Mccomb Samples

Samples by Patrick McComb 734-757-7355 • [email protected]

Excerpts from Science Reporting Blog: Diamonds in Quantum Computing Raymond Scott 100 The Legacy of War of the Worlds Mathematician Sophie Germain Global Sunblock Using Sulfur

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A Response to Paul Davies

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Songs: The Latest Guess of Everything How Long is the Coast of Britain? Mech and Manabozho

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Information Graphics: Relativistic Baseball Chord Head US Poverty by State

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Two-Digit Math

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sciencereporting.blogspot.com

Diamonds in Quantum Computing Quantum particles have the bizarre capacity to contain a variety of different states at once. This is called superposition. A quantum particle may be in a superposition of states but it will break down into one of those states once it is observed. In fact, it will break down if the particle interacts too much with the external environment. This delicate property makes the quantum world appealing to computer scientists. By exploiting superposition, many different mathematical values may be explored simultaneously. That would make computers thousands of times faster and solve mathematical problems that are too complex for classical machines. But the difficulty of keeping those quantum bits in causal isolation is a huge technical challenge. Often, it has required cooling materials close to absolute zero.

Diamond is now showing promise as a material that can perform quantum computing functions at room temperature. "The beauty of diamond is that it brings all of this physics to a desktop," says David Awschalom of the University of California, Santa Barbara. Science News posts an article about how diamonds -- or more precisely, flaws in diamonds -- are showing promise. In a natural diamond lattice, flaws are inevitable. The most common impurity is a nitrogen atom. Another kind of flaw is a vacancy in the lattice where a carbon would otherwise sit. When a diamond crystal contains a nitrogen and a vacancy next to each other, something strange happens. Electrons from the nitrogen will orbit the vacancy as though an atom is there. This virtual molecule, called a nitrogen-vacancy (NV) center, possesses spin, the quantum form of magnetism. Spins are like microscopic bar magnets and can encode and store information by pointing in different directions. A single unit of information, called a bit, can be, say, a 1 if the spin points up or a 0 if it points down. ...Researchers have so far managed to store and manipulate only a handful of qubits [quantum bits] in superbly well-controlled systems, such as single ions suspended in an electromagnetic trap or superconducting materials cooled to very low temperatures. In a paper to be published in Science, Awschalom and his collaborators describe how they achieved a similar level of control over NV centers in diamond. The October 2007 issue of Scientific American had an excellent article on this research [subscription]: Diamond has a track record of extremes, including ultrahardness, higher thermal conductivity than any other solid material and transparency to ultraviolet light. In addition, diamond has recently become much more attractive for solid-state electronics, with the development of techniques to grow high-purity, single-crystal synthetic diamonds and insert suitable impurities into them (doping). Pure diamond is an electrical insulator, but doped, it can become a semiconductor with exceptional properties. It could be used for detecting ultraviolet light,

ultraviolet light-emitting diodes and optics, and high-power microwave electronics. But the application that has many researchers excited is quantum spintronics, which could lead to a practical quantum computer—capable of feats believed impossible for regular computers— and ultrasecure communication.

Raymond Scott 100 "It's all very well to write screwy music, and imitate things like wooden Indians and powerhouses, but just writing screwy music isn't enough. If it's screwy music you want, there's plenty of that in Stravinsky..." -- Harold Taylor, 1939, from the Rhythm Magazine article, You Can Keep Raymond Scott In addition to making some of the most joyously intricate and distinctive melodies of the 20th Century, Raymond Scott was also a leading pioneer in multi-track recording, electronic music and collaborated with the likes of Robert Moog, Jim Henson and Motown. But odds are you will recognize his tunes from Warner Brothers cartoons. He is arguably one of the most influential musician/inventors in American music. Here is his signature song, "Powerhouse," as performed by the band Racalmuto. "The compositions of Raymond Scott are etched, it seems, into the fabric of 20th century culture like some strand of DNA sequence coding our collective memory for future-mutations." -- Paul D. Miller, a.k.a. Dj Spooky Raymond's six-piece band was called the "Raymond Scott Quintette." (Apparently, Raymond thought the word "sextet" would distract from the music and the Frenchie "ette" lent a touch of class.) While the music was classified as jazz, jazz critics were frequently hostile. Despite the critics, the music proved highly popular with the buying public. It was not so popular with the band members. Raymond coerced them into upwards of 60 takes, performing dizzying riffs -- and sometimes under weird acoustic circumstances in order to achieve a particular sound. Unlike other jazz acts, improvisation was not allowed. The songs are intricately assembled as though they were designed by an engineer. Band members could not deviate from the strict tune structure any more than parts manufacturers could deviate from an engine design. Raymond didn't use sheet music either. He recorded the players, edited the strips, played them back and asked the players to play the re-ordered arrangements from memory.

