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“If you don't make mistakes, you're not working on hard enough problems. And that's a mistake.”
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“Two obsessions are the hallmarks of Nature's artistic style:
Symmetry- a love of harmony, balance, and proportion
Economy- satisfaction in producing an abundance of effects from very limited means”
― A Beautiful Question: Finding Nature's Deep Design
Symmetry- a love of harmony, balance, and proportion
Economy- satisfaction in producing an abundance of effects from very limited means”
― A Beautiful Question: Finding Nature's Deep Design
“In physics, you don't have to go around making trouble for yourself - nature does it for you.”
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“Transient and Eternal
The state of the world is in flux, and every object within it is subject to change.
Concepts live outside of time and, because All Things Are Number, liberate us from it.”
― A Beautiful Question: Finding Nature's Deep Design
The state of the world is in flux, and every object within it is subject to change.
Concepts live outside of time and, because All Things Are Number, liberate us from it.”
― A Beautiful Question: Finding Nature's Deep Design
“When religion talks about our aspirations and our sense of morality, I do not believe that science can contradict it. However, when religion contradicts science on matters of fact, religion must yield.”
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“The answer to the ancient question 'Why is there something rather than nothing?' would then be that ‘nothing’ is unstable.”
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“Thus far our meditation on quantum reality has revealed that the world of everyday matter, when properly understood, embodies concepts of extraordinary beauty. Indeed, ordinary matter is built up from atoms that are, in a rich and precise sense, tiny musical instruments. In their interplay with light, they realize a mathematical Music of the Spheres that surpasses the visions of Pythagoras, Plato, and Kepler. In molecules and ordered materials, those atomic instruments play together as harmonious ensembles and synchronized orchestras.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“The legendary Danish physicist Niels Bohr distinguished two kinds of truths. An ordinary truth is a statement whose opposite is a falsehood. A profound truth is a statement whose opposite is also a profound truth.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“Supersymmetry, if correct, will be a profound new embodiment of beauty in the world. Because the transformations of supersymmetry turn substance particles into force particles, and vice versa, supersymmetry can explain, based on symmetry, why neither of those things can exist without the other: Both are the same thing, seen from different perspectives. Supersymmetry reconciles apparent opposites, in the spirit of yin-yang.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“Mythic Background
Describing his approach to science, Einstein said something that sounds distinctly prescientific, and hearkens back to those ancient Greeks he admired:
What really interests me is whether God had any choice in the creation of the world.
Einstein's suggestion that God-or a world-making Artisan-might not have choices would have scandalized Newton or Maxwell. It fits very well, however, with the Pythagorean search for universal harmony, or with Plato's concept of a changeless Ideal.
If the Artisan had no choice: Why not? What might constrain a world-making Artisan?
One possibility arises if the Artisan is at heart an artist. Then the constraint is desire for beauty. I'd like to (and do) infer that Einstein thought along the line of our Question-Does the world embody beautiful ideas?-and put his faith in the answer "yes!"
Beauty is a vague concept. But so, to begin with, were concepts like "force" and "energy." Through dialogue with Nature, scientists learned to refine the meaning of "force" and "energy," to bring their use into line with important aspects of reality.
So too, by studying the Artisan's handiwork, we evolve refined concepts of "symmetry," and ultimately of "beauty"-concepts that reflect important aspects of reality, while remaining true to the spirit of their use in common language.”
― A Beautiful Question: Finding Nature's Deep Design
Describing his approach to science, Einstein said something that sounds distinctly prescientific, and hearkens back to those ancient Greeks he admired:
What really interests me is whether God had any choice in the creation of the world.
Einstein's suggestion that God-or a world-making Artisan-might not have choices would have scandalized Newton or Maxwell. It fits very well, however, with the Pythagorean search for universal harmony, or with Plato's concept of a changeless Ideal.
If the Artisan had no choice: Why not? What might constrain a world-making Artisan?
One possibility arises if the Artisan is at heart an artist. Then the constraint is desire for beauty. I'd like to (and do) infer that Einstein thought along the line of our Question-Does the world embody beautiful ideas?-and put his faith in the answer "yes!"
