Theory Of Relativity Musical Quotes

Einstein was remarkable for his powers of concentration; he could work uninterruptedly for hours and even days on the same problem. Some of the topics that interested him remained on his mind for decades. For relaxation he turned to music and to sailing, but often his work would continue during these moments as well; he usually had a notebook in his pocket so that he could jot down any idea that came to him. Once, after the theory of relativity had been put forth, he confessed to his colleague Wolfgang Pauli, "For the rest of my life I want to reflect on what light is." It is perhaps not entirely an accident that a focus on light is also the first visual act of the newborn child.

In other words, if an observer looks at another frame of reference (like a moving train), he or she will still see that the speed of light is the same even though that frame of reference is moving relative to it. It is because of this symmetry that our standard theory of light, or electromagnetism, cannot accommodate a varying speed of light in empty space. But when a wave of light moves in a different medium, such as glass, Lorentz symmetry is no longer preserved, and light can change speed relative to empty space. This was the essence of Joao's contention. It could be that there is a quantum effect on space-time that fundamentally violates Einstein's cherished Lorentz symmetry, resulting in a variation of the speed of light in the early universe. As it turns out, the shape of extra dimensions in string theory can indeed cause certain constants, including the speed of light, to vary throughout the space-time fabric.

Intellectual property rights are sometimes hailed as the mother of creativity and invention. However, Marshall Brain points out that many of the finest examples of human creativity—from scientific discoveries to creation of literature, art, music and design—were motivated not by a desire for profit but by other human emotions, such as curiosity, an urge to create, or the reward of peer appreciation. Money didn’t motivate Einstein to invent special relativity theory any more than it motivated Linus Torvalds to create the free Linux operating system. In contrast, many people today fail to realize their full creative potential because they need to devote time and energy to less creative activities just to earn a living. By freeing scientists, artists, inventors and designers from their chores and enabling them to create from genuine desire, Marshall Brain’s utopian society enjoys higher levels of innovation than today and correspondingly superior technology and standard of living.

In the same movie, Emperor Joseph II offers Mozart some musical advice: "Your work is ingenious. It's quality work. And there are simply too many notes, that's all. Just cut a few and it will be perfect." The emperor was put off by the surface complexity of Mozart's music. He didn't see that each note served a purpose-to make a promise or fulfill one, to complete a pattern or vary one. Similarly, at first encounter people are sometimes put off by the superficial complexity of fundamental physics. Too many gluons! But each of the eight color gluons is there for a purpose. Together, they fulfill complete symmetry among the color charges. Take one gluon away, or change its properties, and the structure would fall. Specifically, if you make such a change, then the theory formerly known as QCD begins to predict gibberish; some particles are produced with negative probabilities, and others with probability greater than 1. Such a perfectly rigid theory, one that doesn't allow consistent modification, is extremely vulnerable. If any of its predictions are wrong, there's nowhere to hide. No fudge factors or tweaks are available. On the other hand, a perfectly rigid theory, once it shows significant success, becomes very powerful indeed. Because if it's approximately right and can't be changed, then it must be exactly right! Salieri's criteria explain why symmetry is such an appealing principle for theory building. Systems with symmetry are well on the path to Salieri's perfection. The equations governing different objects and different situations must be strictly related, or the symmetry is diminished. With enough violations all pattern is lost, and the symmetry falls. Symmetry helps us make perfect theories. So the crux of the matter is not the number of notes or the number of particles or equations. It is the perfection of the designs they embody. If removing any one would spoil the design, then the number is exactly what it should be. Mozart's answer to the emperor was superb: "Which few did you have in mind, Majesty?