"What can you say about a man who inspired cartoon melodies and bebop, invented Frank Zappa and electronic music, and still found time to work for Motown?" -- Andy Partridge, XTC Here is the Raymond Scott Quintette performing War Dance for Wooden Indians. The image to the left is from a comic strip biography of Raymond Scott by Justin Green, available at the Official Raymond Scott site. The 1940's saw a lot of changes for Raymond Scott. In 1941, he sold his compositions (finally rendered in musical notation) to Warner Brothers. The music was enthusiastically seized upon by Carl Stalling, the man who scored the Warner Brothers cartoons -- which is largely why these tunes are so embedded in our consciousness. (To this day, people think Raymond wrote for cartoons, but he never did. He never even watched cartoons.) "The music of Raymond Scott is positively exhilarating. Its intricacies mesmerize, because they're part of a unique and utterly disarming musical tapestry." -- Leonard Maltin, film critic In 1942, he became Music Director for CBS Radio and made history by hiring black musicians. His CBS band was the first racially integrated band for radio. In 1946, he founded Manhattan Research Inc, "the world's most extensive facility for the creation of Electronic Music and Musique Concrete." It was the first electronic music studio. Raymond's brother Mark Warnow died in 1949 and Raymond took over Mark's job: Orchestra Leader for Your Hit Parade. Raymond Scott and his wife, Dorothy Collins, became early TV celebrities. Here is the Raymond Scott Quintette performing "Powerhouse" on Your Hit Parade. Raymond called it a "rent gig." In fact, he used his handsome salary to invest in electronic equipment. In the late 40's, along with Les Paul, Raymond started experimenting with a new recording technique called multi-track. "Raymond Scott was like an audio version of Andy Warhol; he preceded Pop-Art sensibilities, and he played with that line between commercial art and fine art, mixing elements of both worlds together. I love and respect Raymond Scott's work, and it influenced me a lot. I'm a big fan.'' -- Mark Mothersbaugh, Devo In 1949, Raymond said, "Perhaps within the next hundred years, science will perfect a process of thought transference from composer to listener. The composer will sit alone on the concert stage and merely think his idealized conception of his music. Instead of recordings of actual music sound, recordings

will carry the brainwaves of the composer directly to the mind of the listener."

By the mid-50's his studio began to look (according to friends such as Robert Moog) like a science fiction set. Over the years, Raymond invented numerous electronic musical instruments including the Clavivox and the Electronium. Robert Moog credits Raymond as an important influence on the invention of the Moog Synthesizer. In 1962 and 1963, Raymond released Soothing Sounds for Baby. It was entirely electronic music he composed as an "aural toy" for children. While it was a commercial failure at the time, some now regard it as a strong pre-cursor to ambient music (over a decade before Brian Eno's recordings). Electronic music can suffer from an outdated sound very quickly. However, Raymond Scott's electronic music from the 60's still hold up today. In a 1962 lecture, Raymond said, "To say that we haven't scratched the surface in this field wouldn't be exactly right. Because every time we scratch we find the surface thicker and thicker and thicker. For the possibilities in electronic music are really quite infinite." "It's those front-line types that go into uncharted areas, and pave the way for others. Always go to the source, sources like Raymond Scott." -- Henry Rollins, Black Flag, Rollins Band In the early 70's, Raymond was hired by Barry Gordy to develop new electronic sounds when Motown was positioning itself as a leader in cutting-edge music. Today, we don't know the degree of influence Raymond had on the 70's Motown sound. (If you've seen "Standing in the Shadows of Motown" you know that the Motown star-machine, as policy, kept the support crew on the down-low.) One very unique collaboration was with an up-and-coming puppeteer. Raymond

