Category: Misc

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

 

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

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

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

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 6^th 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.

 

 

 

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.

The Greatest Tweet

I am not a big social media guy.  I do have a Facebook page, but it is under a pen name.  I never visit it and don’t believe I have ever posted on it.  I don’t feel social media is necessary for me; if I have anything to say, I can speak up here.  Of course, this blog is also written under a pen name.  I guess the real version of me has very little to say at all.

So, how did I come across a tweet?  This one made national news, and I instantly realized why.  When the Twitter platform was conceived, the creators could never have imagined something so wonderful and insightful delivered through their code.  And yet, here we are.  I admit I am a novice and have no Twitter experience, but I can say with certain authority that what follows is the greatest tweet in history.  Let me slightly amend that; this is the most fabulous tweet possible.  People who tweet in the future can only hope for second place when the history of great tweets is written.  Behold…

This image was shared the other day.  The left-hand side shows 13 metrics that the team uses to evaluate players.  In the lower right, they tell us that the team assigns each player a score from 0 – 100 based on their analysis.  The revolutionary aspect of this visualization is the “analytics cylinder,” complete with the Bears’ logo.  I have been studying analytics and data visualization for decades, and honestly, this is the greatest thing I have ever seen.

Think about this, did the Bears risk giving away any proprietary information relating to their analytical process?  If anything, the Analytics Cylinder (yes, that deserves to be capitalized) creates more mystery.  What exactly are they doing?  Are they using Python, SQL, and R, or alien technology from Area 51 in concert with quantum computers to pick the most promising players for their team?  I don’t know, but I am interested.  Before I saw the tweet, I didn’t care one bit about how the Bears went about their data analytics.  Now, I assure you, I can’t get enough.  I might set up an account just so I can follow them.  Who knows, maybe a Database Rhombus is next.

 

Datasaurus!

Well…that is something.
Buford Lister (personal communication)

That is in the top seven of the coolest things I have ever seen.
Warren Andrew Slay (personal communication)

This post takes off where the last one (Anscombe’s Quartet) ended.  Anscombe had four data sets, whereas the mighty Datasaurus file has 13.  Yes, it is either a Baker’s Dozen or you can think of it as the dino plot along with 12 others (the Datasaurus Dozen) that illuminate its glory.  Either way, prepare to be dazzled.

As with Anscombe, the summary statistics for all these plots are virtually identical.  (x mean = 54.26, y mean = 47.83, x SD = 16.76, y SD = 26.93). Yeah, yeah, the 4^th or 5^th decimal place is different.  So what?  If you think that is important, I can’t help you.  Please just relax and behold the Datasaurus Dataset.  And yes, please be careful with your data when engaging in a project.  That just might be the point of the following plots.

I hope you are astonished.  I find it fascinating that all these plots share the summary statistics I mentioned earlier.  Considering those commonalities, I wouldn’t have thought it was possible to get this kind of variability.

If you want to learn more about these graphs, search for Alberto Cairo and the team of  Justin Matejka and George Fitzmaurice.  They have done good work.  They all want us to think carefully about our data.  I could not agree more.

 

Anscombe’s Quartet

Let’s be Frank; this data set is interesting.
Buford Lister (personal communication)

 

Yale statistician Frank Anscombe published a short paper in 1973.  As I recall, around that time, Tony Orlando hoped to see a yellow ribbon wrapped around an old oak tree while The Godfather dominated award season in the film industry.  As for me, I can’t recall, but I am sure I was wearing bell-bottom pants and a flimsy shirt to the local grade school.  Anscombe’s paper and The Godfather have fared much better than those bizarre jeans (the huge ones were called elephant pants, my flavor of choice).

In Anscombe’s paper, he introduced what has become known as Anscombe’s Quarter, one of the most famous data sets in the world.  Pay careful attention to the summary statistics at the bottom of the table.

Do you see it?  The summary statistics are virtually identical.  Back in the day, before computers were ubiquitous, many relied upon these summaries to get a general idea of their data.  After all, what else were they supposed to do?  Believe it or not, Box Plots and Stem and Leaf Plots were not commonplace.  Anscombe’s brother-in-law, the great John Tukey, introduced them and other exploratory data analysis techniques during this time.

I am sure many of you are ahead of the game.  You know the data set wouldn’t be famous, and I wouldn’t write about it unless there is something extraordinary about the data.  Take a look at the following graphs.

I only recently came upon this dataset.  I am currently learning Python and SQL.  I am also brushing up on R, a statistical package I have been fighting with for decades.  For those of you too young to remember the baby version of R, it consisted of a command prompt and numerous 1,400-page manuals.  Things are much better today.

This data set has appeared more than once in my recent studies.  It usually appears as a cautionary tale against making assumptions and refusing to think when you may be tired and want to go to bed.  Also, it serves as a stunning reminder to never forget to plot your data.  As you can see, the plots are essential to truly understand the data you are analyzing.

Even though I am done with this essay, I am just beginning with my “data” themed posts.  I have lots of information burning a hole in my hard drives.  I assure you, Anscombe’s Quartet, as brilliant and illuminating as it is, is just the beginning.

P.S.  Don’t forget to check out the regression equations.  Amazing.

A Few Thoughts from the Big City

Do any of us set out to live an uneventful, pedestrian life? My guess is that, yes, many of us want nothing more than a decent partner, a job that pays the bills, and kids that don’t end up as axe murderers. In the land of low expectations, you could do a lot worse.

