Group 1: Anacrusis, Frisson, John P. Sousa, Tempo (Music) Group 2: Planck scale, Fusion, Wavelength, Schrodinger (Physics) Group 3: Maillard reaction, Convection, Puree, Greens (Cooking) Group 4: Sodium Chloride, Covalent, Dimitri Mendeleev, Isotope (Chemistry) Physics and Chemistry are my favorite sciences, and in my free time I can often be found cooking or practicing my skills as an intermediate musician. My favorite part of the Connections puzzles is deciphering their red herrings and mixed definitions. Sousa, Schrodinger, and Mendeleev are all revered pioneers of their respective fields, but my choice to omit a fourth name removes that as a possible category. An anacrusis is the separated beginning of a musical phrase, a pickup note/measure. Frisson is the scientific name for the chills or goosebumps you get from superb orchestration. The Planck scale might sound musically related, but it really refers to the group of measurements defined by the Planck constant, or the link between photon frequency and energy, a keystone of particle physics. Commercializing fusion is the holy grail of nuclear physics. Wavelengths are fundamental to understanding acoustics and therefore music, but acoustics is a sub-branch of physics, and wavelength frequently refers to elementary particles. Convection is the transfer of heat by fluids/gases, as opposed to direct contact (conduction). This is a thermodynamic (and thus a physical) process, but obviously inseparable from the culinary arts. Purees are pulverized fruit blends, and 'greens' colloquially refers to vegetables. The Maillard reaction could be grouped under chemistry, but it's the process that gives browned foods their flavors, from cookies to bread. The average layman will readily recognize Sodium Chloride as table salt, but the scientific label keeps it under the chemistry tab. Isotopes are neutron-poor/rich atoms, chemicals unique for their nuclear properties. Covalent bonds are one of the primary ways atoms bond, where electrons are shared between atoms.

I’ve had an affinity for the art of rhythms and melodies since I was a child, but it was live concerts that taught me the meaning of music. The first live concert I can remember attending was a musical performed by my (then) older high-school cousins. I was only twelve but I can still recall the melee of drill routines, glaring spotlights, and teenage voices trying to come together as a tribute to animated movie music. At the time I could only focus on the sea of excitement, and I missed the true spectacle. Crowds made me uncomfortable, and it was only afterward that I could contemplate the meaning of the music. From ‘Be a Man’ to ‘Everything is Awesome’, each number had a hidden message. Anyone can triumph through effort; the world is amazing if you take a step back to look at it. Music could express encouragement and optimism, help people to unwind and press forward. It was never enough for me to merely listen to music. Because of my inquisitive nature I had to play it, to learn how it was done. When I joined our concert band it was no coincidence that I chose the trombone. I found its tone and intuitive slide appealing, but I loved it most for its power and dominance over a concert atmosphere. Though I chose to prioritize STEM classes for a future career in science, I relished the chance to take a break in concert (and later Symphonic) band. I could have studied all the music theory I wanted without a band, but through those years I also learned about the insider’s perspective. Music isn’t just a psychological phenomenon or hobby, but a real force binding society. The simple pleasure of notes and rhythms gives kids something to socialize over, and learning to understand the themes expressed through music corroborates emotional intelligence. Marching contests and symphonic festivals were just as much about listening to and meeting other bands as the competition. I’ve seen many concerts in my school years, from live music movies to piano recitals and dozens of band gigs. Recently I’ve also explored my abilities as a solo pianist on stage. But if I had to pick my favorite concert memory, it would be when I watched the United States Air Force band live and in person. The sound was crisp but not overbearing, imbued with the kind of excellence that breeds faith in the future of America. But beyond that, it was one of the few band trips where we weren’t expected to play anything, just be there for the experience with our peers. The refined classical tones were a welcome break from the chaos of marching band. I was losing my love for music during that time, and I missed the sense of quality that we used to have as a band. There are many reasons people learn to love notes and rhythms, but it’s usually because music hits them at the right time. Music is both visceral and corporeal. It means different things to different people, but that doesn’t make its power any less real. Though chemistry and the physical sciences are my forte, I have great respect for the power live music has to shape individuals and communities.

