52!

I woke up this morning and decided I was going to do something never before seen in the history of the universe. I started to solve the Riemann Hypothesis, but then thought better of it. Turns out, it is far easier to shuffle a deck of playing cards.

How many different possible combinations are there? More than a couple. Here is the answer in scientific notation:

Here is the number written out:

 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000

Let’s change that number to seconds. If you were to shuffle a standard deck of cards every second, starting at the Big Bang and continuing until today, you would not make a dent in the number. You would need this many years to exhaust all possible combinations:

The age of the universe in years:

So…yeah. Each time you properly shuffle a deck of playing cards, you are creating a sequence that most certainly has never been seen before and will never be seen again. 

Notice that in this instance, uniqueness emerges from permutation. There is nothing special about the sequences, no narrative that can give them meaning. It is simply about the arrangement of playing cards. You might find that astonishing.

The Delightful Louise Stonham

I was in the middle of writing another math post when I came across a “tok” on my phone (OK, a YouTube short). Mississippi State University has a young track and cross country runner named Louise Stonham who keeps randomly showing up on my feed. Today, I realized that we are kindred spirits.

Ok, so well over four decades ago, I was a D1 athlete. I have a letter and a mug somewhere in my house to prove it. For the last several weeks, it has been apparent to me that Ms. Stonham is very proud of her status as a D1 athlete, as she should be. It is a big deal. Not everyone can claim such an honor.

I always smile when she shows up on my phone, dancing and bouncing around like a promising young person with her entire life in front of her. What a joy she is. Today I saw something a little different.

Her latest post shows her running on the track. I am guessing it is a 10k race. The caption reads “When the hardest part of running isn’t the running itself… It’s battling the voice in your head.”

Truer words have never been spoken. I never have trouble getting out to run, the problem always comes when I am out there and the voice, that substantial and inevitable voice, tells me to slow down or cut the workout short. It happens all the time to me now, just as it has for decades.

I usually run 5 miles a day. Today, I gave in to the voice and stopped after 4 miles. “Stop…slow down…you have been running too hard…you are old…you don’t want to get hurt…you should have taken a day off…” You get it. This happens to me almost every day.

I just want to thank Ms. Stonham for letting me know I am not alone in my battle with myself. This is the first time I have ever heard another runner talk about this issue, a problem that has plagued me throughout my life.

Well, young lady, I am rooting for you. As I sit here in mythical Iriquois County, Ohio, I only wish you fulfillment and happiness. Do your best to never lose your joy for running or your passion for life. You are an inspiration. And, good grief, whatever happens, do not stop posting!

 

Wayne’s Wife’s Uncle

Herb Powell – Uncle Herb sounds so formal. Do you think you could call me Unky Herb?
Bart Simpson – No problemo, Unky Herb.

 

Most of my academic training has been in archaeology. There are two distinct camps among archaeologists. There are “artifact people,” those who study the past because of a fascination with material culture, and others (a distinct minority) find their way into the discipline for methodological and theoretical reasons. I am most certainly not an artifact person; I have never felt a thrill from holding a projectile point a thousand years old. To me, artifacts are data. The patterns they create are vastly more interesting than the material itself.

Archaeologists study artifacts to bolster theories of cultural and human evolution. Every dig, if properly executed, adds to our collective knowledge. A Marshalltown trowel placed in the dirt uncovers evidence that either supports or refutes specific scientific theories addressing changes in human behavior over time. That is why I studied archaeology; I was interested in how we get to “big idea” theories from material dug out of the ground.

For me, archaeology has always been a fundamentally mathematical and statistical discipline. If something couldn’t be quantified, it was of little interest to me. Knowledge and progress come from numbers, at least in my corner of the world. I spent decades studying the scientific method, specifically how statistical methods can be used for theory building. Archaeology was always a severe test case for me. Recreating entire cultures from stuff pulled from the dirt always struck me as a hard and interesting problem. Sometimes I think I know less now than when I started.

In 1985, I arrived in Cambridge, Massachusetts. For the first and only time in my life, I felt at home. I haven’t been back in nearly 35 years, but I still think about that place every day and dream about it every night. While there, I found my people. Those times were, without question, the best days of my life. There is no close second. A vignette about a day in my life on campus might be appropriate.

I remember one day when I was talking with my advisor, Bob, in his office in The Peabody Museum. This office was across the hall with a door with several names, including “Danson.” I recognized the other names, but Danson was unfamiliar to me. It seems that Harvard University kept the names of anyone who had occupied that office on the doors. My advisor’s office had the name “Kidder” listed on the door, for Alfred V. Kidder, an important and influential archaeologist who died in 1963. Bob and I often wondered if Kidder would approve of the conversations we had in his old office. We thought that he would.

So, what about this Danson character? Turns out it was the father of actor Ted Danson, widely known for his role as Sam Malone on Cheers. Ned Danson received his PhD in anthropology from Harvard in 1952. Who knew?

I mention the Danson story because, on the day I noticed the name on the door, Bob and I were discussing Ethnographic Analogy, a research method central to archaeology. Archaeologists use analogy to compare an unknown culture with other documented groups. Cultures in similar environments or with similar artifact assemblages are assumed to have much in common when reconstructing their political, religious, and social systems.

I remember that conversation because as I was explaining my objections to the methodology, Bob told me that an archaeologist needn’t use analogy when reconstructing past societies. I gave him a quizzical look as he said, “You can use metaphor!” I think my sigh was heard across campus. His point (and attempt at humor) was well taken: analogies (or metaphors) are integral to the thought process, despite the inherent problems and limitations of the procedures.

Shortly after our talk about ethnographic analogy, we crossed the street to get lunch. There, we had a chance encounter with a guy named Wally. He sat down and told us an unbelievable story about a mimeograph machine. If you ever run into me, ask me about it. I usually save it for special occasions (same with my Superman impression), but you never know, you might get lucky. I always say that the story includes two Nobel Laureates, a Harvard Professor, a beautiful, mysterious woman in a lab coat, and me. I will leave it to your imagination to figure out which person does not belong. That said, the necessary background is in place, and we can move to the material evidence.

 

32 CDs

 

Famous for burying the lede (it is my nature), I can finally get to Wayne’s wife’s uncle. I went to high school with Wayne. I met his wife once, and I don’t know any details about her uncle. The only thing I know is that he recently passed away. Wayne told me that he had a big library that they sold for pennies on the dollar. I really wish I could have gotten my hands on that library (more on that later). Wayne told me that he also had a large CD collection that they were going to throw away. I told him I would be happy to take it. I was already thinking about reconstructing this mysterious man’s life from the CDs. Think of this as my own version of a modern-day pseudo-archaeological study. I will treat each CD as I would an artifact from an archaeological site.

Wayne brought over two large cases, apparently full of CDs. They were strapped shut, so I didn’t have instance access. What I did have was 32 CDs in the CD player that Wayne also dropped off.

Of course, my first inclination was to do as much statistical analysis as possible on the CDs I had ready access to. I was severely limited in what I could do, largely because the sample I had was not random. It seems reasonable to assume they were selected with a specific purpose in mind. This is what I found.

 

 

I have several observations made from these 32 data points. The first is that Unky Rick (I finally asked Wayne for his name) was either a fan of J.S. Bach or in a serious Bach phase when he passed away. I found 5 CDs in this sample dedicated to Bach’s music, including two performed on 8-string guitars. I must admit I did not know that 8-string guitars are a thing. Subsequently, I have found that they are popular in Scandinavian Heavy Metal Music, less popular in Jazz, and even rarer in Classical Music circles.

I am guessing that many of you do not realize that Bach is, by far, the most influential classical composer among modern rock musicians. Bach is the one they always talk about when it comes to their classical music influences. Was Unky Rick a rock musician? Doubtful. I do believe he had knowledge of and appreciated Bach’s well-known genius in what is known as contrapuntal composition.

