How to Get from Jazz to Math in Sixty Seconds

In my post of June 29, I talked about connections among people, types of music, inspiration for writers, etc. Sometimes it's fun to play a game of "connect the dots." Here's a series of connections I recently picked up on:

Beginning with jazz

My wife and I recognize that we were not born with the gene for appreciating jazz. I have a feeling that that would apply to "progressive" jazz as well (if not more so). 

But progressive rock is a different story. I appreciate it a great deal, and my wife appreciates some of it too. This genre of music is represented by many bands, including Dream Theater (official website here), perhaps my favorite band of all time.

... to a progressive rock guitarist

Dream Theater's lead guitarist, John Petrucci, is an award-winning virtuoso.

Petrucci has also had a side gig, a band called Liquid Tension Experiment.

... and on to math

Liquid Tension Experiment is a favorite band of two German mathematicians, Peter Scholze and Johan Commelin.

"Liquid Tensor Experiment" was the title of a post on mathematician Kevin Buzzard's blog in December 2020, in which Peter Scholze described some of his recent work.

This work included the use of mathematical objects called liquid real vector spaces in a proof that was verified by a breakthrough computer system named "Lean".

Try it yourself!

Start with this and see where you can go with it: "The Girl With the Hungry Eyes", a song by Jefferson Starship whose lyrics reference Einstein: "I like to move at the speed of light / Albert says I can't but I can".

Marching to the Beat of a Different Drummer

My Alesis Nitro Mesh expanded set.

My wife professes to be weird. Sometimes she claims I'm weird too. I try to tell her neither one of us is weird -- we're "unique." Each of us is a statistical outlier in various ways. The old cliche, "marching to the beat of a different drummer" comes to mind. 

But the cliche is about to become literal! After a wait of about fifty years, I've started down the path of learning to play drums as I once wanted to do. The path to get here was a circular one.

"Paper" drums and "plastic" guitars

In my teenage years, when I began to listen to rock and was exposed to it at school dances, I wanted to play drums. Unfortunately, I couldn't afford a set of drums, and I had no room in our little house to set some up. And, it would be too noisy. I made do for a while by laying out pieces of paper on my bed to represent the different drums and cymbals and practicing with a couple of "real" drumsticks. When my parents bought me a cheap snare drum (one step above a toy) one Christmas, I had visions of going on to slowly build a collection somehow.

But it didn't happen. Instead, I got interested in guitar. It started with a plastic body acoustic guitar my sister had, that only had one string. I made up a song on it, and called it "Twenty-two Man." It involved playing only two notes on one string, and throwing in some lyrics I made up. It was awful. (The guitar, the song, my skill level ...) 

Graduating to "real" guitars and loud amplifiers

The following Christmas, I started down a path that would last me for decades. I progressed from a cheap guitar and a "baby" guitar amp to a larger and better guitar, a semi-acoustic Silvertone with a Bigsby tailpiece. (I couldn't yet afford the guitar of my dreams, a Gibson SG.) I graduated to a small but larger amp to play through. My father made me play through headphones so the neighbors wouldn't complain, and so he could get some work done in his office. Next, I secured a loan from my grandmother to purchase a 300-watt (125 watt RMS) Peavey 240 Standard solid-state amp with a speaker cabinet holding two 15" speakers. It was appropriately loud -- I seldom turned the volume control higher than 2 1/2. Once, in college, I plugged in a high-frequency horn and I was told people a mile away were able to hear me.

Alas, the Big Whoppin' Amp was not easy to transport back and forth to my dorm room. When it came time to buy a train ticket to travel to upstate New York and marry my first wife, I sold the amp and downsized.

Eventually I found a used Gibson SG I could afford. I purchased and played 6- and 12-string Ovation acoustic/electric guitars. I picked up a Yamaha bass guitar and learned to play it. I experimented with various synthesizers (a Casio CZ-101, a Yamaha DX7, a Kawai, a Roland, a KORG KROSS2). I played, off and on, with friends; did a few one-off gigs with people I knew; and contributed to praise bands in different churches.

Moving on to drums

Many years later, I decided I could afford some drums and I had room to set them up. Volume would be a problem, though, so I opted for electronic drums. I recently purchased an Alesis Nitro Mesh expanded (10-piece) set.  Modern-day mesh drumheads are quiet enough that if I'm listening to the drums through headphones, the tapping on the drumheads is almost inaudible. (Although the tapping noise from the electronic cymbals is another story.)

