The top row shows the fundamental frequency, the one you hear as the pitch — say it’s a violin string playing A 440. The second row shows the first harmonic, the string vibrating in halves, producing A 880. The harmonic is quieter than the fundamental, so you aren’t necessarily conscious of it, but you can isolate it by lightly touching the string at its halfway point while playing. The other rows show other harmonics, vibrations of the string in integer ratios, each producing a pitch that’s an integer multiple of the fundamental frequency. The second harmonic is E 1320; the third is A 1760; the fourth is C# 2200.

In an ideal string, the harmonics would continue to get infinitely higher, beyond the range of your hearing. As the harmonics get higher, they also get quieter and subtler. Still, they all have an impact on the overall sound of the instrument. All musical instruments have overtones: winds, the human throat, speaker cones, even well-tuned drumheads.

Read more about how harmonics form the basis of western music theory.

Original post on Quora

The picture shows a stylized nucleus with red protons and blue neutrons, surrounded by three grey electrons. It’s an attractive and iconic image. It makes a nice logo. Unfortunately, it’s also totally wrong. There’s an extent to which subatomic particles are like little marbles, but it’s a limited extent. Electrons do move around the nucleus, but they don’t do it in elliptical paths as if they’re little moons orbiting a planet. The true nature of electrons in atoms is way weirder and cooler.

Pictures are a terrible way to understand the nature of quantum particles. Music theory is much better.

Quantum particles are waves

The problem with textbook images like the one above is that they mislead you into thinking of particles as “things.” Particles aren’t things. They pop in and out of being in a rapid, flickery way that’s more like the way we think of energy. What we call “particles” are really just knots or bundles of energy fields.

Protons and electrons pull on each other the way refrigerators and magnets do. If electrons really were like little moons orbiting a planet, it seems like they could orbit at any distance, and could easily fall into the nucleus to collide with the protons. And yet, this never happens. Electrons always organize themselves into very specific spatial arrangements around the nucleus. This fact was totally mysterious until scientists started conceiving of electrons as probability waves in an energy field.

You can get a good idea of how particles really behave by looking at television static, which consists of huge numbers of electrons being fired at the screen at random. Now try to imagine “static” surrounding the nucleus of an atom, and you’ll get a much better picture of what’s going on than you get from imagining moons orbiting a planet.

When electrons are in orbit around an atom or molecule, their pattern of static isn’t random the way it is in TV static. When electrons orbit atoms, their energy fields are organized into patterns of overlapping ripples. You can explore these patterns with Paul Falstad’s interactive visualizations of the subatomic world — scroll down to the Quantum Mechanics sections for his simulated hydrogen atom. The colorful blobs show the probability of electrons being found in a particular place.

So what does this have to do with music theory? The electron field’s vibrations around an atom behave like harmonic oscillators. Electrons have harmonics, just like guitar strings do. Electron harmonics are three-dimensional instead of the one-dimensional harmonics of strings, but the underlying math is the same. These harmonics determine the arrangement and interactions of the electron wave, the same way that harmonics of a string form the basis of chords and scales. The electron field’s harmonics are called orbitals.

The physical world is made of electron harmonics

This screenshot of Falstad’s quantum harmonic oscillator applet shows the first harmonic of the electron field around an H2 molecule, two hydrogen atoms, each with one proton and one electron. This is the electron equivalent of the twelfth fret harmonic on a guitar string.

The blue blob represents the position of one electron, and the red blob is the other. At higher energy levels, the orbitals take on more complex shapes. There’s a direct analogy here to the more complex musical intervals that come from the higher harmonics in a guitar string.

You can think of the orbitals as a structure of cubbyholes, each of which can be occupied by one electron. The cubbyholes come in pairs, and electrons “prefer” to live in filled pairs of cubbyholes. All of the structure of objects and chemistry in the world arises from the way that atoms’ outer orbitals interact. If an atom’s outermost cubbyholes are unfilled, electrons from other atoms with unfilled orbitals can fill them, locking the atoms together into molecules. All solid and liquid materials are held together by this sharing of electrons between orbitals.

Here’s the molecular structure of ice, as rendered by Masakazu Matsumoto. The red balls are oxygen atoms. The blue ones are hydrogen atoms. The yellow rods represent the bonds caused by electrons shared between the oxygen and hydrogen atoms’ outermost orbitals.

The “sixness” of ice’s structure emerges from the way that hydrogen and oxygen orbitals combine to make open slots in groups of six. You can see the “sixness” repeated up at the macroscopic scale in the shape of snowflakes and frost.

If you raise the ice’s temperature to the melting point, what you’re really doing is shooting photons at the ice, knocking the electrons out of their orbitals so they can skip more freely from atom to atom. The atoms still stick together, but not as tightly, and not in so rigid an arrangement:

If you zap even more photons into the water, you can sever the bonds between the molecules completely, freeing them to bounce around independently in the state we perceive as steam. If you zap even more photons at the steam, you can rip the molecules apart and tear the electrons from the nuclei to form plasma. Even more energy will rip the nuclei into protons and neutrons, and ridiculously more energy will rip the protons and neutrons into their constituent up and down quarks. The quarks, protons, neutrons, nuclei, atoms and molecules are all vibrating energy fields with waveforms and harmonics of their own.

Whenever I’m bored, I like to try to imagine everything around me, all the matter and energy, as resonating energy fields, cohering the way pitches cohere into chords. Who says science isn’t fun?

Teaching science with music

Albert Einstein told interviewers that he often “thought in terms of musical architectures.” Einstein was an enthusiastic amateur violinist, and an early architect of quantum mechanics. These two facts are probably related.

