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Brought to you from his new EIB Studio in heaven
(Please note: This is a fictional video for entertainment purposes. Rush went to be with his Maker on February 14, 2021. With talent on loan from God, he wanted to share his take on some current events so he asked if I could do the honors with some technical wizardry. I consented but only on the condition that I could make it clear this is only a simulation.)
Keeper Password Manager is a cybersecurity platform that allows users to securely store and manage their passwords, personal information, and sensitive files across multiple devices, utilizing strong encryption and a “zero-knowledge” security model to ensure only the user has access to their data; essentially acting as a digital vault to protect login credentials and other important details from cyber threats.
I started using Keeper a year ago. I didn’t want to use weak passwords and I needed someplace secure I could store and retrieve access to many different accounts. The best part about Keeper is that you can use it on any device anywhere. There are apps for your mobile devices and computers (desktop and notebook). You can also get to your vault using any browser. And any updates you make are immediately accessible all across your devices, computers, and browers.
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This app is very easy to use. If you add their browser extension, all it takes is a single click to open a website and login. This mean you will no longer need to stay logged in to sites for easy access.
Keeper has a record history for each account making it easy go back after you’ve changed the password and retrieve an earlier version. Because many websites ask for the current password when changing it, Keeper has you covered in case you changed the password in Keeper before realizing the website still needed your current password.
Keeper is also perfect for storing other sensitive data like your credit card numbers, bank information, contact numbers in case you need to report something lost or stolen. You and only you can access what you need, when you need it, no matter where you are.
Frankly, I don’t know how I ever got along without it. If you’re not sure, just try it out and you won’t regret it.
Zero-knowledge security:
This means that even Keeper itself cannot access your passwords, as they are encrypted locally on your device.
Strong encryption:
Keeper uses AES 256-bit encryption to protect your data.
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You can access your stored passwords on various devices like computers, smartphones, and tablets.
Family plans:
Allows sharing passwords with family members, with the ability to organize access based on categories.
Enterprise solutions:
Offers plans specifically designed for businesses to manage employee passwords and sensitive data.
Brought to you from his new EIB Studio in heaven
(Please note: This is a fictional video for entertainment purposes. Rush went to be with his Maker on February 14, 2021. With talent on loan from God, he wanted to share his take on some current events so he asked if I could do the honors with some technical wizardry. I consented but only on the condition that I could make it clear this is only a simulation.)
Brought to you from his new EIB Studio in heaven
(Please note: This is a fictional video for entertainment purposes. Rush went to be with his Maker on February 14, 2021. With talent on loan from God, he wanted to share his take on some current events so he asked if I could do the honors with some technical wizardry. I consented but only on the condition that I could make it clear this is only a simulation.)
An original short story by Stephen Jones
Dr. Samuel Larkin, a quantum physicist, had always been fascinated by the mysteries of the universe. He dedicated his life to understanding the strange and elusive world of quantum mechanics. Samuel’s work at the National Quantum Research Institute involved studying quantum states and their potential applications. Little did he know that his research would lead him to discover something far more extraordinary than he could ever have imagined.
One fateful day, while conducting an experiment involving quantum entanglement, a malfunction occurred. A surge of energy burst from the equipment, enveloping Samuel. He felt a strange sensation, like his very atoms were being stretched and twisted. Then, as quickly as it had started, it was over.
Samuel was left disoriented but seemingly unharmed. He chalked it up to a bizarre side effect of the malfunction and decided to return home to rest. As he reached for his keys, however, he found himself suddenly standing in his living room. He was bewildered. Had he fallen asleep and dreamt the whole incident? But no, his lab coat was still singed from the energy burst.
As a scientist, Samuel was compelled to test this phenomenon. He thought of his office at the institute and, in an instant, he was there. It was teleportation, a concept he had only theorized about. But there was more. He discovered he could also duplicate objects, even himself, by manipulating their quantum states. Samuel was both thrilled and terrified by his newfound abilities.
News of the lab incident had leaked, and it wasn’t long before a shadowy organization, known only as the Quantum Syndicate, caught wind of Samuel’s abilities. They saw his powers not as a scientific marvel but as a weapon to be harnessed.
One evening, as Samuel was experimenting with his powers, he felt a sudden chill. He turned to see a group of strangers in black suits. “Dr. Larkin,” the leader said, “we’ve been expecting you.”
Samuel tried to teleport, but he couldn’t. The men had some sort of device that disrupted his abilities. They explained that they were from the Quantum Syndicate and that they needed his powers for their own purposes. Samuel was a pacifist, a man of science. He refused to be a part of their violent plans.
The Syndicate, however, wasn’t taking no for an answer. They kidnapped Samuel, taking him to a secret facility where they attempted to extract and replicate his powers. But Samuel was not just a physicist; he was a genius. He had been studying his abilities, understanding their mechanisms, and he had a plan.
Using his knowledge of quantum states, he manipulated his own body at the atomic level, becoming intangible and slipping free of his restraints. He then duplicated himself, creating a diversion while he sabotaged the Syndicate’s equipment.
The facility was thrown into chaos. Alarms blared, lights flashed, and Samuel used the confusion to make his escape. He teleported to the safety of his home, but he knew he couldn’t stay. The Syndicate would come after him, and he couldn’t risk the lives of those he cared about.
So, Samuel went into hiding, using his abilities to stay one step ahead of his pursuers. He became a ghost, a phantom, always on the move. But he wasn’t just running; he was planning. He was determined to stop the Syndicate and protect his research.
In the following months, Samuel used his powers to infiltrate the Syndicate’s operations, gathering information and sabotaging their efforts to replicate his abilities. He was a one-man rebellion, a thorn in their side. But he was also growing tired. His powers, while extraordinary, were not infinite. He needed help.
Samuel reached out to his colleagues at the National Quantum Research Institute. He revealed his abilities and the existence of the Quantum Syndicate. They were skeptical at first, but they trusted Samuel. Together, they formed a resistance, using their collective knowledge to combat the Syndicate.
The battle was long and hard-fought. The Syndicate was powerful and ruthless, but Samuel and his allies were determined. They used science as their weapon, countering the Syndicate’s tactics with their own innovations.
In the end, it was Samuel’s understanding of his own powers that proved to be the Syndicate’s undoing. He created a quantum field that neutralized their weapons and disrupted their control over the quantum states. The Syndicate was defeated, their plans to weaponize Samuel’s abilities thwarted.
In the aftermath, Samuel returned to the institute. He continued his research, but with a new perspective. He had seen the potential dangers of his work, but also its potential for good. He was more cautious, more aware, but he was not deterred. He was a scientist, after all, and the mysteries of the universe were still waiting to be unraveled.
