LAIS people are language

People

are

Language

18th April, 2015

by

Dustin R. BurchettColorado 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

2 CONTENTS

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.

12 CHAPTER 2. DATA CAPTURING

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

Documents

LAIS people are language