Notes & Lines discusses the
intersection of math, science, and technology with performing and visual arts.
Topics include bizarre instruments, technically-minded musicians, and cross-pollination of science and art.
Several months ago, an acquaintance decided to try out a
speech recognition software program to cure writer's block. He found it to be
quite "intelligent" for a $50 piece of software - the calibration process was
copious but effective, and the program supposedly "learns" based on corrected
mistakes in order to eliminate future mistakes before they occur. By his
account, the program was difficult to adjust to and absolutely mangled European
names, but on the whole he was happy with it.
Speech recognition programs fall within the realm of natural
language processing (NLP), which combines computer science, linguistics, and
artificial intelligence principles with an eye toward reliable interaction
between computers and natural human language. Like other AI fields, NLP has
made great progress but still leaves a lot to be desired. Language is heavily
rule-based but is also capable of great ambiguity, which of course leads to
difficulties even in human-to-human communication. Throughout history,
lexicographers and great thinkers alike have developed ambiguous example
sentences to demonstrate the subtlety and craftiness which makes human language
unique and baffling.
Ambiguity often depends on punctuation, as witnessed by recent
memes demonstrating the importance of commas using the statements "Let's eat,
grandma!" and "Let's eat grandma!" One of the earliest examples of this type of
lexical ambiguity dates to 1327. Shortly after the murder of Edward II of England
in that year, one of the king's prison officers received a note which read "Edwardum
occidere nolite timere bonum est." This statement could mean one of two very
different things depending on how it's punctuated. Place a semicolon after nolite
and it means "Do not kill Edward; it is good to be afraid of doing this", while
a semicolon after timere renders it "Do not be afraid to kill Edward;
doing so is good." The meaning of this note has been widely discussed for
Homonyms - words which share
identical spelling and (usually) pronunciation but have different meanings -
also contribute significantly to ambiguity. This phrase was crafted by William
Rapaport, a professor at the University of Buffalo, in 1972:
Through the use of homonyms,
Rapaport designed this grammatical sentence to appear nonsensical. The sentence
relies on three different forms of the word "buffalo": as a proper noun (the
city in New York), a noun (the large ungulates also known as "bison"), and a
verb ("to bully"). By interpreting these usages we can translate the sentence
as "Buffalo bison [that other] Buffalo bison bully, [themselves] bully Buffalo
The most common thread behind
miscommunication is syntactic ambiguity, or the simple fact that identical
sentences and words may carry different contextual meanings. A famous example
which plays on the words "fly" and "like" is the sentence pair "Time flies like
an arrow. Fruit flies like a banana."
Other instances include:
"We saw her duck."
"Flying planes can be dangerous."
"He saw that gas can explode."
Logical statements can be made
even more confusing by combining multiple ambiguities. For example, the
statement "The old man the boats" appears to be nonsensical because of the
common qualified noun "old man." By playing into our immediate assumption that
"old" qualifies "man," this sentence leads us to believe that it's gibberish,
but by rereading it and considering "old" as a noun and "man" as a verb we find
that it's grammatical. This sentence in particular serves as a kind of verbal optical illusion: by blocking out "the boats" we see the noun "old
man," but considering the whole sentence we interpret something completely
NLP will probably follow the same
old AI destiny: it can make inanimate objects appear intelligent, but
they still won't understand meaning or context. (Even Siri's legendary snarkiness is just programming, after all.) And, as this post
hopefully shows, even human-to-human speech can be impossibly confusing based
on misinterpretation of meaning and context. Besides, eschewing ambiguity would
also result in the loss of scores of classic jokes; ask Groucho about that one.
Image credits: Information Insights | Speculative Grammarian
As the eyes of the world shift from Russia and Sochi
following the 2014 Winter Olympics, it might be neat to focus on a sorely
neglected topic here in the West: Russian music. Most mentions of Russian
composers are buried in music textbooks and stand out due to their unpronounceable
names and tales of extreme poverty and alcoholism (sounds a bit like your first
frat party, doesn't it?). But the influence of many Russians - including The
Five, a circle of late-19th-century musicians who helped define Russian
nationalism - is still evident today. This group is particularly interesting in
that the backgrounds of all five men contain significant ties to science,
mathematics, and engineering.
The Five: Balakirev, Borodin, Cui, Mussorgsky, and Rimsky-Korsakov
Alexander Borodin is a prime example. He attended the Medical-Surgical
Academy in St. Petersburg and followed his education with several years of
advanced study in chemistry. In 1862, he received a professorship in chemistry
at the Academy and spent his days lecturing, conducting research, and as a
practicing physician. His research, including nucleophilic displacement and
other reactions of aldehydes, was influential. He independently discovered the
Aldol reaction in 1872 and is listed as a co-creator. The Soviet Union went so
far as to promote the 1939 Hunsdiecker reaction as the "Borodin reaction,"
claiming their long-deceased denizen did more significant work toward the
discovery than the Hunsdieckers did.