Samuel’s story became a legend in the scientific community, a tale of courage and determination in the face of adversity. He was a hero, not for his powers, but for his heart. He was a man who used science not as a weapon, but as a tool for understanding, a beacon of hope in a world of uncertainty. And above all, he was a reminder that even in the face of extraordinary power, the greatest strength lies in the pursuit of knowledge.
Have you ever wondered why certain musical compositions feel so naturally pleasing to the ear? The answer might lie in a mathematical concept that has fascinated artists, architects, and now musicians for millennia – the Golden Ratio, or Phi (φ). This mysterious number, approximately equal to 1.618, appears throughout nature in everything from spiral seashells to galaxy formations, and its presence in music is equally remarkable. From the structure of Mozart’s sonatas to the climactic moments in modern pop songs, Phi has been quietly shaping the way we experience and create music, often without us even realizing it. Understanding how this mathematical principle influences musical composition not only deepens our appreciation for the art form but also reveals the fascinating intersection of mathematics and creativity that makes music truly universal.
The Golden Ratio, represented by the Greek letter Φ (phi) and approximately equal to 1.618, has long been recognized as a fundamental principle of aesthetic beauty in nature, architecture, and art. This mathematical relationship, also known as the divine proportion, has intriguingly found its way into the realm of music, where it manifests in both composition structure and the physical properties of sound itself.
Throughout history, composers from Mozart to Debussy have, either consciously or intuitively, incorporated the Golden Ratio into their works, creating pieces that resonate with a natural sense of balance and harmony. The presence of phi in music extends beyond mere compositional techniques, influencing everything from the placement of climactic moments in symphonies to the design of musical instruments and even the harmonic relationships between musical frequencies. This mathematical constant serves as a bridge between the rational world of numbers and the emotional impact of musical expression, demonstrating how universal principles can shape our artistic experiences.
The concept of the golden ratio, denoted by the Greek letter Phi (φ), has fascinated mathematicians, artists, and philosophers for millennia. First formally documented by ancient Greek mathematicians, particularly in Euclid’s “Elements” around 300 BCE, this mathematical constant (approximately 1.618033988749895) was originally studied in relation to geometry and architecture. The Pythagoreans, who believed that mathematical relationships were the foundation of the universe, were among the first to recognize the aesthetic and harmonic properties of this ratio.
Throughout history, the golden ratio has transcended its mathematical origins to influence various forms of artistic expression, including music. During the Renaissance, theoretical musicians and composers began to consciously incorporate Phi into their work, believing it represented divine proportion and perfect harmony. This mathematical relationship was found to naturally occur in the harmonic series, which forms the basis of Western musical scales, and has been observed in the structural composition of numerous classical masterpieces, from Mozart to Beethoven, though whether this was intentional or intuitive remains a subject of scholarly debate.
The mathematical foundation of Phi (φ), also known as the Golden Ratio, is rooted in the Fibonacci sequence and can be expressed as approximately 1.618033988749895. This irrational number emerges from the relationship where a line is divided into two parts, such that the ratio of the larger part to the smaller part equals the ratio of the whole line to the larger part. Mathematically, this can be written as (a+b)/a = a/b = φ, where ‘a’ represents the longer segment and ‘b’ the shorter one.
The Golden Ratio’s mathematical significance extends beyond its numerical value, as it appears naturally in geometric constructions and growth patterns throughout nature. It can be derived through various mathematical methods, including the quadratic equation x² – x – 1 = 0, where the positive solution yields φ. This fundamental relationship has fascinated mathematicians, artists, and musicians for millennia, serving as a bridge between pure mathematics and aesthetic harmony. The ratio’s recursive nature, where φ can be expressed as 1 + 1/φ, demonstrates its self-referential properties and hints at its deep connection to natural phenomena and artistic expression.
The golden ratio (φ ≈ 1.618) manifests itself throughout musical composition and structure in ways both deliberate and intuitive. From the arrangement of intervals in classical pieces to the placement of climactic moments in contemporary songwriting, this mathematical proportion has been observed in works spanning centuries and genres. Composers like Béla Bartók and Claude Debussy have consciously incorporated phi into their compositions, while analysis of works by Mozart and Beethoven reveals natural occurrences of golden ratio principles in their musical architecture.
The applications of the golden ratio in music extend beyond mere compositional structure to influence elements such as rhythm patterns, harmonic progressions, and even instrument design. In musical form, phi often appears at crucial transition points, typically around the 61.8% mark of a piece’s duration, creating what many theorists consider to be naturally pleasing proportions. This mathematical relationship can be found in the construction of scales, the relationship between frequencies in harmonious intervals, and even in the physical design of instruments like violins and pianos, where craftsmen have long used golden ratio proportions to achieve optimal acoustic properties.
The Golden Ratio, mathematically expressed as approximately 1.618034 (often denoted by the Greek letter φ), represents a unique proportional relationship found throughout nature and art. This mathematical concept occurs when a line is divided into two parts in such a way that the ratio of the longer segment to the shorter segment equals the ratio of the whole line to the longer segment. The resulting proportion has fascinated mathematicians, artists, and musicians for millennia, as it seems to embody a fundamental principle of aesthetic harmony.
What makes the Golden Ratio particularly intriguing is its recursive nature and its connection to the Fibonacci sequence, where each number is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, 13, etc.). As this sequence progresses, the ratio between consecutive numbers increasingly approaches φ. This mathematical property has profound implications in various fields, including music theory, where it manifests in the structure of scales, the composition of melodic phrases, and even in the physical design of musical instruments. The ratio’s presence in music isn’t merely coincidental; it often corresponds to points of natural emphasis and resolution that musicians have intuitively recognized throughout history.
The Golden Ratio, mathematically represented as φ (phi) and approximately equal to 1.618033988749895, is a unique mathematical constant that emerges when a line is divided into two segments in such a way that the ratio of the longer segment to the shorter segment equals the ratio of the whole line to the longer segment. This divine proportion can be expressed algebraically as (a+b)/a = a/b = φ, where ‘a’ represents the longer segment and ‘b’ the shorter one. The Golden Ratio is also closely related to the Fibonacci sequence, where each number is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, 13…), as the ratio between consecutive Fibonacci numbers increasingly approaches φ as the sequence progresses.
What makes the Golden Ratio particularly fascinating is its recursive nature and its appearance in various mathematical constructs. When expressed as a continued fraction, it takes the form 1 + 1/(1 + 1/(1 + 1/…)), making it the most irrational of all irrational numbers. The Golden Ratio also manifests in geometric shapes, most notably in the Golden Rectangle, where the ratio of length to width is φ:1. When a square is removed from a Golden Rectangle, the remaining rectangle is also a Golden Rectangle, creating an infinite spiral pattern that frequently appears in nature and has been deliberately incorporated into various forms of artistic expression, including musical composition.