Scott and Jim Henson collaborated on "Limbo - The Organized Mind" a very unique performance which appeared on The Tonight Show with Johnny Carson. "Raymond Scott was definitely in the forefront of developing electronic music technology, and in the forefront of using it commercially as a musician." -- Bob Moog, inventor of Moog synthesizers Scott fans include Igor Stravinsky, Henry Rollins, XTC, Elvis Costello, the Kronos Quartet, They Might Be Giants, Devo, Jascha Heifetz, Art Blakey and Danny Elfman. You can hear Scott's influence in Benny Goodman, bebop, ambient, electronica and The Simpsons theme. In 1986, Raymond composed his last known work, "Beautiful Little Butterfly," in Midi. In 1992, a retrospective of Raymond Scott's work, Reckless Nights and Turkish Twilights, brought Raymond Scott to a new audience. Raymond died in 1994. Concordia University in Montreal recently hosted a Raymond Scott Centennial Tribute Concert: 157 West 57th Street Boy Scout in Switzerland Dinner Music for a Pack of Hungry Cannibals A Message from Where The Rhythm Modulator Twilight in Turkey War Dance for Wooden Indians As more music lovers discover him, Raymond Scott is gradually becoming recognized as one of the great innovators in American music. September 10th of 2008, will be Scott's 100th birthday. For much more, here is the official Raymond Scott site, the Raymond Scott Blog and the Raymond Scott MySpace page. "Being introduced to the music of Raymond Scott was like being given the name of a composer I feel I have heard my whole life, who until now was nameless. Clearly he is a major American composer." -- David Harrington, Kronos Quartet

The Legacy of War of the Worlds This coming Halloween will mark the 70th anniversary of Orson Welles' radiovérité broadcast of "War of the Worlds." Radiolab just posted an outstanding podcast of the "War of the Wolds" legacy. Why did it fool people then? And why does it continue to fool people?

First they look at the context of the times - the recent destruction of the Hindenburg and the new media form of the day which is now part of our mental furniture. It starts, "We interrupt this program..." As Hitler continued his attacks throughout Europe, special bulletins became an authoritative and attention-getting feature of radio. A feature Welles exploited. Interestingly, many of the listener's fooled by Welles' broadcast believed that it was Germans attacking, rather than Martians. Other radio stations have staged their own versions of "War of the Worlds" over the years. And again people were fooled. The most disastrous example is the profoundly ill-advised broadcast in the capital city of Ecuador, Quito. The Quito broadcast was produced without any warning to anyone. In fact, the producer planted fictitious stories of strange phenomena in the days preceding the broadcast -- to whip up paranoia. At the end of the evening, the radio station was set on fire by an angry mob. Six people died that night. Buffalo's WKBW (my hometown and my favorite station in the 70's) first broadcast "War of the Worlds" in 1968 -- modernized and set in the Western New York landscape. The 1971 WKBW broadcast is available online. The page contains a link to the full show (with great opening music) plus a making-of video. The climax of the '71 broadcast has iconic TV news anchor Irv Weinstein reporting from a rooftop like Edward R. Murrow – except Irv is reporting on an approaching robot. It's really quite brilliant.

Mathematician Sophie Germain Science News posts a two-part series on Sophie Germain [Wiki] -- a mathematician born in France in 1776. The article describes Germain as "the first woman known to have discovered significant mathematical theorems." (Hypatia from the 4th Century is worth noting, though she is not known for any particular theorems) Germain assumed the identity of a male student and

took classes from Lagrange. She read class notes and sent in assignments under the name of the male drop-out. Lagrange found out her secret: According to a commentator at the time, Lagrange "went to her to express his astonishment in the most flattering of terms," and the commentator goes on to say that "the appearance of this young 'geomètre' made quite a stir." Nevertheless, the barriers against Germain's inclusion in the mathematical community didn't come tumbling down. Later, she corresponded with Gauss under the male pseudonym, "AntoineAugust LeBlanc." Gauss too discovered her real identity: In 1806, Napoleon's armies were marching into Prussia, and Germain became concerned that Gauss might be in danger. She asked a friend who was a commander in the French artillery to find Gauss and ensure his safety. Her friend followed her request—but revealed her identity in the process. Gauss initially responded with delight, writing to Germain: "The taste for the abstract sciences in general and, above all, for the mysteries of numbers, is very rare.… But when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarizing herself with their knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius." Gauss broke off correspondence with her shortly thereafter -- saying he was turning to astronomy and would have no more time for math. Germain worked in isolation, taking on one of the most difficult problems in math, Fermat's Last Theorem. (It was not until 1995 that the theory was proven by Andrew Wiles, and that was in a roundabout fashion.) She defined what would be called Sophie Germain primes and worked on the math of elastic surfaces. Gauss convinced the University of Göttingen to give her an honorary degree. Unfortunately she died in 1831 before receiving it. The two-part series on Sophie Germain: 1, 2.