Borodin's aldol reaction and bust.
Borodin treated music as more of a serious hobby, but some
of his works are still performed today. His Slavic opera Prince Igor and the similarly exotic In the Steppes of Central Asia are regarded as cornerstones of
Russian nationalist music. The popular 1953 song "Stranger in Paradise" was
adapted from a Borodin melody heard in Prince
Cesar Cui, another of The Five, was born in present-day
Lithuania to French and Russian parents. He attended the Military
Engineering-Technical University in St. Petersburg for secondary and advanced
studies and devoted his professional life to the study of fortifications after
graduating in 1857. Cui became an expert on the subject: he published numerous
books and papers on military architecture and served as fortifications adviser
to the Imperial family. After a frontline assignment in the Russo-Turkish War,
he secured a professorship in 1880 and became a general in 1906. Cui's music is
less-performed than that of other members of The Five, and he is best
remembered as an influential music critic, producing nearly 800 articles over
the course of his lifetime.
Other members of The Five had similar backgrounds, but
ultimately attempted music as a profession, with varying degrees of success:
-Modest Mussorgsky attended Cadet School to facilitate a
military career but wound up working most of his life as a civil servant in
various offices. He's best known for his highly original pieces Pictures at an Exhibition and St. John's Eve on Bald Mountain (usually
known as Night on Bald Mountain).
Mussorgsky's professional and musical careers were both cut short by severe
alcoholism, which ultimately killed him in 1881 at the age of 42. His final
portrait painted days before his death, shown here, is often cited as a classic
depiction of the ravages of alcoholism.
-Nikolai Rimsky-Korsakov studied mathematics and
navigational sciences in St. Petersburg before ultimately joining the Russian
navy. He was soon composing full-time, however, and became one of the most
important Russian composers in history. His works, including Scheherazade, musical treatises, and
"corrected" versions of Mussorgsky's pieces, are frequently encountered today. (The
closing number from Disney's Fantasia,
in fact, is a hacked up version of Rimsky-Korsakov's edition of Mussorgsky's Bald Mountain.)
-Mily Balakirev, often thought of as the leader of The Five,
studied mathematics at university but immediately focused on music upon
graduating. He made his (meager) living as a piano and composition teacher and
burned out relatively early, breaking with The Five and suffering several
nervous breakdowns with periods of acute depression.
It's difficult to determine whether The Five's common roots
in math and science were due to their shared musicality or simply the state of
Russian education at the time. Interestingly, their works don't show a
particularly mathematical flavor as do those of contemporary pieces by Brahms,
for example. It's since been proven that there's a concrete link between
musicality and performance in math and science, so maybe the music came first?
Image credits: Naxos | John Wiley and Sons | Lafayette College
a musician, I am foremost a singer. I love to play my vocal chords.
Unfortunately, it's not always easy and fun to make music without an
instrument behind the singing. Enter the guitar, one of the few
instruments that allows the freedom to sing and play at the same time.
My first came into my hands about 9 years ago, and I haven't looked back
The acoustic guitar is one of the most versatile instruments ever
made, as evidenced by the use and evolution of guitar-like instruments
through the centuries. It is also (in my opinion) one of the most
beautiful sounding and beautifully made. The earliest "guitarish"
stringed instruments called tanburs date back to Ancient Egypt,
3500-4000 years ago. Designs changed as time passed and ideas were
passed through different cultures; most, like the European lute, were
small bodied with less than five strings. It wasn't until the mid 19th
century that the modern six string acoustic guitar began to take shape,
with Antonion Torres' invention of the classical guitar. The larger body
size and modified proportions improved the guitar's volume and tone;
over 160 years later, this design remains largely the same.
Dan Bouillez's new guitar design is an attempt to change that. His
guitar is shaped and sized like a regular guitar, with one major
difference - the soundboard.
soundboard on a guitar is the top face of wood where most of the sound
generation occurs. When a note on a guitar is played, the vibration from
the string is channeled through the bridge to the soundboard, which
then also vibrates and causes the tone to resonate into the body and
project (typically) out the soundhole in the center. Most acoustic
guitars have a fixed soundboard attached around its perimeter to the
The Bouillez guitar is different. It boasts a "floating" soundboard
that is not connected to the guitar sides at all, but instead is
connected to the rest of the guitar only at the bridge. The soundboard
is pressed against the neck block and tail block inside the body, and is
supported by the "downward and tensile force of the strings". In
addition, the soundboard uses a goatskin material, and its thickness is
1/10 of that of a normal guitar board. The Bouillez design allows the
soundboard more freedom to vibrate, supposedly creating clearer tones,
improved response, and better tone.