The geometric representation of the Golden Ratio (φ ≈ 1.618033988749895) can be visualized through several elegant constructions, most notably the golden rectangle and the golden spiral. A golden rectangle is formed when the ratio of its length to its width is equal to φ, and when this rectangle is subdivided into a square and a smaller rectangle, the smaller rectangle maintains the same proportions as the original. This self-similar property creates an infinite recursive pattern that naturally occurs throughout nature and has been deliberately incorporated into various art forms, including musical composition.
When connecting the vertices of nested golden rectangles with a curved line, the resulting shape forms a logarithmic spiral known as the golden spiral. This spiral’s growth factor is φ, meaning each quarter turn expands the spiral’s radius by the golden ratio. In musical contexts, this geometric progression has been found to correlate with the spacing of frequencies in harmonic series and the physical construction of instruments, particularly in the design of stringed instruments where the placement of frets or the curvature of acoustic chambers often exhibits golden proportions. The visual representation of these geometric principles helps musicians and composers understand and implement the golden ratio in their work, creating compositions that many find naturally pleasing to the ear.
The Golden Ratio’s presence in nature is both profound and pervasive, appearing in patterns that range from the microscopic to the cosmic scale. In the spiral arrangement of seeds in sunflowers, the branching patterns of trees, and the shell formation of the nautilus, phi (φ ≈ 1.618) emerges as a fundamental organizing principle. This mathematical relationship is also observed in the growth patterns of various organisms, where each new stage of development maintains the golden proportion with its previous state.
What makes these natural occurrences particularly remarkable is their connection to efficiency and stability in biological systems. The golden spiral, formed by connecting quarter-circles drawn in adjacent squares of Fibonacci dimensions, is frequently found in weather patterns, galaxy formations, and even DNA molecules. Plants often grow new cells in spiral patterns that conform to phi, maximizing their exposure to sunlight and rain while maintaining structural integrity. This widespread presence of the Golden Ratio in nature suggests its role as a fundamental principle of optimal design and growth, rather than mere coincidence.
The golden ratio (φ ≈ 1.618) has been observed in the structural composition of numerous musical works, particularly in the placement of significant moments such as climactic points, key changes, and thematic transitions. Composers like Béla Bartók and Claude Debussy have consciously incorporated phi into their compositions, with Bartók notably using the Fibonacci sequence (closely related to the golden ratio) to structure his “Music for Strings, Percussion, and Celesta.” In this piece, the climax occurs precisely at bar 89 in a 144-bar movement, creating a proportion that closely approximates the golden ratio.
The application of the golden ratio in musical composition extends beyond classical works into various genres and forms. Composers often place pivotal moments, such as the entrance of a new instrument or a dramatic shift in dynamics, at points that divide the piece according to phi proportions. This mathematical approach to composition creates a natural sense of balance and aesthetic pleasure that listeners intuitively recognize, even if they aren’t consciously aware of the underlying mathematical principles. Studies have shown that when these proportions are present, whether intentionally implemented or naturally occurring, they tend to contribute to the overall perceived beauty and coherence of the musical work.
The golden ratio’s influence on melodic structure has been observed in numerous musical compositions throughout history, particularly in works where composers consciously or intuitively placed significant melodic transitions, climaxes, or thematic changes at points that correspond to phi (approximately 0.618 or 61.8% through the piece). This mathematical relationship creates a naturally pleasing sense of balance and progression that listeners often find aesthetically satisfying, even without consciously recognizing the underlying mathematical principle.
In analyzing melodic structures, we find that many celebrated compositions position their main melodic apex or crucial harmonic shifts at the golden section point of the overall piece. For instance, in some classical sonata forms, the development section often begins near this proportional point, while in popular music, the bridge or key change frequently occurs at approximately 61.8% of the song’s duration. This strategic placement creates a sense of organic flow and musical tension that aligns with human perception of natural proportions, contributing to the composition’s overall emotional impact and memorability.
In musical composition, the golden ratio (φ ≈ 1.618) manifests itself through rhythmic patterns that naturally create aesthetically pleasing proportions. Composers have long utilized these mathematical relationships, whether consciously or intuitively, to structure their rhythmic phrases and establish dynamic tension and resolution. This can be observed in the way rhythmic sequences often divide into sections that approximate the golden ratio, with longer patterns naturally breaking down into smaller subdivisions that maintain this proportional relationship.
The application of the golden ratio in rhythmic patterns extends beyond simple time signatures and into more complex polyrhythmic structures. For instance, when examining West African drumming patterns or Baroque compositions, we frequently find rhythmic cycles that divide at points corresponding to golden ratio proportions (roughly 62% and 38% of the total pattern length). These divisions often occur at significant musical moments, such as the introduction of new rhythmic elements or the resolution of rhythmic tension, creating a sense of natural balance that listeners instinctively recognize as pleasing, even if they aren’t consciously aware of the mathematical principles at work.
The golden ratio’s influence on harmonic relationships in music manifests through the natural overtone series and the mathematical relationships between musical intervals. When examining the frequency ratios of musical intervals, we find that those closest to the golden ratio (approximately 1.618) tend to be particularly pleasing to the human ear. The perfect fifth, with its frequency ratio of 3:2 (1.5), and the major sixth, with a ratio of 5:3 (1.667), bracket the golden ratio and are considered among the most consonant intervals in Western music.
These harmonic relationships extend beyond simple intervals to inform the structure of chord progressions and voice leading. The Fibonacci sequence, intimately connected to the golden ratio, appears in the overtone series of musical instruments, where each subsequent partial is related to the fundamental frequency through whole number ratios. This natural occurrence of Fibonacci numbers in harmonics helps explain why certain combinations of notes create more stable and aesthetically pleasing sounds than others, providing a mathematical foundation for what musicians have intuitively understood for centuries through practice and tradition.
The golden ratio’s influence on musical form and structure has been observed in numerous compositions throughout history, particularly in the placement of significant musical moments and the overall architectural design of pieces. Composers, whether consciously or intuitively, have often positioned crucial elements—such as climactic passages, key modulations, or thematic transitions—at points that correspond to phi (approximately 0.618) within the total duration of their works. This mathematical relationship creates a natural sense of balance and aesthetic satisfaction, as evidenced in works like Béla Bartók’s Music for Strings, Percussion, and Celesta, where the climax occurs precisely at the golden section of the first movement.
The structural application of the golden ratio extends beyond single movements to entire musical forms, influencing the proportional relationships between sections in sonata form, rondo form, and other classical structures. In sonata form, for instance, the development section often begins near the golden section of the exposition, while the recapitulation frequently appears at the golden section of the entire movement. This mathematical precision in formal organization contributes to the work’s overall coherence and artistic impact, creating a subtle but powerful sense of structural harmony that listeners perceive as naturally pleasing, even if they’re not consciously aware of the underlying mathematical relationships.
