LAIS people are language

People
are
Language
18th April, 2015
by
Dustin R. Burchett
Colorado School of Mines
Abstract
The purpose of this paper is to develop the idea that mathematicians
and musicians are more similar than the definitions of each give
credit to. We will treat each as a separate culture, and draw isomorphisms
between the two through testing and analysis. The similarities
between mathematicians and musicians are beyond just similarities
in communication techniques; both cultures require definition and
pursue the description of the world to achieve satisfaction. This
paper should be viewed by someone who wishes to know more about
mathematics and those who practice it as a culture.

Contents
1 Mathematicians and Musicians, Isomorphisms 3
1.1 Overview of Premise . . . . . . . . . . . . . . . . 3
1.2 A Quick Look at the Depth of Music . . . . . . . . 5
1.3 Isomorphisms Emerge . . . . . . . . . . . . . . . . 6
1.4 How to Capture the Physical Data . . . . . . . . . 6
2 Data Capturing 9
2.1 Intent . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Technical Aspects on Data Capturing . . . . . . . . 10
3 Synopsis 13
3.1 "The Fedora" Math in Music Series Results . . . . . 13
3.1.1 Dr Jon Collis . . . . . . . . . . . . . . . . 14
3.1.2 Dr Paul Constantine . . . . . . . . . . . . . 15
3.1.3 Data Loss . . . . . . . . . . . . . . . . . . 16
3.1.4 Prof Rod Switzer . . . . . . . . . . . . . . 17
3.1.5 Prof Scott Strong . . . . . . . . . . . . . . 18
3.1.6 Dr Stephen Pankavich . . . . . . . . . . . . 19
3.1.7 Dr Mike Nicholas . . . . . . . . . . . . . . 20
3.1.8 Prof Jon Cullison . . . . . . . . . . . . . . 21
3.2 Conclusions . . . . . . . . . . . . . . . . . . . . 22
3.2.1 The "Tribe" . . . . . . . . . . . . . . . . . 23
3.2.2 Isomorphisms . . . . . . . . . . . . . . . . 24
3.3 Further insight . . . . . . . . . . . . . . . . . . 26
4 Addendum: Future Work and Considerations 27
1

Chapter 1
Mathematicians and
Musicians, Isomorphisms
Mathematics: the intellectual conversation that happens between
man and universe. Based upon a set of rules and definitions, mathematics
in all directions is the language that connects truth and reality
within the Universe to interactions between physical phenomena and
the people that witness it. Without mathematics, there is no underlying
reason behind how or why things are. Even without numerical analysis,
mathematics sets a foundation of logic that acts as a barrier between
what is true and what is fallible.
1.1 Overview of Premise
More than just a tool of logic, mathematics is a type of communication.
In fact, mathematics isn’t far removed from other forms of linguistic
communication, such as English. English is what linguists and mathematicians
alike call a recursively enumerable language. Technically speaking,
this is what sets the difference between a codified language such
as mathematics or music (called context sensitive languages), and
a language like English. A recursively enumerable language speaks
to the uncountability of combinations of words and phrases that
can occur in such language. In contrast, a context sensitive language
can only be formed based off ideas from a recursively enumerable
language, so as a byproduct the combinations of words and phrases
are a mere subset of the latter [1]. However, the differences are
negligible (more so irrelevant) for this paper. The important idea
3

4 CHAPTER 1. MATHEMATICIANS AND MUSICIANS, ISOMORPHISMS
to grasp from this is that any codified structure such as mathematics
or music is, in effect, a language. In fact, this idea is what
has led me to study a particular group on campus that has their
own language: the professors of the Applied Mathematics and Statistics
department.
Since every culture has their own "language", it is important
to analyze its formation, and impact of its application in practice.
Realistically, we need not consider the formation and origins of
the mathematical language. But, briefly, mathematics is an ancient
yet ever-growing blend of Arabic, German, and English symbols that
remains pretty consistent throughout many cultures without much
distinction. Hence, we will take a broader look at the culture
surrounding the mathematicians here at Colorado School of Mines,
and consider mathematics as a language subset of English (i.e. everything
in mathematics can be defined literally by a specific grouping of
English words). This leaves us with examining the impact of its
application and not necessarily its formation. Part of the question
that needs to be posed is, due to the structure of the mathematical
language, does learning it as a cultural staple lead to a difference
in musical preference and interpretation? More succinctly, does
a mathematician view music in a specific way due to a codified language
and, also, what are the commonalities between how mathematicians
describe the world and how musicians describe the world that may
be unique from the rest of the world?
In order to do this, we can analyze the music preferences of
some of the individuals in the group; our newfound "tribe" of mathematicians
can be used as study material for empirical data. The goal of this
particular study is to ensure quality and thorough record of multiple
applied mathematicians, in regards to both math and music background,
and then to analyze the obtained data. Each personality should
bring together different, perhaps even disjoint, qualities to be
presented for analysis. The commonalities that will exist between
multiple subjects are more than likely to be abstract, e.g. none
of the mathematicians may have a repeated artist that is liked,
but perhaps there remains an isomorphism between why a particular
set of artists is preferred. Just because one person likes Buckethead
and another prefers JoJo Mayer doesn’t mean those artists aren’t
effectively the same for each person. It is conceivable that one
person is a guitarist and one person is a drummer, making the appeal
of each artist the aspects of technical ability or maybe pattern-building