Music of the Grid: A Poem in Two Equations _________________________ The masses of particles sound the frequencies with which space vibrates, when played. This Music of the Grid betters the old mystic mainstay, "Music of the Spheres," both in fantasy and in realism. LET US COMBINE Einstein's second law m=E/C^2 (1) with another fundamental equation, the Planck-Einstein-Schrodinger formula E = hv The Planck-Einstein-Schrodinger formula relates the energy E of a quantum-mechanical state to the frequency v at which its wave function vibrates. Here h is Planck's constant. Planck introduced it in his revolutionary hypothesis (1899) that launched quantum theory: that atoms emit or absorb light of frequency v only in packets of energy E = hv. Einstein went a big step further with his photon hypothesis (1905): that light of frequency v is always organized into packets with energy E = hv. Finally Schrodinger made it the basis of his basic equation for wave functions-the Schrodinger equation (1926). This gave birth to the modern, universal interpretation: the wave function of any state with energy E vibrates at a frequency v given by v = E/h. By combining Einstein with Schrodinger we arrive at a marvelous bit of poetry: (*) v = mc^2/h (*) The ancients had a concept called "Music of the Spheres" that inspired many scientists (notably Johannes Kepler) and even more mystics. Because periodic motion (vibration) of musical instruments causes their sustained tones, the idea goes, the periodic motions of the planets, as they fulfill their orbits, must be accompanied by a sort of music. Though picturesque and soundscape-esque, this inspiring anticipation of multimedia never became a very precise or fruitful scientific idea. It was never more than a vague metaphor, so it remains shrouded in equation marks: "Music of the Spheres." Our equation (*) is a more fantastic yet more realistic embodiment of the same inspiration. Rather than plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combinations of quarks, gluons, electrons, photons,... (that is, the Bits that represent these Its) and let them settle until they reach equilibrium with the spontaneous activity of Grid. Neither planets nor any material constructions compromise the pure ideality of our instrument. It settles into one of its possible vibratory motions, with different frequencies v, depending on how we do the plunking, and with what. These vibrations represent particles of different mass m, according to (*). The masses of particles sound the Music of the Grid.

None,” Einstein said. “Relativity is a purely scientific matter and has nothing to do with religion.”51 That was no doubt true. However, there was a more complex relationship between Einstein’s theories and the whole witch’s brew of ideas and emotions in the early twentieth century that bubbled up from the highly charged cauldron of modernism. In his novel Balthazar, Lawrence Durrell had his character declare, “The Relativity proposition was directly responsible for abstract painting, atonal music, and formless literature.” The relativity proposition, of course, was not directly responsible for any of this. Instead, its relationship with modernism was more mysteriously interactive. There are historical moments when an alignment of forces causes a shift in human outlook. It happened to art and philosophy and science at the beginning of the Renaissance, and again at the beginning of the Enlightenment. Now, in the early twentieth century, modernism was born by the breaking of the old strictures and verities. A spontaneous combustion occurred that included the works of Einstein, Picasso, Matisse, Stravinsky, Schoenberg, Joyce, Eliot, Proust, Diaghilev, Freud, Wittgenstein, and dozens of other path-breakers who seemed to break the bonds of classical thinking.52 In his book Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc, the historian of science and philosophy Arthur I. Miller explored the common wellsprings that produced, for example, the 1905 special theory of relativity and Picasso’s 1907 modernist masterpiece Les Demoiselles d’Avignon.

It might be imagined that certain people in history—the naturally gifted, the geniuses—have either somehow bypassed the Apprenticeship Phase or have greatly shortened it because of their inherent brilliance. To support such an argument, people will bring up the classic examples of Mozart and Einstein, who seemed to have emerged as creative geniuses out of nowhere. With the case of Mozart, however, it is generally agreed among classical music critics that he did not write an original and substantial piece of music until well after ten years of composing. In fact, a study of some seventy great classical composers determined that with only three exceptions, all of the composers had needed at least ten years to produce their first great work, and the exceptions had somehow managed to create theirs in nine years. Einstein began his serious thought experiments at the age of sixteen. Ten years later he came up with his first revolutionary theory of relativity. It is impossible to quantify the time he spent honing his theoretical skills in those ten years, but is not hard to imagine him working three hours a day on this particular problem, which would yield more than 10,000 hours after a decade. What in fact separates Mozart and Einstein from others is the extreme youth with which they began their apprenticeships and the intensity with which they practiced, stemming from their total immersion in the subject. It is often the case that in our younger years we learn faster, absorb more deeply, and yet retain a kind of creative verve that tends to fade as we get older.

