages because they fulfill
the four essential requirements of language. They both have the functions
of announcement, expression, narration, and decoration.
I have enjoyed addressing this question on your behalf. If you feel that
any part of my answer requires correction or amplification, please inform
me through a Clarification Request so that I have chance to fully meet
your needs before you assign a rating.
Regards,
leapinglizard |