As for me, I am a serious Wolfgang Mozart man. I believe that it is the greatest cosmic ripoff in the history of the universe that he was taken from us at such a young age. I have sat through numerous courses on Mozart, read all the books, and I listen to his music daily. Piano Concerto in D (K. 175) is playing in the background as I bang this post out right now.

Unfortunately, Unky Rick had only 1 (odds bodkins, just 1!) Mozart CD queued up on his player when I received it. I am in a forgiving mood, so I will let it slide and wait to see if there is more in the cases.

The next observation that gave me pause was discovering that Unky Rick had an affinity for modern classical composers. Many people, including me, who love classical music, do not bother with living composers. It simply is not done. Why would I listen to some random dude when I could bask in the genius of Mozart? For better or worse, the vast majority of people feel that way. Unky Rick was a clear exception.

I found one CD among the 32 that astonished me. This one data point instantly made me realize that had I met Unky Rick, we would have become instant friends. He and I, even though we never met and never will, were, are, and will remain kindred spirits. How is that possible from a single CD? I will make you wait for that answer because I just decided to open the cases. I am going to take an initial, random, non-scientific look at the contents.

 

1000 to 1100 CDs

 

OK… first of all, no Ludwig van Beethoven. I don’t see a single disc. Is that odd? Yes. I don’t listen to Beethoven because I do not think very highly of him. He ripped off Mozart, then stole from him some more, and then decided to “borrow” even more from my man. I really wonder why Unky Rick doesn’t have any. Did he feel the same way? I don’t think so. If he did, I would expect more Mozart in the collection than I found.

Perhaps even more curious is the following. No opera. Let me say that again, I could not find a single disc containing an opera in the entire collection. Like me, did he find the vocals distracting when he was studying or working? I must admit I am really surprised by this. Every classical music fan has to have some opera, right? Maybe? Is there a rule somewhere requiring it? I’ll look into it, but I am pretty sure that if you are sent the super secret opera decoder ring, you’ll need to provide proof of opera ownership. Did he have the ring? I do not know, but my guess is that his fingers were bare.

This next piece of information is very strange. I examined over 200 CDs, and I could not find a single one released after 1999. Why did he stop buying music for the last 25 or so years of his life? Did he start downloading new music? This is around the time Napster appeared in all its glory. That seems like the most logical explanation. I do not think that he lost interest in music and gave up. That doesn’t seem plausible at all.

Archaeologists have a specific term for this type of situation, terminus ante quem (TAQ). It is always good to throw a little Latin into a post, don’t you think? Since I found no CDs released after 1999, the collection has a TAQ of 1999. Nothing in that assemblage is later than that date. In archaeological terms, it is like a sealed layer that must predate a known event.

As the 32 discs imply, many present-day composers are represented in the cases, far more than the usual suspects. I did find a lot more Mozart and Bach, but the CDs are dominated by those who are alive today or are recently deceased.

So, was Unky Rick a professional musicologist or a music professor? I don’t think so. The CDs were not organized in any apparent fashion. They seemed haphazardly placed on the shelves. There were no categories indicated, nor were the performers or composers alphabetized in any form. A CD of didgeridoo music was next to a Gregorian Chants recording, which was beside a Dennison University Choir performance.

After this cursory glance, it is time to get to some real work.

 

Sampling

 

It is difficult for me to relate how much time I have spent studying sampling. I sat through course after course, book after book, and read article after article. I am still studying these procedures and am excited to learn more about Bayesian sampling techniques, a topic I know little about. Of course, I am familiar with Bayesian inference, but I have never had to take a sample within that paradigm.

One of the reasons I started this blog was to educate potential scientists. I want to give just enough information to pique the interest of someone who might one day want to take a much deeper dive into the topics I am interested in.

I bring this up because I decided to take an appropriate, scientifically valid sample of Unky Rick’s CD collection. I took an explicitly frequentist approach to this sample. Rest assured, I did not slop this together; I gave it careful thought. Hopefully, someone reading this post will be interested enough to take a more in-depth look at why I chose this exact equation.

Here is the sampling equation I utilized:

 

Where
N = population size (≈1050 CDs)
z = z-score for confidence level (1.96 for 95%)
p = estimated proportion (0.5 is used when unknown)
e = margin of error

 

The output from the equation means I can get a result at the 95% confidence interval with a +/- 6% error if I sample 200 CDs. Believe it or not, if he had an infinite number of CDs, all I would need is a sample of 384 to achieve a +/- 6% error range at this confidence interval. I have always found that fascinating. It is an unexpected outcome (maybe a quirk?) of statistical analysis. Since I received a little over 1000 CDs, I decided to pull out a random sample of 200 CDs. Here are the results.

 

 

OK, the man had strong musical tastes. He knew what he liked, that much is certain. I immediately wanted to know how concentrated his CD collection is. The CD collection is focused on a few musical categories, with the majority of recordings falling into the classical and choral traditions. Earlier, I mentioned that I want to quantify all that is quantifiable. There is a metric that addresses the issue: the Herfindahl–Hirschman Index (HHI). I have never needed to use it, and I am glad it has come up now.

The Herfindahl–Hirschman Index (HHI) is a measure of concentration that describes how evenly or unevenly observations are distributed across categories. It is calculated by summing the squares of the proportions of each category:

 

 

where pi is the proportion of observations in category i and k is the number of categories.

Because the proportions are squared, categories with larger shares contribute more heavily to the index. The HHI ranges from 0 to 1, with lower values indicating a more diverse distribution and higher values indicating greater concentration in a few categories.

Based on this sample and an HHI ≈ of 0.327, the CD collection is moderately to highly concentrated. It is reasonable to say “So what?” This type of index becomes more important when multiple cases are studied and compared. So, does anyone else have an interesting uncle?

I have to admit, this man is becoming increasingly fascinating as I delve deeper into what he left behind. He was unusual in the best kind of way.

 

Arvo Pärt and the Sound of Stillness

 

I still get a big kick out of learning new things. It sustains and elevates me. I remember one day, walking down a hallway on campus in Cambridge, I came across a remarkable door. What initially caught my eye was a large image of a very old, bearded man with a cane, struggling to carry several books under his arm. The caption read “Learning Until the Day I Die.” As I was looking over the image, the professor emerged from his office. I apologized for blocking his exit. He laughed and told me, “You know, that is why I post all the things on my door. I hope that someone might one day become inspired by something I taped up.” Well, I viewed that image 40 years or so ago, and I never forgot it. Well done, professor.

I am happy to report that I have learned a great deal while writing this post. I had to research Gregorian Chants, a staple of Unky Rick’s chosen material, and Arvo Pärt, the most performed living classical composer in the world. It will surprise no one that Gregorian Chant deeply influences Pärt’s canon.

I noticed CD after CD with Pärt’s name on the cover. Of course, I became curious about this man and set to my task. I have listened to hours of his music, and I am now thoroughly convinced that Unky Rick had a sophisticated musical knowledge far beyond mine. If this were an official “Archeological Dig,” I would call in experts to consult.

I can, though, relate what my research has uncovered. At a surface level, both traditions, Gregorian Chant and the Pärt School, share an obvious feature: slowness. Gregorian chant unfolds without rhythm in the modern sense. It moves like breath, displaying an ethereal quality. Pärt’s music, especially in his tintinnabuli style (a method he invented), is similarly restrained. The sparse notes appear with deliberate spacing, often surrounded by large fields of silence. For the casual listener, this can feel uneventful. For the informed and devoted listener, however, the silence is not emptiness; it is structure.

This distinction matters, especially to those who take this music seriously.

People who gravitate toward these musical forms often demonstrate a high tolerance for stillness. They are comfortable with and enthusiastically welcome environments that others might label ‘quiet’ or ‘uneventful’. Perhaps more importantly, they do not experience silence as an uncomfortable or awkward gap. Instead, silence becomes an integral element of the experience itself. In a sense, the listener participates in the music by providing patience.