In many fields—literature, music, architecture—the label ‘Modern’ stretches back to the early 20th century. Philosophy is odd in starting its Modern period almost 400 years earlier. This oddity is explained in large measure by a radical 16th century shift in our understanding of nature, a shift that also transformed our understanding of knowledge itself. On our Modern side of this line, thinkers as far back as Galileo Galilei (1564–1642) are engaged in research projects recognizably similar to our own. If we look back to the Pre-Modern era, we see something alien: this era features very different ways of thinking about how nature worked, and how it could be known. To sample the strange flavour of pre-Modern thinking, try the following passage from the Renaissance thinker Paracelsus (1493–1541): The whole world surrounds man as a circle surrounds one point. From this it follows that all things are related to this one point, no differently from an apple seed which is surrounded and preserved by the fruit … Everything that astronomical theory has profoundly fathomed by studying the planetary aspects and the stars … can also be applied to the firmament of the body. Thinkers in this tradition took the universe to revolve around humanity, and sought to gain knowledge of nature by finding parallels between us and the heavens, seeing reality as a symbolic work of art composed with us in mind (see Figure 3). By the 16th century, the idea that everything revolved around and reflected humanity was in danger, threatened by a number of unsettling discoveries, not least the proposal, advanced by Nicolaus Copernicus (1473–1543), that the earth was not actually at the centre of the universe. The old tradition struggled against the rise of the new. Faced with the news that Galileo’s telescopes had detected moons orbiting Jupiter, the traditionally minded scholar Francesco Sizzi argued that such observations were obviously mistaken. According to Sizzi, there could not possibly be more than seven ‘roving planets’ (or heavenly bodies other than the stars), given that there are seven holes in an animal’s head (two eyes, two ears, two nostrils and a mouth), seven metals, and seven days in a week. Sizzi didn’t win that battle. It’s not just that we agree with Galileo that there are more than seven things moving around in the solar system. More fundamentally, we have a different way of thinking about nature and knowledge. We no longer expect there to be any special human significance to natural facts (‘Why seven planets as opposed to eight or 15?’) and we think knowledge will be gained by systematic and open-minded observations of nature rather than the sorts of analogies and patterns to which Sizzi appeals. However, the transition into the Modern era was not an easy one. The pattern-oriented ways of thinking characteristic of pre-Modern thought naturally appeal to meaning-hungry creatures like us. These ways of thinking are found in a great variety of cultures: in classical Chinese thought, for example, the five traditional elements (wood, water, fire, earth, and metal) are matched up with the five senses in a similar correspondence between the inner and the outer. As a further attraction, pre-Modern views often fit more smoothly with our everyday sense experience: naively, the earth looks to be stable and fixed while the sun moves across the sky, and it takes some serious discipline to convince oneself that the mathematically more simple models (like the sun-centred model of the solar system) are right.

To the eye, the key signatures of relative keys are identical. Minor key signatures are laid out on the staff just like major key signatures. The sharps and flats are in the same octave and same order. Only by analyzing the melody to locate the tonic can a key signature be visually identified as major or minor.

Theories of generational difference make sense if they are expressed as theories of environmental difference rather than of psychological difference. People, especially young people, will respond to incentives because they have much to gain and little to lose from experimentation. To understand why people are spending so much time and energy exploring new forms of connection, you have to overcome the fundamental attribution error and extend to other people the set of explanations that you use to describe your own behavior: you respond to new opportunities, and so does everybody else, and these changes feed on one another, amplifying some kinds of behavior and damping others. People in my generation and older often tut-tut about young people’s disclosing so much of their lives on social networks like Facebook, contrasting that behavior with our own relative virtue in that regard: “You exhibitionists! We didn’t behave like that when we were your age!” This comparison conveniently ignores the fact that we didn’t behave that way because no one offered us the opportunity (and from what I remember of my twenties, I think we would have happily behaved that way if we’d had the chance). The generational explanations of Napster’s success fall apart because of the fundamental attribution error. The recording industry made that error when it became convinced that young people were willing to share because their generation was morally inferior (a complaint with obvious conceptual appeal to the elders). This thesis never made sense. If young people had become generally lawless, we’d expect to see a rise not just in sharing music but also in shoplifting and other forms of theft.

The Great Library holds the blueprint for the whole universe. People from your world sometimes refer to it as “source code”, although it is in no way digital. It is much more fundamental and ancient than that. Every book in the library controls some aspect of reality. Section 04F concerns the Big Bang, for example. Section 03B is music theory. The numbers 20-29G deal with quantum physics. And 18 and 19G are relativity. We have dictionaries for every language ever spoken. It’s very important that the books are not disturbed. We look after them, read them, maintain them… It takes all our time. But looking after the Great Library is one of the most important jobs in the whole universe.