My current gear includes the Alesis electronic drums and cymbals, a Behringer Xenyx Q1202 mixer to blend instrument input as well as music from an Amazon Echo, and an inexpensive Sony receiver with output to some old Bose bookshelf speakers.

It took many years to get here, but I have now returned to my percussive "first love".

Celtic Rock, Appalachian Stories, and Knowledge Maps

Six Degrees of Separation

Most people know of the "six degrees of separation" concept because of the popularity of the "six degrees of Kevin Bacon" game. On average, any two actors in the world can be connected through a chain of movies in which actors have co-starred. 

More broadly, network science tells us that any two people in the world can be connected through social connections by no more than six jumps. Here are a few examples of my own:

1. I am one degree from the deceased actor Vincent Price -- I once shook his hand at a college event. Anyone he knows, or starred in a movie with, is only two degrees from me. (Admittedly the social connection was not a remarkable one. LOL)
2. I have met two Nobel Prize winners, which places me one degree away from each of them, and two degrees from the King of Sweden, who hands the prizes to each winner. 
3. I have a relative who was a campaign manager for Senator Bob Dole years ago, which places me two steps from Dole and three steps from everyone Dole knew in Congress and Washington, DC. 
4. Thanks to my father, who got Project Mercury astronaut Wally Schirra's autograph in 1964, I am three degrees from just about everyone in NASA's early space program. 
5. Sadly, I am one degree from at least three people who took their own lives, and only two degrees from a political assassination in Venezuela.

Connections

Six degrees of separation is a social phenomenon. Work at digging up who is connected to whom, and you can wind up with a huge network of connections. Then, you can follow the network from one point to the next and uncover connections you didn't know about.

But what about other networks? A clever programmer could "scrape" (as they call it) book recommendations from Amazon's website and come up with a map of related books that might show you recommendations that were two or three or four steps away from a book you're looking at, instead of only one step away.

Still, these examples are only focused on connections between the same kinds of things (people with people, books with books). There's no a priori reason why we can't derive a network connecting different kinds of things that are related. A more sophisticated example using Amazon recommendations would include authors as well as books. Each author could be connected to every book that author has written, books could be connected to co-authors, and authors within a certain genre could all be connected. This would be useful if you wanted to use authors for recommendations, and not just books.

Discovery and knowledge

To take this one step further, consider an example network I created that connects certain authors, books, musicians, genres, and influences on musicians. The example network, shown at the bottom of this post, is something I developed using the yEd and yEd Live network drawing software, both of which are free software products from the software company yWorks. (An interactive version of this network, which includes hyperlinks, can be accessed via this link.)

At the top of the diagram are three authors, including J. R. R. Tolkien, Alex Bledsoe, and Sharyn McCrumb. (For more on Sharyn McCrumb, see this recent post of mine.) Beneath each author is an icon showing something that author has written. The Lord of the Rings is fantasy, of course, as are Bledsoe's "Tufa" stories, set in a modern-day part of the mountains of Tennessee. Many of Sharyn McCrumb's novels are set in the Appalachians.

Below that part of the diagram is the musician Dave Brons. Brons, who composes and performs progressive rock with a "Celtic symphonic twist", found inspiration in The Lord of the Rings. Bledsoe's "Tufa" novels inspired a group of musicians known as Tuatha Dea, also shown on the diagram, who compose and perform what they call "Appalachian Rock." Both Brons and Tuatha Dea have been influenced by Celtic culture. (And, Tuatha Dea has also been influenced by "steampunk.")

Final Remarks

The diagram I created is a small example of a knowledge map. It captures a set of connections I thought were interesting, that I can share with others, and that may lead others to consider artists or authors or works they might not realize were connected. As a knowledge map, it can be extended to include as many connections as I would like.

Knowledge map created using the free tools, yEd and yEd Live. See text for link.
Copyright Mark E. Lacy, 2021.

Guest Blogger Sharyn McCrumb on the Roots of Appalachian Culture

A novel of a historian following the trail of
a young woman who escaped the Shawnee in 1799.