Education is a great tool in life, but for me, it’s also one of my lifelong quests, a legacy of generations past. Planet Earth wouldn’t be the same without the men and women in history who had the courage to theorize outside the box. Learning isn’t about memorizing arcane knowledge, but the opportunity to continue where others left off. Few have the pleasure to make the pursuit of groundbreaking research into their career, but the drive to decipher our universe must be protected at all costs. Without science we would still be stuck in the dark ages, with no modern conveniences, institutions, or notions of equality. But if we continue advancing my favorite fields of astrophysics and chemistry, humankind’s record of progress has only begun. I was born and raised in rural Washington; essentially the middle of nowhere. However, isolation from the big city has one niche advantage: stargazing. Since childhood I have been fascinated by the night sky. I idolized Hubble’s views, saved up to buy a telescope, and wasn’t afraid of checking out textbooks way over my head. The mission of astronomy is to satisfy our innate curiosity of what’s out there, what is real. What else could have inspired pioneers like Galileo, who had the audacity to defy the powers of the church and state over fledgling theories of the heavens? Science grows when we challenge our understanding of the universe, find errors in our models. To learn is to correct misunderstanding, find the enlightenment to fuel perseverance. Despite their genius, the great minds of astronomy were still human. Copernicus was right about heliocentricity but clung to the belief that orbits were perfectly circular. Galileo couldn’t accept the moon causes tides and spent hours staring at the sun through his telescopes. Even Isaac Newton, the discoverer of gravity and calculus drank mercury for its supposed benefits. But what is he most remembered for? His contribution to the quest to quantify reality. The battle between what we think we know and what we observe is key to science. What branches are more at odds today than physics and astronomy? To understand the universe at large we need astrophysics, their union. The sooner we learn the true factors at play, the sooner we can figure out how to explore the universe. As humans have worked toward these goals it has become clear that the study of the large is dependent on the study of the small. Put simply, one can’t expect to understand the great beyond without taking a look at what they have in front of their nose. We’re surrounded by matter, which we intuitively know is governed by forces, actions and reactions. What has taken ages cto codify is chemistry, the math behind their make-up and properties. But looking back on today, the journey was well worth it. Alchemical quests led to the discovery of the first ‘new’ element, phosphorus. The idea that matter could be broken into indivisible elements led to the idea of atoms, and the beginnings of the periodic table as designed by Dimitri Mendeleev. Chemistry allowed scientists to manipulate the workings of chemical bonds to make invaluable discoveries and begin to uncover the physics underpinning the fundamental forces. But our chemical databases are by no means complete. Only 1% of all chemicals have been discovered by some estimates. Chemistry is responsible for the creation of transistors, plastics, and chemical weapons. Virtually all the innovations enabling modern technology had their roots in its advances. The only way we’ve progressed so far was by looking back. I believe that the quest for knowledge is one of humanity’s most important tasks because it is what sets us apart as a species. We are not helplessly carried about by the winds of evolution but have instead learned to control our environment through daring to comprehend the universe. The study of chemistry and astronomy help us to understand what’s around us so we can reach for greater heights. The progress we have made is nothing short of astounding, and I plan to be a part of the work to better our future, because it would be a disgrace to generations past if we stopped now.

Why do I love math? Because I would be insane not to! In the modern world where misinformation runs rampant, the notion of truth is no longer an abstract concept that one might do without, but an essential ingredient for life. Math is the foundation of science, the art of efficiency, and saves the day when all guesswork fails. This love comes naturally to science aficionados like myself, but may not register for the uninitiated. However, I believe every student should crave math, and inwardly does, whether consciously or not. When I first learned algebra it was a milestone, but also a turning point, where the mathematicians of my school were sorted from the rest. Why then? Because algebra is the first branch of math to deal with the ‘abstract’. However, the nuance of math, and especially algebra, is that it’s anything but abstract. Algebra revolves around the principle of conservation, the requirement of “an equal and opposite reaction.” For all closed systems, a change in one state must be duly reciprocated. The only abstract thing about the concept of physical consequences is the terminology to codify it. Math is not only about reason, but the presence of order in the universe; the existence of justice, if you will. What do humans seek in life? In our culture it’s a given that everyone wants happiness, which is often enhanced by a sense of meaning and purpose. But how should one get there? By factoring out obstacles, rechecking the truth, and not being afraid to critically think. A world without math has no justice or equivalency, no base for moral systems or economics. Algebra helps us solve the unknowns from the knowns. Calculus shows the acceleration of change, essential to kinematics and diverse applications. Even linear algebra, one of the most seemingly abstract levels, finds itself indispensable in the field of computer science. Mathematics beyond simple arithmetic is portrayed in our culture as the domain of robots, a sort of Kardashian subject that no healthy human should love. But in the end, what makes homo sapiens distinct from all other species? Our ability to think, reason, and establish priorities. The study of math enhances and fulfills our potential to understand the when(s), where(s), and what(s) of reality. Knowledge is power, and as I always say, there is no such thing as luck, only uncalculated math.