The Marland definition of giftedness (page 499) broadened the view of giftedness from one based strictly on IQ to one encompassing six areas of outstanding or potentially outstanding performance. The passage of Public Law 94–142, the Education for All Handicapped Children Act, in 1975 led to an increased interest in and awareness of individual differences and exceptionalities. PL 94–142, however, was a missed opportunity for gifted children, as there was no national mandate to serve them. Mandates to provide services for children and youth who are gifted and talented are the result of state rather than federal legislation. The 1980s and 1990s: The Field Matures and Provides Focus for School Reform Building on Guilford’s multifaceted view of intelligence, Howard Gardner and Robert Sternberg advanced their own theories of multiple intelligences in the 1980s. Gardner (1983) originally identified seven intelligences—linguistic, logical-mathematical, spatial, bodily-kinesthetic, musical, interpersonal, and intrapersonal (see Table 15.2). Describing these intelligences as relatively independent of one another, he later added naturalistic as an eighth intelligence (Gardner, 1993). Sternberg (1985) presented a triarchic view of “successful intelligence,” encompassing practical, creative, and executive intelligences. Using these models, the field of gifted education has expanded its understanding of intelligence while not abandoning IQ as a criterion for identifying intellectually gifted children. A Nation at Risk (National Commission on Excellence in Education, 1983) described the state of education in U.S. schools as abysmal. The report made a connection between the education of children who are gifted and our country’s future. This commission found that 50 percent of the school-age gifted population was not performing to full potential and that mathematics and science were in deplorable conditions in the schools. The message in this report percolated across the country and was responsible for a renewed interest in gifted education as well as in massive education reform that occurred nationally and state by state.

We live in a wave universe, cycling forward for all eternity, and ruled by wave mathematics: Fourier mathematics. Fourier mathematics is the basis of music theory, light theory, wave theory, quantum mechanics, and holography. It uniquely explains mind, and solves the problem of Cartesian mind-matter interaction. Einstein’s relativity theory is a spacetime misinterpretation of Fourier mathematics, deriving from Einstein’s inability to conceive of a Singularity outside space and time as the mysterious “ether” that provides the absolute framework for spacetime reality. If humanity turned its entire attention to holography, and Fourier mathematics, we would be Gods living in paradise in just one generation. What are we waiting for?

e=mc^2. I know. I promised there would be no equations and, except for a few footnotes, I've kept my promise. But I think you will forgive me for making an exception for the world's most famous equation-the only equation to have its biography written. And the thing is this: e = mc^2 pops right out of QFT. Einstein had to work hard to find it (it was published in a separate paper that followed his breakthrough paper on relativity theory in 1905), but in QFT it appears as an almost trivial consequence of the two previous results. Since both mass and energy are associated with oscillations in the field, it doesn't take an Einstein to see that there must be a relationship between the two. Any schoolboy can combine the two equations and find (big drum roll, please) e = mc^2. Not only does the equation tumble right out of QFT, its meaning is seen in the oscillations or "shimmer" of the fields. Frank Wilczek calls these oscillations "a marvelous bit of poetry" that create a "Music of the Grid" (Wilczek's term for space seen as a lattice of points): Rather than plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combinations of quarks, gluons, electrons, photons,...and let them settle until they reach equilibrium with the spontaneous activity of Grid...These vibrations represent particles of different mass m...The masses of particles sound the Music of the Grid. ----- Frank Wilczek

Her exposition took the form of notes lettered A through G, extending to nearly three times the length of Menabrea’s essay. They offered a vision of the future more general and more prescient than any expressed by Babbage himself. How general? The engine did not just calculate; it performed operations, she said, defining an operation as “any process which alters the mutual relation of two or more things,” and declaring: “This is the most general definition, and would include all subjects in the universe.” The science of operations, as she conceived it, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.… One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used. Symbols and meaning: she was emphatically not speaking of mathematics alone. The engine “might act upon other things besides number.” Babbage had inscribed numerals on those thousands of dials, but their working could represent symbols more abstractly. The engine might process any meaningful relationships. It might manipulate language. It might create music. “Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