In my post of April 20, Deep Geographic Memory, Bagpipes, and Electronic Music, I mentioned New York Times bestselling author Sharyn McCrumb. It is my pleasure to share with you, courtesy of Sharyn, a piece that she wrote on the topic of how the early American settlers brought with them, as they journeyed west into the Appalachians, music and stories from England, Scotland, and Ireland. That culture, once transplanted, acquired small differences, but it reflected--and still reflects--the "old country", even as the Appalachians reflect the landscape of the hills and valleys that these settlers would've called their original home.

I thank Sharyn for giving me permission to reprint this! Please see her bio at the bottom of this post. You can learn more about her and her work at www.SharynMcCrumb.com and www.facebook.com/SharynMcCrumbAuthor.

Wayfaring Strangers

By Sharyn McCrumb 

from the 2017 Mountains of Music Magazine
for The Crooked Road, Virginia's Musical Heritage Trail

Copyright 2017 Sharyn McCrumb

My home’s across the Blue Ridge Mountains
My home’s across the Blue Ridge Mountains
My home’s across the Blue Ridge Mountains
And I never expect to see you anymore.

They must have felt that way once—more than a century before that song was written—when the settlers rolled down the Great Wagon Road that followed the valleys between the wall of mountains that stretched on forever. When the settlers reached the middle of Virginia—about where Roanoke is today—some of them headed west on the Wilderness Road, ending up on the 18th century frontier, in southwest Virginia, east Tennessee, eastern Kentucky, and western North Carolina.

They, or their recent forebears, had already made one perilous journey in a lifetime, across the Atlantic from Scotland or Ireland or England, to settle in the New World, but the eastern seaboard was already getting crowded by the late eighteenth century, mostly full of the people they left Britain to get away from. (Besides: you could see the neighbors.) So they ventured deeper into the mountains, looking for a place that felt like home. They never knew how close they were to being back home; nearly two more centuries would pass before geologists put together the ancient puzzle of earth’s Triassic period to discover that millions of years ago the Appalachians had been part of those same mountains in Britain from which many of the settlers themselves had come.

The new people brought what they could from home—not material things, because the ships were small, so you had to pack light—but they carried with them everything they could fit into their heads, because memories were all they had left of the places they’d come from, and they treasured them. They handed down these memories to their children and grandchildren, which is why in 1914 musicologist Cecil Sharpe found the traditional folksongs he was looking for, not in Britain where they had originated, but in the southern Appalachians, where they were cherished remnants of the past.

Things changed a bit in the new world. If you came over with an unusual name—Rhys (Welsh) or O’Laoghaire (Irish) or McDiarmuid (Scots)—sooner or later some census taker would standardize you to “Reese,” “O’Leary,” and “McDermott.” The songs and stories got naturalized, too. The Wexford Girl became The Knoxville Girl, and Lady Margaret of the Child Ballad was demoted to Little Margaret over here, but the plots of the songs stayed the same, and the tunes were still recognizable. When The Lily of the West was composed, back in Ireland, the “West” was the coast of Ireland: Galway or Connemara. Many years later when people sang the song in America, the “West” they pictured was Kentucky (“When first I came to Louisville, some pleasure there to find…”)

You never know when the family resemblance is going to peek out at you. Years ago, I took a newly-arrived Scottish professor to an Appalachian storytelling festival. The speaker began a tale about an old farmer who was fishing in a mountain stream and caught a big old trout. As the story wound on to the part where the farmer found a gold ring in the belly of the fish, the Scottish professor began to nudge me with his elbow. Finally when the story ended, I asked him what he had wanted so urgently to tell me. “Right,” he said. “About that story the fellow told. First of all, it wasn’t an old farmer; it was St. Mungo of Glasgow; and it wasn’t a mountain stream; it was the Firth of Clyde. And it wasn’t a trout; it was a salmon. – But the rest of the story is correct.”

They brought their fiddle tunes from Scotland, their knowledge of whisky-making from Ireland, and their quilt patterns from a time before history began. (The Hangman’s Beautiful Daughter.)  But just as English timothy hay became Kentucky bluegrass in the New World, sooner or later almost everything that the settlers brought with them got a North American spin. We were a long way from where we started, but if you look closely, you can see where we hailed from.