Since I was a child one of my defining traits has been an obsession with the sciences. I can still remember trying to check out a college astronomy textbook in the first grade, and trying to memorize the periodic table soon after. I read such books at first for the cool pictures, but I soon saw nonfiction for what it was. Fiction is created to seem relatable and entertaining, which is fine, but that’s all it is. I knew science had relevance to my world, however abstract, and if my teachers thought I was too young for such ideas then that was all the more reason to try. But I wasn't just a book learner. I was active in scouts, took piano lessons, and had chores on our family farm. Like many kids I was inspired by aviation. The few vacations my parents could take often featured museums, from dinosaur parks to the Seattle Museum of Flight. There I got to see an SR-71 Blackbird and walk through the cabin of a Concorde. Seeing some of the greatest supersonic aircraft ever built was inspiring, but I always had to return to my home in the desert. As my family grew larger we couldn’t afford such trips, and my summers were resigned to farmwork. I often looked back on those times as an adventure, occasions when I could experience the world outside of my rural domain, and get involved in the bigger picture of human progress. Despite my wishes to be elsewhere, I found purpose outside school volunteering and serving my local community. For my Eagle Scout Project, I arranged and performed in a series of summer concerts to entertain residents of a local nursing home. After scouting I joined my church youth group, which sponsored fundraisers and frequent services. Every December I would serve with the youth from various clubs for our canned food drive, the Christmas Baskets. Our mission was to deliver a Christmas dinner’s worth of goods to all the low-income families we could in our town. Over the years I volunteered personally in various positions, from sorting stock in the weeks leading up to last-minute organizing on delivery day. Giving my time to these and other efforts taught me how little many in this world possess, and that serving others is a cornerstone of good character. In high school I delved into chemistry, and that became a springboard for scientific understanding. Chemistry is the central science, the quest to discover the constituents of matter. Its growth has given thousands of commercially invaluable discoveries, but also a core understanding of the elements. From that physics was formalized to explain the workings of the atom, and became the base for the Standard Model. Though my scientific interests to that point had been very eclectic, I discovered chemistry tied into them all with ease. The SR-71 was possible because of the properties of titanium. Modern astronomy relies on spectroscopy, derived from electron orbital theory. Pianos depend on high-carbon steel alloys and chemically-engineered substitutes for ivory and rare woods. Going into college my current aim is for a bachelor's degree in chemistry with an emphasis on physics. Science is about learning how the world works, and exploiting those laws of nature to benefit humankind. After centuries, there still are many things to improve with the study of chemistry. After all, graphene has yet to be truly commercialized. My time in Othello has taught me a lot about the service of volunteering, but I can’t wait to take the next step in my pursuit of a career as a research scientist.