1.2. A QUICK LOOK AT THE DEPTH OF MUSIC 5
in the music. This would be a trait that is commonly shared between
one artist to the next, or if it isn’t shared then it is contrasted.
Point being, the goal is not to isolate an era, genre, artist, or
set of instrumentation preferences for the math department as a
collective, but to utilize an assumption that the implications of
the music, moods, uses, or even origins of the music is more revealing.
If the rest (being genres, eras or instrumentations) come out to
be correlative, then it can be used--but let that not produce misassumptions
by mixing correlation with causation.
1.2 A Quick Look at the Depth of Music
As we looked a little bit at "codifying" languages, we have drawn
a simple, assumed, isomorphism between mathematics and music as
languages. Hence, it will be useful in the future to use the study
of the connection between mathematicians and their musical intrigue
as a means to gain insight to the math culture (as a side-note,
think inverse problem). To do this we need to take a closer look
at the isomorphism (evaluate the connection through the study of
the elements being connected), and hope to be assured that there
exists a strong possibility for mapping to and from each element.
In particular, we will create a pool of information on the music
side that we will use later as a base to construct how to interpret
the data gotten from the mathematicians.
It is difficult to pinpoint the origins of music. Without doubt,
the original intents for music are incredibly varied. Religion
and work motivation were likely the first uses of music as it came
to be more realized. With spirituality being a large part of music
throughout the ages, societies would use music to get closer to
nature as well as to become closer to each other in a community.
Of course, music was also used for learning, as to help people memorize
scripture. For a long time, however, music was regarded less of
an art, and more of a tool. Eventually, being a musician was a
profession in entertainment, but an artist would typically compose
and perform all their own music--making their music die with them
or forced to be carried on through the word and interpretation of
others. Once music became a written and codified substance, music
became art: a competition for beauty.
At this point the merging of intangibles, a sequence of specific

and deliberate ideas makes a collection of sounds become music.
Where sound exists as a series of pressure differentials in air,
it simultaneously exists as an ordering of the mind and emotion
when it is music. The music language, coded formally by Bach perhaps,
is an attempt at bringing largely abstract and subjective pressure
differentials into a concrete world designed by rules. It is thus
a musician’s job to view the world in light of this codified language
and draw connections between one abstraction and another abstraction.
Also, it is then important to strengthen definitions and rules,
add reinforcing qualities to what is known, in order to keep an
ever-evolving grasp on what everything is and how it exists [2].
1.3 Isomorphisms Emerge
Is it then hard to see that a connection between mathematics and
music could exist, if not by nature then by application or fortune?
One should not need to be both a musician and a mathematician in
order to build a bridge between the two (though, any person who
is one or the other should be able to walk upon that bridge without
toll.) In other words, it may be helpful to determine your own
eye-colour by asking someone else to look at them for you, but a
similar result can be achieved by looking in a mirror. A mathematician
may be able to look at music in the exact way a mathematician looks
at everything whilst retaining accuracy in its interpretation. The
description a mathematician may give on behalf of a musical note
or series of rhythmic patterns may not appear on first glance the
same definition as a musician gives, but may very well be the same
description.
This is what we can use to our advantage. The same bridge that
is built as a musician in communication may be built as a mathematician,
if not painted a different hue or tinted with a thicker paint. We
will travel to both ends of bridge built by the mathematics-based
"tribe" and compare it to the bridge formed by the musicians in
order to gather the required information.
1.4 How to Capture the Physical Data
To start, this project will be funded in resources through Mines
Internet Radio. As an excuse to get the tribe recorded, interviewed,

1.4. HOW TO CAPTURE THE PHYSICAL DATA 7
and observed, we will host different members of the mathematical
family here at Mines on my personal radio show, "The Fedora". This
method is hypothesized to be culture-preserving, meaning there should
not be any damage to the culture in any way, and what is observed
from the culture will be pure. This is a byproduct in the design
of how the interviews will be setup. Every contestant on the show
will be there voluntarily. Aside from bias accrued from "showing
off" to a public audience, there shouldn’t be a disturbance in the
cultural aspects on the interview in any way (and even that phenomena
could be described as culturally significant).
Typically this manner of interviewing will occur one at a time,
though in the case where multiple are interviewed at the same time
there shouldn’t be any major differences. In fact, this should
be at least once achieved as an interaction between multiple members
of the community can be observed and extrapolated upon.
Interviewing will be an important aspect to each interaction.
Interviewing will occur on the spot, so that instinctual answers
can be given, and recorded. The questions will contain a variety
of topic manners, including (but not restricted to): general hobbies,
strengths and weaknesses within the [math] community, math background,
music background, etc. The questions are meant to vary between
person to person, such that a wide variety of information can be
extracted from the community over time. Variations within the answers
could lead to certain biases, but we will assume that unless obvious
reason, each subject has some positive value of being representative
of others in the community.
Each interview will be captured via standard radio-show microphones
(as mentioned, they will be provided by Mines Internet Radio). There
should be seven interviews, totaling at least 10 hours of contact
time with the "tribe". Each member will also be suggested to bring
in a playlist of nearly an hour long to be shared with people listening
to the radio, and during this time there will be ample opportunity
to study the reactions to the music each professor has, as well
as ask them more personal questions and interact even more candidly
off-air. This interaction will not be recorded, though will still
hold great value to the study.