From an analogical perspective, this suggests a reflective disposition. My research suggests that individuals attracted to Gregorian Chant and Pärt are often curious about deeper questions. Philosophy, theology, history, and even mathematics often appear somewhere in their intellectual orbit. The music itself invites this orientation. A medieval chant carries nearly a millennium of cultural continuity. A Pärt composition often hides a precise structural logic beneath its simple surface. Both traditions reward attention to pattern. Of course, a look at Unky Rick’s elusive library would answer those questions.

Interestingly, pattern recognition, the heart of mathematical thinking, is central here. Gregorian chant follows modal systems rather than modern harmonic progressions. The listener gradually learns the contours of these modes, much as one recognizes the grammar of a language. Pärt’s work is even more explicit in its architecture. The tintinnabuli technique pairs melodic lines with triadic tones in carefully constrained relationships. The resulting sound is spare, yet mathematically coherent.

I normally write the beginning of a post last. After learning more about the music in the cases, I revised the initial paragraphs because it is clear to me that, if Unky Rick had been an archaeologist, he would not have been an artifact guy. He experienced his music in a very sophisticated way, through the patterns present and implied. I think this also explains his interest in Jazz. Serious officianiados of that genre consider the notes not played as well as those performed.

For analytically inclined minds, this pattern recognition is the point.

Another shared characteristic of these listeners is a preference for depth over novelty. In contemporary culture, novelty functions as currency. Streaming platforms encourage constant movement between songs, artists, and genres. Chant and Pärt operate under a completely different logic. The value of the music often increases with repetition. A piece heard dozens, or hundreds, of times reveals details that initially pass unnoticed.

Perhaps most importantly, this listening pattern cultivates a particular emotional tone. The experience is not dramatic in the cinematic sense. Instead, it produces something closer to equilibrium. The music does not overwhelm the listener. This may be why there was no opera in the collection. He did not wish to be overwhelmed by the music; he wanted a more subtle, perhaps meditative, experience.

This is where the personality profile, derived through the analogy process we previously discussed, becomes especially interesting. The typical admirer of chant or Pärt often feels deeply, but expresses it with restraint. There is an appreciation for sincerity without theatricality. Beauty emerges through subtlety rather than intensity.

Importantly, this aesthetic preference frequently extends beyond music. Minimalist architecture, clean typography, uncluttered workspaces, and carefully organized data structures often appeal to the same individuals. The underlying principle remains consistent: remove the unnecessary elements, thereby allowing the structure to speak.

There is also a historical dimension. Gregorian chant connects the listener to an unbroken musical tradition reaching back through monasteries, manuscripts, and medieval cathedrals. Even for a secular listener, the sense of temporal continuity is striking. One hears not only a melody, but a fragment of cultural memory.

Pärt’s music operates similarly, though in a modern context. His work feels ancient, even though it was composed recently. The sound suggests continuity with something older than modernity itself.

Perhaps most importantly, this musical preference reveals an unusual relationship with time. Chant and Pärt slow perception. They create a space where minutes stretch, and attention deepens. In a culture built on acceleration, this becomes a quiet act of resistance.

The listener who loves this music is therefore not simply nostalgic or eccentric. He is practicing a different mode of attention.

At the core, that may be the real attraction. Silence, when properly structured, becomes a kind of equilibrium. And equilibrium, as it turns out, has its own music.

Oddly enough, and this is another extraordinary bit of synchronicity, I do have knowledge of specific aspects of the medieval world. I took around a half-dozen seminars on the history of medieval science back in the 1980s. I was tracing the shift from the demon-haunted world of that day to the more enlightened one of the Scientific Revolution. During all that time, the importance of music never came up. I can’t remember it ever being mentioned, and I never considered the musical tastes of the day to be relevant to anything I was studying.

Now I can conclude this section of the post. How? How else but with a discussion of French High Brow Cinema.

 

Zbigniew Preisner

 

I have a young friend (is a rapid approach toward 30 considered young?) named Sage who recently completed a master’s degree in English. I tagged along for the entire program. I read the assignments, watched the things they watched, and looked over her papers before she turned them in. Truth told, she didn’t need me to look over anything. She is a very smart and extraordinarily capable lady.

One of the last classes she took addressed the French Philosopher Jacques Derrida and his thoughts on what is known as Narrative Framing. Yeah, yeah… I know, not your run-of-the-mill topic. The professor had everyone watch three movies by the brilliant Polish director Krzysztof Kieślowski, a true person of genius. Known as Three Colours (Blue, White, and Red), the films are masterpieces of European (particularly French) Cinema. I believe I fall in love with Irene Jacob, the brilliant actress, again and again every time I rewatch Red, my favorite of the trilogy.

Sage’s professor repeatedly mentioned that the music throughout the trilogy was sublime and deserving of serious study. Her professor was correct. You have probably figured out that Preisner wrote the music for all three movies and that Unky Rick had a Preisner CD among the initial 32 that I found.

When I told Sage what I had discovered, she thought the same thing I did: “How cool!”  The CD, Requiem For My Friend, is a tribute that Preisner wrote for Kieślowski upon his death in 1996. Unky Rick surely knew of the trilogy and appreciated the genius of these two men. That one CD, more than the entirety of the whole collection, convinced me that Unky Rick and I would have enjoyed talking about his love of music.

I would have been happy to share a meal with him as we discussed what he found special about Preisner’s music. I am convinced he would have had some illuminating insights, and it is unfortunate I will never hear them.

 

Conclusion

 

As I write this post, I find myself constantly returning to the tragic events of July 12, 1562. A Franciscan friar (whom I refuse to name), a dimwitted individual from Spain, burned nearly all of the written records of Mayan civilization. They were, in his estimation, works of the devil produced by ignorant heathens. For the sake of all that is good and holy, God himself told the friar that the materials needed to be destroyed. To this day, only four Maya codices survive.

While the destruction of the written records of the Mayan civilization is a tragedy, the disappearance of Unky Rick’s library is nothing more than a footnote in history. Yet, from an archaeological perspective, the situation is the same. The materials are gone, and nothing can be done about it. There was a lot to be learned, but circumstances got in the way.

Why am I fixated on Unky Rick’s library? I have written about my own substantial library. Decades ago, I had hoped it could be kept together and passed down to someone who would appreciate it. I now know that it is a pipe dream. No one will care, and the removal of the books from my home after I am gone will be more of a burden than an opportunity for discovery (good luck, Sage). That doesn’t make me sad; it only makes me shrug my shoulders.

As for Unky Rick’s library, did he have any books about the movie trilogy? Was his copy of Plato’s Republic worn out? I bet he had texts on Aristotle and knew that Socrates didn’t want anyone to write anything down. Did he have any materials about his favorite violinist (Esther Abrami, anyone?) or did he not bother with such trivialities? Would his library tell more about him than the CDs? That is a very good question, and I don’t have a good answer. I do know that my library would expose me.

I have some final, purely speculative, thoughts on Wayne’s wife’s uncle. I don’t think he ever married; there was nothing overtly kid-friendly in the cases. I believe he was highly educated and deeply religious. He certainly could have been a member of the clergy. He was a man who might have felt he was born out of time, believing that the 1300s or 1400s were better times to live in. He watched The Name of the Rose more than once (as I have) and had a highly cultivated mystical (make that spiritual) side (as I do not have).

I believe he lived near Columbus, Ohio, and probably attended Denison University or had a close relationship with it. I gathered this information from the CDs; many were purchased in Columbus, and several feature performances by Dennison orchestras and choirs.

He was a thoughtful, intelligent man in a progressively dense and reactionary world. I would have been delighted to have some tacos and beer with him as we discussed how Preisner’s music informed and framed Kieślowski’s narrative vision. I am convinced he would have had some interesting insights. Finally, I hope he had people in his life who appreciated him, and I really wish I had known him.

 

 

The Guitar Man (Flash Fiction)

It was one of those nights when Daniel felt the weight of his existence pressing down on him. Everyone in his circle had conspired to make him feel small and insignificant, and he realized they had won. His guitar, a sunburst Telecaster, sat propped against the corner of his cluttered apartment, its wooden body glowing dimly in the light of a single table lamp. The coffee table was littered with takeout boxes, sheet music, and rejection letters from record labels. He hadn’t played a gig in months, and even when he did, no one cared.