Since childhood one of my defining traits has been my interest in the sciences. I can still remember trying to check out a college astronomy textbook in the first grade and trying to memorize the periodic table for the first time. I read such books at first for the cool pictures, but I soon saw nonfiction for what it was. Fiction is created to seem relatable and entertaining, but in the end that’s all it is. However abstract science seemed to others, I recognized its relevance to the world, and if my teachers thought I was too young to read it then that was all the more reason to do so. But I wasn't just a book learner. I was involved in scouts, took piano lessons, and had chores on our family farm. My childhood obsessions also included aviation. The few vacations my parents could take often featured museums, from dinosaur parks to the Seattle Museum of Flight. I got to see an SR-71 Blackbird, to walk through the cabin of a Concorde. Seeing some of the greatest aircraft in person was inspiring, but after such excursions I would always have to return home to the desert. As my family grew larger we couldn’t afford such trips. I came to look back on those times as an adventure, occasions when I could experience the grander world outside of my small domain, learn things outside of books. Though I didn’t see it then, having to stay in my small town taught me to appreciate what our community had to offer. I learned to adjust to the necessities of rural life, which taught me the importance of hard work. Despite your reservations, when there is a job to be done, you better be prepared to do it right. Without that preemptive attitude I wouldn’t have done as well in school, or have earned the rank of Eagle Scout. I was proud to be involved in the community, but between working on the farm, schooling, and youth groups I had little time to myself, and had put little thought towards my future. When the COVID pandemic struck, I found the spare time to start studying again. I delved back into chemistry, and that became a springboard for scientific understanding. Chemistry is like the central science, a story of discovery, as scientists broke matter into its constituent, often dangerous elements, and found chemical combinations with invaluable properties. From that physics was formalized to explain the workings of the atom and eventually became the base for the Standard Model. While my scientific interests to that point had been very eclectic, I discovered chemistry could tie into them all with ease. Back at school, I had changed. In contrast to many returning from distance learning I was more focused on my academics. High school also introduced me to the wider world of music. My schedule grew to include many band events, from solo performances to fundraisers and field trips. Those times were fun, but they awakened me to the reality that I was still living in the middle of nowhere. Unless I was willing to put in the effort to chase my dreams, I would be stuck, trapped. I doubled down on my schoolwork and started to plan for the future. Going into college my current aim is a bachelor's degree in chemistry. I have grown to love many things about my rural town, but I can't wait to go to university and begin to pursue a career as a research scientist.

Since I was a child one of my defining characteristics has been my interest in the sciences. I can still remember trying to check out a college astronomy textbook in the first grade and memorize the periodic table. I read such books at first for the cool pictures, but later I saw nonfiction for what it was. Fiction is created to seem relatable and entertaining, but in the end that’s all it is. However abstract it seemed to others, nonfiction possessed an ethereal relevance to my world, and if my teachers thought I was too young to read it then that was all the more reason to do so. But I wasn't just a book learner. I was involved in scouts, took piano lessons, and had chores on our family farm. If school was trying then my summers were tenfold. My childhood obsessions also included aviation. The few vacations my parents could take often featured museums, from dinosaur parks to the Seattle Museum of Flight. I got to see a SR-71 blackbird, walk through the cabin of the last Concorde to fly in the U.S.. Seeing such aircraft in person was inspiring, but after such excursions I would always have to return home to the desert. As my family grew larger we couldn’t afford such trips. I came to look back on those times as an adventure, a series of ethereal experiences, times when I could experience the grander world outside of my small domain, learn things outside of books. Though I didn’t see it then, having to stay in our small town taught me to appreciate what our community had to offer. I learned to adjust to the necessities of rural life, which among other things taught me the importance of hard work. Despite your reservations, when there is a job to be done, you better be prepared to do it right. Without that preemptive attitude I wouldn’t have done as well in school, or have earned the rank of Eagle Scout. After Boy Scouts I remained involved in youth groups throughout high school, often sponsoring service projects. There were annual fundraisers, lawn repair services, and the Christmas Baskets, where youth from various clubs would go door-to-door for canned food donations to be given to low-income families. Over the years I played various roles. I donated directly, collected, organized, packaged, and almost always was around to deliver. These experiences helped me appreciate what I had, and brought me to realize how little some people in this world have. My family has a saying. Where much is given, much is required. It comes from the Bible (Luke 12:48). My parents’ objective as parents was to teach us about the blessings of life so that we would understand the need to give back, and participate in the community. But as my workload increased, the push took a toll on my health. I was proud to do my duty to my family- they’re who raised me, after all, but I desperately needed time to myself. I had become the kind of person that some might call a jack-of-all-trades. I played multiple instruments, took all the advanced classes available despite my remoteness, studied subjects from linguistics to physics on my own time, and devoted quite a few nights to the rigors of marching band, not to mention religious commitments. Despite my involvement, I lost motivation for it all. Because I was seemingly involved in everything, I was committed to nothing. I learned that while it’s good to be involved in the community, in the end, life is about carving out your own path. Though my childhood was filled with forces pushing me in different directions, I realized all along that my love for science, and chemistry in particular, had remained intact. My drive to explore and learn from experiences was what kept me going. I still have work to find my career, but majoring in chemistry is a great start to many. I’ve learned a lot already, but as I go to college I look forward to learning the rest of the skills I’ll need to make an impact in the world, both for myself and my future community.