You said to get involved with people, that I can’t learn about connections in a vacuum.” I agreed. “So what’s not working?” She pulled a long list from her purse. “This,” Linda said, “is a list I put together of all the involvements I’ve had in the past few months. And nothing’s happening.” I read the list, which looked something like this: Dancing lessons: ballroom, disco, and line Sports: sailing, rollerblading, golf, and tennis Music: opera, modern, and piano lessons Art: ceramics and museums Spiritual: Bible study, worship, and missions Career: Ongoing training, night school to earn an MBA “What are you grinning at?” Linda asked me. I wasn’t even aware I was smiling. I told her, “This is a proud moment for me. I’ve never met a real live renaissance woman.” “Now I’m really confused,” Linda said. I explained, “Linda, this is the most well-rounded, comprehensive, and exhausting list I’ve ever seen. I can’t imagine how you can even get up in the mornings. But it’s not solving your problem. “These are all great activities, designed to develop you and help you in your life. But each of them is primarily functional, rather than relational. Their goal is competence in some skill, or recreation, or learning more about God’s creation. But relationship isn’t the goal. These are ‘doing’ things, not ‘connecting’ things.” Linda started to get it. “You know, I’ve noticed that I am talking to people at these activities. But all the talk is about tennis or management theories. I’ve wondered when someone in the classroom was going to ask me about my emotional and spiritual life.” “Don’t hold your breath,” I said.

Einstein, likewise, realized how important it is to interweave the arts and the sciences. When he felt stymied in his quest for the theory of general relativity, he would pull out his violin and play Mozart, saying that the music helped connect him to the harmony of the spheres.

On a deeper level, modes show the relationships between chords and scales, and they are completely relative to the chords that are playing underneath in the background, or on the backing track. This concept will be extremely important when it comes to 7-note scales,

In his book The Art of Yoga, B. K. S. Iyengar calls Yoga a “disciplinary art which develops the faculties of the body, mind and intellect” and whose “purpose is to refine man.”4 Initially he practiced Yoga for health reasons, but gradually he developed the yogic postures into an art form bringing “charm and delicacy, poise and peace, harmony and delight in presentations.”5 Undoubtedly he relates in this artistic way to the rest of Yoga as well. At the same time, Iyengar—whose method of āsana practice is the most exacting of all—makes it clear that the yogic techniques, if practiced correctly, have predictable results. Iyengar sees the relationship between art and science as follows: “Art in its initial stages is science; science in its highest form is art.”6 That is to say, at first the artist must master technique (the scientific part of art), just as the scientist who wants to master science must see beauty in truth. The delight and awe of mathematicians when looking at a particularly concise formula is a well-known manifestation of artistic sensibility. Long ago, Pythagoras knew of the meeting place of science (in the form of mathematics) and art (in the form of music). Even before him, the Indians had discovered the same connection, as expressed in their Shulba-Sūtras. Yoga practitioners look upon their own body-mind as an artistic instrument that can be explored fairly precisely by carefully observing the timehonored rules of the yogic heritage. This effort yields what the Western esoteric traditions call the “music of the spheres”—the mystical sound om reverberating throughout the cosmos followed by the wondrous realization of absolute oneness (ekatva) beyond all qualities.

the preparation and resolution of a dis-c(5rd ; the transition from a point of rest to one of unrest, and thence to a new point of rest, which is one of the great underlying prmciples of musical art. Concords, and discords, and the sys-tematisation of tones into scales, are all inextricably mixed up together, and Debussy's departure from what has hitherto been the ordered procedure in relation to chords has involved a proportionate departure, or nearly so, as regards scales. This, again, it is possible to consider as an addition to, rather than a destruction of the proved resources of music. The universal employment of the major and minor modes exclusively, was born of expedience. They made for elasticity and security ; but at the same time the door was thereby closed upon the old Church modes, and with them, upon a range of effects which belonged to these old-world modes alone. Many of these effects Debussy has revived, but in this only treading more continuously in a path which has been adventured upon by various composers, from Beethoven to Weingartner. Not the construction of music, however, but its effect, is the main subject of consideration so far as the non-professional public is concerned. In this connection there are a few points which it will be worth while to consider with some little attention, for upon this consideration will it depend very much whether one takes a reasonable view, or the reverse, of Debussy's music. and the reverse, it should be mentioned, may equally well be laudatory or hostile ; adulation or detraction alike insufficiently informed. In the first place it is to be borne in mind that Debussy's music overrides a good many established theories, or rather the limitations within which the operation of these theories has hitherto been confined.