Global Sunblock Using Sulfur Last week's podcast of CBC's Quirks and Quarks discusses the radical idea of blocking the sun's rays to mitigate climate change. Bob McDonald interviews Dr. David Keith, the Canada Research Chair in Energy and the Environment at the University of Calgary. Keith is not necessarily recommending the idea but he does believe we should put it on the research agenda. One option -- a pretty shocking one -- is to release sulfur into the upper atmosphere. From volcanic activity in the past, we already know this would have an immediate cooling effect on the climate. Nobel Prize winning atmospheric chemist Paul Crutzen^ also recommends looking into such research [PDF]. But he warns: I must stress here that the albedo enhancement scheme should only be deployed when there are proven net advantages and in particular when rapid climate warming is developing, paradoxically, in part due to improvements in worldwide air quality. Importantly, its possibility should not be used to justify inadequate climate policies, but merely to create a possibility to combat potentially drastic climate heating. Keith says in the podcast that many climate scientists are reluctant to discuss this because it would only treat the symptoms of climate change and not the cause. At the same time, he found policy-makers who were all too eager to deploy such a program. In this panel discussion on geoengineering, Harvard geochemist Dan Schrag^ points out: If we're going to use the Earth as an experiment -- which we're already doing by adding greenhouse gases -- if we're going to do an experiment by testing injection of reflective material, say, sulfur, into the stratosphere, we don't have a control. And so if something happens, it's almost impossible, given the complexity of the system, to attribute it either to the CO2 or the sulfur. Sulfur injection into the upper atmosphere, says Keith, is within the power of poorer nations and even within the power of the richest individuals. And like the current trend in climate change, there would be winners and losers. Since we are already altering the atmosphere, is this something we should consider? And if so, who would be responsible? Who should be allowed to fiddle with the global thermostat?

A Response to Paul Davies on the Nature of Science "People say to me, 'Are you looking for the ultimate laws of physics?' No, I'm not... If it turns out there is a simple ultimate law which explains everything, so be it — that would be very nice to discover. If it turns out it's like an onion with millions of layers... then that's the way it is." -- Richard Feynman from "The Pleasure of Finding Things Out" Paul Davies' Op-Ed in the New York Times, "Taking Science on Faith" (November 24, 2007) makes a familiar argument. If he had used the light version of the argument, I might have agreed. But he uses the strong version which is just wrong. The light argument is: Everyone works with metaphysical assumptions. For example, I have a working assumption that the universe is comprised of matter and energy -- and everything we experience emerges from those two properties. Maybe there is more to the universe than I am guessing. I just haven't seen convincing evidence of anything else yet. So yes, I have a metaphysical assumption and it might be wrong. Davies argues a much stronger version of this. He states, "science has its own faith-based belief system. All science proceeds on the assumption that nature is ordered in a rational and intelligible way." That is demonstrably false. Quantum physics is not rational or intelligible. On the quantum scale, sometimes "if A then B" -- sometimes "if A then not-B." No one understands why this is the case. But if we perform enough experiments resulting in B or not-B, we can statistically chart the probabilities. That is a rational approach to something we don't understand. The use of probabilities delivers extremely reliable results over the long term. But the actual workings of the quantum world remain mysterious. Physicists Richard Feynman and John von Neumann are both attributed saying, "You don't understand quantum mechanics, you just get used to it." The world is not so orderly -- and this is already accepted by scientists. There is a difference between rationality in nature and using rationality to study nature. Davies conflates the two ideas. Davies continues, "The laws of gravitation and electromagnetism, the laws that regulate the world within the atom, the laws of motion — all are expressed as tidy mathematical relationships. But where do these laws come from? And why do they have the form that they do?" Davies presents these as questions that science ignores. Actually, these are vital and pressing questions in the physics community. The mathematical relationships that he describes as "tidy" are actually pretty hairy. The relationship between gravity and electromagnetism has been a mystery for decades and is the impetus for studies in supersymmetry and string theory. When relativity and quantum mechanics are combined on the small scale, they generate messy infinities. The sexiest and busiest theoretical