Did Einstein make an explicit connection between musical harmonics and quantum harmonics? Maybe we’ll never know, but the connection exists, and future scientists can benefit from it. The concept of electron orbitals is really hard. When I was in high school, my (excellent) chemistry teacher told us not to even bother trying to visualize the true nature of electrons. She was right to not try to condescend to us or mislead us, but she gave up too easily. True, she didn’t have cool interactive computer visualizations, but the school did have a great music department. If I ever get a chance to teach chemistry, first I’m going to make sure the kids get some hands-on experience with harmonics. I’ll have them experience the way that it takes more energy to produce higher harmonics, and the way those higher harmonics produce more complex musical sounds. Then we’ll go back to chemistry class and I’ll bet the kids will have an easier time.

Using instruments like the Hubble Space Telescope, it’s possible to literally see the warping of spacetime by very massive objects like galaxies and huge conglomerations of dark matter. When you’re looking at a very distant object and there’s a large mass along your line of site, it warps spacetime to produce a visual effect known as gravitational lensing. Here’s a schematic diagram showing how it works.

Here’s a real-world example of gravitational lensing, an “Einstein cross” — a single quasar is distorted by a massive object along our line of sight so it appears to be a cross of four quasars.

The arcs in this image are disc-shaped galaxies that appear warped by dark matter along our line of sight.

Here are some examples of Einstein rings, a lensing effect similar to Einstein crosses, where a massive object warps the galaxy behind it into a ring shape.

Finally, here’s a simulation of how the Milky Way disc would be lensed gravitationally if a black hole passed between us and it.

The really weird thing about gravity is that it warps time, not just space. In fact, at the scale of the earth, the time warping is more noticeable than the space warping. GPS satellites and the like need to account for the fact that they’re moving through time at a slightly different rate than objects on the ground. Pretty cool!

So how does gravity “really work” at the fundamental level? No one knows. There’s a lot of intense speculation going on in the physics community. String theory is one attractive approach.The idea is that all particles are different vibrational modes of tiny loops of one-dimensional “strings” of energy. One vibrational pattern produces electrons; a different one produces photons, and so on. If string theory is right, then one of the vibrational patterns produces gravitons, which communicate gravitational force the same way that photons communicate the electromagnetic force. In order for string theory to work, there need to be ten or eleven dimensions of space, which is either preposterous or intriguing, depending on your philosophical tastes.

No one has ever observed a graviton, and nor are we expecting to anytime soon, since gravity is so weak compared to the other forces. In general, string theory is difficult to test experimentally, so for now it remains an attractive mathematical construct in search of evidence to support it.

Another approach is called loop quantum gravity. The idea here is that spacetime is made of a tiny discrete network of loops. All of the fields and forces, including gravity, emerge from knots, links and kinks in the network.

There’s some indication that string theory and loop quantum gravity are different mathematical expressions of a single underlying theory. As with string theory, probing spacetime experimentally at the tiny scale of loop quantum gravity is very far out reach technologically, so for now, it too remains speculation, though it’s well-motivated mathematically. Only time will tell what the true story is.

Original question on Quora

Let me tell you a story. In ninth grade math, we took a break from all the trigonometry to do a little section on probability. It wasn’t anything exotic, just the likelihood of pulling certain cards out of a deck, stuff like that. I had been a straight-A math student my whole life until that point, and I couldn’t wrap my head around probability at all. I could memorize the equations well enough, but I was used to intuitively understanding the rationale behind the equations, and with probability I just could not do it. When you flip a coin and it winds up tails, where does the heads outcome “go?” How does the coin “know” it’s supposed to converge on a fifty-fifty ratio of heads and tails as you flip it more and more times? I almost flunked the test on that unit, I was so baffled.

I forgot the whole thing until more recently when I started learning about quantum mechanics. That’s where the probability questions get to be way more philosophically disturbing than in coin-flipping and card-choosing.

The situation is summed up best by the famous double-slit experiment. In this experiment, you shine light through a screen with a pair of slits in it onto photographic film. You get a stripy interference pattern as the waves of light coming from each slit overlap each other, the way overlapping ripples in a pond do. In this case, what’s “waving” is the probability density of a given photon passing through a given slit and landing at a given spot on the screen. Just the thought of probability having a physical density gives me intense vertigo, but it gets worse.

If you shoot a single photon at a time through the slits onto the film, the result looks like this:

Each individual photon somehow “knows” that there are two slits, and that the probability waves emanating from each slit interfere with each other. So even when the photons come one at a time and don’t interact with each other at all, they still obey the same probability distribution as if you fired them all at once. What’s even weirder is that you can get this same result with any quantum particle, and even entire molecules like buckyballs.

You can interpret this situation to mean that the probability waves are some sort of physical entity, a “pilot” wave that tells each photon what to do, which somehow extends forwards and backwards in time. I find this idea repugnant. You could also interpret the experiment to mean that space and time are nonlocal in some way that lets the single photon go through both slits at once. I also find this idea repugnant.

The only explanation of the double-slit experiment that makes any sense to me is the many-worlds interpretation. Because the left-slit universe and the right-slit universes are so similar, they overlap and mutually interfere, and that’s what produces the stripy pattern. It took me some time to get used to many-worlds, but once I got comfortable with it, I’ve become much more relaxed when I think about probabilities. Now I just see the different possible outcomes as all happening in some universe, and the “probability density” is just the density of the different universes. If I flip a coin, there’s an equal number of universes where it lands heads or tails, plus a very small number of universes where all the particles in the coin spontaneously jump into the Andromeda galaxy.

I’m not a mathematician or a scientist. I’m just a humanities guy who likes math and science. So if you’re a professional in one of these fields and you can correct me or clarify what I’m trying to say here, please do, I want to understand this stuff more clearly.

Original post on Quora

Okay. So. The Higgs boson is involved in the weak nuclear force, which is the weirdest and least famous of the basic four forces in the standard model of particle physics. I have a pretty firm handle on the other three. There’s gravity, you know what that is. There’s electromagnetism, which is behind pretty much everything in our direct experience aside from gravity. And there’s the strong force, which sticks quarks together into protons and neutrons, and sticks those together into atomic nuclei.