Let’s call it the theory of receptivity. It’s the idea, often cited by young people in their case against the relevance of even marginally older people, that one’s taste—in music or film, literature or fine cuisine—petrifies during life’s peak of happiness or nadir of misery. Or maybe it’s not that simple. Maybe a subtler spike on the charts—upward, downward, anomalous points in between—might qualify, so long as it’s formative. Let’s say that receptivity, anyway, can be tied to the moments when, for whatever reason, a person opens herself to the things we can all agree make life worth living in a new and definitive way, whether curiosity has her chasing down the world’s pleasures, or the world has torn a strip from her, exposing raw surface area to the winds. During these moments—sleepaway camp right before your bar mitzvah; the year you were captain of the hockey team and the baseball team; the time after you got your license and before you totaled the Volvo—you are closely attuned to your culture, reaching out and in to consume it in vast quantities. When this period ends, your senses seal off what they have absorbed and build a sensibility that becomes, for better or worse, definitive: This is the stuff I like. These films/books/artists tell the story of who I am. There is no better-suited hairstyle. This is as good/bad as it gets for me. The theory suggests that we only get a couple of these moments in life, a couple of sound tracks, and that timing is paramount. If you came of age in the early eighties, for instance, you may hold a relatively shitty cultural moment to be the last time anything was any good simply because that was the last time you were open and engaged with what was happening around you, the last time you felt anything really—appallingly—deeply. I worry about this theory. I worry because it suggests that receptivity is tied closely to youth, and firsts, and also because as with many otherwise highly rejectable theories—Reaganomics and communism come to mind—there is that insolent nub of truth in it.

While this signifier can be difficult to pin down with precision, it can clearly be heard in the records of Duane Eddy and many other guitarists of the period. It usually involves a relatively nondistorted electric guitar timbre articulated with a strong attack and a melody played on the lower strings. Reverberation is ubiquitous, and almost equally common were echo, amplifier tremolo, and use of the guitar’s vibrato bar. This overall guitar sound is often called a Fender sound, but that is a bit misleading, since Gretsch guitars were equally specialized for the purpose, and many other brands were also used. What makes the twang guitar interesting in topical terms is that it not only signified the western topic but also was key to a linked set of genres that intersect one another in complex ways: western, spy, and surf. Because these were all signified by overlapping musical features and in turn resemble one another in some of their broader connotations, we could speak of a twang guitar continuum: a range of topics that coalesced only shortly before psychedelia and were cognate with it in a variety of ways. Philip Tagg and Bob Clarida point out that the twang guitar, often in a minor mode with a flat seventh, was a common factor between spaghetti western and Bond/spy scores in the late 1950s and early 1960s. I would add surf guitar to the list, with its sonic experimentation and general relationship to fun, escape, and exoticism: “[The twang guitar] probably owes some of its immediate success as a spy sound to its similarity with various pre-rock ‘Viennese intrigue’ sounds like Anton Karas’s Third Man zither licks (1949). But in the 1962–64 period that produced The Virginian (1962), Dr. No (1963) and Leone’s A Fistful of Dollars (1964), steely Fender guitar was well on its way to becoming an all-purpose excitement/adventure timbre” (Tagg and Clarida 2003, 367).

Supergravity is a version of Einstein's theory of general relativity, dressed up with supersymmetry-a symmetry that draws a connection between bosons and fermions, matching one boson for every fermion into "superpartners." Bosons are the entities responsible for transmitting forces, such as the photon that transmits the electromagnetic force. On the other hand, fermions are both matter particles, such as electrons and quarks, and the antiparticles of all these subatomic entities. Looking in the mirror is an example of how symmetry works. The image you see closely resembles how you appear to others because of your bilateral symmetry, even though the mirror switches your left side for your right. Think of supersymmetry as a mirror that switches Bosons for fermions without changing the behavior of the physical system.