physics happening from Einstein to today has been the attempt to reconcile this problem. But Davies portrays the scientists as in a blithe disregard. Davies reports, "Over the years I have often asked my physicist colleagues why the laws of physics are what they are. The answers vary from 'that's not a scientific question' to 'nobody knows.' The favorite reply is, 'There is no reason they are what they are — they just are.'" First, "nobody knows" is perfectly legitimate answer. It's the kind of answer that gets scientists out of bed in the morning. It's a mystery to solve. Nobody knows, but maybe we can find out. Second, we can't assume there is an ultimate explanation. If we found one, that would be nice, just as Feynman said at the top quote. But we can't currently assume such an explanation will be found. Davies rebukes, "The idea that the laws exist reasonlessly is deeply antirational." Again, we can't assume that nature has any reasons. But we can still use our rationality to study nature. Nature is what it is. Our rationality helps us discover nature. But we should not assume we will find rationality staring back at us. Davies argues, "If one traces these reasons all the way down to the bedrock of reality — the laws of physics — only to find that reason then deserts us, it makes a mockery of science." No, it just means that some phenomena are unintelligible -- as in quantum physics. A few words about the "laws" of physics. The use of the term "laws" carries some baggage. Plus, it invites additional baggage from those who want to assume a "lawmaker." Let's take the law of gravity as an example. The law of gravity is one of the most respected ideas in physics. Galileo measured falling bodies at 32 feet/sec/sec. But that measurement turned out to be true only locally. Newton revised this by showing that the strength of gravity is inversely proportional to distance, and in doing so explained planetary motion. Einstein revised Newton, describing gravity in terms of space-time geometry -- which fit better with the Mercury’s orbit around the sun. Now Einstein may be under revision as we try to understand the apparently accelerating expansion of the visible universe. Like our secular laws, physical laws are open to revision. What's more, our current physical laws break down when we go back in time within the Big Bang model. Our use of the word "laws" is a relic from science's past. Greater minds may be able to think up a better word. But it is important to realize that any scientific explanation is tentative, open to revision, maybe true at one time but not in another time. Modern cosmology now treats "laws" as mutable. Davies talks about his science education, "The laws were treated as 'given' — imprinted on the universe like a maker’s mark at the moment of cosmic birth — and fixed forevermore." It sounds like that education was a disservice. The Big Bang and inflationary models contradict these assumptions.

Leaving the Big Bang aside, let's concentrate on the consistency of scientific findings. Consistency of experimental results is the norm today and makes science possible. The current universe, to our best evidence, is very consistent. That does not necessarily mean that, at its root, the universe is intelligible or has "laws" for a "reason." Consistency and rationality are two different things. For example, the quantum world is consistently and dependably irrational. Davies then touches on the multiverse speculation. This is the idea that our universe is only one of many universes. The other universes may have different physics which may or may not be stable or hospitable to life. He writes, "In this 'multiverse,' life will arise only in those patches with biofriendly bylaws, so it is no surprise that we find ourselves in a Goldilocks universe — one that is just right for life. We have selected it by our very existence." Davies is responding to a line of questioning often called the anthropic principle. "Why is the universe so suited for our existence?" is a way of summarizing the idea. The problem with the anthropic principle is that explores the universe by looking through the wrong end of the telescope. In the novella Candide, Voltaire ridicules this kind of thinking with the character Dr. Pangloss. Pangloss argues we live in the best of all possible worlds. Evidence for this assertion is that our noses are perfectly designed for resting eyeglasses. Actually, most of the universe is hostile to human existence. We are not adapted to survive in the vacuum of space (the vast majority of the universe). And if the earth happened to form near the center of our galaxy, the turbulence may have made it impossible for creatures to evolve to the point where they could ask teleological questions. A better question might be "Why is our universe productive enough to create life at all?" That might be interesting except that it's likely unanswerable. Our sample set of universes is limited to one. And we don't know what portion of this one is visible to us. While it's unlikely we are the first life in the universe, we're the only ones we have found. The universe is not teeming with life forms except very locally. A few miles up or a few miles down and you're escaping our humble biota. If Davies is dissatisfied with speculating on a multiverse, we are in agreement, except... Davies argues, "Both religion and science are founded on faith — namely, on belief in the existence of something outside the universe, like an unexplained God or an unexplained set of physical laws, maybe even a huge ensemble of unseen universes, too." Wow. This misconstrues the search for "physical laws" as necessarily appealing to something "outside" the universe. And it throws in the problematic multiverse idea for good measure. Then comes the zinger, "For that reason, both monotheistic religion and