But then the weak force. This one is harder to nail down in a single pithy sentence. When you get to the section on the weak force in most popularly-oriented physics texts, the language becomes vague and evasive. There’s usually a feeble bit about how the weak force “is involved in certain kinds of radioactive decay.” This is true, but it doesn’t begin to tell the story. What the weak force really does is transform one kind of particle into another.

Here’s the weak force at work, transforming a neutron into a proton.

This might be happening inside an unstable atom, like nitrogen-16 (nitrogen with too many neutrons.) Time goes from bottom to top, as indicated by the arrow. At the bottom is the neutron, with its three quarks: up, down and down. As the nucleus wobbles, it’s possible for its components to come within the weak force’s extremely short range. A weak force carrier particle, represented by the wavy line labeled W-, changes the flavor of one quark from down to up. That changes the neutron into a proton, and in the process spits out an electron and an antineutrino. With its new proton, the former nitrogen atom is now oxygen. Shazam!

Weak interactions are part of the fusion reactions powering the sun. They’re the reverse of the one pictured above, since the sun turns protons into neutrons, spitting out positrons and neutrinos. Weak interactions produce some of the heat coming from the Earth’s core, and there are more weak interactions in the upper atmosphere as high-energy particles slam into air molecules. Aside from nuclear reactors and particle accelerators, there isn’t too much weak force happening in our day to day lives. Your best chance to experience the weak force first hand is in a hospital PET scanner. Anna asks, looking over my shoulder, if it scans to see if you have any pets. Um, no.

Before you lie down in the scanner, you get injected with a radiotracer containing unstable isotopes of oxygen, nitrogen or some other biologically-oriented element. These isotopes come attached to glucose or water molecules. You lie in the scanner, and as your body metabolizes the radiotracers, weak interactions emit positrons (thus the term Positron Emission Tomography.) The positrons are antimatter, and they don’t get far before they smack into electrons, mutually annihilating into pairs of high-energy photons that zip away in exactly opposite directions. The scanner ring registers all the photons hitting it, and devotes mammoth amounts of computer power to ignoring all of them except the ones originating on opposite sides of the ring. From there, the computer can deduct where the photons are originating, and voila, you get a 3D animated picture of your metabolism in action.

There are a couple of weird and cool things about the weak force. One is that it has a preferred handedness. All particles spin, either clockwise or counterclockwise. Physicists call these spin directions right-handed and left-handed. If you think of your thumb as your spin axis, then your fingers curl in the direction of spin. The weak force defies common sense by only acting on left-handed particles (and right-handed antiparticles.) This is a startlingly odd asymmetry. Gravity and electromagnetism act the same on left and right-handed particles and there’s no obvious reason why the other forces shouldn’t behave the same way. Could this asymmetry could be related to the slight imbalance between matter and antimatter produced by the big bang? Is it necessary for a universe that’s hospitable to our existence? What do you say, scientists?

Another weird and cool thing about the weak force is its relationship to electromagnetism. They turn out to be different aspects of the same force. This is where the Higgs boson comes in. It’s the particle aspect of the Higgs field, which is thought to pervade all of space. The standard model of particle physics credits this invisible energy field with giving the various force-carrying particles their various masses. The idea is that the Higgs field gives the universe a weak force charge, the way electric charge pervades a cloud before a thunderstorm. The weak force has such a short range because the W and Z particles that convey it drag against the Higgs field and quickly lose their juice. Photons have an infinite range because they don’t interact weakly, so they pass right through the Higgs field.

So here’s the thing. At very high temperatures, the Higgs field evaporates. W and Z particles no longer drag, so they become massless and indistinguishable from photons. In other words, electromagnetism and the weak force reveal themselves to be different aspects of the same force, the electroweak force. The standard model predicts this, and experiments have confirmed it. This fact gives physicists hope that at higher energy levels still, the electroweak force will unify with the strong force, and at even more ridiculously high energy levels, they’ll all unify with gravity. Sadly, testing the unification of the electroweak and strong forces is very far out of our technological reach. Testing to see if the other forces unify with gravity would require a particle accelerator bigger than the solar system. That hasn’t stop physicists from dreaming of finding a single unified theory of the forces, a mathematical description of the entire universe that would fit on a t-shirt. Einstein spent decades of his life searching for such a theory, without success.

The Higgs boson is the particle form of the Higgs field, the way the photon is the particle form of the electromagnetic field, and the electron is the particle form of the lepton field. The Higgs boson has never been spotted. It’s assumed that it takes more energy to produce Higgs bosons than particle accelerators have been able to bring to bear. A major mission of the Large Hadron Collider is to produce Higgs bosons.

Here’s what Higgs boson production would look like on the LHC computers:

And so who is this Higgs guy? Here’s what he looks like.

He was one of the major movers behind the electroweak theory and is presumably twiddling his thumbs in a university office somewhere, waiting to see if they do indeed find his particle. I’m rooting for him.

The sun was on my mind today anyway, it being so nice and cloudless outside. But days like today also cause me anxiety. I’m a fair-haired sunburn-prone type, and my dad died from skin cancer, a combination of Scandinavian genes and long hours as a young guy on a ladder helping Grandpa paint houses, plus many more hours on boats and beaches with no sunblock. I stick to the shade, wear hats and generally play it very safe, but still, I feel some dread about the amount of radiation I’m getting from the great thermonuclear reactor in the sky.

My dread does have an upside. It’s fueled a lot of fascination. The sun is a bottomless source of interest if you’re a science geek like me. They tell you in ninth grade biology that all life on earth is powered by the sun. Technically, this isn’t true, since there are those cool little ecosystems living around undersea volcanos that are powered by nuclear reactions in the Earth’s core. But the sun is the prime mover for you and me and all the organisms we interact with. The sun also powers all of our technology, since we’re burning fossilized plants for fuel. You can think of coal, oil and natural gas as a conveniently stable and portable form of sunlight.