From a young age I have been very inclined to science and its way of thinking. I can still remember trying to check out a college astronomy textbook in the first grade. I would dream of future inventions, try to discover new phenomena. Growing up on a farm I had to learn how to work early on, but I also learned the purpose of work: to live to learn and explore the universe. Those who view science as merely applied math miss the point. Science is not an opposition to art, but its companion. Knowledge empowers; art encourages. If art is about self-expression, science enables self-assertion. My desire for understanding led me to pursue chemistry and astronomy at a young age, and later the rest of the sciences, with a bent on physics. There are projects every science lover hopes will change the world, from the much-anticipated rise of graphene to room-temperature superconductors. There was a reason for the fiasco last summer over LK-99 (which is still under review according to some sources). A verified breakthrough with either could be the bridge to the next technological revolution. The JWST has gained worldwide renown for its achievements in only two years, and its future promises untold insight. Even non-astronomers would be thrilled by the unmasking of dark matter or habitable exoplanets. As a child, I never knew what facet of science I wanted to pursue. As I grew, my uncertainty remained. My ambition was not to work only towards specializing in one field, but to understand all to some degree. During family vacations I often pushed to visit museums, from dinosaur parks to the Seattle Museum of Flight. There I got to see an SR-71, walk along the cabin of a retired Concorde. I saw such marvels not as mere tools, but as works of art. Being there made me feel connected, as if I was part of that legacy of progress. Yet after such excursions I would always have to return to my rural life in the seeming middle of nowhere. When summer workdays grew long I survived by thinking back to those times, pondering the workings of what I’d seen. But then the day came when I realized that I had no skills in comparison, no powers comparable to those who built such machines. I would grow up and be stuck in this desert, unless I chose to learn. When the COVID pandemic hit I found the time I needed to start studying on my own. I covered many fields, but came to appreciate the field of chemistry for its role as the central science. That appreciation grew stronger for physics, the roots of all engineering and science. Though I am still considering my career choice, I am confident in my plan to major in chemistry. I liked the study of atoms and their working on its own, but I came to love it for its multitude of applications. Curious how transistors work? That takes an explanation of semiconductivity. Doing spectroscopy in space? Made possible by electron orbital theory. Need to understand homeostasis in the human body? Chemical knowledge is indispensable. Even chefs would find it impossible to do their work without knowing some of its key tenets. Getting a bachelor's degree in chemistry opens up paths to many different careers, and can help me get into whatever field of STEM I ultimately choose to innovate the world. I love science and art because they're not as separate as they seem. Science is a tool to create art, and art inspires us to seek out science.

As a child I was often labeled precocious, and later in school, an overachiever. I did well in class but I didn’t learn to take pride in my skills. I was content to abide by the invisible moral standard, the rules for life that had been drilled into me as a kid. But as I grew older, it became harder to converse or relate with people, as if they were on a foreign plane of existence. Because of my rural upbringing, I was so wrapped up in my parents’ world of work and chores that I was unable to put myself out there, accomplish something for myself. I was rarely up to date with trends and had little time to learn about the world. The last place I was willing to take advice from was in a movie. But that changed when I watched National Treasure. The plot followed Benjamin Gates and the legacy of the Knights Templar, a hidden treasure too great for any one man to possess. Yet that didn’t stop the Gates family from trying. Despite his dad’s disenfranchisement Ben believed his grandfather. We jump to modern day to learn Ben built his life around the hunt for the treasure, only to find with millionaire Ian’s help that the next clue was on the back of the Declaration of Independence, safely locked away. If Ian hadn’t split from him then, Ben would be at a dead end, with no excuse to steal it and continue the hunt. Most of the fun in the movie is just his plan to infiltrate the preservation room, taking advantage of unsuspecting gadgets and clever timing. I realized it was also symbolic. The sequence sets up the brains versus brawn contest structuring the rest of the film, but also speaks to the power of the individual. As Gates paraphrased: “...those who have the ability to take action have the responsibility to take action.” I realized from the start that this wasn’t the typical hero’s journey. This wasn’t a treasure hunt with a patriotic twist, but an allegory for the American dream. Then things started to click for me. What was the titular national treasure? Not the Declaration, or even the Freemasons’ gold. As Ben’s grandfather said, it was never about the money. Life is about the journey, not just a destination. Ben devoted his life to finding the treasure because it was his dream, his legacy, and he understood it was his right to pursue it. If that meant protecting the Declaration by stealing it along the way, that was just what had to be done. The treasure of all treasures is an archetype of success, the opportunity for which was laid out by the founding fathers. Our nation is great because it allows its people to pursue greatness. Life isn’t easy, even for the fortunate, but treasures can be found if you are willing to work for them. Though in school I was an outsider from the middle of nowhere, by being born in America I was in the top one percent. Though few shared my academic standards, I learned to persevere. I took harder courses online that weren’t offered by my high school. I learned to learn on my own time and rose to the top of my class. Going into college I will once again be an underdog, but also an American citizen, ready to work for my place in life. Because of National Treasure, I remember that ultimately, a difference can only be made by people willing to be different.