 

Sharyn McCrumb

​Sharyn McCrumb, an award-winning Southern writer, is best known for her Appalachian “Ballad” novels, including the New York Times best sellers The Ballad of Tom Dooley, The Ballad of Frankie Silver, and The Songcatcher. Ghost Riders won the Wilma Dykeman Award for Literature from the East Tennessee Historical Society and the national Audie Award for Best Recorded Book..        
       Sharyn McCrumb, named a Virginia Woman of History by the Library of Virginia and a Woman of the Arts by the national Daughters of the American Revolution, was given a merit award for literature by the West Virginia Library Association (2017) and the Mary Hobson Prize for Arts & Letters (2014). Her books have been named New York Times and Los Angeles Times Notable Books, and have been translated into eleven languages.

When Hymns Come In Handy

Me, age 3 1/2, leading music in my Sunday School class.
Note that no one is paying attention to me.

In January 2015 I was looking out over the ocean, thinking (and praying) about my father's decline in health, his admission to a nursing home, getting him and my mother on the right Medicare supplemental insurance, getting their finances in order, and working with an attorney's office on setting up the right legal paperwork so I could help meet their needs in the coming years. I was plagued by anxiety and confusion and fear that things would not work out right. Through a whipping rain (but behind the shield of a pair of sliding glass doors), I watched waves fighting each other and pounding the beach. I was reminded of the hymn, "It Is Well With My Soul":

    When peace, like a river, attendeth my way,
    When sorrows like sea billows roll;
    Whatever my lot, Thou hast taught me to say,
    It is well, it is well with my soul.

I did not feel like all was well with my soul. And peace did not "attendeth my way." Far from it. Instead, I felt buffeted by relentless forces standing in the way of caring for my parents. But in those times of distress, I prayed for peace, and wisdom to make the right choices as I upheld the Fifth Commandment.

Growing up with hymns

In my formative years I was -- thanks to my parents and several Baptist churches -- introduced to a great deal of church hymns. In Sunday School we learned the old standards, "Jesus Loves Me" and "Jesus Loves the Little Children." (See Matt. 19:13-15). As a three-year old I stood on a little chair in my Sunday School class to lead the music for us. (See photo above.) And whenever I see a sycamore tree I'm reminded of another song we learned as children in Sunday School (see Luke 19:1-10):

    Zacchaeus was a wee little man and a wee little man was he!
    He climbed up in a sycamore tree for the Lord he wanted to see ...

One of my earliest memories is of my mother doing a solo at church of "His Eye Is On the Sparrow." She sang in the church choir. My father could have been part of the choir. He had a good voice, but we could never get him to join. Perhaps he was too self-conscious.

There was only one hymn I was told my father didn't like: "The Old Rugged Cross," because he considered it idolatrous. Philosophers refer to this as confusing the map [the representation] with the territory [what is being represented]. The lyrics of this hymn don't say we should worship the cross. The cross, as it says in the first verse, is "the emblem of suffering and shame." It is a representation of Christ's death and what it means to Christians.

As I sang in church, growing up, I realized I had a knack for picking up harmony while the congregation sang hymns. But it was not until I joined our church's youth choir that my harmonizing found the structure it needed as I started learning to read music and sing tenor alongside my choir friend Bob DuBois.

Nowadays, hymns are something I seldom hear, but they remain in my heart. They frequently come in handy, as when I contemplate a never-ending list of chores and responsibilities and hear in my mind the refrain of the hymn, "We'll Work Till Jesus Comes":

    We'll work till Jesus comes,
    We'll work till Jesus comes!
    We'll work till Jesus comes
    And we'll be gathered home.

I just hope He comes soon so I can get some rest!

What hymns and contemporary Christian music mean for me today

In the past fifty years Christian music has changed radically. In many churches where hymns are still sung, hymnals are a thing of the past. The lyrics are projected on a screen for all to see, but for those of us who read notes while singing harmony, we have no notes to guide us. I have to fall back on improvising, and not singing too loud in case I pick a discordant note by accident.

Twenty-five years ago my wife and I joined a church that had a "blended" traditional/contemporary service. We felt like we were getting the best of both worlds. (I made the "mistake" of singing tenor where the choir director could hear me, and soon I was drafted!) But blended services are increasingly difficult to find in our part of Ohio. And "praise bands" leading music in contemporary non-denominational churches, at least in our region, stick strictly to a repertoire of contemporary Christian music (CCM). This may be an important part of attracting younger families. Older church members are dying out, and that may also contribute to the shift from hymns to CCM.