I’ve known for as long as I can remember that the sun makes all of its energy from fusing hydrogen into helium, but it was only in the past few years that I tried to figure out what that actually means. Here on Earth, hydrogen molecules repel each other like the north ends of little magnets. The sun is so big that its gravity smacks the hydrogen molecules into each other hard enough to tear them apart into their constituent protons and electrons. In the center of the sun, the protons get jammed into each other so hard that they can come within the tiny range of the nuclear forces. This is when the really weird and exciting physics happens.

Inside each proton are two up quarks and a down quark. When the protons come close enough together, the weak nuclear force can come into play, transforming one of the up quarks into a down quark. This reaction makes the proton turn into a neutron, spitting out a positron and a neutrino in the process.

The positron is the antimatter counterpart to the electron. It quickly seeks out the closest electron in an electromagnetic death spiral that annihilates both particles and creating a pair of very high energy photons. These photons bounce from atom to atom in the sun, being absorbed and re-emitted, until they finally make their way to the surface and zip off into space. I would have naively guessed this ping-ponging around to take a few seconds or minutes, but NASA says that it can take anywhere from a hundred thousand to fifty million years for a photon to get from the core to the surface.

Meanwhile, the newly made neutrons combine with protons to make helium, a much more stable atom than hydrogen. The sun isn’t big enough to fuse helium, so once it runs out of hydrogen, it’ll burn out. The good news is that there’s about five billion years worth of hydrogen left. The bad news is that as it runs out of juice, the sun will get bigger and hotter until it vaporizes the Earth. So, clock’s ticking.

If burning fossilized plankton and ferns is stored fusion power, why can’t we just cut out the middleman? Why don’t our cars run on the fusion of hydrogen into helium? There’s plenty of hydrogen in the planet’s water, and helium is as harmless a waste product as you could ask for. The problem is that it takes a high temperature and/or ridiculously extreme pressure to make atomic nuclei overcome their mutual electromagnetic repulsion and get the nuclear forces doing their thing. Driving around with a tank full of gasoline is dangerous enough; imagine driving around with a reactor whose interior is at ten million degrees. So we shouldn’t be holding our breath for fusion-powered cars.

The sun converts four and a quarter million metric tons of matter into energy every second, and science writers are always comparing it a constantly exploding thermonuclear bomb. But pound for pound, the sun turns out not to be all that energetic. At its center, the power production density per cubic foot is about as intense as an iguana’s metabolism, or the chemical reactions in an active compost heap. The sun is pumping out so much juice because of its humungous size.

Okay, enough science. Here’s an awesome duet version of the George Harrison song that he played with Paul Simon on Saturday Night Live:

Nina Simone did a nice version too. Here’s a cool electronica remix:

Seriously, people, wear that sunblock.

A harmonic oscillator produces sine waves, or their mathematical cousins sawtooth and square waves. For most of technological history, our oscillators were mechanical systems of skins or reeds or metal. For the past hundred-ish years we’ve also been using electronic oscillators connected to speaker cones. Making a steady mechanical oscillator is expensive and challenging. Even making a reliable tuning fork or pendulum takes some crafty engineering. A side benefit of the computer revolution is that we’ve figured out how to mass-produce very cheap electronic oscillators out of quartz crystals and microchips, so now we’re surrounded by them in our cell phones and computers.

Sine wave oscillations are thermodynamically unlikely and hard to produce. Noise is everywhere and easy to produce. In mechanical systems the big challenge is to limit it. In electronic systems, pure sine waves are easy to make and sustain. Now that we’ve had a chance to listen to them, we’ve come to appreciate the musical value of noise better. Pure sine waves sound unearthly and fake. Part of what gives a cello its distinctive tone is the noise of the bow scraping against the strings. Percussion is mostly shaped noise.

Once you have your blend of sine waves and noise, you want to be able to control when they start and stop, how loud they are, and what pitch they’re at. Ideally you also want to be able to shape the overtones to give nuance to your tone. In mechanical instruments the control surface is the whole object. In electronic systems, the control surface and the sound generation system can be totally separate devices. Using computers it’s possible to produce any recorded or synthesized sound at all from a keyboard or even video game controllers and cell phones.

Finally, you probably need to boost your signal to make a loud enough sound that people can hear it. For that, you need a resonator, something that vibrates sympathetically with your signal. For electronic instruments the resonator is an electronic amplifier hooked to speakers, headphones or the business end of a recording device.

Here are some widely-used music tools in terms of the basic four components.

Your voice

• Oscillator: vocal folds
• Noise: plosives and fricatives
• Modulation: shape of mouth, position of tongue, lips and teeth
• Resonator: chest, sinus cavities

Beer bottle

• Oscillator: air at bottle mouth
• Noise: overblowing
• Modulation: blowing angle and intensity, amount of water inside
• Resonator: bottle interior

Clarinet

• Oscillator: reed
• Noise: overblowing
• Modulation: keys, embouchure
• Resonator: body

Piano

• Oscillator: strings
• Noise: none, unless you put ball bearings or something on the strings
• Modulation: timing and intensity of key presses and releases, sustain pedal
• Resonator: body

Acoustic guitar

• Oscillator: strings
• Noise: pick scraping, strings buzzing against fretboard
• Modulation: fingers on fretboard, pick angle and attack
• Resonator: body

Electric guitar

• Oscillator: strings, amp speaker driver
• Noise: pick scraping, string buzzing, amp distortion, electrical interference
• Modulation: fingers on fretboard, pick angle and attack, whammy bar, tone switches and knobs, effects units and expression pedals, amp settings…
• Resonator: amp speaker cone

Snare drum

• Oscillator: drum head
• Noise: snares
• Modulation: angle, location and intensity of whacking, makeup of striking implement (wood or rattan sticks, brushes, mallets, bare hands, etc)
• Resonator: body

Record player

• Oscillator: needle in the groove. The groove is shaped by the electromagnetic oscillations captured on the master tape, which follows the electrical signal from the microphones and mixing console in the original recording, and so on.
• Noise: dust on the needle and in the groove, electrical interference
• Modulation: speed knob, DJ scratching and crossfading
• Resonator: speaker cone

Drum machine

• Oscillator: Electromagnetic oscillators and crystal clocks
• Noise: Electromagnetic noisemakers
• Modulation: Buttons and knobs
• Resonator: speaker cone

Nintendo Entertainment System

• Oscillator: Electromagnetic oscillators and crystal clocks
• Noise: Electromagnetic noisemakers
• Modulation: Software on the game cartridge controlling voltages on the oscillators and noisemakers, as specified by the assembly language translation of Kōji Kondō’s score
• Resonator: TV speaker cones

Here’s a documentary about the wah:

Cry Baby: The Pedal That Rocks The World from Joey Tosi on Vimeo.