Chapter 2
Data Capturing
Broken down, the purpose of this study is to:
1) assume a culture (being the Applied Mathematicians on
campus here at Mines),
2) directly target what makes this culture unique, and
3) map those traits to that which is unique to musicians
(as an assumed culture) by isomorphism (using 1 and 2).
2.1 Intent
Item 3 is especially important, as finding results that positively
support this will establish a bridge between the math world and
the music world; it will bring two unique cultures just a little
bit closer together. In application, this could mean that the communication
between two subsets of people drastically increases and, hence,
increases production of either side as well as expands the variety
of output on either side. In this study, I will be taking the observational
role of "musician", where I establish a generic pool of traits that
belong to musicians, and then I will participate in a field study
as to get closer to the community of mathematicians on campus. Of
course, my roots in math cannot be set aside during this study,
even if I consciously tried. This should not be a hindrance as
many people invoke a cultural study as a means of becoming closer
with their own heritage. The typical biases produced by this relation
might be that there is less of a chance of criticizing one’s own
heritage (though that will hopefully be nullified as it is consciously
9

10 CHAPTER 2. DATA CAPTURING
recognized), but also that there is more motivation to study said
culture (which is not a hindrance to data collection or interpretation,
so that need not be avoided). I will be treating the mathematicians
as a foreign, but not disjoint, entity that I need to gather data
from as objectively as I can.
In concept, what physically needs to be done is to gather information
on mathematicians based off things in their world, and then also
gather data on what they think about the music world (my world).
In some cases, it may be readily available that a mathematician
has set foot into "my" world. In a broader sense, I am taking data
from a subset of people who positively identify as a certain subset
of people, even though they may secondarily identify as something
else (so the sets upon inspection may not be mutually exclusive).
This is fine, as cultural studies today often have a similar modernistic
twist in which there are a very few amount of people in any culture
who are actually "pure" to one culture. There exists many dilutions
due to how media diffuses, technology is spread, and information
is gathered. Studying these dilutions still gives us relevant data.
2.2 Technical Aspects on Data Capturing
Not much hardware and technology is actually needed to accurately
capture this "tribe". Since all the interviews are volunteer only,
there is no need for fancy, sleuthing tactics or technology for
data capturing. In fact, the recording techniques come from the
microphones and resources available at Mines Internet Radio, where
I will be conducting the interviews.
Mines Internet radio has three studio microphones available for
use with producers and DJs. Luckily, I am both so I get to use
them when I need to. The microphones are all Shure-SM27s. They
are multipurpose microphones, good for a studio that cover a wide
range of purposes. The reviews on this particular model are nearly
perfect. For 300 bucks, a person can own a microphone capable of
capturing voice and guitars with outstanding quality, and even act
as good overhead microphones on a drum set. The range has an extended
low end range for recording, which helps boost clarity for instrument
recordings, but really the one thing it shouldn’t be used for is
recording something that is prominently bass [3].
The Shures extend the microphoning area by having a large diaphragm

2.2. TECHNICAL ASPECTS ON DATA CAPTURING 11
and uses a cardioid pattern on the sides. The microphones are condensers
and have "superior transient response" according to their website.
Also, there is a large reduction in unnecessary "white noise" picked
up by the microphone’s self-noise, and there are three layers as
the mesh of the contact area for sound pickup--making the microphones
good at reducing wind and breath noises [3].
All in all, the microphones are pretty universally regarded as
impressive for their price. For use, there isn’t much that needs
to be considered when recording the mathematicians. As in every
good radio show, there is certain etiquette that serves as an effective
guideline between user and tools. Of course, since the mathematicians
will be on my radio show "The Fedora", this will be considered.
First off, all spatial adjustments to the microphones need to be
made prior to the recording of the shows. If microphones are adjusted
during recording, there will exist a series of loud crackles and
pops between the microphone and the input interface. This is bad,
as they are not just unwanted sounds but the are sometimes uncomfortable
to listen to because of clipping. Another key element of recording
is pre-gain editing. It is important to engage the person being
recorded in a candid sense in order to achieve their dynamic decibel
range. (If I was to tell you to whisper and yell into the microphone
then I would be preparing for an unrealistic decibel range, which
would result in a loss of clarity for the actual representative
range. Hence, a candid range during a normal conversation in preparation
of a slightly wider dynamic range typically yields better results.)
Once a dynamic range is set, it is important to also evaluate
the dynamic range of the recorded music presentations asked of the
mathematicians. Except for in rare, typically unique, cases, the
music is played by auxiliary port on the mixing board from the mathematician’s
very own computer. Since the music they play is likely not normalized
to the same volume, then some songs are going to be compressed to
a louder volume than the previous. The goal in every radio show
is to maintain consistent volume between the talking, to one song,
and then to the next song. Luckily, there are tools at my disposal
to do this.
The process isn’t so bad. First, I will maximize my volume on
the aux channel, and ask the mathematician to minimize their volume.
Then, I have them slowly increase volume until I just reach a peak
on my recording. This gives me a pretty good upper bound that I
can finely tune to fit the exact song using a fadein.

Chapter 3
Synopsis
The physical data has been all captured at this point--at least
to a point in which the data has become "usable". The sample size
for the data is objectively small, though we will consider it to
be representative of the entire Applied Mathematics and Statistics
group here on campus. In fact, the relative size is fairly high
which will give us some good bearing on the weight our conclusions
carry. In the following section, we will take a brief look at each
candidate and review the data we collected. In the next section
we will explore the analysis of the captured data. In particular,
we will derive conclusions based off the given information.
3.1 "The Fedora" Math in Music Series Results
Below is a short overview of each interview that was conducted for
this study. Included in each is a background on their profession,
what they do at Mines, and then a little bit about their obvious
connections with music. Then, the relative summary of the playlists
they brought in will be explored and then brief summary of interactions
with that professor both on and off air. Each professor (excluding
one) will be introduced with a direct quote, in which I have asked
them to describe any one thing of their choice (be it a concept,
person, place, feeling, etc.) in 3-5 sentences. The interviews
will be included with the paper in hardcopy, as audio, along with
a few compositions from two of the professors via DVD.
13