I like and I appreciate CCM. I enjoy the "rock" feel to it. I've even attempted solos of a couple of pieces of CCM in church, with backing tracks, and I've enjoyed playing guitar and bass in a few praise bands. But CCM does not easily lend itself to congregational singing. There is a much greater variety to draw on, compared to the old hymns, but unless you listen to CCM on the radio/Spotify, you probably won't know how to sing the melody, let alone some kind of harmony.

A related problem, in my mind, is this. Too often, it feels like the praise band leading CCM is putting on a performance instead of gathering voices from all over the church in praise to God. Darkened auditoriums with spots on the praise band only bolster that impression. Congregational singing consequently falls by the wayside. Without a strong participation by the congregation, the church misses out on "the fellowship of kindred minds" who together proclaim the glory of God in song.

Deep Geographic Memory, Bagpipes, and Electronic Music

MacDuffee Clan Society Tartan (modern)

This past weekend I attended the graveside service of a dear cousin of mine. Just before the service began, a bagpiper approached playing a solemn tune. When the service was finished, he departed the same way he had come, slowly crossing a rise in the cemetery, signifying the departure of my cousin from this earthly life. We were moved by the occasion, and we were moved by the music.

I was reminded of heritage, and music. I was reminded of writing, and our sense of place on this planet.

Geographic Memory

Cherokee linguist Tom Belt is a descendant of the Native Americans who left their homelands in the Southeast U.S., forced to follow the "Trail of Tears" and relocate in Oklahoma in the 1830s. Robert Moor, in his book On Trails: An Exploration, explains that as a child in Oklahoma, Tom Belt would fantasize, while playing war games on the prairie, "that he was in a land of mountain slopes, soaring trees, and murmuring brooks." It wasn't until Belt moved to North Carolina at the age of forty that he realized this was the landscape he had been imagining. It's like a "sense of deep geographic memory," writes Moor. And while it "may seem mystical ... it isn't--or at least, isn't entirely--because the landscape is 'encoded' directly into the [Cherokee] language."

Scots-Irish Heritage

I believe this would resonate with Sharyn McCrumb, award-winning author of a number of historic novels set in the Appalachian mountains of Tennessee and North Carolina. I was fortunate to hear Sharyn speak at the first Lost State Writers Conference in the foothills of the Appalachians in 1998. Many of us in the audience were descendants of the Scots-Irish who came to America in the 18th and 19th centuries, and we have roots in the Appalachians. Sharyn said that our Scots-Irish heritage has followed us in our music, our writing, and especially our choice of where to live, for the Appalachians closely resemble the Scottish Highlands. While my McDuffee ancestors were not Highlanders (they came from the island of Colonsay in the Inner Hebrides off the coast of Scotland), surely some of my ancestors were Highlanders.

Bagpipes, Drones, and Electric Guitar

Scots-Irish heritage following us in our music?! And not just music played on a hammered dulcimer. Take the bagpipes, for instance. The Great Highland bagpipe. When I was somewhat taller and older than a wee lad, I really wanted an electric guitar effect (similar to a "fuzz box" or a "wah-wah pedal") that would allow me to create a drone on the electric guitar. As far as I know, it wasn't until advances in digital signal processing made it possible that one could purchase and use a drone effect. (Or, use what is called a "pad" on a synthesizer.) And I wonder, did my desire to create a drone on a guitar arise from what Robert Moor referred to as a "sense of deep geographic memory"?

The Drive Home

Not long after my cousin's graveside service, near Chattanooga, Tennessee, I got back in my car and headed home to Ohio. There is something I've not yet put my finger on that causes me to feel like "I'm in the right place" when I'm in Tennessee. It could be topography, natural history, or the fact I was born there. Though I never really lived much in Tennessee, I consider it home. This is something I will have to explore.

Music, Soundtracks, and Accompaniment for an Apocalypse

Pleasant surprises

We all know the power that music has to evoke emotions. Several months ago, as I was driving home at the end of a long day, a colorful sunset lit the sky. I felt enraptured as I listened to "Jupiter, the Bringer of Jollity" from The Planets, by Gustav Holst. My favorite part of "Jupiter" comes as a surprise (see "Rock Music and the Element of Surprise"): a slower-tempo segment of grandeur sandwiched in between frivolity. I have no idea why Holst composed "Jupiter" the way he did. The segment I so appreciate was later turned into a tune used for the hymn "I Vow to Thee My Country," a patriotic piece particularly appreciated by the British and performed (for example) at the funeral of Winston Churchill.