Combined with a guitar, the wah can do more than vowel glides. When you mute the strings and strum through a wah, you get a percussive sound ranging from “chicka chicka” to “chucka chucka.” By filtering the overtones differently, you can make other vocal sounds too. I have a digital effects unit that can make the guitar say the word “yeah” pretty convincingly. These kinds of effects give a guitarist the emotional immediacy of the voice combined with the guitar’s wide range of pitches and richness of harmonic possibility.

The guitar isn’t the only instrument you can use with a wah, and it wasn’t the first. The pedal was invented somewhat by accident when the Thomas Organ Company was developing a tone modifier for amplifiers. The first instrument they tried with it was an amplified saxophone, and the company thought they might market it for wind instruments in big bands, as an electronic version of the Harmon mute. A guitarist who worked for the company named Del Casher heard the possibilities of the new tone modifier, and he was the first person to make a recording of it in 1966.

Frank Zappa was an early adopter, and he introduced it to Jimi Hendrix, who would be the first to break it into mass consciousness with “Voodoo Child (Slight Return).” Jimi also introduced the percussive “chicka chicka” on “Little Miss Lover.” Jimi’s solos on “All Along The Watchtower” is another distinctive early adventure with wah. Plenty of other hippie rockers followed suit. George Harrison has a song called “Wah-Wah” on All Things Must Pass, named both for the pedal and for the Beatles’ whining during their final sessions together. Eric Clapton uses wah with Cream on “Tales of Brave Ulysses” and “White Room”.

Pop culturally, wah is most associated with seventies funk and soul, like on “Theme From Shaft” by Isaac Hayes, with Charles Pitts on guitar. Curtis Mayfield also had a distinctive and much-imitated wah style. From blaxploitation soundtracks it was a short jump to the porn movies that imitated them, which is why funky wah guitar is an effective comedy shorthand for getting busy. But wah doesn’t have to be seductive. Eddie Hazel of Funkadelic used it for a dark, spacey cry on “Maggot Brain.” Click here to listen to some standard wah techniques on electric guitar. The wah pedal sounds especially good on E9, the mother of all funk chords.

Hard rock and metal guitarists have found a vocabulary for wah drawing more on Hendrix and Zappa than on funk. Zappa used it less like a speech effect and more like a simple adjustable filter. He would leave it partially open to filter the high frequencies over the course of an entire song. Distortion exaggerates out the guitar’s upper harmonics and other partials, and the wah makes a great envelope controller. Jimmy Page used it on Led Zeppelin’s “Dazed and Confused,” “Whole Lotta Love,” “No Quarter” and “Custard Pie”. Slash used it with Guns N’ Roses, and Kirk Hammett leans heavily on it with Metallica.

Bassists sometimes use the wah too, especially in the funk and soul world. Michael Henderson played with one on Miles Davis’s album On the Corner. Other wah-loving bassists include Metallica’s Cliff Burton and Black Sabbath’s Geezer Butler.

Electric pianos and harpsichords operate in very much the same way as electric guitars, so it was only a matter of time before keyboard players started investigating guitar effects. Clavinet with wah sounds so much like guitar that it’s hard to tell them apart. Garth Hudson plays some pretty groovy clav with The Band on “Up On Cripple Creek”, but nothing is as funky as Stevie Wonder on “Superstition,” “Higher Ground” and his other seventies classics. Electric piano also sounds great through wah, again because of its guitar-like tone when played through an amp with distortion. Richard Wright uses it on Pink Floyd’s “Money”, and it’s on tons of Miles Davis electric recordings, especially the ones with Keith Jarrett and Chick Corea.

Any instrument that’s amplified can be played through a wah. Miles Davis got a devastating trumpet tone with wah on Live-Evil and his other darker funk records. A few saxophone players have experimented with it too, as the pedal’s original inventors intended. David Sanborn played with one on the David Bowie album Young Americans, and Dana Colley used it with Morphine.

Violin sounds great with wah. The leading practitioners are Jean-Luc Ponty in the Mahavishnu Orchestra and Boyd Tinsley in the Dave Matthews Band. Pink Floyd even tried some wah on an acoustic piano in their song “Echoes”, which also includes wah guitar made to sound like crying birds. I myself have found that wah sounds terrific on mandolin. I’ve also tried it on harmonica, but there it’s redundant since you can do the wah effect so easily with your mouth.

Wah is just one flavor of the envelope filtering you can do with a synthesizer. A lot of the craft of electronic music comes down to creative rhythmic use of the filter. A standard technique is to get a repetitive loop happening and then sloooowwwly open and close the filter over the course of a phrase or section. Since a sequencer or computer can play the actual synthesizer notes, it frees up the musician’s hands for complex multi-parameter filter control using knobs or touchscreens. We’re only at the beginning of our collective exploration of the artificial vowel glide in music.

Daniel Dennett has a nice phrase describing evolution in his book Darwin’s dangerous idea: threads of actuality in design space. The space in question is the set of all possible physical manifestations of life, and the threads of actuality are the bodies that have actually appeared. Dennett thinks that human artifacts and culture are a continuous branch of the same design space that includes our teeth, hair and fingers. I see a smooth continuity between the bagworm moth caterpillar’s use of sticks and the neanderthal’s.