I applaud Dan Bouillez for engineering a unique alternative to
today's all-too-familiar guitar construction. But how does it sound?
After listening to this video
of Jesse Solomon playing the Bouillez, I think the sound has the slight
flavor of a banjo, fast response and clear tones but a bit metallic and
mechanical. Music is in the ears of the listener, of course, and to be
sure the music would be better with a higher quality recording. But take
a listen and tell me what you think.
Brian Eno has worn many hats over the course of his 64-year
life: glam rocker, experimental composer,
influential producer (for no less than David Bowie, Talking Heads, Devo, U2,
and Coldplay), artist,
and political activist. As of late, the English musician has brought his
unique talents to the completely different arena of healthcare.
Independent recently reported that Eno had installed two "ambient sound
installations" - for the purpose of creating a serene environment for patrons -
at the newly-renovated Montefiore Hospital in Hove, East Sussex, England. One
of the installations is generative
- created to constantly evolve and never repeat using complex algorithms -
while the other is a predetermined soundtrack album accompanied by ambient
lighting and art. (The image at right shows Eno with one the art installations
at Montefiore.) Public music installations are not unfamiliar to Eno: his
well-known 1978 album Ambient 1: Music
for Airports was devised to calm nervous fliers in airport terminals.
As an electronic music pioneer, Eno was instrumental in the
conception and development of both ambient and "discreet" (a term of his own
invention) music. Ambient music is defined as that which focuses more on sonic
textures than the more traditional cornerstones of rhythm and melody. Most of
Eno's ambient music is very slow and sprawling, with gradual musical changes.
(Eno himself has confessed that he typically plays and records his ambient
pieces at a normal pace, then slows down the tape.) Discreet music is a type
of ambient music - based on the eccentric "furniture music"
derived by early-20th century French impressionists - designed not
to be explicitly heard but to blend in with an environment and its surroundings
and be perceived like a piece of furniture. This probably explains why the
hospital was so eager to contract with Eno to enhance their "three-dimensional,
all-embracing means of treating patients" - the idea is for the patient or
visitor to be comforted and soothed without explicit awareness of what is
Just as Eno is no stranger to ambient music, the medical
profession is well-acquainted with the benefits of music therapy. Decades of
research has shown that music improves patients afflicted with mood disorders,
schizophrenia, aftereffects of stroke, Alzheimer's, dementia, and heart
disease, as well as children with developmental disabilities. If Eno's ambient
installations prove successful at Montefiore, I would hope other medical
centers follow their lead and proactively work to comfort those likely to be
experiencing stress or trauma.
Most would agree that the technological development of music
players during the past twenty years has been astounding. From the bulky
portable cassette players of my childhood through portable CD players, MiniDisc
players, and increasingly-smaller digital media players, portable music has
become ubiquitous in most international communities. It's perhaps not
surprising that noise-induced hearing loss (NIHL) is also on the rise and is
becoming an increasingly prevalent concern for both the medical and musical
The National Institute on Deafness defines NIHL
as damage to the inner ear from overexposure to harmful environmental noise. This
overexposure can take two forms. Acoustic trauma is defined as a one-time overexposure
that causes permanent damage due to high-intensity sounds like gunfire, a
single loud drum hit, or firecrackers. Gradually developing NIHL, on the other
hand, is caused by repeated exposure to dangerously loud sounds. This type
tends to develop as a result of combined sound intensity and time of exposure
to loud sounds. (I supposed the guy in this
well-documented case would place himself between these two extremes.) OSHA
states that exposure to 85 dB of noise for eight hours a day has the potential to cause permanent hearing
Most organizations recommend specific techniques to curb
NIHL, namely to first avoid exposure to excessively loud sounds as often as
possible (and let's face it, this is more difficult than it sounds). Many
industrial workers - including those working in manufacturing, agriculture,
transportation, and around aircraft - have little choice but to be exposed.
While ear protection standards is well-established in these industries, most
individuals planning to attend loud concerts or nightclubs skip ear protection
due to embarrassment, lack of comfort, and reduced sound quality.
The NIHL discussion becomes a little more interesting - and
controversial - when applying it to musicians. It may come as no surprise that
many (if not most) rock musicians suffer from resultant hearing loss, but
orchestral musicians and conductors are now considered susceptible as well. Hearing
researchers have avoided making broad generalizations because of the lack of
conclusive research, but many believe that musicians' exposure to sound levels
on par with harmful industrial noise renders much of the research on
occupational noise applicable to the art music world. The fact that orchestral
musicians depend on hearing themselves clearly to make a living, and therefore
are unable to use earplugs or other protective devices, adds an interesting wrinkle
to the debate.