“Just another face in a sea of struggling musicians,” he muttered, kicking an empty can of beer across the room. He knew that when he died, there would be little evidence that he ever lived. He flopped onto his couch, staring at the ceiling.

Daniel had dreamt of being a musician ever since he could remember, but the universe had other plans. The gigs that came through were sparse and unpaid, his songwriting was stagnant and derivative, and his social media accounts were filled with dismal and indifferent silence. He scrolled through his phone, looking at pictures of famous musicians, the people he envied and tried to emulate. Their lives seemed effortlessly glamorous—beautiful women, sleek cars, sold-out shows. How often do those people have to worry about coming up with the rent? What would it be like to be someone like that?

The thought lingered as he set his phone down and reached for his guitar.

The moment his fingers brushed the strings, something strange happened. He felt a jolt of static shoot up his arm. He flinched, shaking his hand, but the sensation faded almost as quickly as it had come. Weird. He shrugged it off and tuned the guitar, plucking each string with expert precision.

The first chord he played was a G major, the quintessential cowboy chord, a familiar sound that usually brought him some comfort. But tonight, it felt… different. The notes hung in the air longer than usual, vibrating through his skull as if the sound had turned physical. It was then that Daniel noticed the room had begun to shift. His fingers kept moving, strumming a melody he didn’t recognize, his body acting independently.

The walls blurred, and his vision seemed to stretch and twist, pulling him through some invisible tunnel. His fingers kept strumming, and he kept playing the unknown song. And then, everything stopped.

Daniel blinked, finding himself standing in the middle of a crowded club. A stage with bright lights. The electric hum of an audience waiting in anticipation. He looked down at his hands. They were gripping a guitar—a Stratocaster that wasn’t his. The strings hummed beneath his fingers, a warm buzz of anticipation. But it wasn’t just the guitar that was different.

He was different.

Daniel stumbled back, his mind scrambling to understand what had just happened. A glance at the mirror behind the bar stopped him cold. He wasn’t looking at his own reflection. Staring back at him was someone else—a man with sharp cheekbones, styled dark hair, and a leather jacket that looked like it cost more than his monthly rent. His hands, calloused and weathered from years of playing, were smooth and adorned with rings.

“What the hell?” he whispered, his voice sounding foreign in his own ears.

A voice crackled over the speakers before he could fully process what was happening. “Ladies and gentlemen, give it up for John Wisher!”

The crowd erupted into cheers, and Daniel—or John, apparently—felt his legs carry him to the microphone. His body moved with an effortless swagger as if it knew exactly what to do. Muscle memory. Without thinking, he strummed the guitar, hung down much lower than he was used to, and began to play. The song flowed out of him effortlessly, like he had played it a thousand times before. His fingers danced along the fretboard, and John’s voice boomed through the speakers, captivating the crowd.

For a moment, he was lost in it. The music, the applause, the energy of the room. He felt alive in a way he hadn’t in years. But as the song ended and the cheers died, reality hit him like a punch. This wasn’t his life. This wasn’t his body. He was… someone else.

Panicking, Daniel rushed off the stage, ducking into the club’s back alley. His heart pounded in his chest, his mind racing. How was this possible? Was he dreaming? Was he dead?

He clutched the guitar tightly, his fingers trembling as he plucked the strings again, desperate to find a way back. The same strange melody came to his hands, unwelcome and unintentional, and the world around him began to warp again.

With a rush of sound and light, Daniel was back in his apartment, staring at his reflection. His heart hammered, but the relief was overwhelming. He was himself again.

For days, he avoided his Telecaster, afraid to touch it. The experience felt too real to be a hallucination, but he couldn’t make sense of it. Was it magic? Some kind of curse? He didn’t know. All he knew was that playing those notes had transported him into another person’s life.

But curiosity gnawed at him, whispering to him in the quiet moments. He couldn’t stop thinking about the rush of being John Wisher—the thrill of the crowd, the feeling of success. That was what he had always wanted, wasn’t it? To be someone? To live a life that mattered?

Finally, Daniel gave in.

Sitting on the edge of his bed, he picked up his sunburst Telecaster again, his fingers trembling as he played the same mysterious melody. Once more, the room warped and spun, and when the world settled, he was somewhere new.

This time, he was in a recording studio. His reflection in the glass showed a different man—a polished, clean-cut singer in his mid-30s, headphones around his neck, a crowd of producers nodding in approval from the other side.

The life he’d stepped into was equally glamorous. The day was a whirlwind of recording sessions, photo shoots, and catered dinners at expensive restaurants. For a while, it was everything Daniel had dreamed of. He felt important. Admired. Successful.

But as the days went by, something began to gnaw at him. Each time he returned to his own life, his apartment felt more foreign, more distant. The simple act of waking up as Daniel in his shabby apartment became painful. It was as if he had tasted something sweet, only to have it ripped away again.

He began to spend more and more time in other people’s lives. A rockstar in one life, a wealthy and prominent composer in another. With each guitar strum, he was someone new—someone better. But the more he switched, the harder it became to remember who he really was. He would wake up in a stranger’s body and struggle to recall his own face. His own name.

Soon, the lines began to blur. He would return to his apartment after a week spent as some famous DJ, only to feel like he was stepping into a stranger’s home. He no longer felt like Daniel. He no longer wanted to be Daniel.

One night, after an especially wild show as the frontman of an explosive punk group, Daniel—or the person who had once been Daniel—sat in a luxurious hotel room, staring at the Strat. His fingers trembled as he picked it up again, the strings humming softly. He couldn’t remember the last time he had been himself, and he didn’t want to go back.

His life memories were fading like distant dreams—shadows of another existence. He could barely recall his face in the mirror or the sound of his voice.

As he played the familiar melody, the room began to spin, and he smiled. He no longer cared where the guitar would take him as long as he never had to return to the emptiness of his old life.

The last chord faded, and Daniel disappeared, swallowed by the endless stream of lives he would never fully belong to, lost in a symphony of borrowed faces and forgotten names.

In a state of existential despair, Daniel hoped to “become music” and live an infinite supernatural existence. All I know, all that anyone knows, is that if you visit a run-down building in the southern part of Iroquois County, Ohio, you will find a sunburst Telecaster in the corner of a dusty, abandoned apartment, waiting for its next player.

 

 

The Unopened Letter (Flash Fiction)

The Unopened Letter

 

A soft thud echoed from the hallway. Marie looked up from her computer screen, her glasses slipping down the bridge of her nose. The mail had arrived. She sighed and went to the front door. Bills, advertisements, a postcard from some real estate agent—nothing unusual.

But there was one letter that caught her eye.

It was different. No return address, no postage stamp. Just her name scrawled in a familiar hand. Her hand. Marie’s breath hitched in her throat. She turned the envelope over, but it was sealed shut with an embossed wax stamp. Her intuition told her this wasn’t some prank. She had written the letter. But how? When?

She stepped back inside, the world outside the door suddenly too sharp, too loud. Sitting at her kitchen table, she stared at the envelope, her fingers tracing the edges of the paper. The handwriting was unmistakable. The way her “r” curled slightly, the way she looped her “e”—it was her own. But she hadn’t written a letter to herself, had she?

Marie’s heart quickened. The edges of the world seemed to blur, like reality had bent just slightly. The envelope weighed heavier in her hand than any ordinary letter should.

The air in the kitchen felt stifling. Her fingers twitched, wanting to tear it open and read the words. Yet, something held her back. Fear. What could it say? Was this some kind of cruel joke, was her intuition deceiving her, or was it… something more?

She shook her head. This was ridiculous. Letters didn’t just appear out of nowhere. There had to be a logical explanation. Maybe she’d written it and forgotten, right? But then how did it get delivered?

Her phone rang, her boss demanded a report be submitted by the end of the workday. Marie knew it was due, and she had already done much of the work, so she quickly hung up and went into her home office.