14 CHAPTER 3. SYNOPSIS
3.1.1 Dr Jon Collis
Jon Collis:
Green’s function: In mathematics, a function that represents
the particular solution to a different equation in response
to a delta function, i.e., an impulse, forcing term. In
electrical engineering, a Green’s function is used in signal
processing to represent the time series associated with
the measured source signal. In geophysics, a Green’s function
is the time series collected by a seismometer, representing
the source event, for example an earthquake [5].
Dr Jon Collis is the acoustics specialist here on campus, or
an "acoustician". His primary responsibility within the department
is to do research, namely in underwater acoustics. In the department,
he teaches Differential Equations, but has also taught higher-level
classes such as Applied Mathematics (graduate level). He claims
to be an avid outdoorsman, lives in Boulder, and enjoy watches "nerdy"
movies and shows. Jon Collis considers himself removed from the
musical community in terms of playing instruments. He tried to
pick up piano as well as recorder when he was younger but came to
the conclusion that he had "no beat and no rhythm", which forced
his prospects elsewhere. When asked what instrument he would choose
to become a master at, he chose the clarinet.
Currently Dr Collis is an avid jazz fan, and he even supports
his local jazz radio. Inspired by the "heart and soul" of jazz,
Collis decided to put a playlist of afro-cuban music on air to showcase
his involvement in music. The playlist consisted of about 45 minutes
in length, and was fairly pure in terms of sticking to the selected
theme of afro-cuban. The playlist included American Jazz roots
such as Miles Davis (and we talked extensively about Herbie Hancock),
but also had more fine-tuned cultural jazz music stars such as Benny
More and Los Camelos Blancos.
The selection process that Dr Collis went through to find music
for the playlist wasn’t necessarily clear cut. He described his
tastes as being "ever-evolving", and though he had plenty of favourites
in the genre of jazz, he wanted to provide something that less people
were familiar with. Some of the songs, being actually Cuban, are
supposed to hold cultural significance--which is why Collis wished
to play them. Some talk about reviving the heritage of traditional

3.1. "THE FEDORA" MATH IN MUSIC SERIES RESULTS 15
Cuban music, while others sing about revolution. The second track
on the playlist by Fela Kuti (Nigeria) is a historical autobiographical
afro-tune, in which Fela Kuti describes how his mother was killed
by Nigerian politics, so there is obvious cultural and sociopolitical
insight given to Nigeria that Collis wanted to share on air.
The rhythmic element of jazz is typically very intricate. I
would have to say, however, that as a person who doesn’t listen
to any Cuban music, hearing it play as a variation of a "jazz-type"
genre, I thought the music was even more so rhythmically intricate
than I give average jazz credit to. I was a little impressed with
Collis, because though he claimed not to be a musician, there was
an obvious "feeling" about and towards the music that was played.
Off-air, he was tapping on the table and dancing in his chair a
little bit. On-air, he had plenty to say about each artist and
could provide historical references and cultural significance of
each song.
3.1.2 Dr Paul Constantine
Paul Constantine:
My inbox is full. It’s an unending to-do list. Some things
are urgent. Some are important. Some of the things get
lost on the second page, forever invisible from view. Only
Google machine marketers know the inner thoughts of my
inbox’s second page. [6]
Dr Paul Constantine is a new professor within the math faculty
family. With just under two years of Mines experience , Constantine
seems to have grown to be a shining young math professor, valuable
at Mines through his research and knowledge in "uncertainty quantification"
and "active subspaces" (in fact, just over a month ago Constantine
released his first book, which is called textitActive Subspaces:
Emerging Ideas for Dimension Reduction and Parameter Studies).
Dr Constantine began his collegiate journey generally undecided
in what he wanted to graduate in, at a Baptist university in Arkansas.
He initially came in thinking he was going to work on behalf of
the church under a double major of philosophy and physics. Quickly,
within a year, he decided that that path was not the correct path
for him. He moved to Texas A&M (where he began playing the drums).
Before finally settling in mathematics, he switched to just a single

major in physics, bounced around the idea of doing economics, and
then quit at A&M to go to Europe for a few months (funded by selling
his car). Interestingly enough, Constantine decided to go back
to school (University of North Texas this time), and then finally
fell in love with math in which he graduated with a bachelors in
mathematics, and a minor in music. Dr Constantine explained that
he did math to get a good job, but did music because it was something
he loved.
Dr Constantine started playing music in college, being trained
professionally by the jazz program at Texas A&M, played a little
bit of piano along the way, and then graduated in math with a minor
in music. Dr Constantine enjoys a range of genres in music, including
but not exclusive to Grunge, funk, and even classical. However,
Constantine is an afro-cuban percussionist and hence enjoys that
genre, and jazz, the most.
The playlist this professor brought in defiantly characterized
the range of music that Constantine was inspired by. Lots of afro-cuban,
some jazz, a little bit of hip-hop and catchy licks of the recent
years was thrown in, as well as some Squarepusher and a song that
Constantine himself wrote, reflecting some of the techniques Squarepusher
utilizes in his song writing. In college, in addition to playing
in a few bands, Constantine composed and mixed an album called textitWhat’s
Your Condition Number? under the alias ILL-CONDITIONED (a reference
to a branch of math theory). This album is electronic, with a late
90s techno feel and obvious Squarepusher, and Aphex Twin allusions.
On air, Constantine was comfortable and bright in demeanor. Off
air he wasn’t much different, and out of all the Professors probably
had the most laughs. A lot of things were discussed about music,
including the differences of genres, classifying the kind of people
who listen to particular sets of music, and even analyzing differences
of the importance of historical figures in music such as Mozart
and Beethoven. Dr Constantine was also very literate in music,
such as Dr Jon Collis was about the music he brought in.
3.1.3 Data Loss
Unfortunately, the recording for Switzer and Strong were on the
same file, and it got lost due to storage problems on MIR’s computer.
Hence, the data has not been able to be reviewed. Luckily, I have
the playlist of each professor, as well as a CD recording from Prof

