The ambient field is filled with talented composers who for various reasons have not produced as many albums as the guys I've profiled in the last two chapters. Yet some of these albums from the less prolific folks are absolute gems.

I begin with Paul Avgerinos, a music producer in southern Connecticut. His Studio Unicorn is his livelihood, and in that studio, among all the other film, TV, and popular music he does, he has made a number of fine albums under his own name. (They are available for sale on his website.) Avgerinos is a classically trained bassist, who can also play jazz and just about anything else. In his ambient work, he uses the string and electric bass as both lead instrument and drone, sometimes electronically modified. It's certainly a difficult and unwieldy instrument to use as a melody carrier, but he makes it sing. Avgerinos is of Greek ancestry and he has used Classical Greek culture as a theme in his two best albums, MUSE OF THE ROUND SKY (1992) and SKY OF GRACE (1998). On these albums he has gathered with him some of the best jazz and Middle Eastern musicians of our time, among them guitarist Brian Keane and Turkish/Egyptian multi-instrumentalist Omar Farouk Tekbilek. MUSE is filled with Mediterranean instruments and rhythms, but also can float away on gorgeous tone-clusters from smooth synthesizers. Perhaps because of his extensive commercial experience, as well as his classical music background, Avgerinos tends to have a "slicker" and more accessible sound, with more familiar harmonies, than composers like Roach or Rich. SKY OF GRACE is one of my favorite ambient albums of all time, full of spiritual longing and languorous flights of sonic fantasy. In 2002 he released another album, WORDS TOUCH, which looks to be along the same lines as SKY OF GRACE, though I have only heard excerpts from it. Paul Avgerinos consciously avoids "dark ambient," preferring to provide his listeners with an uplifting sound full of a sense of wonder.

From Paul Avgerinos' sunny Greece we move on to electric China, the virtual world of Forrest Fang. By workday, the Chinese-American Fang is a lawyer in the San Francisco area; the rest of the time, he is a dazzlingly gifted avant-garde musician specializing in violin and Asian stringed instruments. Like Avgerinos, he began as a classical string player. But Fang is also trained in classical Chinese stringed instruments, which he plays on many ambient albums. He's most often heard as a guest player, especially with Robert Rich on Rich's albums PROPAGATION and SEVEN VEILS. But he also has two solo albums, THE BLIND MESSENGER (1997) and GONGLAND (2000). THE BLIND MESSENGER is an album that makes me sit up and go "Yikes!" every time I hear it. It's definitely not "comforting" ambient. Composed with Fang's strings as well as a wide array of percussion and electronics, it rips along with jagged rhythms, dissonant and Asian harmonies, masses of dizzying fractal-fueled whirling chords, and adventures in mathematical structures made into themes and variations. It's one of the most original techno-ambient albums I've ever heard — relentlessly intellectual and unsentimental, definitely not New Age sweet. GONGLAND is quite different from its predecessor. The Asian harmonies and instruments are still present, but it is much softer and less aggressive, misty and nocturnal, a subtler sound all around. You can find these albums, and more information, on Forrest Fang's home page.

Jeff Pearce opens the door to Heaven with his guitar. This may sound silly, but if you listen to Pierce's metaphysical playing, you'll perceive that heavenly light, too. All his sounds are produced with electric guitar and electronic modification; no crowded cabinets of world instruments nor stacks of synthesizers are necessary. The electronics modify the guitar so thoroughly that you will be unaware that he is not using synthesizers, and yet often his simple, innocent playing comes through almost as if he were just sitting on the porch next to you. Take some sophisticated jazz chords based on 7ths, 9ths, and 11ths, strum them on an electric guitar and stretch them out to infinity in a soft cloud of sound, and you will have a good idea of what Jeff's music sounds like. He has a number of albums, not all of them available. I recommend three albums. The first is TO THE SHORES OF HEAVEN (2000) which is a gentle narrative in slow ambient, from despair to exaltation. Next is its followup, THE LIGHT BEYOND (2001) which has one of my favorite single ambient tracks of all time, "Across the Infinite Sea." This album also has a 44-minute (yes, that long!) track which was recorded live at a concert in 2000, "A Farther Shore." Listen to this for sweet sleepy trance dreams. A more recent album is BLEED (2002) which has a more melancholy tone than the mystical warmth of his previous albums. Ambient music rarely says so much with so little instrumentation. You can find Jeff Pearce's information, and links to his recordings, at the Jeff Pearce webpage maintained by "Star's End," the ambient music organization at whose concert "A Farther Shore" was recorded.

If you like the quiet, melancholy tone of Pearce's work, you will probably also like the music of Tim Story, who combines piano with long-sustain electric guitar and other instruments to create minimalist melodic miniatures. Like Pearce, he does a lot with a little; just one or two motifs, repeating and varying, can convey an entire universe of mood. He's put out quite a number of albums, all of which feature his highly individual sound. There's GLASS GREEN (1987), BEGUILED (1991), THE PERFECT FLAW (1994) and more recently, SHADOWPLAY (2001). My favorite for pure sense of wonder and quiet is BEGUILED, though GLASS GREEN is also good. When you listen to Tim Story, it is always a rainy February twilight, and you've just lost someone you desperately love. SHADOWPLAY is so sad that I can't bear to listen to it. Share the tears at Tim Story's website.