orthodox science fail to provide a complete account of physical existence." This is a subset of the general rule: "no one can provide a complete account of physical existence." This is not a controversial point. The advantage of scientific inquiry is that it admits this ignorance. But Davies tries to use our shared ignorance as a basis for false equivalence. There is a difference between saying "The universe seemed to start with a Big Bang, I wonder why?" and "The universe seemed to start with a Big Bang, I wonder who made it?" The second question assumes a particular kind of answer. The first question is more open-ended and parsimonious. Davies' argument falsely equates the two. It does this by misrepresenting the quest for physical "laws" as a faith-based initiative. Today's cosmology is not so certain. If Davies was arguing that we are all ignorant of any full explanation of physical reality and we do our best with our assumptions, I would agree. But he goes further to argue that all scientific inquiry is like religion. In practice, the answer "God made it that way," tends to stop inquiry (and generates an unwarranted amount of certainty these days). On the other hand, all scientific knowledge is tentative. Currently, physicists are using ideas of symmetry to gain an understanding of the subatomic world. They are exploring it as a good hunch. But maybe it's not true, maybe nature is not symmetric. Symmetry in nature does have a good track record, but even a good track record is not the final word in science. On the other hand, the idea that "a creator made it so" has not produced anything usefully testable. Even a discovery as well revered as gravity is under continuous scrutiny and revision. Under what circumstances does the God speculation get revised?

SONGS THE LATEST GUESS OF EVERYTHING By Patrick McComb 2001 G G7 F#aug Faug F#aug Long ago when scientists were ancient and Greek C Eaug A G#aug Gdim You could learn to whole of physics in the course of a week G G7 C D Earth, air, water and fire G G7 Em Faug Were everything you needed if your heart desired elementals

G G7 F#aug Faug F#aug Centuries later, these elements changed C Eaug A G#aug Gdim And the Periodic Table has them neatly arranged G G7 C D But as dozens of atoms came into the sprawl G G7 D Perhaps those elements weren’t elemental at all Chorus G F# F E We kept on discovering more C C# D Varieties increased until

E7

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G F# F E We knew we hadn’t reached the core

Bdim

C Cmaj7 C Cmaj7 C E7 D7 F#aug G It must be made of something else, a something else that’s tinier still G7 Gdim F#aug So we gave those atoms a look-and-see To find their subatomical constituency Protons, neutron and electrons provide Everything you needed if your heart desired fundamentals That theory worked until we tested the guess Smashed some atoms all apart and measured the mess Tiny bits of matter scattered copiously A zoo of quantum particles we didn’t foresee Chorus We kept on discovering more Varieties increased until We knew we hadn’t reached the core It must be made of something else, a something else that’s simpler still Now we’re asking questions in the quantum range Where the old-school science rules begin to change Energy, matter, cause and effect Uncertainly break down to waves of accidents and incidentals We measure all this randomness with complex math As we seek a simple pattern in the cosmic bath

Supersymmetric ten-dimensional strings Provide the latest guess addressing everything Chorus We keep on discovering more Varieties increase until We know we haven’t reached the core It must be made of something else, a something else more elegant still In this loopy point of view some problems persist Predicting universes that don’t seem to exist Walking the Planck-space Vibrating at a scale too small to test Creating more dimensions than our brains can address Gyrating to the rhythm of our latest guess of everything Our latest guess of everything