Switzer. This was a n unexpected hiccup in the interviewing process,
and it should be noted that the data I will be citing is entirely
from memory.
3.1.4 Prof Rod Switzer
Prof Rod Switzer went to school in Minnesota, and graduated with
a Master’s degree in mathematics, and a minor in music. Switzer
has been working as an adjunct at Mines for quite some time, teaching
a range of classes since he started. Now, mostly, Switzer teaches
Calculus classes.
While talking one on one with Switzer, it seemed apparent that
Switzer’s heart lied more in music than in math. Switzer started
playing music prior to college, but once he was in college he became
involved in the school radio, as well as played in a few bands.
Like Constantine, he plays drums and piano primarily and considers
himself more of a drummer, but has also had a little bit of experience
with the trumpet. Switzer also has his own part in a band called
"Patch", in which he is the drummer and primary studio-mixer/producer.
Switzer has a recording studio in the basement of his house, and
reportedly has produced for a set of other artists in his spare
time.
But his musical resume doesn’t give good insight into his play
in music. Even being several generations apart from me, and never
having me in any of his classes, upon the first meeting Switzer
was exited to share with me a text on the relations of math and
music called textitMusicmathics (and let me borrow it for an extensive
amount of time). Also, he was more than happy to burn a copy of
his CD for me textitPatch (self-titled). He even gave me insight
on a few record festivals and upcoming concerts that he was signed
up for, and gave me invitation to see the collection of records,
music memorabilia he kept in his recording studio when I expressed
interest in some shared band interests (he allegedly has nearly
5000 CDs and at least 1500 vinyls).
His playlist was one of the most distinctly unique in regards
to the other professors. The span of music ranged from music in
the 1950s or so to the 1970s or so, nearly 20-30 years prior to
most of the other professors, on average. However, this was not
the most interesting aspect. Almost all of the music that was brought
in held some sort of whimsical or numerous value to it. The theme

of his playlist was "Things I liked to listen to in college", and
all of it was very good-feeling, smile invoking music. (This will
be touched on later in analysis.)
3.1.5 Prof Scott Strong
Scott Strong:
The powers that be force us to live like we do and bring
me to my knees when I see what they’ve done to you. But
I’ll die as I stand here today, knowing that deep in my
heart that they’ll fall to ruin one day for making us part.
I found a picture of you, those were the happiest days
of my life. Like a break in the battle was your part,
in the wretched life of a lonely heart. [8]
Scott Strong is currently working on his PhD during his professorship
at Colorado School of Mines. He has taught classes ranging from
Calculus to Advanced Engineering Mathematics, and is typically regarded
as one of the most fun teachers on campus. This is his native school,
as Scott Strong graduated from here with his math degree initially.
Now, Strong holds some power within the department as one of the
department heads.
Scott Strong actually came on air just after Rod Switzer, though
Rod Switzer and Scott Strong are close knit when it comes to music-speak
so Rod Switzer decided to stick around. Apparently, the two talk
about music quite often and even inspire each other to find new
music outside of the other’s generational knowledge. Scott Strong
had requested not to break up any of his music except for perhaps
right in the middle, because his philosophy on radio time was that
people come to listen to music, perhaps while they are working,
and deserve a non-interrupted song list. Hence, aside from the
initial interview there was little to no interaction on air and
the focus of my study was conducted mostly off-air observing the
two professors converse about music.
The playlist was difficult for Strong to make. He said that
he had a hard time finding the right "vibes" he wanted to portray
in his mix. Because MIR has a strict policy on lyrics, Scott Strong
had to significantly filter the material he wanted to play. Scott
Strong thinks that music should be emotionally charged, and that
a lot of early rap from the 80s and metal from the similar era was

about rebellion and fighting for good causes. However, since most
of those songs included profane lyrics, he couldn’t play any of
it. Aside from this issue, to make a playlist that is about an
hour in length is really limiting to what one can express.
Scott Strong doesn’t really have a big musical background. He
may have played a little bit of grade-school band, but he never
continued playing through college. Granted, he can tell you quite
a lot about music technology and, as the previous professors can,
ramble quite a lot about music history and background on current
musicians. However, Scott Strong was the only one to bring an actually
"mixed" playlist. He gave it to me as a lossless compression wave
file, and the file included his own fade outs and EQ--making not
just an interesting playlist, but a list of songs that flowed into
one another, a list that was planned to work around the surrounding
songs.
3.1.6 Dr Stephen Pankavich
Stephen Pankavich:
Partial Differential Equations, or PDEs, are ubiquitous
throughout engineering and the sciences. Their use is
seemingly infinite as they can describe phenomena as seemingly
diverse and distinct as wave propagation, fluid flow, cancerous
tumor growth and chemotherapeutic treatment, climate change,
glacial assembly and melting, chemical kinetics, gene expression,
properties of advanced materials, and even quantum mechanics.
In addition, the study of PDEs has facilitated many of
the greatest mathematical discoveries of the 20th and 21st
centuries, such as the proof of the Poincare Conjecture,
the crucial understanding of Nonlinear Schrodinger Equations
and Landau Damping, and the continuing quest to solve the
regularity problem for the Navier-Stokes equations [9].
Dr Stephen Pankavich could be considered a differential equation
specialist. He has been working in the department for several years
now, and married recently to Dr Rebecca Swanson (a pure mathematician
in the department). Aside from teaching and research, Pankavich
also co-heads the department’s bi-monthly Putnam club. He describes
every faculty member’s role in the department as being three things:
teaching, research, and service. When asked specifically what he