The power of spectacular soundtracks

Like many people, I appreciate spectacular soundtracks for movies. I remember, when I was a boy, repeatedly resetting the needle on my father's turntable as I listened to his LP for How the West Was Won (1962), long before I was able to actually see the movie for myself. By that point, I had already pictured much of the story from the titles and musical dynamics of the tracks on the LP.

But I can't begin to express what I felt, at age 13, when I heard, for the first time, Richard Strauss' Also Sprach Zarathustra, used in both the opening sequence and the ending of 2001: A Space Odyssey (1968). I had to purchase the LP  for the soundtrack so I could listen to this piece again and again. And, feel the sadness behind the Adagio from Khachaturian's Gayane Ballet Suite #3, another piece from the soundtrack for 2001. This soundtrack was just as much an act of genius as the visuals of the movie, given how the skillful use of these pieces helped to convey the vastness and mystery of space.

Inspiration for writing

For both inspiration and pure enjoyment, while I was writing my Civil War stories (MISSING IN ACTION, 1863, and Battlefront and Homefront), I must have listened to the soundtrack of Gettysburg (1993) hundreds of times. While writing fantasy I've listened to Scheherazade, by Rimsky-Korsakov, to put me in an inspired state of mind.

Endings, and an apocalypse

But some of the most moving of orchestral pieces are those used at the climax of movies. Samuel Barber's Adagio for Strings, like Khachaturian's Adagio from Gayane, is a slow and sad composition. Barber's Adagio was famously used for the pathos of the final scene in Platoon (1986). 

And I cannot think of the sci-fi movie, Knowing (2009), without pondering the apocalyptic conclusion to the movie. SPOILER ALERT: At the end of the movie, devastation runs rampant as the world comes to an end. The power of this ending is a result of two things. First, there is neither dialogue nor voiceover. And second, the first part of Beethoven's Symphony No. 7 in A major, opus 92, II. Allegretto is used to communicate the depths of despair as both the movie and life on earth comes to an end.

Rock Music and the Element of Surprise

My latest book, The Trail Behind Me, includes a short memoir titled, "Embracing the Element of Surprise." In it, I give several examples from my youth, growing up in Florida and exploring the wild with my friends, where surprise found us and made our experiences more exciting and memorable.

The element of surprise in music can do the same thing.

When I was going to college in South Florida, eons ago, a band named McKendree Spring gave us a concert one evening. I had no idea what kind of music they played, but it didn't matter. It was the end of a balmy spring day and it felt good just to sit out on the lawn, in front of the stage, and experience something new. 

In addition to a number of original songs, McKendree Spring played a cover of "Down by the River" by Neil Young. The first verse was played in much the same style as Neil Young had played it, but when they came to the chorus, they let loose. Fortissimo! Power chords! I was floored. It was totally unexpected. The surprise was exciting. They were loud, and tight, and sounded like The Who had just come on stage for the chorus. Just as exciting was the transition back to the melodic second verse, mezzo-forte.

Since that time, I've come to appreciate a lot of rock music that begins with a soft, melodic intro that changes, with maybe little warning, into something pulsing with volume and energy. (Some classify these songs as power ballads.) 

Styx performed several songs like this, including "Lady" (1973), "Suite Madame Blue" (1975), and "Come Sail Away" (1977). Grand Funk did this with a short intro to "Sin's a Good Man's Brother" from the album Closer to Home (1970). And there are many others, including "Glory of the Empire" (2005) by the Norwegian progressive rock band, Circus Maximus. "The Shadow Hunter" (2004) by the Brazilian prog rock band Angra begins with a lively Spanish (Portuguese) guitar and some castanets and up-tempo percussion before (at 0:45) bursting with power chords. 

The intros for songs like these are frequently performed on piano or acoustic guitar before electric guitars, bass, and percussion come in with a bang. Certainly, the more you listen to one of these songs, the less the surprise, but even when you expect the shift from "light" to "heavy," it can send a thrill down your spine.