The end of the day was approaching when Marie got another call. The main office needed numerous items added to the report. She took a deep breath and worked late into the night.

The following morning, Marie was awakened by her phone. A text message from Greg:
Hey, are we still on for dinner tonight?
A normal text. Everyday life, pulling her back into routine. She swallowed, glancing between her phone and the letter on her nightstand.

Yeah, she typed back, 7 p.m. at Luca’s, right?
Right.

She felt relieved by the prospect of a night out. She picked up the envelope and brought it into the kitchen. She picked up a butterknife to use as a letter opener but quickly put it back. Her fingers hovered over the edge of the envelope once more before she tucked the letter into a drawer. Later. She would deal with it later. She wasn’t ready now. It can wait.

But Marie couldn’t forget the letter.

Back at work, she found herself distracted, staring at her computer screen but seeing only the envelope. During her lunch break, she examined her desk, half-expecting the letter to have magically appeared. She had to consciously stop herself from running into the kitchen, tearing it open, and confronting whatever lay inside.

The anxiety clawed at her all afternoon. What could the letter say? How did it end up at her door? The thought gnawed at her, and by the time she had finished the day’s tasks, it was all she could think about.

When she turned off her computer, the first thing she did was head to the kitchen drawer. She stood there, staring at it for a long time, her hand resting on the handle. Slowly, she opened the drawer and pulled out the envelope. Her heart hammered in her chest as she sat down with it again.

“Okay,” she whispered to herself. “Okay.”

Her thumb slid under the flap of the envelope, and—

A knock at the door startled her so badly that she dropped the letter.

Marie stared at the door, her pulse racing. She wasn’t expecting anyone, was she?

Another knock, this one more insistent. The letter lay on the floor, unopened.

She left it there and crossed the room cautiously. When she opened the door, Greg was standing on the porch, his hands stuffed in his jacket pockets. His smile wavered as he took in her frazzled expression.

“Hey, you okay? You didn’t respond to my last text. I thought I’d just come by and make sure we were still good for dinner.”

Marie blinked, her mind whirling. She had completely forgotten.

“Yeah, dinner. Right.” She glanced over her shoulder at the letter on the floor, still sealed. “I… uh… just lost track of time.”

Greg raised an eyebrow but didn’t push. “You sure you’re alright? You look like you’ve seen a ghost.”

“I’m fine,” she said quickly, rubbing her arms. “Just… distracted.”

His eyes followed hers to the envelope on the floor, but he didn’t comment. “Okay, well, if you need to reschedule…”

“No,” she interrupted, forcing a smile. “Dinner sounds great. Let me just grab my coat.”

Throughout dinner, Marie tried to push the letter from her mind, but it was impossible. Greg’s voice became background noise as she ran through every possible scenario. If she had sent herself a letter, it had to be important. Urgent. But what if opening it changed everything? What if reading the letter caused something terrible to happen?

“Marie?”

She blinked, suddenly aware that Greg had been talking to her. “Sorry, what?”

He frowned. “You haven’t heard a word I’ve said, have you?”

“I’m sorry, I just—” She paused, lowering her fork. “Something weird happened yesterday.”

Greg leaned forward. “Weird, how?”

“I got a letter. From me.”

His brow furrowed. “From you?”

“Yeah, like… it was in my handwriting. My name, no return address. It just showed up, and I have no idea how.”

Greg sat back, his face a mix of confusion and mild amusement. “Maybe it’s some kind of prank?”

“I thought of that, but… I don’t know. It felt too real.” She shook her head. “I haven’t opened it yet.”

“Why not?”

“Because… because what if it’s something I’m not ready to know? What if it’s a warning or…” Her voice trailed off, her chest tightening.

Greg was silent for a long moment. “Marie, if you wrote this letter to yourself, there’s a reason. Maybe it’s something you need to hear.”

She stared down at her plate, her appetite gone. “I’m scared.”

“I get that,” Greg said softly. “But maybe the fact that you’re scared means you need to read it.”

That night, Marie sat on her bed, the letter resting in her lap. The edges of the envelope were soft now from all the times she’d handled it, but it was still sealed. Still waiting.

She took a deep breath, trying to steady her nerves. Her hands trembled as she finally slid her finger under the flap and tore it open. A faint yellow glow surrounded her hands as she removed the sheet of paper.

The letter inside was short, only a few lines. Her heart pounded as she unfolded the paper and began to read.

In her own handwriting, the message was simple:
Don’t open the door tomorrow.

The words blurred before her eyes as the realization hit her like a punch to the gut.

Tomorrow.

 

In the Presence of Shadows (Flash Fiction)

In the Presence of Shadows

 

When Jacob first woke, the air in his bedroom felt thick, like a smothering weight pressing down on him. His eyes blinked open to the familiar shape of his bedside lamp, the faint glow of morning just barely filtering through the curtains. But there was something else.

Someone was standing at the foot of his bed.

His heart leaped into his throat. A tall, shadowy figure, darker than the rest of the room, seemed to loom over him. Jacob froze, his body paralyzed with a cold, creeping terror that crawled up his spine. He tried to blink it away, telling himself it couldn’t be real. His fingers clutched the sheets, the pulse in his ears deafening.

But the figure didn’t move.

A breath caught in his throat, sharp and painful. Then, in an instant, like a trick of the light, the shadow was gone. There was nothing there—just the familiar shapes of his dresser, the door slightly ajar, the room as it always had been. Jacob sat up, swallowing hard, his hands trembling as he dragged them through his sleep-tousled hair.

It was a hallucination, just a figment of his groggy, half-asleep mind. It had to be. He’d been stressed—work had been hell lately, and his sleep schedule was a mess. This kind of thing could happen to anyone, right?

He swung his legs over the edge of the bed and planted his feet on the cool hardwood floor. He rubbed his face, trying to shake off the lingering unease. He’d been on edge for days, running on caffeine and fumes. The vision had been a warning from his overworked brain, no more, no less.

Jacob stood, stretched, and padded toward the bathroom. The rest of the morning was supposed to be mundane—shower, shave, breakfast—but as he went down the hallway, he felt… off. His steps seemed too loud on the floor; his skin tingled like it didn’t fit quite right. The quiet of the house had a strange weight to it, like it was watching him.

Shaking his head, he tried to dismiss the thought, but the sensation persisted, an inexplicable tightness in his chest.

When he stood at the kitchen counter, pouring himself a cup of coffee, the unease had settled into something more tangible. Every so often, he’d catch a flicker of movement from the corner of his eye—a shadow darting across the wall, a figure slipping behind a corner. His head would snap toward it, only to find nothing there. Empty spaces. Ordinary silence.

Jacob clenched his jaw, forcing himself to focus. “Get it together, man,” he muttered, gripping the coffee mug too tightly, his knuckles going white.

The momentary distraction helped. He busied himself with making toast, methodically buttering the bread, the warmth of the kitchen offering some comfort. But as he reached for the silverware drawer, his hand brushed something cold.

Startled, Jacob looked down. His fingers had grazed the handle of a knife, but the metal felt icy, far colder than it should have been. He pulled his hand back, and in the reflection of the knife’s blade, he saw something move behind him.

He whirled around.

Nothing.

The kitchen was empty, just as it had been. His eyes scanned the space, his heart hammering in his chest. His mind was playing tricks on him, indeed. But the knife…

He stared down at the butter knife. It was just a regular utensil sitting innocently on the counter. Maybe the air conditioning had kicked on. Maybe—

A sharp pain shot through his right hand, causing him to drop the knife with a clatter. He gasped, clutching his hand, his pinky throbbing like he’d jammed it in a door. He flexed his fingers carefully, but something wasn’t right. The pinky seemed… off. It was bent at an unnatural angle, swollen and discolored.

“What the hell?”

His breath came faster now. He hadn’t hit it on anything. He hadn’t even touched anything hard enough to break a bone. Panic began to bubble up inside him, mixing with the strange, disorienting feelings that had been plaguing him since he woke. His skin felt too tight again, his thoughts scattered.