The materials might be different, but I don’t see any fundamental conceptual difference between this drawing and any organism replicating itself:

All living things generate waste. Our problem is that we’re cranking out waste faster than the rest of our ecosystem can process it. Making a single cell phone motherboard generates two hundred twenty pounds of waste. America exports most of its nastiest e-waste, but as the planet shrinks, we won’t be able to avoid the byproducts of our lifestyle forever.

It would be easy at this point to get judgmental and say that our consumption-oriented ways are evil, and that if environmental catastrophe befalls us it’ll be just what we deserve. I don’t think those kinds of judgments are constructive. Nobody wants to destroy the earth. But we feel genuine competitive pressures within and among our social groups, and showing off our tools has been part of our sexual selection since the stone age. How do we balance our need to compete with each other with a more abstract but equally pressing need to restrain ourselves? I don’t have a good single answer, but I think that more reflection on the consequences of our actions is a necessary start.

Let’s start with the face. Einstein’s iconic white hair and wrinkles coexisted with an unusually childlike face. Einstein had large, widely-spaced eyes on a large head. The combination of infantile and ancient is psychologically intense. I wasn’t surprised to find out that Einstein’s face inspired the design of Yoda and ET.

Einstein’s parents worried about his intellectual development as a child. He didn’t start speaking until he was three, and he wasn’t completely fluent until nine. A picture emerges of an eccentric and inward kid, with a lot of attention devoted to his own imagination and thoughts, and not much attention left over for everything else. I don’t believe that Einstein was born with a superior brain. His spectacular spatial reasoning and mental imaging abilities came at the expense to his social skills and his personal happiness. History remembers his achievements and tends to gloss over his failed marriage and depression.

Einstein loved to tell the story of being five years old and being shown a small pocket compass by his father. He was elated to discover that something in “empty” space acted on the needle. Einstein would later describe his first brush with the Earth’s magnetic field as one of the most revelatory events of his life. As a kid, he built models and mechanical devices for fun, and he showed mathematical ability early on. In 1891, he taught himself Euclidean geometry from a school booklet (for fun, whee!) and began to study calculus. The teenage Einstein sounds like the consummate math nerd, antisocial and hostile to authority. He only completed one term of the equivalent of high school before dropping out in the spring of 1895.

Einstein’s family was Jewish, but not observant, and he went to a Catholic elementary school. I’m guessing that the contradictions he experienced there were a source for his later outspoken secular humanism.

The same year he dropped out of school at age sixteen, Einstein performed a famous thought experiment with the speed of light. He was trying to wrap his head around one of his era’s most baffling scientific problems. There were these equations, the Maxwell equations, that describe electricity and magnetism extremely accurately. The equations predict that the speed of the light (around 667 million miles per hour) is always the same, regardless of how fast you’re moving when you observe it. If you’re sitting still and you turn on your flashlight, the light zips away from you at 667 million mph. No mystery there. But the Maxwell equations say that if you’re zipping along in a spaceship at 666 million mph and you turn on your headlights, the beams will still race away in front of you at 667 million mph. Scientists in 1895 were making the first really accurate measurement of the speed of light under various conditions, and they were hoping to prove this prediction wrong. Much to their horror, every experiment proved the Maxwell equations right. Einstein was trying to figure out a way out of the paradox by imagining himself to be in that spaceship and turning on your headlights.

Like a lot of scientists, Einstein was a musical person. He frequently used musical terms to express physics concepts. At the insistence of his mother, he took classical violin lessons as a kid, and like most people, disliked them and eventually stopped them. Like dishearteningly few people, Einstein returned to music in adulthood, and became a dedicated amateur classical violinist.

He once said:

If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music.

Einstein eventually attended university, where he studied math and science in the hopes of getting a science teaching gig. He managed to graduate, but his antagonistic relationship with his professors didn’t help with recommendations or job offers. Instead, the father of a classmate helped him get an unglamorous position as an assistant examiner at the Swiss patent office. It turned out to be a good day job for him. The pace was undemanding and it gave him the opportunity to ponder his favorite subject, the electromagnetic force, at length.

Here’s a fun Java applet that lets you play with a simulated electromagnetic field. We take the field’s physicality for granted in modern life, since we’re always walking through metal detectors and such, but a hundred years ago you could have been forgiven for doubting that such a weird idea could possibly be true. The field concept is not an easy one, and if we weren’t intimately familiar with evidence of its existence, it might sound like a paranoid delusion. The math isn’t much help in making fields more accessible to our common sense, because it requires frightening calculus. It’s humbling to consider Einstein trying to puzzle through electromagnetism for fun while he worked his slacker job in the earliest years of the twentieth century.

During 1905, in his spare time and sometimes during work when no one was looking, Einstein wrote four short articles for publication in Annalen Der Physik, then the leading journal in the field. He wrote them without much scientific literature to refer to or many fellow scientists to talk with. The only science library in town was closed on his only day off. People call them the Annus Mirabilis papers, from Latin for ‘miracle year.’

The first Annus Mirabilis paper was titled On A Heuristic Viewpoint Concerning The Production And Transformation Of Light. (Heuristic means hands-on or practical.) It was a response to Max Planck’s hypothesis that energy comes bundled in tiny little discrete chunks or particles called quanta (singular quantum.) Einstein’s key contribution was to say that energy quantization is a general, intrinsic property of all other electromagnetic energy, not just light. He showed how these little chunks of energy are mathematically related to the energy’s frequency. This later developed into the concept of photons. So that’s the first paper.

Einstein’s second article of 1905 was called On the Motion, Required by the Molecular Kinetic Theory of Heat, of Small Particles Suspended in a Stationary Liquid. It covered his study of Brownian motion, the random jostling of dust motes in the air, or the swirling of milk in coffee. Einstein used mathematical analysis of Brownian motion to provide empirical evidence for the existence of atoms. Before this paper, atoms were recognized as a useful concept, but physicists and chemists debated whether they were real things or just mathematical abstractions. Einstein’s statistical discussion of atomic behavior gave experimentalists a way to count atoms by looking through an ordinary microscope.