Throughout musical history, numerous composers have consciously or unconsciously incorporated the golden ratio (φ) into their compositions, particularly during the Classical and Romantic periods. Wolfgang Amadeus Mozart, for instance, employed phi proportions in his piano sonatas, with the development and recapitulation often occurring at points that divide the pieces according to the golden ratio. Similarly, Béla Bartók was known for his deliberate use of the Fibonacci sequence and golden ratio in works such as “Music for Strings, Percussion, and Celesta,” where the climax occurs precisely at the phi point of the first movement.
The influence of the golden ratio extends beyond individual compositions to the very structure of musical instruments. The placement of sound holes in Stradivarius violins, crafted by the legendary Antonio Stradivari in the 17th and 18th centuries, demonstrates proportions closely aligned with phi. Claude Debussy, though less explicit in his mathematical approach, created works like “Reflets dans l’eau” that exhibit golden ratio proportions in their climactic moments and overall formal structure. These historical applications suggest that the golden ratio served not only as a mathematical curiosity but as a fundamental principle of aesthetic beauty in classical music composition.
Mozart’s ingenious application of the golden ratio in his compositions, particularly in his sonatas, demonstrates a sophisticated understanding of mathematical proportion in music. In his Piano Sonatas, notably K.279, K.280, and K.282, Mozart frequently positioned significant musical events—such as key changes, development sections, and recapitulations—at points that closely correspond to the golden section (approximately 0.618) of the total length of the movement. This deliberate structural organization creates a natural sense of balance and progression that listeners find inherently pleasing, even if they aren’t consciously aware of the mathematical underpinning.
Analysis of Mozart’s Symphony No. 41 (“Jupiter”) reveals an even more intricate implementation of golden ratio principles. The proportions between different sections of the first movement, as well as the relationship between melodic phrases and their development, often align with phi. While some scholars debate whether Mozart consciously employed these proportions or if they emerged naturally from his intuitive sense of musical balance, the presence of these golden ratios contributes to the enduring appeal and mathematical elegance of his compositions. This mathematical precision, combined with his extraordinary melodic gift, helps explain why Mozart’s works continue to be regarded as pinnacles of Classical period composition.
Bach’s masterful application of mathematical principles, particularly the golden ratio, is evident throughout his compositions, most notably in his “The Well-Tempered Clavier” and the “Art of Fugue.” Studies have shown that Bach frequently positioned significant musical transitions, cadences, and structural elements at points that closely correspond to phi proportions within his pieces. The mathematical precision in his work extends beyond mere coincidence, as Bach was known to employ numerical symbolism and precise mathematical relationships in his compositional techniques.
In the first movement of Brandenburg Concerto No. 5, researchers have identified golden ratio proportions in both the macro structure and micro elements of the piece. The climactic moment occurs approximately 0.618 through the movement, aligning with phi’s proportions. Additionally, Bach’s use of counterpoint and harmonic progressions often creates a balanced architectural framework that reflects the natural harmony found in the golden ratio. This mathematical approach to composition, while maintaining musical expressiveness, demonstrates Bach’s unique ability to merge artistic creativity with mathematical precision, setting a standard that influenced composers for generations to come.
Beethoven’s meticulous approach to composition often revealed a profound understanding of mathematical relationships, including the golden ratio. In his Piano Sonata No. 14 (“Moonlight Sonata”), the proportions between sections closely align with phi, particularly in the first movement where the development and recapitulation occur approximately 0.618 through the piece. This mathematical precision is not merely coincidental, as similar proportions appear in other works like his Fifth Symphony, where the famous four-note motif and its structural development demonstrate golden ratio relationships in both micro and macro levels of the composition.
Further analysis of Beethoven’s manuscripts reveals his careful attention to structural balance, with sketches showing numerous calculations and revisions to achieve precise proportional relationships. The final movement of his Hammerklavier Sonata (Op. 106) exemplifies this mathematical rigor, where the fugue’s primary themes and subsequent variations are spaced according to proportions remarkably close to phi. While debate continues among musicologists about whether Beethoven consciously employed the golden ratio, the consistent appearance of these proportions throughout his work suggests an intuitive or deliberate application of these mathematical principles in his compositional process.
Modern applications of the golden ratio in music extend far beyond classical composition, finding its way into contemporary production and sound design. Digital audio workstations (DAWs) and music software now incorporate phi-based algorithms to create aesthetically pleasing arrangements, while some producers consciously place key elements of their tracks at golden ratio points (approximately 61.8% through the composition) to create naturally satisfying climaxes and transitions. Notable examples include tool-assisted composition methods that use the Fibonacci sequence to determine optimal placement of breaks, drops, and melodic peaks.
The golden ratio also influences modern mixing and mastering techniques, where engineers often utilize phi-based proportions in equalizer settings and dynamic processing. Some contemporary artists and producers, including electronic music pioneers like Aphex Twin and Brian Eno, have experimented with mathematical relationships based on phi to create complex, evolving soundscapes. Additionally, certain modern synthesizer designs incorporate golden ratio harmonics in their oscillator relationships, resulting in uniquely pleasing timbres that feel organic despite their electronic origin.
Contemporary classical composers have increasingly incorporated the golden ratio (φ) into their compositional techniques, using it as both a structural framework and an aesthetic principle. Composers like Béla Bartók, who famously employed the Fibonacci sequence in works such as “Music for Strings, Percussion, and Celesta,” and György Ligeti, whose “Piano Études” demonstrate phi-based proportions, have helped establish golden ratio applications as a legitimate tool in modern classical composition.
The integration of φ in contemporary classical music extends beyond mere temporal divisions to influence pitch organization, harmonic progression, and even spatial arrangements in performance. Composers like Per Nørgård have developed sophisticated systems, such as his “infinity series,” which uses golden ratio principles to generate melodic and rhythmic patterns. This mathematical approach to composition has become particularly relevant in the age of computer-assisted composition, where algorithms based on φ can generate complex musical structures that maintain natural, organic qualities despite their mathematical origins.
Contemporary analysis of popular music has revealed numerous intentional and unintentional applications of the golden ratio (φ), particularly in song structure and climactic moments. Studies have shown that in many hit songs, the most significant emotional peak or transition often occurs approximately 61.8% through the piece, aligning with φ’s proportions. Notable examples include “God Only Knows” by The Beach Boys, where the key change occurs precisely at this golden moment, and Pink Floyd’s “Echoes,” which features its major transition at the φ point of its 23-minute duration.
The golden ratio’s influence extends beyond timing to melodic construction and arrangement choices in modern popular music. Musicians and producers, whether consciously or intuitively, frequently employ φ-based proportions in verse-chorus relationships and instrumental breaks. Analysis of Billboard Hot 100 hits from the past several decades reveals a tendency for hook placement and bridge sections to align with golden ratio proportions, suggesting that these naturally pleasing mathematical relationships may contribute to a song’s commercial success. This mathematical framework has become a valuable tool for contemporary songwriters and producers seeking to create more engaging and structurally balanced compositions.