If I could have everyone on Earth read at least one book in their lifetime, I would have to take careful consideration. Our planet is home to billions, from ultra-elite to humble farmers, the indigenous to the metropolitan. Whether or not one novel could impact all, or how is not the question, but must be considered to find what book might best do the job. But what venue should I broadcast for? To find the book to go to the ends of the earth, we must first find a cause. Historically, the only books claiming universal appeal spoke of faith or natural laws. Religious texts were preached with zeal by their followers for their supposed universal tenets. Math is a subject of study, the primordial rules scaffolding science. Everyone searches for truth, looking to science and/or religion for solace. If I wished for a unified global society, the introductory book for worldwide learning must start by codifying arithmetic or religion. But I wouldn’t want to force a curriculum on anybody. Failure to walk the line between merely promoting first-grade education and forcing globalized ideals could easily backfire. What about fictional books, one might ask? Though many are works of art, serving as both allegories and entertainment, literature in my experience seems quite divisive. Fiction is philosophical, often political. Few seem to agree on what makes a book truly artistic, or which are. Too many are products of mass marketing, built on tropes and stereotypes. I can’t name one inclusive enough to please my relatives, let alone the majority of humanity. I wish not to offend, but inspire. With this resolution in mind, one of the most simply inspiring books I know is the Hubble: Legacy Edition atlas, which chronicles the story of the Hubble Space Telescope. If there is one thing humanity can share, it’s our home planet's night sky, the natural desire to know what’s out there. I daresay that at the end of the day the awe of the universe has inspired all, from the poorest sleeping under the stars to Elon Musk, CEO of SpaceX. Why did NASA pay millions for four orbital missions to repair Hubble’s aging parts, and billions for its successor, the JWST? Because those views continue to be an inspiration to all of humanity. And if there is one thing everyone should get from reading a book in their lifetime, it's inspiration.

Calculus is a centerpiece of higher math, vital to calculations almost everywhere in the STEM fields. When students learn math they soon realize that it builds upon itself. Math is the primordial foundation of science; it underpins reality. Math builds upon itself because it was codified into branches as it was discovered over the ages. Calculus is well-renowned for its complexity, but not so much for its concepts or use outside the classroom. Algebra operates on the principle of conservation. Geometry and trig extend the tenets of algebra to the properties of shapes and vectors. But it takes calculus to fully model the real world, where forces at play continuously change concerning time and other factors. The first lessons of calculus are about derivatives. A derivative of a function gives the slope of a line tangent to a given point on the line. A derivative graph reveals the properties of its parent graph. The x-intercepts (zeros) correspond to the extrema of the parent function. If a complex situation can be modeled on a graph, calculus can be applied to analyze it. Derivatives of derivatives also exist. The second derivative shows concavity, or change in slope. Velocity is the derivative of the position-time function, and acceleration is the second derivative. If we know how an object accelerates, we can use calculus to show the object’s motion. The derivative (or change) of acceleration is what we call jerk. The derivative of momentum (mass times velocity) with respect to time is the net force acting on an object. These tenets tie calculus to kinematics, the theoretical framework for all systems of motion. The second theme of calculus is integration, which is essentially doing derivatives in reverse, namely antiderivatives. It starts with the problem of how to calculate a given area bounded by a curve. This is extremely important, not just conceptually, but anywhere in ergonomics and design where curves and contours are ellipsoidal. Where would we be if we couldn’t calculate the volumes of complex non-linear shapes? The area under a curve can be estimated with circumscribed bars. The more bars there are, the closer the result. Integration takes the limit as that number approaches infinity, disregarding the constant C of the parent equation to give an approximation. Integrals also relate to kinematics. When velocity changes over time, integration is employed to find displacement. Multivariable calculus extends derivatives and integrals to the third dimension, allowing for the complete calculation of volume, surface area, and real-world free-body diagrams. Beyond geometry, calculus helps quantify thermodynamics and electromagnetism. Ultimately, calculus is at play about anywhere where exponential change occurs. With it, one can calculate the growth rate of bacteria cultures, voltage through electronic components, mechanics of acoustics due to friction, and the effects of gravity. Calculus underpins every field of STEM. Pure science is concerned with the behavior of particles like electrons, relying on calculus to describe their field potentials. Technology is a product of the other three fields but employs calculus directly for machine learning and optimization algorithms. Calculus also ties momentum and velocity into kinematics, the foundation of engineering. The study of continuous change deserves its reputation as one of the most notorious branches of math.