does in the department, he said that he "does quite a few of those
things".
Originally, Dr Pankavich pursued computer science, but decided
quickly against. He switched to mathematics at Carnegie Melon Hall
in Pittsburg. Pankavich fell in love with mathematics because of
a class called the Calculus of Variations, a topic that deals with
hard optimization problems and physical representations of differential
equations and its variations, but stays away from topics such as
Abstract Algebra because it stretches his brain in uncomfortable
ways. Now, he is trying to fulfill a role of "mentor" in respect
to the inspiration he found in college when he had no direction.
In fact, Pankavich to this day is grateful for having inspiration
to continue in math by this professor, and attributes part of his
successes to him.
Dr Pankavich had expressed very strong inclination toward rhythmically
motivated songs, and this is because he is a drummer (one of at
least three in the department). First learning how to basically
play the guitar, Pankavich leaned toward the art of rhythm, to which
he was been playing drums for almost two decades (with a large break
in the middle supposedly).
Pankavich struggled to create a playlist, for similar reasons
as to why Scott Strong had struggled a little bit. Luckily, he
was able to find edited or clean versions for some of the songs
he thought we would not be able to put onto air due to censorship
problems. The playlist featured some rap/hip-hop of the late 90’s
and early 2000’s, as well as a fair amount of rock/metal from the
90s including music composed and played by one of his long-time
friends. The playlist even included the song Lateralus by Tool,
a song based rhythmically (and not coincidentally) off the Fibonacci
Sequence.
3.1.7 Dr Mike Nicholas
Mike Nicholas:
I wear a cast on my lower left arm to protect a broken
wrist while it heals. The cast is made of plastic and
was fit to my arm. It comes off, so I can remove it and
wash it once a week. In 3 weeks, I get to take it off
permanently [10].

Dr Mike Nicholas is, like a few other professors interviewed,
fairly new to campus. In fact, I was in his first class here at
Mines back in my first semester (in that way, he is really the first
math professor I had contact with at this school). Since he has
been here he has taught Calc II, Diff EQ, and Intro to Scientific
Computing. His first degrees were at the University of Duke, where
he doubled in math and physics. Then, he went to Duke University
where he got his PhD in Applied Mathematics. Unlike Dr Pankavich,
Dr Nicholas’s favorite class as an undergrad was Abstract Algebra,
where he really enjoyed the puzzle solving aspect of that particular
branch of mathematics. Now, Nicholas is researching for the school
and considering pursuing a Master’s degree in Statistics here at
Mines. Dr Nick (as most people refer to him) currently co-sponsors
the Math club for the department
Dr Nicholas claims not to know much about the connection between
math and music, and claims specifically to be not a musician (even
though he plays the harmonica). Though maybe musically inept, it
is important for him to be involved in campus spirit during his
school activities. The playlist he wanted to do at MIR consisted
of numbers and surveys, where he brought in a long list of songs
with numbers in them and the listeners were required to vote on
a song to represent every number 0-9. This turned out to be fairly
successful, even though no one voted for Bob Dylan (and Bob Dylan
is one of Dr Nick’s favorites.)
Like all previous contestants on the show, Dr Nick had a fairly
large wealth of knowledge to draw on when talking about each song.
The music that he brought in ranged anywhere from classic rock and
psychedelia to foreign pop and even some newer rap. Though he was
shy in first on air, he quickly adapted and seemed to display relative
comfort within minutes. The show was fast-paced and more user-interactive
than any other show to date, and that may have helped him be distracted
from stage fright.
3.1.8 Prof Jon Cullison
Jon Cullison:
Songs, more than any other medium, transport me to a specific
time and place. When I hear an "important" song, I can
describe the place I was, the person I was with, smells,

textures, etc. I’m not sure what this says about me psychologically,
but it’s an instant thing [11].
Jon Cullison, bassist and professor here at Colorado School of
Mines, brings a little bit of heart and soul to the students in
the music program. Unlike the mathematicians, this data point was
uniquely collected. This interview did not happen over MIR, and
the interview lasted 10%-25% as long as any of the other interviews.
And, although a playlist was given, essentially none of the music
was actually played with the professor being there. Data was collected,
but not quite at the depth or the magnitude as the other interviews.
(To note, one of the other candidates for music-professor interviewing
would not reply to my emails for an interview).
Cullison was introduced to music early on, by means of parental
influences. The pool of music that Cullison typically leans to
is Jazz, though he also enjoys some new-wave, metal, and the occasional
EDM song. Good music in Cullison’s eyes comes from the concepts
of "power" (music that is emotionally charged). This relates to
the concept of "nostalgia", where there is plenty of music that
Cullison enjoys purely because of an associated memory.
Cullison is a bassist by nature and definition, though dabbles
in other instruments including piano and drums. When asked which
instrument he’d like to have a complete knowledge and skill-set
over, he said piano (in which he would want the ability of a player
named Brad Meldan). It seems as if Cullison recognizes a type of
link between music and math, though, like most people, he may have
a hard time describing it. According to Cullison, there was never
a personal connection between himself and math, at any level. Geometry
made the most sense to him, though algebra II may have even been
his worst/least-favorite class of all time.
3.2 Conclusions
We will now, first, interpret the raw data in terms of things that
are similar (i.e. what traits do members of our tribe share or
have in common). This is important as it will help shape the profile
of what it means to be a member of this tribes "culture", such as
means to establish a concrete definition between those who are mathematicians
and those who are not. Secondly, we will then interpret the tribe’s
profile and conclude existing relative isomorphisms between mathematicians