In electronic music production, the golden ratio (φ) has found innovative applications in both sound design and composition structure. Modern digital audio workstations (DAWs) and synthesizers allow producers to precisely implement phi-based relationships in parameters such as filter cutoff frequencies, delay times, and modulation rates. For instance, applying the golden ratio to time-based effects can create naturally evolving rhythmic patterns, while using phi to determine frequency relationships in synthesis can produce harmonically rich timbres that feel organically balanced to the human ear.
The influence of the golden ratio extends to the arrangement and mixing stages of electronic music production as well. Producers often utilize phi-based proportions to determine optimal placement of key musical elements within the frequency spectrum, creating mixes that exhibit natural separation and clarity. Additionally, the golden ratio can guide decisions about track automation, helping to create gradual builds and releases that mirror natural growth patterns found in nature. This mathematical approach to electronic music design has been embraced by numerous contemporary artists and has contributed to the development of more sophisticated and aesthetically pleasing electronic compositions.
The influence of the golden ratio (φ) in musical instrument design has been documented across various cultures and time periods, most notably in the craftsmanship of classical string instruments. The legendary Stradivari violins, considered among the finest ever made, incorporate phi proportions in their construction, particularly in the placement of the f-holes and the overall body dimensions. These precise mathematical relationships contribute to the instruments’ superior acoustic properties and renowned tonal qualities.
Beyond string instruments, phi appears in the design of modern piano keyboards, where the ratio between black and white keys closely approximates the golden ratio. Similarly, pipe organs often display phi proportions in their pipe lengths and arrangements. Wind instruments like flutes and trumpets frequently exhibit golden ratio relationships in their tube lengths and finger hole placements, though whether these occurrences are intentional design choices or natural acoustic optimization remains a subject of ongoing research in organology, the study of musical instruments.
The relationship between string lengths and the golden ratio (φ) manifests prominently in various stringed instruments, particularly in the violin family. Master luthiers, including the legendary Antonio Stradivari, are believed to have incorporated phi proportions in their instrument designs, with the placement of the f-holes and the overall body proportions closely adhering to golden ratio measurements. The length ratios between strings on many instruments also demonstrate mathematical relationships that approximate phi, contributing to their harmonic resonance and tonal quality.
When examining string length relationships in musical instruments, we find that adjacent strings often follow ratios that create pleasing harmonic intervals. For instance, in a properly designed string instrument, the ratio between string lengths frequently approximates 1.618:1, matching the golden ratio. This mathematical relationship not only influences the instrument’s aesthetic appeal but also plays a crucial role in its acoustic properties, as these proportions help create optimal vibration patterns and sound projection. The presence of these golden proportions in string lengths has been observed across diverse musical traditions and cultures, suggesting an inherent connection between phi and natural acoustic principles.
The influence of the golden ratio in wind instrument design can be observed in both historical and modern instruments, particularly in the placement of tone holes and the proportions of instrument components. In woodwind instruments like the flute, clarinet, and saxophone, the spacing between tone holes often corresponds to logarithmic patterns that closely align with phi-based relationships. This mathematical precision isn’t merely coincidental; it contributes to the instrument’s acoustic properties and helps achieve optimal resonance and tonal quality.
The internal bore design of brass instruments also demonstrates phi-based proportions, particularly in the rate at which the tubing expands from mouthpiece to bell. Master instrument makers, whether consciously or intuitively, have long crafted instruments whose proportions approximate the golden ratio, resulting in instruments that not only produce superior sound quality but also feel naturally balanced in the player’s hands. This relationship between form and function has been particularly evident in the work of renowned manufacturers like Stradivari, who applied similar principles to both string and wind instrument design.
The golden ratio’s influence extends into the realm of percussion instruments, particularly in the spacing and arrangement of drums and other struck instruments. In many traditional drum sets and orchestral percussion layouts, the placement of drums often naturally follows proportions close to phi, creating both ergonomic efficiency and aesthetic balance. This can be observed in the positioning of tom-toms, where the distance between each drum often corresponds to logarithmic spacing that approximates the golden ratio, allowing drummers to maintain optimal playing positions while accessing multiple drums with minimal movement.
The application of phi in percussion spacing isn’t limited to modern drum sets; it appears in traditional instruments from various cultures as well. For instance, the arrangement of gamelan metallophones from Indonesia and the spacing of African talking drums in ceremonial setups often display golden ratio proportions. These arrangements not only facilitate better playing technique but also contribute to the visual harmony of the instrument setup. Contemporary percussion manufacturers have also begun incorporating these principles into their designs, using phi-based measurements to determine optimal distances between playing surfaces and strike zones.
The psychological impact of the golden ratio in music extends beyond mere mathematical curiosity, influencing how listeners perceive and process musical compositions. Research suggests that when musical elements are structured according to phi proportions, whether in timing, frequency relationships, or overall form, they often create a sense of natural balance and aesthetic pleasure in the listener. This phenomenon may be attributed to our brain’s inherent recognition of patterns that occur frequently in nature, making compositions that incorporate the golden ratio feel both familiar and inherently satisfying.
Studies in psychoacoustics have shown that musical pieces incorporating golden ratio proportions in their climax points, phrase lengths, or harmonic progressions tend to elicit stronger emotional responses from listeners. The human brain appears to be particularly receptive to these proportions, possibly due to their prevalence in natural phenomena and their role in human cognitive development. This neurological preference may explain why compositions that consciously or unconsciously employ phi relationships often achieve a balance that listeners describe as both compelling and aesthetically pleasing, even without their conscious awareness of the mathematical principles at work.
The human brain’s natural affinity for the golden ratio (φ ≈ 1.618) extends deeply into our perception of musical structures and compositions. Research has shown that when musical elements are arranged according to golden ratio proportions, listeners often report heightened emotional responses and a stronger sense of aesthetic satisfaction. This phenomenon appears to be rooted in our neurological makeup, as the human brain demonstrates particular activation patterns when processing sequences and harmonies that incorporate phi-based relationships.
Studies in psychoacoustics have revealed that compositions utilizing the golden ratio in their timing, progression, and climax points tend to create what listeners describe as “natural” or “perfect” tension and release cycles. This mathematical relationship appears frequently in works that have stood the test of time, from classical masterpieces to modern compositions, suggesting that our psychological preference for golden ratio proportions may be hardwired into our cognitive processing of music. The effect is particularly noticeable in the placement of key changes, dynamic shifts, and structural transitions, where golden ratio positioning often correlates with moments of peak listener engagement and emotional response.
The psychological impact of the golden ratio in music extends beyond mere mathematical precision, delving into the realm of aesthetic pleasure and emotional response. Research has shown that musical compositions incorporating phi-based proportions in their structure, timing, and harmonic relationships often create a sense of natural balance and satisfaction in listeners. This phenomenon may be attributed to humanity’s inherent recognition of golden ratio patterns found throughout nature, suggesting an evolutionary predisposition to find such proportions inherently pleasing.