Particle theory explains that all matter is made of many small particles that are always moving. There are particles in solids, liquids, and gases, and all of them continually vibrate, in varying directions, speeds, and intensities.17 Particles can only interact with matter by transferring energy. Waves are the counterpart to particles. There are three ways to regard waves: •​A disturbance in a medium through which energy is transferred from one particle within the medium to another, without making a change in the medium. •​A picture of this disturbance over time. •​A single cycle representing this disturbance. Waves have a constructive influence on matter when they superimpose or interact by creating other waves. They have a destructive influence when reflected waves cancel each other out. Scientists used to believe that particles were different from waves, but this is not always true, as you will see in the definition of wave-particle duality in this section. Waves, or particles operating in wave mode, oscillate, or swing between two points in a rhythmic motion. These oscillations create fields, which can in turn create more fields. For instance, oscillating charged electrons form an electrical field, which generates a magnetic field, which in turn creates an electrical field. Superposition in relation to waves means that a field can create effects in other objects, and in turn be affected itself. Imagine that a field stimulates oscillations in an atom. In turn, this atom makes its own waves and fields. This new movement can force a change in the wave that started it all. This principle allows us to combine waves; the result is the superposition. We can also subtract waves from each other. Energy healing often involves the conscious or inadvertent addition or subtraction of waves. In addition, this principle helps explain the influence of music, which often involves combining two or more frequencies to form a chord or another harmonic. A harmonic is an important concept in healing, as each person operates at a unique harmonic or set of frequencies. A harmonic is defined as an integer multiple of a fundamental frequency. This means that a fundamental tone generates higher-frequency tones called overtones. These shorter, faster waves oscillate between two ends of a string or air column. As these reflected waves interact, the frequencies of wavelengths that do not divide into even proportions are suppressed, and the remaining vibrations are called the harmonics. Energy healing is often a matter of suppressing the “bad tones” and lifting the “good tones.” But all healing starts with oscillation, which is the basis of frequency. Frequency is the periodic speed at which something vibrates. It is measured in hertz (Hz), or cycles per second. Vibration occurs when something is moving back and forth. More formally, it is defined as a continuing period oscillation relative to a fixed point—or one full oscillation.

Lovelace defined as an ‘operation’ the control of material and symbolic entities beyond the second-order language of mathematics (like the idea, discussed in chapter 1, of an algorithmic thinking beyond the boundary of computer science). In a visionary way, Lovelace seemed to suggest that mathematics is not the universal theory par excellence but a particular case of the science of operations. Following this insight, she envisioned the capacity of numerical computers qua universal machines to represent and manipulate numerical relations in the most diverse disciplines and generate, among other things, complex musical artefacts: [The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine … Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

Flower of life: A figure composed of evenly-spaced, overlapping circles creating a flower-like pattern. Images of the Platonic solids and other sacred geometrical figures can be discerned within its pattern. FIGURE 3.14 FLOWER OF LIFE The Platonic solids: Five three-dimensional solid shapes, each containing all congruent angles and sides. If circumscribed with a sphere, all vertices would touch the edge of that sphere. Linked by Plato to the four primary elements and heaven. FIGURE 3.15 PENTACHORON The applications of these shapes to music are important to sound healing theory. The ancients have always professed a belief in the “music of the spheres,” a vibrational ordering to the universe. Pythagorus is famous for interconnecting geometry and math to music. He determined that stopping a string halfway along its length created an octave; a ratio of three to two resulted in a fifth; and a ratio of four to three produced a fourth. These ratios were seen as forming harmonics that could restore a disharmonic body—or heal. Hans Jenny furthered this work through the study of cymatics, discussed later in this chapter, and the contemporary sound healer and author Jonathan Goldman considers the proportions of the body to relate to the golden mean, with ratios in relation to the major sixth (3:5) and the minor sixth (5:8).100 Geometry also seems to serve as an “interdimensional glue,” according to a relatively new theory called causal dynamical triangulation (CDT), which portrays the walls of time—and of the different dimensions—as triangulated. According to CDT, time-space is divided into tiny triangulated pieces, with the building block being a pentachoron. A pentachoron is made of five tetrahedral cells and a triangle combined with a tetrahedron. Each simple, triangulated piece is geometrically flat, but they are “glued together” to create curved time-spaces. This theory allows the transfer of energy from one dimension to another, but unlike many other time-space theories, this one makes certain that a cause precedes an event and also showcases the geometric nature of reality.101 The creation of geometry figures at macro- and microlevels can perhaps be explained by the notion called spin, first introduced in Chapter 1. Everything spins, the term spin describing the rotation of an object or particle around its own axis. Orbital spin references the spinning of an object around another object, such as the moon around the earth. Both types of spin are measured by angular momentum, a combination of mass, the distance from the center of travel, and speed. Spinning particles create forms where they “touch” in space.