3.2. CONCLUSIONS 23
and musicians (i.e. what are things that mathematicians and musicians
do that are dissimilar, that might hold equivalent meaning and importance
within each culture).
3.2.1 The "Tribe"
Primarily we will define some of the basics; the who, what, when,
where, and then the why.
The tribe is based off of a "who", which is the mathematicians
here at CSM. Of course, the "when" and "where" are also defined
in generally the same manner. There does seem to be a defining
cuisine choice within the math department, as Pankavich points out:
We always go to Thai Golden.
This does say a little bit about our tribe. There is a sense of
communal activity between eating a meal and being with each other.
Typically, this event will occur over the summer, during grading
periods, when welcoming new professors into the pack, and celebrations.
The food is relatively costly, which speaks to the relative wealth
of this particular tribe. However, the important thing to note
about this particular favorite gathering between the professors
is that it is entirely a unique way to "force" communication, something
that will be touched on in the next section.
What are some of the "whats" that bring this particular group
together? There does appear to be a fair amount of shared traits
between the mathematicians. Of easy note, but of significant importance,
there is an obvious appreciation (and a lot of times textitimmersion)
within musical topics. The fact that half of the sample not only
identifies as musicians but identify as textitdrummers, means that
there exists a special trait or common occurrence between mathematicians.
Of course, the three that didn’t consider themselves musicians still
had experience playing instruments at some point in their life and
still very actively listen to music (at any age). This may be slightly
a product of bias since the participants were voluntarily chosen
to come onto a show about music, but since the total tribe size
is so small and still this number of people from the tribe exhibit
these traits suggests this commonality holds come weight.

3.2.2 Isomorphisms
The physical observations and date recording leads to interesting
obvious conclusions, such as what the tribe can be defined as, and
perhaps even easy mappings between how a mathematician and musician
are similar. However, we will let the readers review the previous
aspect of the paper and draw their own conclusions there. Instead,
we will focus on a particular mapping that gives us a large similarity:
the idea of communication.
First let us define, particularly, how we will be defining communication.
Communication by application is already a mapping from one "type"
of person to another "type" of person. i.e. if a person from Portugal
is trying to communicate with another person from Portugal that
something they are holding is yellow, the obvious tool of communication
would be the language of Portuguese. This tool has been molded
and shaped from other, similar, tools of communication and is the
base level from which we derive a meaning of any concept between
person and person. In fact, there are easy "signs" in that language
that already place meaning on what yellow is, and it can be communicated
from one person to the next efficiently without expending much energy.
Now we can make it more complicated by adding dimensionality.
Now, consider a straight, single man from Portugal trying to communicate
to an attractive single woman from Spain. Suddenly, appropriate
communication becomes more complex. We have added the idea that
there is a motive between at least one of the parties, in which
a tool to communicate is needed, but also a fine tuning in how the
tool is used in order to properly get to an interpretation of the
communication tool.
Essentially, this man (as referred to in the previous paragraph)
has to convert his language to the language of the listener, alter
it in some way that may be common throughout all languages, and
try to convey a specific message or idea to this woman. This is
a large growth in complexity from the previous example, in which
something closer to a "sign" was used to communicate between people
using the same tools (language) of communication. Now the idea
of "symbolism" comes into play, in which the language itself may
not give a perfect idea of what is trying to be conveyed, and how
the man says what he is trying to say will hold a large weight in
interpretation value.
So what does it mean for a musician to communicate? The words

3.2. CONCLUSIONS 25
that first might come in to mind are, "feeling’, "emotion", "mood",
all of which allude to the concept of "internalization" on an idea.
In other words, a musician may make the connection between the physical
world and how it affects them personally in order to communicate
to someone what it is. Remember that music, as math is, is a context
sensitive language. There is a music "language" that can be used
to describe an incredible amount of things, some of which are more
complex than what a recursively enumerable language can achieve,
but there isn’t a one-to-one mapping (think about the english words
"the", or "dog", or "capitalism", there are no words in music that
directly describe these terms). However, there is an injection
in the music language because everything that can be expressed in
music can be written out (even if verbosely) in complete, precise,
english words. So when a musician communicates by method of music,
the entire idea of using music instead of english words is this
extra dimensionality on communication that is already partially
defined. You can take a 10-minute long piece and describe people,
places, and ideas and make people feel things for more intensely
than you could in words.
We will assert that a mathematician communicates in a way that
is identical. The language structures already prove similarities
in how communication is accomplished. Granted, the subject matter
tends often to be non-identical or dissimilar. In a lot of ways
there is anti-symmetry. This means, whereas a musician will "internalize",
deriving emotions that makes sense to them based off what is physical,
or abstractly tangible, a mathematician will "externalize" an interpretation
of an idea or solution where emotion can’t affect its meaning. It’s
like giving back to the universe, taking yourself out of the equation
and expressing what you "know" is.
The good news is that this is how we can draw the isomorphism.
There seems to be an anti-symmetry between math and music, in terms
of communication, that allows us to suggest that the motive behind
doing what each "culture" does as a "culture" is similar to one
another. We can equate to the want, sometimes need to "internalize"
a concept, to then interpret it, and then explain to others, to
needing to "externalize" that concept. i.e. a musician that wishes
to explain the concept of love first has to acknowledge what that
means to them, figure out how to convey that to others, and then
externalize that interpretation so that others get a chance to internalize
it. A mathematician works backwards from this, though the motive