Something was wrong. Really wrong.

The coffee mug slipped from his grasp, shattering on the floor. The sound rang in his ears, louder than it should have been, like a gunshot. Jacob flinched, his pulse racing.

It was enough. He grabbed his phone, fumbled for his car keys, and within minutes he was out the door, driving with one hand while his broken pinky throbbed in time with his heartbeat.

The fluorescent lights buzzed overhead at the emergency room, casting a sterile glow over the rows of plastic chairs and the low hum of chatter. Jacob sat with his right hand cradled in his lap, his mind still spinning. He kept running his thumb over the curve of his pinky, feeling the break, the way the bone didn’t line up quite right anymore.

A nurse finally called his name, leading him into a small exam room. The doctor arrived soon after—a tall, wiry man with graying hair and a kind smile. He introduced himself as Dr. Fields, gave Jacob’s hand a cursory glance, and immediately ordered an X-ray.

That creeping sensation returned as Jacob sat on the examination table, waiting for the nurse to return with the X-ray machine. The room felt too cold, and shadows seemed to pool in the corners where the overhead light didn’t reach.

He glanced toward the open door and saw something. A figure, tall and thin, standing just out of sight in the hallway.

His chest tightened. He could barely breathe. His vision wavered, like heat rising off asphalt. He blinked, and the figure was gone, swallowed by the sterile white light of the hospital.

The nurse wheeled in the X-ray machine, oblivious to the tension thrumming through him. He forced himself to sit still, to focus on her instructions as she positioned his hand for the scan. But his heart wouldn’t slow down. His mind raced.

The hallucinations were getting worse.

The scan took only a few minutes, and soon, Dr. Fields returned with the results. He slid the black-and-white film onto the lightbox and flipped the switch, illuminating the delicate bones of Jacob’s hand.

“Well, Mr. Hale,” Dr. Fields said, his brow furrowed as he examined the X-ray. “It’s definitely broken, but… it’s odd.”

“What do you mean?” Jacob asked, his voice tight.

“This kind of fracture is more common in crush injuries or severe trauma. It’s clean, but with enough force applied directly to the bone to cause significant displacement.”

Jacob swallowed. “But I didn’t do anything to it. I mean, I didn’t hit it or crush it or anything.”

Dr. Fields looked at him thoughtfully, concern flickering in his eyes. “You don’t remember any impact at all? No recent accidents?”

Jacob shook his head. His hand throbbed again, the pain sharp and insistent.

“I’ll put a splint on it for now,” the doctor said, “but I’d recommend seeing an orthopedist in the next few days. This isn’t a typical break.”

Jacob nodded, barely hearing him. As the doctor left to retrieve the splinting supplies, Jacob’s gaze drifted back to the X-ray film. His bones seemed fine, normal, except for the fractured pinky. But behind the bright white lines of his skeleton, deep in the shadows of the film, something strange caught his eye.

There, nestled between the bones of his hand, was a faint, dark outline. It was almost imperceptible, but once Jacob saw it, he couldn’t unsee it.

A shape. Like a hand—thin and skeletal—resting over his.

A shiver ran down his spine. His breath caught in his throat.

He stared at it, unblinking, as the cold hospital room grew darker around him.

 

Twilight Embrace (Flash Fiction)

Twilight Embrace

Roland stood on the edge of the pier, the salty sea breeze ruffling his thinning gray hair. The sunset cast a golden glow on the water, turning it into a shimmering mirror. He’d always loved this time of day, when the world seemed to slow down, the chaos of life pausing to catch its breath. But tonight, the sunset was more than just a daily spectacle; it was a backdrop to the thoughts that weighed heavily on his mind.

He heard her footsteps before he saw her, the soft patter of sandals on wood. He didn’t need to turn around to know it was Lila. She had a way of walking that was almost musical, each step a note in a melody that only he could hear. When she reached his side, she leaned on the railing, her youthful face glowing in the fading light.

“It’s beautiful, isn’t it?” she said, her voice as light and airy as the breeze.

Roland nodded, his eyes lingering on the horizon. “It is,” he agreed, though he wasn’t sure if he was still talking about the sunset.

He stole a glance at her, his heart tugging in that familiar, bittersweet way. Lila was young, vibrant, full of life—everything he no longer was. Her hair was a cascade of chestnut curls, her skin smooth and untouched by time. But it wasn’t just her youth that captivated him; it was the way she looked at the world, with wide-eyed wonder and an unshakable belief in endless possibilities.

He’d met her at the community center where he volunteered, teaching a creative writing class. She’d signed up on a whim, she’d said, looking for something to fill her summer days. But from the moment she walked in, Roland had been drawn to her. It wasn’t a sudden attraction, like a lightning strike. No, it had been gradual, a slow unfolding of admiration, respect, and something deeper that he hadn’t felt in years.

They’d spent hours talking after class, about books, music, and the dreams she had for her future. Lila was open, honest, her emotions unfiltered. Roland found himself sharing parts of himself that he’d kept hidden for decades. He felt alive in her presence, like a man much younger than his 63 years.

But as much as he cherished their connection, he couldn’t ignore the nagging voice in the back of his mind. He was old enough to be her father, perhaps even her grandfather. What could she possibly see in him? The thought haunted him, twisting his emotions into knots. Was it wrong to feel this way? Was it foolish?

Lila turned to him, her eyes catching the last rays of the sun. “Roland, you’re awfully quiet tonight.”

He forced a smile, hoping it didn’t look as strained as it felt. “Just lost in thought, I guess.”

She tilted her head, studying him in that way she had, as if she could see right through to the core of him. “You know, age is just a number,” she said softly, as if reading his mind.

His breath caught in his throat. “Lila, I—”

She reached out, placing a hand over his. It was warm, comforting, grounding him in the moment. “You make me happy, Roland. Isn’t that what matters?”

The simplicity of her words hit him like a wave. All the doubts, the fears, the self-recrimination—they seemed to dissipate in that instant, carried away on the breeze. He looked into her eyes, seeing only sincerity there, and something that might have been love.

He squeezed her hand gently. “Yes, Lila. That’s all that matters.”

And as the sun dipped below the horizon, casting the world into twilight, Roland felt something within him shift. He didn’t know what the future held for them, but for the first time in a long time, he was willing to embrace the unknown.

 

Steps Forward (Flash Fiction)

Steps Forward

Sergio stood at the edge of his driveway, phone in hand, staring down the quiet, leaf-strewn road that led to the harbor. The late September air was cool, tinged with the smell of damp earth and the first hints of winter. Lake Erie was only three miles away, a place he’d gone a thousand times before, but tonight was different. Tonight, he needed the walk. He needed the beer.

He scrolled through his contacts, hoping someone might answer, someone who could drive him down to the old pub by the harbor—Murphy’s Place. It was a spot he’d frequented in better days, back when life felt less like a cage. But now, it was just a distant reminder of the way things had changed.

The first call went to voicemail. “Hey, this is Dan. Leave a message.” Sergio didn’t bother. He tried a few more numbers—each one met with the same silence, or a polite but firm excuse. “Busy tonight, Sergio. Maybe another time.”

He let out a long sigh, shoving the phone into his jacket pocket. No one was coming. It seemed fitting, really. In the last year, most of his friends had drifted away, and those who hadn’t were more like acquaintances now—people with lives too busy for someone who’d become a shadow of his former self. It was easy to let that happen, Sergio thought, when you spent more time with a bottle than with people.

He started walking, his footsteps heavy on the pavement. The streetlights were spaced far apart, leaving long stretches of darkness between them. Sergio welcomed it. The shadows felt like a shroud, something to hide in, away from the prying eyes of a world that no longer made sense.

As he walked, the memories crept in. The accident. The year he’d spent trying to piece his life back together after losing his wife, Ellen. The guilt, the what-ifs that gnawed at him day and night. He’d been driving that night, too tired from work, too stubborn to admit he needed rest. And then the truck, the blinding lights, and the sound of metal tearing like paper.