Studies in psychoacoustics and music cognition have demonstrated that when musical elements are arranged according to golden ratio principles, listeners report heightened emotional engagement and a stronger sense of resolution. Whether in the placement of climactic moments, the structuring of melodic phrases, or the distribution of harmonic tension and release, compositions that consciously or unconsciously employ phi-based relationships tend to resonate more deeply with audiences. This aesthetic pleasure appears to transcend cultural boundaries, suggesting that the golden ratio’s influence on musical appreciation may be rooted in fundamental aspects of human perception rather than learned cultural preferences.
Research has shown that the human brain exhibits a natural affinity for processing musical structures that incorporate the golden ratio (φ), potentially due to its prevalence in natural phenomena and its mathematical elegance. Studies in neuroscience suggest that when listeners encounter musical compositions structured around phi proportions, their cognitive processing demonstrates enhanced pattern recognition and emotional resonance. This alignment with naturally occurring mathematical relationships may contribute to the ease with which our brains process and interpret such musical information.
The cognitive processing of phi-based musical elements appears to activate multiple neural networks simultaneously, engaging both analytical and emotional centers of the brain. When listeners experience music composed with golden ratio proportions—whether in rhythm, melody, or formal structure—their brains show increased activity in areas associated with both mathematical processing and aesthetic appreciation. This dual activation may explain why compositions incorporating the golden ratio often feel both intellectually satisfying and emotionally compelling, suggesting that our cognitive architecture is particularly well-suited to processing these mathematical relationships in musical contexts.
The presence of the Golden Ratio (φ) in music demonstrates the profound connection between mathematics and musical composition, revealing an underlying natural order that humans have intuitively recognized and implemented throughout musical history. From the structural organization of classical masterpieces to the climactic moments in contemporary compositions, phi continues to serve as both a conscious tool and an unconscious guide for composers seeking balance and aesthetic appeal in their work.
While some skeptics argue that the appearance of the Golden Ratio in music is merely coincidental, the overwhelming evidence of its occurrence in everything from sonata forms to phrase lengths, and from rhythm patterns to frequency relationships, suggests otherwise. As our understanding of this mathematical principle deepens, musicians and composers can more deliberately harness its power to create works that resonate with the same natural harmony found throughout the universe, from the spiral of a nautilus shell to the arrangement of leaves on a plant stem. The Golden Ratio remains a testament to the intricate relationship between mathematical precision and artistic expression in music.
Throughout this exploration of the Golden Ratio’s presence in music, we’ve uncovered compelling evidence of phi’s influence across various musical elements, from composition structure to rhythm and harmonic relationships. The mathematical proportion of approximately 1.618 appears consistently in classical masterpieces, modern compositions, and even in the physical design of instruments, suggesting that this universal constant may be inherently connected to our perception of musical beauty and balance.
The findings demonstrate that while some applications of the Golden Ratio in music may be intentional, others appear to emerge naturally through composers’ intuitive sense of proportion and harmony. This relationship between mathematics and musical aesthetics reinforces the ancient Greek philosophy that music and mathematics are intrinsically linked, providing a fascinating bridge between objective mathematical principles and subjective artistic expression. Whether conscious or unconscious, the presence of phi in music continues to influence contemporary composers and theorists, offering a valuable framework for understanding musical structure and composition.
The potential future applications of the golden ratio in music are both exciting and far-reaching. As artificial intelligence and machine learning continue to evolve, composers and producers can leverage phi-based algorithms to create more naturally appealing compositions. These technologies could analyze existing successful musical pieces through the lens of golden ratio proportions, helping to identify patterns that resonate with human perception and potentially establishing new frameworks for musical composition that integrate these mathematical principles more deliberately.
Furthermore, the golden ratio’s application in music may extend beyond traditional composition into emerging fields such as sound therapy and neuroaesthetics. Research suggests that music structured around phi might have particular psychological and physiological effects on listeners, opening new possibilities in therapeutic applications and cognitive enhancement. As our understanding of the relationship between mathematical harmony and human perception deepens, we may discover innovative ways to incorporate the golden ratio into everything from educational music programs to acoustic architecture, potentially revolutionizing how we create and experience musical works in the future.
The pervasive presence of Phi in musical composition and structure demonstrates the profound connection between mathematics and artistic expression. From the placement of climactic moments in classical pieces to the architectural framework of sonata form, the Golden Ratio serves as both a natural organizing principle and a tool for creating aesthetic balance. While some composers consciously incorporated these proportions into their works, others may have intuitively followed these patterns, suggesting that our appreciation for Golden Ratio relationships might be deeply embedded in human perception.
As we continue to explore and understand the relationship between mathematics and music, the Golden Ratio remains a fascinating lens through which to analyze and create musical works. Whether used as a compositional technique or discovered through analysis, Phi’s presence in music reinforces its status as a fundamental principle of natural harmony and beauty. This mathematical constant not only bridges the gap between science and art but also provides insight into why certain musical structures and proportions consistently resonate with listeners across cultures and throughout history.
Looking back from our “more enlightened” age at our founding fathers and the birth of America as a new nation gives a loft sense of giddy superiority. What were they thinking by continuing to allow slavery when they wrote the Constitution?
And this, folks, is how easy it is to feel some kind of moral superiority to those poor, ignorant, miscreants (aka scumbags) who practiced slavery, the ultimate cruelty perpetrated by man against another human being.
Funny how the use of the phrase “more enlightened” just rolls off the tongue as if it’s self-evident that we are so advanced and superior these days. I actually wrote this with a tinge of sarcasm because I believe a case could be made for the opposite. We may have many technological advancements but we can’t truthfully say we ended slavery.
That’s right. Slavery is alive and well in the world. It’s even alive and well in the good old USA. You can pretend you didn’t know all you like but it’s just called something else these days: human trafficking, or sex slave trade. Some of the trafficked victims actually end up doing manual labor against their will.
Back in colonial America, before we gained our independence, the tradition and practice of slavery was imported from Europe. I’m not suggesting its origin as some excuse. And there were many different kinds of slavery. Securing passage to the New World from Europe was costly, and out of reach for any but the very wealthy. That’s why many would voluntarily offer themselves up as indentured servants as payment in order to get to America. For many, this became a necessity to escape persecution for religious beliefs. For others, this was the prospect of claiming real estate and finding gold.
The reason for my question at hand goes at the very heart of the abortion issue. In those days slavery had become so commonplace that people eventually came to regard the practice as acceptable, even a right. They saw their station in life as an accident of birth so it wasn’t anyone’s fault that they were wealthy enough to have slaves and the slaves were grateful to find a benevolent, rich master able to afford to hire them.