HOW LONG IS THE COAST OF BRITAIN? By Patrick McComb 1997 with thanks to Benoit Mandelbrot Finger 6ths, maj7ths and 2nds E F# B7 B B6 E One day I found myself engrossed Within the length of Britain's coast. E F# B7 B Ab I thought I'd map it by the mile And circumnavigate the isle F# B B6 E But I missed details all the while E F# B7 B Ab So then I measured by the yard Caught my precision off it's guard A C#m A C#m A C#m C# F# 'Cause all those rocky zigs and zags that my straight-edge couldn't reach B7 B B6 E Still scribbled out along the beach A E My calculations grew exotic A F# B7+ B7 B7+ B7 The closer my eyes scrutinized the more that shore turned asymptotic E F# B7 B Ab My next solution was a cinch, or so I thought I'd map the coastline by the inch

A C#m A C#m A C#m C# F# But all that sandy granulation my straight-edge missed before B7 B B6 E Still wriggled 'round along the shore INSTRUMENTAL The instrumental fingers 7ths, #9ths and 4ths (instead of fingering 6ths, maj7ths and 2nds, as in the rest of the song) Em-E F# B Ab C# F# B E F#-G-Ab-A A E Some call it fractional dimension A F# C7 B7 C7 B7 It makes your lines in nature pay more length the more you pay attention E F# I found the answer to my hope (my sense of length restored) B7 B Ab In an electron microscope (I thanked the quantum lord) A C#m A C#m A C#m C# F# F#-F-E-B7 Now all those micro-nanometers around old England's girth B7 B Ab Could circumnavigate the Earth F# B B6 E C# 10,000 times for what it's worth, (and I'm still counting) F# B B6 E 1 million times around the Earth

E7

MECH AND MANABOZHO By Patrick McComb 2000 Em C13 Em A AaddBb A Old Manabozho was a crafty shape-shifter C7 C#7 C7 B7 Who met a funny gadget named Mech one day The machine said, “Let me make your life go swifter You look so inconvenienced in your primitive way” Old Manabozho was hungry for adventure And hadn't seen a creature like Mech before He didn't know the gadget was a masterful entrencher The cost of it's admission wasn't marked on the door A G# G G# A G# G G# Manabozho then elected to step inside to see what Mech did He got deep-fried, heat-convected, spliced, rewinded, vivisected

Unqualified and unexpected, F F# F B7 C7 Em The shiny new machine had swallowed Manabozho whole

Old Manabozho was feeling kind of tired Shrink-wrapped, freeze-framed and singin' the blues He found a naked wire and then he got inspired “A fire in this belly is a thing I could use” Well the machine named Mech laughed “Don't you even try it I heard that story yesterday My memory remembers and my processors apply it Evolving adaptation is the natural way” Old Manabozho changed his voice, he said, “You're the shiniest suit I've seen Your belts and gears are my style of choice I'll be handsome when I'm fashioned in my new machine”

Manabozho changed his shape and the new machine retaliated They both fought and sparred and spated, sneak-attacked and counter-invaded Deconstructed all the day ‘til The shiny new machine had finally given up the ghost

Old Manabozho was a crafty shape-shifter Who fashioned a mechanical suit one day He's worn it ever since and he's always moving swifter Accelerating pranks in his mechanical way He lives inside your switches, knobs and spools Ink pens, toasters and walking sticks If something funny happens with any of your tools C9 B9 C7 B7 Em You'll know that Manabozho is playing one of his many tricks

Information Graphics:

Chord Head - Instructional Guitar Chord Posters:

Two-Digit Math (from The How Gate site, 1999 tinyurl.com/yrcnvu) Counting and arithmetic can be done with just 0 and 1. HIT PRINT: Since this page deals with the kind of math we all learned in school, it will be more useful on a paper print-out. There are some math problems on this page which are more easily handled with a pen or pencil as your interactive medium. ;-) DON'T PANIC: The difficulty of doing math with binary is the numbers all look the same. 111011 and 1110111 look pretty similar. But the quantities they represent are 59 and 119, respectively. When you get into larger numbers, it gets tough guessing the quantities. Below, there will be an explanation of how to translate between binary and base-ten. For now, you can ignore the quantities. Instead, pay attention to how the methods of counting and arithmetic apply to binary numbers.