They told him it wasn’t his fault, that it was a freak accident, but the words never reached him. They couldn’t undo the damage, couldn’t bring her back. So, he’d let the grief consume him, finding solace only in the numbness that came from a bottle.

The harbor came into view, its lights flickering in the distance like tiny beacons. Sergio felt a pull toward it, like it was calling him, offering some small comfort. He reached Murphy’s Place, its neon sign buzzing in the dark. Inside, the warmth and noise greeted him like an old friend. He ordered a beer, the bartender nodding as if he knew. Everyone knew, in a place like this.

But as Sergio lifted the glass to his lips, he paused. The walk had stirred something in him, something he hadn’t felt in a long time. A small, insistent voice that whispered: enough.

He set the beer down, untouched, and walked out of the bar. The night was cold, the air sharp in his lungs as he headed back the way he’d come. Each step felt lighter, the darkness less oppressive. He didn’t know what tomorrow would bring, didn’t have any grand plans to turn his life around. But as he walked back toward his empty home, Sergio knew one thing: he was done running.

The walk had changed something in him, something vital. It wasn’t about the beer, or the harbor, or the friends who no longer answered his calls. It was about the simple act of moving forward, one step at a time. And for the first time in a long time, Sergio felt like he could keep walking.

 

A Crush, A Data Viz, and a Book Long Postponed

A Crush, a Data Viz, and a Book Long Postponed

I have a crush on a YouTuber. There, I said it. I hesitate because there is no chance I would ever approach her and “shoot my shot.”  She is probably half my age…maybe. She might be much younger. I am not delusional; even at my advanced age, I tend to still have my wits about me, so I will choose to keep my powder dry. So, why the crush, and, even more importantly, why would I choose to write about it? Let’s get into that.

Many months ago, I was doing my thing, surfing around the internet in an attempt to find a mathematical basis for the meaning of life (cough, cough), when I came upon an astonishing young woman. Indeed, I wasn’t looking for her, but that is how these things work, right? Most of the interesting things in my life have happened to me while I was standing in a corner, minding my own business, and breathing my own air.

This mysterious YouTuber is a brilliant Ph.D.  in theoretical physics who left academia because…well, that is one of the reasons why she is a content creator. She has many videos detailing why she left the academy to join the corporate world. I was instantly smitten. I was enchanted; I didn’t have a chance to surf away. The deed was done.

Was I instantly attracted to her obvious intelligence? Absolutely.  Was I impressed with her charm and personality? No doubt. And I must say, it didn’t hurt that I found her very attractive.

Immediately after I discovered her, I quit watching her videos. I didn’t need to be reminded of what I was missing while living here in Hillbilly Land. I say from experience and with all confidence that there is no woman like her anywhere near where I live. If such a bright light flickered near me, I imagine we would have crossed paths at some point. As it stands, I have no recollection of such a person. In fact, I just stepped outside and looked up and down my street…nothing. There was a chance she was driving through my town and got a flat tire in front of my house, right? Hold on, I’ll calculate the odds…ah, forget it.

As many of you know, it is much too early for me to reveal the lede (or thesis statement, if you like) as it has not yet been sufficiently buried. Trust me, the payoff is not a bad one. I felt this topic deserved its own essay mainly because I find the whole story unusual and fascinating.

Now, we can leave the present (where I sit overly impressed by a woman I will never meet) and travel back to the mid to late 1980s. The setting is Cambridge, Massachusetts, on the campus of Harvard University. I then was a dude learning graduate-level statistics. Believe it or not, Stem and Leaf Plots and Box and Whisker Plots were on the agenda. Now, kids learn about these things very early. I know a young man presented with these techniques in 6th grade. There are lots of reasons for this. John Tukey, the great statistician, published the seminal book Exploratory Data Analysis in January of 1977. Things take time to filter down to the mathematical masses. The lack of personal computers had something to do with the lag, as did the fact that high school teachers don’t spend much time looking through statistics textbooks. Also, who paid attention to mathematicians back then?   Who read their books? You get the idea. It was about as many people who pay attention to them now, at least on a percentage basis.

Of course, the bigger problem is how long it takes ideas, even great ones, to trickle down to society at large. An idea must go through levels of bureaucracy before it can be included in a public school textbook. No such stipulations apply to university settings. A professor can read a paper and talk about it in class the next day if they are inclined. I was known to do this a time of two. Not that it mattered; I don’t think my students even cared that they were learning something “hot off the press.”  They just yawned and asked if the material would be on the test.

Back then, and to this day, I spent a lot of time studying Tukey’s previously mentioned Exploratory Data Analysis (EDA). His book greatly impacted the study of statistics in general and proved to be a revelation in my little corner of the mathematical universe. I instantly understood the value of visualizing data in the way Tukey described. I wasn’t the only one, as Box Plots are as common today as bar graphs and pie charts.

Inspired by Tukey, I went on numerous statistical  “deep thinks” back in the day. I derived all the equations, both as an exercise and as a way to convince myself of the validity of the methods. It’s not that I didn’t trust the people who set the foundations of statistical thought; I simply thought it was required of me to do so. Many of my professors and I saw it as a way of paying my intellectual dues. Today, there are applied statistics programs that focus on the applications of the methods; they leave the mathematical nuts and bolts to those studying pure statistics. The applied statistics folks are experts at using the techniques; they don’t necessarily care what is under the mathematical hood. Nothing wrong with that. I think there might be an appropriate analogy with those who opt for English degrees instead of the more popular English Literature track.

A central focus of this post relates to an idea I had one day while studying Box Plots, known as Box and Whisker Plots across the pond, and Box and Dot Plots here. Mostly, they are simply called Box Plots, and that is fine. As I was studying a series of plots, not unlike those in the following figure, it started to bother me that the widths of the plots were not diagnostic; they appeared to be totally arbitrary.

Examine the plot illustrating baseball production by position. I created this in R using a dataset I  compiled long ago. The individual plots show the OPS (on-base percentage plus slugging percentage) for different positions in the American League during the 2009 season. The particulars are unnecessary; I just want you to notice the width of the boxes. You will see they all are the same, imparting no valuable information. In fact, the widths reveal no information at all. Shouldn’t the widths of the boxes change to reveal something about the data used to create the plot? Doesn’t that make sense?

 

Figure 1. Box Plots of 2009 AL MLB Hitters by Position.

I considered this issue and decided that the widths could and should reveal some information. I decided to develop a plot with the attributes of a Box Plot but changed widths depending on the number of observations in the data set at each point along the vertical axis of the box. I thought of them as supercharged Box Plots, or Box Plots on steroids, even though I never got to the point where I tried to name them. More on that in a bit.

My task was straightforward and didn’t require much insight to figure out what to do. I put my head down and made some plots, such as the following ones.

Figure 2. Box Plot of OPS for Second Basemen, AL 2009.

As usual, the nature of the data does not matter. This happens to be an OPS Plot of second basemen in the AL from 2009. I used the same data as in Figure 1. Next comes a histogram made from the same data set. Something interesting happened when I fused the two plots together. I say that with hesitation because I was in the extreme minority in my corner of the world.

 

Figure 3. Histogram of same data.

I rotated the histogram 90 degrees and then mirrored it. I then placed those plots on the box plot. It was a very simple process that required no mathematical insight or leap in intuition.

 

Figure 4. Rotated Histogram

 

 

Figure 5. Flipped (Mirrored) Histogram

I came up with the following. It is simply a box plot with varying widths. I wrote up a short paper and started circulating it among my cohorts, professors, passers-by, strangers, and anyone I thought might have an opinion. The results were disappointing.

 

Figure 6. Histogram and Box Plot.

The typical reaction I got was one of confusion. Huh? Why are you doing this? Why are you here? Why would anyone ever need this? This isn’t necessary (the implication being that I wasn’t necessary). I received no positive feedback. I received no neutral feedback. Everyone who saw my plots hated them. I think some people who viewed my plots felt embarrassed for me. It was a disaster.