Beauty is a vague concept. But so, to begin with, were concepts like "force" and "energy." Through dialogue with Nature, scientists learned to refine the meaning of "force" and "energy," to bring their use into line with important aspects of reality.
So too, by studying the Artisan's handiwork, we evolve refined concepts of "symmetry," and ultimately of "beauty"-concepts that reflect important aspects of reality, while remaining true to the spirit of their use in common language.”
― A Beautiful Question: Finding Nature's Deep Design
“Yet it is beautiful to discover that there's another chapter to the story, where we discover deep unity beneath, and supporting, the diversity of appearance. All colors are one thing, seen in different states of motion. That is science's brilliantly poetic answer to Keats's complaint that science "unweaves a rainbow.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“To explain all nature is too difficult a task for any one man or even for any one age. ’Tis much better to do a little with certainty & leave the rest for others that come after you.”
― Fundamentals: Ten Keys to Reality
― Fundamentals: Ten Keys to Reality
“Planck noted that although the Andromedans wouldn't have access to our rulers, scales, or clocks, they would have access to our physical laws, which are the same as theirs. They could measure, in particular, three universal constants:
c: The speed of light.
G: Newton's gravitational constant. In Newton's theory, this is a measure of the strength of gravity. To be precise, in Newton's law of gravity, the gravitational force between the bodies of masses m1, m2 separated by distance r is Gm1m2/r^2.
h: Planck's constant.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
c: The speed of light.
G: Newton's gravitational constant. In Newton's theory, this is a measure of the strength of gravity. To be precise, in Newton's law of gravity, the gravitational force between the bodies of masses m1, m2 separated by distance r is Gm1m2/r^2.
h: Planck's constant.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“In short: the space of color information is infinite-dimensional, but we perceive, as color, only a three-dimensional surface, onto which those infinite dimensions project.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“We know even less about dark energy. It seems to spread out perfectly evenly, with the same density everywhere and everywhen, as if it were an intrinsic property of space-time. Unlike any conventional kind of matter (even supersymmetric particles or axions), the dark energy exerts negative pressure. It tries to pull you apart! Fortunately, although dark energy supplies about 70% of the mass of the universe as a whole, its density is only about 7 X 10 ^-30 times the density of water, and its negative pressure cancels only about 7 X 10 ^-14 of normal atmospheric pressure-less than a part in a trillion. I don't know when we'll have clearer ideas about what the dark energy is. I'd guess not very soon. I hope I'm wrong.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“The entity we perceive as empty space is a multilayered, multicolored superconductor. What an amazing, astonishing, beautiful, breathtaking concept. Extraordinary, too.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“If an energetic and powerful Creator made the world, it could be that what moved Him—or Her, or Them, or It—to create was precisely an impulse to make something beautiful.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“If you don’t make mistakes, you’re not working on hard enough problems”
―
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“So: What is the world made of? Subject, as ever, to addition and correction, here is the multifaceted answer that modern physics provides:
1) The primary ingredient of physical reality, from which all else is formed, fills space and time.
2) Every fragment, each space-time element, has the same basic properties as every other fragment.
3) The primary ingredient of reality is alive with quantum activity. Quantum activity has special characteristics. It is spontaneous and unpredictable. And to observe quantum activity, you must disturb it.
4) The primary ingredient of reality also contains enduring material components. These make the cosmos a multilayered, multicolored superconductor.
5) The primary ingredient of reality contains a metric field that gives space-time rigidity and causes gravity.
6) The primary ingredient of reality weighs, with a universal density.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
1) The primary ingredient of physical reality, from which all else is formed, fills space and time.
2) Every fragment, each space-time element, has the same basic properties as every other fragment.
3) The primary ingredient of reality is alive with quantum activity. Quantum activity has special characteristics. It is spontaneous and unpredictable. And to observe quantum activity, you must disturb it.
4) The primary ingredient of reality also contains enduring material components. These make the cosmos a multilayered, multicolored superconductor.
5) The primary ingredient of reality contains a metric field that gives space-time rigidity and causes gravity.