The third paper was called On The Electrodynamics Of Moving Bodies, and it introduced the special theory of relativity, of which you have probably heard but whose content is probably mysterious to you. It was to me until I started reading Brian Greene books. Relativity is extremely tripped out. Remember how the velocity of light is supposed to be the same, regardless of how fast you’re moving when you measure it? Einstein interpreted this wildly counterintuitive fact as evidence that everything is always moving through space and time at the speed of light. More accurately, everything in the universe is always moving along the three spatial dimensions and the fourth dimension of time at the velocity of light. Whatever your velocity through space is, your velocity through time is the difference between it and the velocity of light. The faster you move through space, the slower you move through time. The slower you move through space, the faster you move through time. No joke. For a photon zipping along through space at the speed of light, time isn’t passing at all.

So if the theory of relativity is true, and every experiment confirms that it is, why hadn’t anyone noticed before 1905? It’s mostly an accident of scale. We and most of the things we encounter in the world move through space a lot slower than 667 million miles an hour, and by cosmic scales we can only change our velocity by miniscule amounts, so our movement through time is barely affected. It’s like the way the curvature of the earth appears to be zero when we’re standing on it, because it’s so much bigger than we are. We would have found out the earth was round much sooner if it was only twenty-seven miles wide instead of twenty-seven thousand. Time dilation is trivial for our poky selves, but it’s a real fact of the universe. It has more serious consequences at higher speeds and energy levels, and larger time and distance scales. Global positioning systems have to account for time dilation between the different satellites as they hurtle around their orbits.

Heavy, right? It gets better (or worse, depending on your tastes.) Brian Greene asks us to imagine the universe as a loaf of bread arranged along the time axis, where each slice is a freezeframe snapshot of everything in space at a particular moment in time. If you and someone else are moving relative to one another, you slice the spacetime loaf at different angles. Here on Earth, the difference in angle between my spacetime slices and yours are imperceptibly tiny. But what a photon or a person on a far-distant planet considers to be the state of the universe “now” is going to be very different. Quoting Brian Greene, italics his:

If you buy the notion that reality consists of the things in your freeze-frame mental image right now, and if you agree that your ‘now’ is no more valid than the ‘now’ of someone located far away in space who can move freely, then reality encompasses all of the events in spacetime. The total loaf exists. Just as we envision all of space as really being out there, as really existing, we should also envision all of time as really being out there, as really existing too. Past, present and future certainly appear to be distinct entities. But as Einstein once said, “For we convinced physicists, the distinction between past, present and future is only an illusion, however persistent.”

My first exposure to this idea was from Kurt Vonnegut in Slaughterhouse-Five. The Tralfamadorans explain to Billy Pilgrim that humans perceive time “passing” the way we’d perceive a landscape passing if we could only see it through a long cardboard tube while being carried along on rails.

In this way of thinking, events, regardless of when they happen from any particular perspective, just are. They all exist. They eternally occupy their particular point in spacetime. There is no flow… It is tough to accept this description, since our worldview so forcefully distinguishes between past, present and future. But if we stare intently at this familiar temporal scheme and confront it with the cold hard facts of modern physics, its only place of refuge seems to lie within the human mind.

I’m a little disturbed by BG’s confrontational tone – “confront”, “cold hard facts”, “place of refuge” — but let’s bracket that and move on.

The feeling that time flows is deeply ingrained in our experiences and thoroughly pervades our thinking and language… But don’t confuse language with reality. Human language is far better at capturing human experience than at expressing deep physical laws.

Does time have an arrow discernible somewhere in the universe outside our collective imaginations? Intuition says yes, since spilled milk doesn’t unspill. But the basic physics equations don’t specify a direction for time or depend on any asymmetry to it. Post-Einstein, you can treat time as just another direction, like left-right, up-down, forwards-backwards. Equations describing the moon’s orbit or electrons in a molecule have time-reversal symmetry. In theory, you could manipulate the particles into unspilling your milk; it would just be very very difficult, and it’s vanishingly unlikely to ever just happen by itself.

Maybe time’s arrow is just our interpretation of the strong overall tendency towards entropy in the world around us, not a fundamental fact of the universe. The Wikipedia article on time says:

Psychological time is, in part, the cataloguing of ever increasing items of memory from continuous changes in perception. In other words, things we remember make up the past, while the future consists of those events that cannot be remembered. The ancient method of comparing unique events to generalized repeating events such as the apparent movement of the sun, moon, and stars provided a convenient grid work to accomplish this. The consistent increase in memory volume creates one mental arrow of time. Another arises because one has the sense that one’s perception is a continuous movement from the unknown (Future) to the known (Past). Anticipating the unknown forms the psychological future which always seems to be something one is moving towards, but, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer.

Okay. So Einstein’s third paper of 1905 undermined the concept of time. His fourth one was called Does The Inertia Of A Body Depend Upon Its Energy Content? From relativity, Einstein showed how one can deduce the famous equation showing the equivalence between matter and energy, E=mc^2. To get the energy equivalence (E) of some amount of mass (m), you multiply the mass by the velocity of light (c), and then you multiply it by the velocity of light again. A very small amount of mass converts to a very large amount of energy. When hydrogen in the sun fuses into helium, part of its mass gets converted to the energy we receive here on Earth.

If Einstein had been hit by a bus in 1906, we’d still be absorbing his output, but there was more big stuff coming. In 1909, he presented a paper called The Development Of Our Views On The Composition And Essence Of Radiation. In this and an earlier 1909 paper, Einstein showed that the energy quanta introduced by Max Planck also carry a well-defined momentum and act in many respects as if they were independent, point-like particles. This paper marks the introduction of the modern photon concept (although the word itself was coined  later). Being able to mathematically describe and predict the behavior of photons has made possible such modern conveniences as computers, TV and supermarket scanners. The behavior of photons suggests more deep weirdness going on behind the world we experience. Einstein showed that light, like all other forms of mass-energy, must simultaneously behave like both a wave and a particle, a revolutionary idea at the time and still a major head-scratcher.