I believe it goes without saying that I shelved my “box plots on steroids” project and went on with my life. If I had heard one word of encouragement, I would have developed the idea into a publishable paper.

I didn’t think of it again…until…a few weeks ago. I was using R, my computer language of choice, when I came across something curious. That is not unusual in and of itself; it happens constantly. What caught my attention was an image of something called a Violin Plot. I instantly recognized it. The output was very similar to my old project. Sure, the edges were smoothed, but the idea was the same.

I took a deep dive into Violin Plots. I realized that my idea from all those decades ago was now a common choice for those looking to create a statistical plot or data visualization, commonly known in data analysis parlance as a Data Viz.

 

Figure 7. Violin plot of Second Base Data.

 

 

Figure 8. Violin Plot overlayed on my original plot.

 

Figure 9. Violin Plot of Figure 1.

It is now time for the payoff to this essay. No, the point is not that I came up with an idea that was apparently way before its time. While interesting, I am sure that being attributed with the creation of Violin Plots wouldn’t have changed my life in any meaningful way. As mentioned, their existence requires no great insight or intuitive leap of significant consequence. No, the curious thing is what happened when I went on my deep dive of Violin Plots.

As I searched in an attempt to learn all I could about the newly revealed Violin Plots, I stumbled into a rabbit hole. I fell in face first, and as I dusted myself off and began my climb back to reality, I came across a scathing video by a young woman who HATES Violin Plots. She methodically went through her case. Many of her points were ones I had heard nearly 40 years ago, e.g., they aren’t necessary, it is easier to just use a histogram, box plots are fine, etc…

She also had one major criticism that had never occurred to me. In the last few weeks, I had spent a great deal of time looking at different Violin Plots, and I never thought they looked like anything other than violins. Seriously, I didn’t. The young woman’s main criticism of the plot is that immature males take their shape to resemble something other than a beautiful-sounding musical instrument. Unfortunately, she has a lot of anecdotal evidence to support her claim that these plots should never be used by anyone for any purpose.

I swear to you that what I will now tell you is accurate. If it wasn’t, I never would have written this essay. I almost feel stupid writing this because I am sure most of you have figured out that my YouTube crush and the young woman who hates Violin Plots are the same person. I would never have written such a scenario in a work of fiction because it sounds too contrived, yet here we are. I’ll slowly shake my head in disbelief as I crack open a beer.

What about the book, the one referenced in the title? I am guilty of more than a little foreshadowing. Yes, it is a book on baseball analytics. I started writing it in 2002. It got put off because I was compelled to write another book in its place. That entire book, The Athena Chapters, is posted on this site. My long overdue baseball book will be completed relatively soon, and much to the disappointment of my YouTuber, it will be full of Violin Plots because I find them diagnostic and beautiful. I know she disagrees, but I don’t see us arguing over their utility and functionality at some fancy dinner party. I’ll apologize in advance, place the plots where I want, and take my chances.

 

 

 

Gas Cards

I am broken…defeated. I fought the good fight, but I lost. Better people than me have experienced a worse fate.  The future I always had planned for myself is dead.  There is nothing I can do about it.

As some of you know, I spent my best years at Harvard University. I was there for about 6 years. Those are my ‘good old days.’  I still dream about the basement I lived in across from Tufts University.  For a time, I had a lab at Vanserg Hall.  It was miles away from my little apartment, but I used to walk. The entire area is charming.

I didn’t want to leave. I really didn’t want to leave. The Harvard community calls it “Exile from Eden” for a reason. They kick you in the butt, give you a mission, and tell you to go.  For the most part, you have to go.  The first time I graduated, I stayed and got another degree.  They really wanted me to leave after that, and so I did.

I like telling people about how remarkable that place is. I could easily sit down at a table with nine other people and know that there was an excellent chance that I was the tenth most interesting person there. Where I live now…not so much.

I have been thinking about Harvard because I am getting old. My brain has betrayed me. I don’t have trouble learning anything, but retention is a different story. Sometimes, I can not remember what I studied five minutes after getting up. That might be the main reason I study so much. Perhaps I am in a constant loop and have no clue. I do know I still love learning. And that brings me to Cliff Stoll.

I have written about the great Cliff Stoll, an astronomer who makes Klein bottles. He is a national treasure. Seek out his TED talk (The Call to Learn); he is a force of nature. He made one of the most profound statements I have ever heard during that 17 minutes. He said that if you do something once, you are a scientist; if you do it twice, you are an engineer; three times makes you a technician. I would add that the fourth effort makes you a trained monkey.

Stoll was talking about the mindset of a scientist, those true-born intellectual explorers. Once scientists have done something, they aren’t interested in ever doing it again. The appeal is to move on to the next problem. What else is unknown? Confirming someone else’s discovery is uninteresting.

One of the great tragedies is when a scientist, through circumstance or bad luck, is forced to do repetitive, soul-crushing monkey work for their entire working life. If you were not born with the spirit of a scientist, I imagine the monkey work is a little easier to take. For the scientists, even those doing the work of an engineer, it is heartbreaking.

Is there a point to this short post? Sure, as always, I like to bury the lede. I want to plant it deeper, but I am tired, worn out. As I said earlier, I am broken.

I fought the good fight; I really did. Some dreams die hard, and I am still shocked that mine passed away. I am shaking my head at the prospect of a dreamless future. I am disappointed. I need more time to reflect on this.  I will wake up tomorrow knowing that I need to win the lottery if I ever want to pursue my life’s work.  I do not anticipate winning the lottery.

At Harvard, people would often ask what equation would be on your tombstone or what the first line of your obituary would say. Yes, it really is that kind of place. As I have gotten older and my abilities have faded, I find myself thinking about that ‘contribution to humanity’ we were supposed to make. They were serious about it. We were all tasked with making the world a better place. It never occurred to me (until now) that I wouldn’t leave the world a better place than I found it.

I have yet to make that contribution; I haven’t done anything substantive, at least not in my eyes. That might be one of the reasons I have not set foot on that campus in over 30 years.

Some of you would disagree with my assessment, but I am the only true arbiter of success or failure. Just as you are with your life. No one else’s opinion is of any consequence.

I have been busy, I have written 16 novels and books under various pennames, but none are extraordinary. One was really good, but that contribution the Harvard people told me to make remains elusive.

I always knew I would spend my last years writing that great novel, the work representing my contribution. I worked hard to put together a plan that has been in place for decades. I was going to get a little place in Portugal or in South Africa, and I was going to drink some warm beer and write…a lot. I would leave behind a record of what it was like to be me.  Now, I am hurt.  If I believed in a soul, I would say mine is wounded.

Pushing my attempt down the road was not ideal, but I had little choice. I kept getting up every morning because I knew the day would come when I could sit by the beach with my computer or notepad. I would fight off inferior insights as The Muses battled for my ear.  That is not going to happen.

I have told friends I prepared for every eventuality except what has now befallen me. The universe broke me. Of course, I always knew it was indifferent to me, but it has been known to go way out of its way to make me feel its destructive power. The evolutionary biologists at Harvard used to constantly remind me that the universe is not cruel; it is simply indifferent.  They had to keep telling me because I had difficulty believing it.  I still don’t know what to think.

I won’t be going to Portugal or Africa. I will remain here in Hillbilly Land, a scientist stuck in the monkey clutches of an apathetic world. The hows and whys of my plight are uninteresting and don’t matter.  I must find a new reason to lift my head from the pillow.

The odds of me writing a great novel while stationed in Hillbilly Land are nil. I can’t fake inspiration; unfortunately, this is this continent’s most uninspired piece of land.   Hope does not spring here; this is where hope comes to die. This town is depressing, the people are (predominantly) uninteresting, and the weather is terrible.  I do not understand where I am supposed to draw the inspiration from.

I will let out a sigh as I contemplate my fate. I am sorry for all the people back in Cambridge who believed in me and expected something substantive. It is unlikely that is going to happen. The New York Times will certainly not notice my demise. As for that tombstone, burn me and throw me to the wind.