After I graduate high school I am planning to start my college experience, aiming for a bachelor's degree in the sciences. I believe a great title for my next chapter would be ‘The Reckoning’. Though chapter titles for books are probably best written in hindsight, I can say that this is a solid choice. At first glance it has all the proper elements of a chapter heading- ominous, but vague; enough to not give away the plot yet be later recognizable. The reason for that title is that no one suddenly crosses a threshold and becomes. Change happens by degrees each day, for better or for worse. Progress takes effort, patience, and the will to go forth even when life doesn't feel like a page-turner. This new chapter will be one of many choices and plans to make, as educators and elders love to remind young adults, but I prefer to think of it as a continuation of life, not a new beginning from scratch. Instead of a heading like ‘The Decision’, ‘The Reckoning’ suggests a culmination, a sum of the work and decisions put forth and in progress, a campaign perhaps to confront and deal with the powers that be. This next chapter in life will be a time when the choices made by me and my peers, if they haven’t paid off, will, for better or for worse. A reckoning implies a crusade, or a resolution of justice, but to reckon also means to formulate, to put yourself out there and voice your conjecture on the issues that be. This is fitting since it is through education and self-discipline that we learn and prepare to deal with reality. In this light ‘The Reckoning’ not just hints at what I plan to do, but how I plan to do it: through continued education and perseverance.

From a young age I have been inclined in the sciences. Like many kids I read nonfiction books at first for the cool pictures, but unlike many students revisiting them later I saw them for what they were. Fictional worlds died; if not by fault of the protagonist then when the storybook was shut for the night. Nonfiction doesn’t work like that. But book learning was by no means all the exposure I had. It was easier for my family to travel when I was younger. During our family vacations I found myself in many museums, from dinosaur parks to the Seattle Museum of Flight, home to a retired Concorde and SR-71 Blackbird. Seeing some of the greatest supersonic planes ever built was inspiring, to say the least. But after the thrill of such excursions I would always have to return home to the desert. As I grew and adjusted to the necessities of life on a farm I met cousins, became an Eagle Scout, and grew personally through service in the community. But I couldn’t help but think back to some of those trips, wondering how, or how and what such machines were built out of. And then the day came when I realized that I had no idea, no talents in comparison to those who had designed such marvels. At least, not unless I chose to learn how. I decided to use what spare time I could in my studies to learn about chemistry, and that became a springboard for understanding. Chemistry is like the central science, a story of discovery, as scientists broke matter into its constituent, often dangerous elements, and found chemical combinations with invaluable properties. From that physics was formalized to explain the workings of the atom and eventually became the base for the Standard Model. Yet for all its intricacies, science is a theory. Tenets never disproven are taken as fundamentals for the next concepts, and engineering simply applies the discoveries. Elementary and middle school never taught science like that. Now, with the best observatories in the history of science up in orbit, astronomers are continually challenging some of the dearest concepts of cosmology. However, the inner workings of science aren’t just for those looking to build the next JWST. Natural physics can explain almost anything, from an electrical lighter on a campout to the acoustics properties of your favorite chords and songs. I’ve always liked attempting puzzles, from exotic Rubik’s cubes to the perfect chocolate chip cookie. One thing I learned is that to comprehend the large scale, you need to understand the smallest part. Perhaps that is why chemistry and physics have resonated so much with me. Going into college I am aiming for at least a Bachelor’s degree in either branch or their respective subfields, possibly looking for a career in research science.