Despite the lack of conclusive research, NIHL among
professional musicians and conductors has steadily increased in recent years.
This awareness affected me on a personal level: during my time playing in
college bands and orchestras, a longtime conductor was diagnosed with NIHL
after years of rehearsing large, noisy ensembles in rooms that were too small
and acoustically poor. Our school responded by installing temporary anechoic
panels in the same rehearsal spaces as a short-term solution, before eventually
renovating all rehearsal spaces to be acoustically safe under high decibel
levels. Several organizations have been founded to raise awareness of NIHL and
its effect on musicians as well as youth, including Don't Lose the Music
and Hearing Education and
Awareness for Rockers (HEAR).
Noise-induced hearing loss is perfectly avoidable, but even
for those already afflicted the prognosis is good thanks to improving hearing
aid technology. Thanks to awareness and forward thinking, advocacy groups are
causing us to think twice about constantly slipping on headphones or burning
out our car speakers with excessive noise.
The neural links between music, math, and technology have
long been studied and established, and a number of great inventors or engineers
have had side interests in the arts. This post will delve into the life of
Laurens Hammond, inventor of one of the most widely-heard electromechanical
instruments of the 20th century.
Laurens Hammond (usually referred to as "Larry") was a
tinkerer from a young age, and this interest led him to pursue a mechanical
engineering degree at Cornell University. After graduating in 1916, he worked
for several Detroit-area automobile manufacturers, although he continued to
invent on the side. In 1919 he invented a silent spring-driven clock, and in
1922 developed a 3-D motion picture projection system called the Teleview. Only one feature
film was made for this system, and although it was a great critical success the
economics of refitting theaters with new projection systems ended the
While working on the Teleview, Hammond perfected his skill
at designing and building increasingly small synchronous motors. In the late
1920s he used this skill to design an electric clock in which the motor was
synchronized with the current frequency of the power grid, resulting in great
precision so long as the current's frequency remained constant. Hammond
patented his clock and formed the Hammond Clock Company, which eventually
produced dozens of models and employed 700 people. Due to the Great Depression
and problems with patent royalties, the company ran into financial problems in
the mid-1930s. Hammond scrambled to invent a lucrative solution: he developed
bridge table that sold well enough to pay off outstanding debts, but this
proved to be a short-lived solution.
Hammond had long toyed with the idea that his synchronous
motors could be put to musical use. While developing the synchronous clock, he had
stumbled upon the fact that if a gear is rotated within a magnetic field, it
will theoretically produce a musical tone if connected to a speaker. (This was
a sort of precursor to the concept of a guitar pickup.)
If Hammond synchronized these "tone wheels" with the frequency of the power
current, the instrument would perpetually stay in tune. Hammond gutted a used
piano, worked with Hammond Clock's treasurer - who was a church organist - to
develop suitable tones, and in 1933 completed his first "Hammond organ." The
instrument contained 91
tone wheels, each of which was connected to nine switches. These switches
activated different harmonics of each tone wheel fundamental, effectively
producing nine different tones for each wheel. Using additive synthesis of
different waveforms produced by the tone wheels, the instrument was capable of
hundreds of different tones and musical colors. Hammond added drawbars, based
on a church organ's register system, so that the performer could precisely
select and alter the organ's range and sound on the fly.
Hammond patented the instrument in 1935, and it was an
immediate success. Churches jumped on the Hammond organ because it was cheaper,
lighter, and easier to maintain than traditional pipe organs, and could
replicate many of the latter's complex layered sounds. The instrument
eventually made its way into jazz and rock, is
featured on various landmark recordings of the 60s and 70s and was revived in
the 90s and 21st century.
Although Hammond developed his own corresponding speaker system, most Hammond
players took to the Leslie
speaker, which was built with a rotating horn to enable a swirling Doppler
Hammond organs were eventually redesigned with transistor
circuitry, but most players still gravitate to the antique tone wheel models.
Interestingly, many design flaws that Laurens Hammond tried and failed to
correct - such as a percussive key click and unintended
crosstalk interference between rotating and stationary tone wheels - are now
highly valued by studio musicians and collectors as integral parts of the
Laurens Hammond was an eccentric fellow who never expected
or enjoyed the fame his invention brought him. He was intimately involved in
the Hammond Organ Company into his later life and also forayed into economics,
publishing an 80-page pamphlet about mathematically eliminating unemployment;
this publication understandably did not catch on. Hammond died in 1975 with
over 100 patents to his name. I find it interesting that, whenever I appreciate
the sound of a Hammond organ, I can thank Larry's bankrupt clock company and
ingenious mind for its invention.