In these <ahem> “enlightened” times we have come to see abortion as one of the many options when it comes to planned parenthood. After all, a woman has right to autonomy over her own body. In fact, to even suggest that she not be permitted to have an abortion seems an injustice on par with rape. She never gave assent to becoming impregnated and now, how dare anyone suggest she be forced to bear the offspring of such a violation. And, even when there is no rape, shouldn’t the mother be able to choose whether to “keep” the baby.
My point is that the practice of abortion is as commonplace as getting a tattoo, a piercing, a nose job, a chin lift, or a gastronomic bypass. It’s just a procedure and the problem goes away. It’s not expensive and many clinics offer the service free of charge. In fact, just regard it as another form of birth control. Bottom line, no painful delivery, no labor, and no postpartum responsibilities of raising the child. And, heaven forbid we ever go back to the days of back alley abortions.
When slavery was the law of the land, the disparity of class meant the slaves had no rights and were unequal to their masters. None of the slaves could stand up and say to their master “I don’t have to take this abuse. I’m out of here.” There were runaway slaves but most of them were caught and either put back into servitude or killed as an example and deterrent to others who might be like-minded. The slaves had no liberty because they were less than human: they were just property to be sold, traded, purchased, or disposed of. Not only were they without rights, they had no representation. They weren’t even considered citizens. You might even say they weren’t even regarded as human.
It has become customary to refer to the unborn child as a “fetus” from the Latin, meaning “offspring, young animal” which has led some to regard it as mass of tissue, not a child, and definitely less than human. This seems strange to me because with any other mammal we have no problem recognizing that what is inside the mother is the infant offspring of said mammal. A pregnant cow most obviously has a baby calf inside. I think the reason some have so much trouble equating “fetus” with “unborn child” has to do with the implications of what abortion means.
What is abortion? According to The American Heritage Dictionary of the English Language, 5th edition, abortion is “induced termination of a pregnancy with destruction of the embryo or fetus.” It would seem less egregious if this were just a removal of some tissue, similar to removing a tumor. I’m pretty sure that’s what most people think of when they think abortion.
Let’s just ask ourselves a simple question: “What if abortion was actual infanticide?” There was a time just asking this question was horrific and unthinkable. Now, there is a new breed of abortion activist that believes it is the mother’s right to kill her baby (infanticide) so it’s a waste of time coming to terms with what is actually going on. This position, though very recent, is more commonplace than you might imagine. No longer is the argument that the fetus is an unborn child, so it’s murder. The mask is off and it’s ugly. There is now a big movement that says it’s within the right of a mother to kill her baby, no matter how late term, even after the baby has been born. To me this is horrifying.
Even though the slave was powerless, he/she could cry out and be heard in their suffering. Not so with the unborn. When babies are being killed in the womb there is none but God to hear their silent cries of pain and anguish. Their death isn’t instantaneous. We now have scientific proof that they can feel pain and suffer an agonizing death as they are ripped apart or burned with chemicals.
As with slavery, abortion these days has become acceptable and we have yet to reach a point in our culture where it has become as widely regarded as an injustice. Maybe it was easier to see slavery as wrong because we could see, hear, and read of the cruelty and inhuman treatment they had to suffer. The slaughter of the unborn through abortions is a modern day holocaust but nobody can hear their screams and no one is forced to even see their ordeal.
My biggest sorrow is that none of the abortion advocates, whether Pro-Choice or Pro-Abortion, will even assent to the proposition we should have less abortions. They love to kill their babies and heaven help anyone who tries to stop them. I’m not sure criminalizing mothers having abortions or doctors performing them is the solution. Neither am I favor of outlawing abortions which will again lead to women dying from botched back alley abortions. What we need is a dialog and more enlightenment so, as a society, we can eventually say it’s wrong so we’re not going to do it anymore. The next generation may very well look back at this time and marvel at our inhumane practice of abortion the same way we look back when slavery was the law of the land. Maybe one day there will be a procedure to transplant the unborn child successfully from an unwilling mother to one who wants the child. i know, I’m a dreamer. But what other choice do I have? Color me silly, but I care about every life, no matter how small or defenseless. Are you with me?
Most of the focus in this recent election has been on who to vote for. Many are under the impression that both campaigns were personality driven, yet it may come as a surprise that we on the right kept waiting to hear what the Harris / Walz platform was other than not to vote for Trump. And, there was plenty of misinformation being heralded by the media about what a Trump presidency would be like. Kamala, Biden, Obama, and pretty much every other well known politician on the left warned that Trump is the biggest threat to our democracy.
Ok, friends, I’m going to ask you put all of that aside for the rest of this blog, because I’m not here to write about that. Instead, I’m going to try to explain what I voted for and not who.
I know you are going to find this hard to swallow, but I voted for everything the left said it was voting for: individual liberty; women’s rights; the right to believe what I want; the right to not have the government dictate what I can or cannot do (unless it violates someone else’s rights); equal protection under the law; no bullying or discrimination over ethnicity, sex, belief, or sexual preference; the right for women to be able to compete with women; the right to privacy; a secure border; freedom from overregulation and federal overreach; the right to earn a living; and a government that puts the interests of its citizens first.
As a Christian I share many beliefs with those of other faiths. I strongly believe that we should love one another. I believe we need to get rid of our anger and put aside our differences so that we can work together for all the things we have in common. In spite of the efforts of some, all of us — I mean every American — have more in common than our differences and we can live together without having to agree on everything. Your citizenship does not require you to have the same beliefs, wants, tastes, or ideas. In the Declaration of Independence, we read that “all men are created equal.” That equality only applies to our worth and rights to equal justice. It is not a guarantee of equal outcome and does not deny us differences in appearance, preference, taste, belief, station in life, ability, aptitude, intelligence, talent, role, etc. Life itself is diverse, of many colors and hues, multifaceted, and full of variety. All snowflakes are snowflakes yet each is unique. All fingerprints are fingerprints yet each is unique. You might look like someone else and you might have a lot in common with many other people but you are unique. Even identical twins are different people.
None of our differences need ever be a cause for separation unless that difference involves actions that cause or threatens harm to another. We believe in freedom of religion but that doesn’t mean we allow human sacrifice. We believe in the sanctity of life and the right to life, which includes the right to self defense and defense of others. We also believe to deprive someone of their life must always be a last resort. We understand the need for law enforcement because not everyone follows the law. We also believe that those given the authority to enforce the law have a responsibility and obligation to discharge their duties responsibly, without bias or prejudice, and should have to answer for their actions whenever they abuse that authority. That being said, we need to support and assist those who are serving on our behalf, putting themselves in dangers way on a regular basis.
We believe in civility and showing respect of others. We oppose bullying and depriving any one of their inalienable rights to life, liberty, and the pursuit of happiness. We also believe that citizenship is privilege not freely given to everyone, but granted according to our immigration laws. This is not only in respect for those born here and those who have obtained their citizenship, but also for anyone seeking to become a citizen. There is value in being a citizen and there is a proper means to becoming one. It is our right as sovereign individuals this be so.