6) The primary ingredient of reality weighs, with a universal density.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“Energy-momentum tells the metric fluid how to flow.
The metric fluid tells energy-momentum how to flow.
Electric charge tells the electromagnetic fluid how to flow.
The electromagnetic fluid tells electric charge how to flow.
Weak charge tells the weak fluid how to flow.
The weak fluid tells weak charge how to flow.
Strong charge tells the strong fluid how to flow.
The strong fluid tells strong charge how to flow.”
― A Beautiful Question: Finding Nature's Deep Design
The metric fluid tells energy-momentum how to flow.
Electric charge tells the electromagnetic fluid how to flow.
The electromagnetic fluid tells electric charge how to flow.
Weak charge tells the weak fluid how to flow.
The weak fluid tells weak charge how to flow.
Strong charge tells the strong fluid how to flow.
The strong fluid tells strong charge how to flow.”
― A Beautiful Question: Finding Nature's Deep Design
“Gravity is the dominant force in astronomy, but only by default. Other interactions are far stronger, but they feature both attractions and repulsions. Normally matter reaches an accurate equilibrium, with the forces cancelled. Temporary imbalances (small ones) among electric forces lead to lightning storms; small temporary imbalances among strong forces induce nuclear explosions. Gross breakdowns of equilibrium cannot stand. Gravity, however, is always attractive. Though feeble at the level of individual basic particles, gravitational forces inexorably add up. The meek inherit the cosmos.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“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.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
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.”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“Science tells us many important things about how things are, but it does not pronounce how things should be, nor forbid us from imagining things that are not.”
― Fundamentals: Ten Keys to Reality
― Fundamentals: Ten Keys to Reality
“With this, in a powerful sense, our Question has been answered. The world, insofar as we speak of the world of Chemistry, biology, astrophysics, engineering, and everyday life, does embody beautiful ideas. The Core, which governs those domains, is profoundly rooted in concepts of symmetry and geometry, as we have seen. And it works its will, in quantum theory, through music-like rules. Symmetry really does determine structure. A pure and perfect Music of the Spheres really does animate the soul of reality. Plato and Pythagoras: We salute you!”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“Dynamical beauty transcends specific objects and phenomena, and invites us to imagine the expanse of possibilities. For example, the sizes and shapes of actual planetary orbits are not simple. They are neither the (compounded) circles of Aristotle, Ptolemy, and Nicolaus Copernicus, nor even the more nearly accurate ellipses of Kepler, but rather curves that must be calculated numerically, as functions of time, evolving in complicated ways that depend on the positions and masses of the Sun and the other planets. There is great beauty and simplicity here, but it is only fully evident when we understand the deep design. The appearance of particular objects does not exhaust the beauty of the laws.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“Subtle is the Lord, but malicious She is not.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“A quantum atom with two electrons is a much more complicated object to visualize, and I'm not aware that it's ever been done very well. The challenge is that for each possible position of one electron, the wave function of the other is a different three-dimensional object. So really, the natural home of the total wave function, for the two-electron system, is a space of 3 + 3 = 6 dimensions. It is quite a challenge to present such an object in a way that human brains find meaningful.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“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?”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
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?”
― The Lightness of Being: Mass, Ether, and the Unification of Forces
“Yet many creative spirits have found inspiration in the idea that the Creator might be, among other things, an artist whose esthetic motivations we can appreciate and share-or even, in daring speculation, that the Creator is primarily a creative artist. Such spirits have engaged our Question, in varied and evolving forms, across many centuries. Thus inspired, they have produced deep philosophy, great science, compelling literature, and striking imagery. Some have produced works that combine several, or all, of those features. These works are a vein of gold running back through our civilization.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design
“For us, the great conclusion is this: all the colors can be obtained from any one of them, by motion, or, as we say, by making Galilean transformations. Because Galilean transformations are symmetries of the laws of Nature, any color is fully equivalent to any other. They all emerge as different views of the same thing, seen from different but equally valid perspectives.”
― A Beautiful Question: Finding Nature's Deep Design
― A Beautiful Question: Finding Nature's Deep Design