I am back at the library, the intellectual and cultural center of this neck of Hillbilly Land. There is a man a table away from me struggling to get his phone charged. He is unhappy with the progress the USB port is giving him. He reached into his duffle bag and pulled out a couple of chargers. Those do not appear to be sufficient either. A mild inconvenience for me could prove disastrous for this man.

I could invent a back story for this homeless person. That is what writers often do. I have done it all my life. One guy is a secret agent, another a fledgling serial killer. See that guy over there?  He is about to steal a large sum of money from work so he can run off with his mistress.  I am not sure any of those random people would be given a backstory that matches their reality. A homeless man’s story is only interesting if they can somehow come out the other side with their wits intact. I am rooting for this guy, I haven’t seen him before, but the other homeless people know him. They are all saying hello or nodding in his direction.

When this man was a child, I doubt he envisioned that he would be an old guy without a home or a job. Perhaps he even had parents who had bright hopes for his future. No one wants to think that they will be the guy sitting by himself at the library, loudly cursing the phone charger that is letting him down. Indeed, no parent would wish that fate on their child.

Could it just be a bad cable? The dollar store sells them, and most of them are good. Still, the occasional defective actor slips through the quality control process. I bought many cables there and have had excellent luck with them.

Author’s Note:  I had a lot of trouble sleeping again last night. The past, a place I have a complicated relationship with, has been tugging at me. Thinking about the deaths of people who die far too soon can do that. Perhaps I am worried about living long enough to finish all my projects. That is probably it, right? Old Killy McGee has come after me twice in the last six or seven years. I have been lucky. I hope I won’t need to dip into that well again soon. It is a morass of stochastics and probability that allows only so many withdrawals before the bean counters take some initiative and do their thing.

A woman, another homeless person I have never seen before, just sat down with the man having phone charger issues. She is much younger than him. She is clearly agitated. I could take off my headphones to get a sense of the conversation, but I would rather listen to Mozart in my headphones rather than their conversation.

An interesting thing just happened. The people at the table are having animated conversations, not with the other person across from them, but with themselves. If I had a solution to this problem, I would present it. I would write it up, send it to anyone I thought would read it, and then work to implement a plan. I have nothing.

Mozart juxtaposed with hopelessness. And here I sit, the eyes through which a nonsensical story with no plot, direction, or purpose, is told. Mozart’s death was an unnecessary slap in the face to humanity.  He was taken from us way too soon in the most significant cosmic ripoff in history. The universe didn’t care that a genius was struck down before reaching his prime. I can’t help but think that the universe has the same attitude toward the two people at the table across from me. Genius, homeless, no matter.

The woman at the table is becoming increasingly animated as the man is loudly mumbling about a local church. I guess they will stop by there and get their lunch. They might be a couple, even though he appears much older. Love, right? Who can know how such things happen. Who understands the chemical, biological, or cosmic forces that work to bring two fragile and precarious people together. I have no thoughts on how such a thing might have happened to them (in particular) or others (in general).

Implied Author’s Note: I tried to publish the post I wrote about Dawn and her memoir yesterday. Things became odd, very odd. My website says that the post was published, and I can see it on my computers at home, but it does not appear on any other computers. I have no idea what is happening. In the past, with hundreds of other posts, I have never had this problem. I spent some time researching the problem, and I came up empty. It must be some kind of omen, right? Maybe not, probably not, most certainly not. I am sure it is some random nonsense that has a technical solution.

The couple just left together. He struggled to lift his backpack from the floor, his arthritis creating problems I am familiar with. She did much better. She had no problem jumping up, her backpack already around her shoulders. I wish them luck, but they will need more than I can offer, a lot more.

Author’s Note:  I do not make New Years’ Resolutions. If a person wants to change, they should simply do it. An arbitrary date on a calendar means nothing to me. That said, I have 8 books I want to get out the door and into the world this year. Some are 90% done, others closer than that. A couple volumes are going to require a lot of revision. Time and energy are in short supply in my general vicinity.

I usually sit and write at the library until I get up to use the bathroom. Old guys need to go a lot. For any young men who might be reading, when you reach my age, you will wake up in the middle of the night, probably multiple times. You are going to plan your travel so that a restroom is always close. The whole thing is an inconvenience and can quickly become a major problem. Hopefully, modern medicine will progress to the point where discussions such as these will be forgotten by the time you are my age. Good luck to all of you.

I have moved upstairs to the nonfiction section at the library. I am very hungry, but I am still on my “post-blood-clots-trying-to-kill-me-diet.” I am hungry all the time. I am hungry when I go to bed and hungry when I wake up. I am hungry all day and into the night. The powers that be tell me that is better than dropping dead. Most days, I tend to agree.

Implied Author’s Note: I recently discovered that nothing I have ever written has influenced a single person. How did I come to such a realization? That is a topic for a novel. If I can get those 8 other books out the door, I can work on that one.    With luck and a cheeseburger or two (something I haven’t had in years), things will be just fine.

Highly unlikely or even inconceivable events do happen on occasion. This might be one of those strange moments in time. Bizarre might be another word for it. I need to leave and go home. Against all odds, my laptop charger is malfunctioning. When I get home, I will try another cable. That’s probably all it is, right? I just need to swap out the cable. If that doesn’t work, I will have to think of other things I might be able to do to fix this mess. Without a charged laptop, there isn’t much for me to do at the library, and there is not much they can do for me. I don’t need any social services; I have a home and a job. I took a shower before I came in this morning. I think I’ll just head home and think about what I want to eat.