We believe in charitable giving and helping those in need. As a believer, I strongly believe this must be something given freely and personally, not under duress, by force, or using someone else’s money. As a nation we have been more than generous and regularly give enormous amounts of money in aid to many nations, including our enemies. Whenever there is any disaster, we are the first to give as we can. There is a mistaken notion that the government should have the right to take money from us against our will as long as it’s for a good cause. This is Machiavellian thinking and the biggest problem with it is the lack of transparency. Doing wrong is never right or justified because a bigger power is doing it. We are aware that there are practices in our government that violate this principle but that doesn’t make the principle itself invalid.
In summary, no matter your party or political affiliation, we are all in this together. We may have our differences, but in the end of the day we share a common heritage and a common hope that we can better ourselves and be that shining city on a hill that our forefathers envisioned. Here in El Paso we have an expression, “If you don’t like the weather, just wait awhile and it will change.” No matter who wins our elections, it serves all of us to have such a form of representative government. If we don’t like who gets elected we will have the chance to elect someone else the next election. Our government doesn’t allow anyone to so radically change our government to ever change that. What’s more important is that we never abandon our principles, the ones that have eternal merit, and that we continue to live together as fellow Americans to see our dream come true.
While it may be debatable how much autonomy (free will) any of us have, there is sufficient evidence to establish free will exists.
Having and making choices is one of our responsibilities as an adult. Even children make choices but their options are necessarily limited by their parent(s) or guardian(s). Sometimes our choices are less evident and sometimes we even forget we have a choice.
As a believer and a philosopher, I believe there is a strong case for the importance of free will to our Creator. To demonstrate this, I ask you to consider soulful, romantic love.
Love that is forced upon us, that is imposed on us against our will, may be many things (including rape) but it isn’t true love. This has always been the case, even if historically many marriages were for reasons other than love. Even in arranged marriages, there wasn’t any pretense that it was for anything other than class, and material concerns.
The tradition of marriage, from time immemorial, has always included (in some for) consent by means of a question, and vows as declaration of will. Even arranged marriages were between people who chose to accept the arrangement.
Consent, or permission, is a part of free will. The best form of consent is informed consent, in which there is transparency about what is being accepted. This is the reason the traditional vows have that peculiar directive: “If anyone knows any reason why these two shouldn’t be joined together in holy matrimony, let him speak now or forever hold his peace.”
In scripture we learn that God is love. It is His nature. Furthermore, we read about the account of creation, where a loving God created man. Quintessential in the creation story is the instruction God gave Adam (and Eve): “You may eat freely from every tree of the garden, but you must not eat from the tree of the knowledge of good and evil; for in the day that you eat of it, you will surely die.”
In being given this commandment, Adam and Eve were presented with a choice: to eat or not to eat. God expressed His desire that they not eat. They chose to eat, an act of free will, and that choice resulted in death. God could have created man without any free will, in which case they never would have disobeyed God. Somehow, and I believe this to be very important, it was by the express will and design of God that man should have free will.
We also learn in scripture that God has and exercise His will. We don’t know about all the heavenly hosts, but we do know angels and archangels also have free will. When Lucifer fell, if we accept this account, he chose to rebel against God and many angels who joined him were cast out.
Let’s stop here and consider the implications of free will as applied to love and worship. I believe this is evidence given to us to know that God is good and loving. God doesn’t just tell us He is loving. He shows us by loving us enough to allow us to make choices. Because of how much Adam’s choice cost the human race, and because of how much God loves us, God himself chose to live as human and die in our place, thus making the ultimate sacrifice and paying for us the cost of our redemption, or salvation.
While the politics of man pale in comparison to the authority of the Kingdom of God, I believe we have been given knowledge useful in making intelligent choices when it comes to the government of man on earth.
While no perfect form of earthly government exists, we have plenty of data to give informed consent where the choice is available to us. By and large, we are limited to those choices provided to us. For some, there is no choice. To rebel against the status quo could mean imprisonment or death. Do you remember the Soviet Gulag Archipelago? Do you remember reading about life under the control of the Third Reich? Under Stalin?
Because God has placed so much importance on free will, I propose that the form of government that provides the most liberty, even if those choices lead to less than perfect circumstances, is the lesser of evils, being compared to other governments, where there is such a level of control, that its subjects are not free, and are deprived of liberty.
I’ll even go one step further and submit that throughout history, it is the forms of government we describe as tyrannical, where liberty is deprived from its subjects, that life and the pursuit of happiness is also up the whim of those in control. Life given or taken was determined by the upward or downward gesture of a thumb.
Think of the forms of government we see around the world today and I believe there is but one that is a shining city on a hill. Even though it is not purely in the same form as when it was born, it was unique experiment in the governance of man. Namely, the United States of America. Not a pure democracy, and definitely not a monarchy, socialist, or communist state, but a constitutional Republic with democratic elements. Whether or not it is supreme, that is not my argument. I’ll leave you to decide. But, it is definitely unique, even considering there are some governments that have a similar form.
In conclusion, I’ll put it this way: No form of government on earth is without its flaws. There is no perfect government where it depends on men, who are not angels, but sinners. Yet, the liberty enshrined the USA, as blueprinted by our Constitution, allows us a remedy should tyranny ever raise its ugly head. Such a remedy is out of reach in other governments where liberty has been denied. Just look at how many are trying to immigrate here compared to those trying to leave communist countries.
Some things in life are chosen for us, others we choose for ourselves. We have no say in our birth and little say, if any, in our death. Yet, choice is how we exercise our liberty.
Having the right to something isn’t the same thing as having it. We have the right to life, but life is fragile. Life should be respected and, if not defended, can be easily lost, not just our life but the lives of others, as well. All those deprived of liberty have the right to it. Also, the pursuit of happiness isn’t always a given.
Most of who we are is a product of our birth and our life choices. Life can be many things. It can be easy. It can be difficult. It can be delightful. It can be unbearable. Circumstance beyond birth can also provide fortune or famine. To a certain extent, all feelings of being in control are illusionary.
Human nature can readily be observed in a classroom. No matter the level, students of all ages will test the boundaries of rules. That’s why experienced teachers are ready for their first test. Yes, teachers get tested because students want to find out which, if any, rules get enforced. If the teacher makes the mistake of boasting meaningless ultimatums, the students will walk all over them.
But, that’s only one side of the equation. Most students want the security that comes from enforced rules, even at the cost of facing discipline. In the novel, Lord of the Flies, we are shown what happens when a group of boys find themselves in a circumstance where no rules are enforced. Of course, the rules of life don’t depend on mankind for enforcement. Life isn’t fair. Life isn’t cruel. It just is.