COUNTING: 0123456789 These symbols form the base-ten Arabic* system we all use. After 9, the numerals turn over to 10 which we pronounce "ten." 01 These symbols form the base-two binary system our computers use. After 1, the numerals turn over to 10 which we can pronounce "two." 0000 is zero 0001 is one 0010 is two 0011 is three 0100 is four 0101 is five 0110 is six 0111 is seven 1000 is eight 1001 is nine, and so on. If you look closely, you can see some patterns in the number sequence.

• Each power of two (4, 8, 16...) is a round number. (100, 1000, 10000...). • Each even number ends in a 0. • Each odd number ends in a 1. • The right-most column of digits reads down as 010101010101. • The next column over reads down as 001100110011. • And the next column: 000011110000. These patterns are true throughout the binary set of whole numbers. (These kinds of patterns also exist in our base-ten system, but they are more pronounced when we count out numbers in binary.) Can you write out the numbers one through twenty in binary? Writing out the binary number sequence can help you get the hang of how they operate.

ARITHMETIC: Binary numbers can be added, subtracted, multiplied and divided just like Arabic numbers. For example: In base-ten we can add 3+4+5. This equals twelve (12). So we write down a 2 and carry the 1 over to the next column. In binary, we can add 1+0+1. This equals two (10). So we write down a 0 and carry the 1 over to the next column. ADDITION Here is an addition problem. In the highlighted column you can see we are adding 1+1+1. The sum, three, is "11" in binary. So we write down 1 and carry the other 1. Just as in normal addition, we are following the same rules of adding and carrying. Try adding 1101 and 11. SUBTRACTION This subtraction shows how borrowing works in binary. When a 0 borrows a 1, its value becomes "10" -- two. In binary, 11(three) minus 1(one) equals 10 (two) and 10 (two) minus 1 (one) equals 1 (one). Try subtracting 10101 from 100011.

MULTIPLICATION and DIVISION The basic methods apply also to multiplication and long division. Once you get past the strangeness of working with a two-digit notation, the math starts to make sense. In the problem to the left, you can see a column of four 1's getting added together. In binary, four is written as 100. In this case, you write the last digit, 0, then carry the 10. Try multiplying 100001 by 100001 in binary. What does 11111111 divided by 11 equal?

The methods we use when we work out math on paper are a series of logical steps. These steps can be mechanized with logic circuits. The adder is a basic circuit that calculators and computers use to do math. TRANSLATING BETWEEN BINARY AND ARABIC Here's a math trick. Turning any Arabic number into a binary number. 1. Draw a horizontal line where you can keep a tally of the 1's and 0's. Fill the tally from right to left. 2. If the number is EVEN, write a 0 in the tally. 3. If the number is ODD, subtract 1, write a 1 in the tally. 4. Divide the Arabic number in half. Go back to step 2 5. Stop when you are down to 0

Let's take the number 2001 and see what it looks like in binary. 2001-1 1000 500 250 125-1 62 31-1 15-1 7-1 3-1 1-1 0 TALLY: 11111010001 This will work with any number. In fact, a number of primitive tribes handle problems of multiplication and division using a system similar to this.

Here's another trick. Turning any binary number into an Arabic number. Let's start with any old string of 1's and 0's:

1|0|0|0|1|0|1|0|1|1 1. Divide up the number into digit places, like above. 2. Starting on the right, label the first digit place with a 1. Label the second with the 2, the next with a 4, the next with an 8. Keep doing this, doubling the value of each label, until you reach the left end. 3. You can ignore the digit places with 0's in them. 4. Take the digit places with 1's in them and add up the labels. In this case, we have: 512 + 32 + 8 + 2 + 1 = 555 Go to the arithmetic problems above and see if you can translate them into Arabic* numerals. * "Arabic numerals" is actually a bit of a misnomer. The Hindus developed our modern number system. Al-Kwarismi, an Arab mathematician, traveled through India and upon his return wrote the book, On The Hindu Art Of Reckoning. Hindu numerals became standard in the Arab world about 1000 years ago. Al-Kwarismi also gave us al-jabr or algebra. The term translates to "the transposition" (jabr is a word for the silt that deposits annually along the banks of the Nile). As for al-Kwarismi himself, his name has been immortalized in the word "algorithm."

Patrick McComb 2009