In November 1915, Einstein unveiled his new theory of gravity, the general theory of relativity. In general relativity, gravity is no longer a force, as it is in Newton’s conception of gravity. Instead, gravity is the warping of spacetime by matter and energy. Empty space itself is the thing being warped in general relativity. As with relativistic time dilation, this warping is a real thing. We don’t notice it because of the scale thing. If there’s a huge amount of mass-energy, spacetime can get stretched like silly putty. You can see it in Hubble Space Telescope photos of very distant galaxies.

General relativity laid the theoretical framework for the big bang theory.

Einstein’s career from 1905 to 1917 was a lot like Paul McCartney’s from Please Please Me through Abbey Road. Einstein’s career after he moved to New Jersey was more like McCartney from Wings through the present: he was a highly visible figure on the landscape, but he didn’t produce any new ideas that anyone cared about. Mathematicians and scientists, like rock stars, are famous for burning out young. Einstein the scientist burned bright and fast, and then coasted amiably along to old age. But Einstein the political figure was just coming into full flower. His authority problems as a kid turned into a principled opposition to fascism and violence as an adult. He was a member of the Rationalist Press Association and an admirer of Ethical Culture. On the much-contested subject of his religious views, here’s what the man himself had to say:

A human being is part of a whole, called by us the Universe, a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest–a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circles of compassion to embrace all living creatures and the whole of nature in its beauty.

He published a paper in Nature in 1940 called Science And Religion:

A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings and aspirations to which he clings because of their super-personal value … regardless of whether any attempt is made to unite this content with a Divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly a religious person is devout in the sense that he has no doubt of the significance of those super-personal objects and goals which neither require nor are capable of rational foundation…In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals, and constantly to strengthen their effects.

The religious and atheistic alike claim him as a hero, but I think if he had to pick a side, he would have come down closer to Darwin and Dawkins:

If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it.

You will hardly find one among the profounder sort of scientific minds without a peculiar religious feeling of his own. But it is different from the religion of the naive man.

For the latter God is a being from whose care one hopes to benefit and whose punishment one fears; a sublimation of a feeling similar to that of a child for its father, a being to whom one stands to some extent in a personal relation, however deeply it may be tinged with awe.

But the scientist is possessed by the sense of universal causation. The future, to him, is every whit as necessary and determined as the past. There is nothing divine about morality, it is a purely human affair. His religious feeling takes the form of a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection.

I believe in Spinoza’s God, who reveals Himself in the lawful harmony of the world, not in a God who concerns Himself with the fate and the doings of mankind.

In 1939, Einstein sent a letter to Franklin Delano Roosevelt urging the study of nuclear fission for military purposes, for fear that the Nazis would develop nuclear weapons first. The letter prompted an investigation that eventually led to the Manhattan Project. Einstein himself didn’t end up working on the bomb, and, according to Linus Pauling, he later regretted having written his letter. Einstein considered himself a pacifist and humanitarian, and in later years, a committed democratic socialist.

I believe Gandhi’s views were the most enlightened of all the political men of our time. We should strive to do things in his spirit: not to use violence for fighting for our cause, but by non-participation of anything you believe is evil.

Einstein was a busy civil rights agitator, and a member the Princeton chapter of the NAACP. With Paul Robeson, he was a co-chair of the American Crusade To End Lynching. When the octogenarian WEB DuBois was frivolously charged with being a communist spy, Einstein volunteered as a character witness in the case, which led to the charges being dismissed. Maybe the biggest compliment America ever paid Einstein was the size of his FBI file: fourteen hundred pages on his activities and movements. The FBI recommended that Einstein be barred from immigrating to the United States under the Alien Exclusion Act, alleging that he “believes in, advises, advocates, or teaches a doctrine which, in a legal sense, as held by the courts in other cases, ‘would allow anarchy to stalk in unmolested’ and result in ‘government in name only.’” Israel offered Einstein the presidency, and he turned it down. He was a supporter of Zionism in the cultural sense but he had some reservations about its nationalistic aspect. In a speech he said:

My awareness of the essential nature of Judaism resists the idea of a Jewish state with borders, an army, and a measure of temporal power, no matter how modest. I am afraid of the inner damage Judaism will sustain.

Anytime I did something dumb in grade school, my friends would say sarcastically, “Nice going, Einstein.” Since then I’ve said it myself more times than I can count. Einstein serves a handy shorthand for the natural genius, the superhuman intellect. He offers the hope that any lazy and undisciplined student might secretly be a genius, one in a zillion. This fantasy isn’t as far-fetched as it seems. People like Einstein aren’t necessarily well-served by the way our society requires us to learn. Sitting at desks in big groups just does not work for all kids. Kids learn a lot from school, but they don’t necessarily learn math and science, they just learn how to pretend to be attentive while managing a lot of boredom.

Einstein donated his brain to science upon his death, and there has been a whole ghoulish cottage industry around its study. Steven Pinker’s theory on Einstein’s brain is that it showed rapid prenatal development of areas of the brain responsible for spatial and analytical reasoning which, in competing for finite bodily real estate, temporarily robbed resources from functions of the brain responsible for speech development. Pinker and others have extended this speculation to explain the development of other famously gifted late-talkers, including mathematician Julia Robinson, pianists Arthur Rubinstein and Clara Schumann, and physicists Richard Feynman and Edward Teller. These people were also said to have shared several of Einstein’s childhood peculiarities, like monumental tantrums, rugged individualism and highly selective interests. Whether or not this is true, it fits well with my larger hypothesis that a genius is basically an obsessive-compulsive who’s lucky enough to be obsessed with something constructive.

By the way, I didn’t have a poster of Einstein in my dorm room, but as an adult I’m proud to have an Einstein action figure sitting on the shelf, above my computer, next to my clock.