is similar. Let the mathematician be describing the sensitivity
of a parameter in a chaotic system. Before deriving personal conclusions,
or receiving intuition on an internal level with a problem, it is
first necessary to map the solution that is equal in meaning to
everyone else by use of mathematics. Then, one can internalize
"interpretation" on something on a less-objective scale.
3.3 Further insight
So that we won’t beat the topic dry, we will let the reader digest
the information while we discuss some of the physical data that
was utilized supporting the idea that the way a mathematician communicates
is isomorphic to the way a musician communicates.
When listening to the professors converse, both to myself or
to an audience or even to each other, I noticed that, different
from a lot of professions, mathematics gives the professors a certain
motivation to make things clear. Much of the topic matter, including
casual conversation had to be "clarified", or instantiated to something
specific, else general. It is astounding listening to people talk
in this way because there is a continual bridge being formed between
all people, where the bridge leads to the same place if the listener
maintains a set of logic. This is what gave me the idea of the
isomorphism because one of the trophy aspects to "artistry" is communication,
and to find that within a culture that is almost always painted
as being "logical" and "definite", pointing away towards the type
of freedom achieved in art, makes me excited. This really makes
me think that though there is a perception of difference, though
the content matter that exists in the separate cultures are nearly
disjoint, each culture is really trying to accomplish the same thing
and is doing it in such a similar fashion. This should be a good
key for either side as to provide an open door between each culture,
to try and utilize this communicative similarities for the production
of new ideas.

Chapter 4
Addendum: Future Work and
Considerations
Unfortunately, I am but one person. A study of this depth and magnitude
really needs to be done within a small team. Even if I try to remove
all of my bias and keep my perspective as wide as possible when
evaluating a culture, or a made-up tribe, my grasp upon perspective
can only be confirmed by myself. Recording all the data isn’t even
the problem, but going back through 10 hours of data and trying
to keep my mind straight for what I am looking for is daunting.
The communication between me and my tribe went smoothly but the
wealth of data that I collected could likely be analyzed much more
in depth that I could realistically provide in this paper.
In retrospect, I think I should have tackled this problem as
an inverse problem. I think my way of thinking, maybe not way of
learning or way of life but my way of thinking, is closer to that
of a mathematician. Hence, I could have applied a similar process
to interviewing a group of musicians about math and I would have
had a great pool of knowledge in math to compare that to and draw
better isomorphisms with. At the very least, mapping data to and
from six "mathematicians" with only one "musician" seems like poor
practice.
Also to note is that I did interview the applied mathematicians,
but no statistics mathematicians, which could have changed the data
and interpretation a bit. However, asking some of the professors
if there was a separation of "clans" within the AMS tribe, Constantine
told me:
27

28 CHAPTER 4. ADDENDUM: FUTURE WORK AND CONSIDERATIONS
Statistics has own culture of formulating problems with
data and uncertainty.
Which makes me think there may be a small perspective shift between
people inside the tribe. Pankavich assured me:
I don’t think there are exclusive groups.
It is then possible that the subset examined was sufficient to give
us insight on the AMS department in entirety.
In the end, I can say that I definitely had a blast and did learn
good substance on a parallel culture. However, I would say that
the original purpose of this paper wasn’t met with as much of a
thorough conclusion as I would have hoped. Luckily, I do think
this paper sets a groundwork for a very effective way in looking
at other cultures for other people. It can be shown logically that
this method is only slightly more expensive in the total time spent,
but also has twice the potential for useful derivations and analyzations
of a foreign culture entity.
I will omit the proof, but I will conclude by thanking everyone
who gave time out of their busy schedule in order to let me toy
with the notion of "people isomorphisms". Thanks to MIR for letting
me use resources on hand to collect my data. Thanks to the math
department for allowing me to advertise my shows to that part of
campus, and lastly, thank you to the music department for letting
me be crazy in my theories and occasionally rant about particularly
odd subject matter.
Quote: Diffusion of idealisms, motivated by dissonance
between tools of communication. A remedy: pose a better
connection between harmonics and critical wave-numbers.
People Language.

Bibliography
[1] Roger S. Recursively Enumerable Languages. Duke University
[2] Andrew Kania The Philosophy of Music Stanford University
[3] Shure SM27 Multi-Purpose Microphone Shure.com
[4] Shure ShureSM27 Large Diaphragm Cond Mic with Shockmount
and Bag. Musician’s Friend
[5] Dustin Burchett Math in Music -- Dr. Jon Collis Interview
on "The Fedora"
[6] Dustin Burchett Math in Music -- Dr. Paul Constantine
Interview on "The Fedora"
[7] Dustin Burchett Math in Music -- Professor Rod Switzer
[8] Dustin Burchett Math in Music -- Professor Scott Strong
[9] Dustin Burchett Math in Music -- Dr. Stephen Pankavich
[10] Dustin Burchett Math in Music -- Dr. Mike Nicholas
[11] Dustin Burchett Math in Music -- Professor John Cullison
Interview
[12] Patch Patch Recording
[13] ILL-CONDITIONED What’s Your Condition Number? Recording

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