I haven't yet talked about the sub-genre of ambient known as "spacemusic," but now's the time for it. This music is not that much different from what I describe as "classic ambient" with its long, sustained synthesizer notes and slow rhythms, but its purpose is more specific. "Spacemusic" is used in planetariums or with films, TV shows, and performances which deal with astronomy, stars, galaxies, and outer space. You know it's spacemusic because you hear those starship "whooshes," tinkling bells and beeps suggesting twinkling stars and cosmic rays, and comforting heroic power-chord harmonies suitable for rocket launches and colorful vistas of nebulae. One of the most prominent composers in this genre is Michael Stearns who has cranked out mass quantities of spacemusic as well as film soundtracks. He's probably the best of the lot when it comes to musical quality. Another spacer is Jonn Serrie who started out as an electronic planetarium composer and has since transformed into a kind of ambient easy listening guy, with pop rhythms and romantic sighing songs added to his repertoire. Kevin Braheny builds his own hybrid electronic/acoustic instruments, and also plays an electric woodwind instrument, the Steiner EWI, which has an easily recognizable sound, kind of like a spacey soprano sax. Braheny has released a few albums on his own, especially the spacemusic classic GALAXIES(1988), but most of his work is as a guest player in many different ambient and jazz ensembles.
In 1992 Michael Stearns and Kevin Braheny joined with Steve Roach to produce a superb album of "desert spacemusic," DESERT SOLITAIRE.

Some rare readers may wonder why all the ambient composers I've mentioned so far are male. It's true; the vast majority of ambient composers and performers are men, a much larger proportion than in the general musical community. When women appear in ambient at all, it is usually either as crooning vocalizers or as guest players on acoustic instruments. I can only theorize as to why there should be such a gender imbalance in ambient; possibly it is because women have not had either the opportunity nor the inclination to work with the complex electronic technology which makes ambient possible. Nevertheless, there are some exceptional female ambient composers (other than Wendy Carlos, who is not doing ambient any more). The one that comes first, in my mind, is Constance Demby, a classically trained musician who has been doing experimental and ambient music as long as any of the guys. As you can see from her web site, she's fond of grand gestures and extravagant presentations, and often enough, her music lives up to it. Her album NOVUS MAGNIFICAT (1986) is an over-the-top journey into mind-blowing transcendence, and her 1989 album SET FREE contains not only catchy New Age tunes (yes, singable tunes) but a set of wild, precipitously dissonant spacetracks suitable for high magical ritual, if you dare.
Another lesser-known female ambient composer is Meg Bowles who, along with her engineer/producer husband Richard Price, has created a small repertoire of tasteful ambient albums. Her 1996 BLUE COSMOS is an understated, quiet set of space ambient with rhythmic bongo drum accents. Another album, FROM THE DARK EARTH (1999) features the interesting combination of trumpet solo (played by David Bilger, the principal trumpeter of the Philadelphia Orchestra) and synthesizers. Unfortunately, the Bowles/Kumatone website is well out of date and I have not been able to find any information about what Bowles is doing now.

If you are one of the patient folks who have read all my ambient installments so far, I hope that by now you have a pretty good idea of what this music is like and who are some of its best people. I want to leave you with a recommendation for just one more ambient album. This album is simply titled 76:14, the amount of time the album takes, and each track has no word title, just its timing number. It was released in 1994 by Global Communication, the pseudonym for Tom Middleton and Mark Pritchard, two British guys with a lot of sound equipment. Their idea in just listing numbers is that you, the listener, will provide the mental imagery to go with the music, and if you hear this album, you will. It's hard to find information about them, and their output is limited to this one and a couple of re-mixes of other, earlier material, such as their 1998 re-mix, PENTAMEROUS METAMORPHOSIS. 76:14, depends on minimalist repetition, mechanical rhythms, sound samples, and synthesizer textures to create an impersonal, brushed-aluminum sound. Yet in this album, these features are used to create haunting, cinematic atmospheres, sometimes wistful, sometimes eerie and UFO-like. There are even moments of wry humor, such as cut number 5, "7:39," where two electronic tracks, playing different rhythms, have a "duel" to see whose rhythm will win out. In a field where many ambient artists take themselves and their music very seriously, the creators of "Global Communications" have a refreshing detachment and light touch. Yet their last piece on 76:14, "12:18," is almost like a repetitive hymn, with big organlike chords and a canned chorus. You don't know whether they are being honestly "spiritual" or just playing at it. It's possible that they are doing both.

Well, it's time to drift on out of the ambient sphere and get back to what I set myself to do, back when I saw the light of physics at Fermilab. I think of ambient as my mathematics and physics background music! All this music depends on those wonderful electrons which flow through the technology which makes it all possible. As I go along I will be talking more about ambient and reviewing albums which I think are worthy of attention. Meanwhile…

Back to math! I forgot the cosine formula!

I've spent so much time composing my series of articles on ambient music that I've been neglecting my first priority, that is, learning math and physics. I went back to my trigonometry books to find that, alas, I've forgotten a lot of what I recently studied, and must review it all. Trigonometric identities, vectors, and that lot. The annoying "Ruritanians" of Barron's study text propose problems which make me feel stupid, because I am not able to solve them. For instance, they list problems where you are supposed to derive a formula from an example and your knowledge of previous formulas. All abstract, something I'm not yet good at. Well, I'll put on some bracing ambient music and get to it.

Posted at 12:10 am | link

In this chapter we move from the sun-bleached desert of Arizona to the moist underground of fungi and the hypnotic-fragrant Near East. Then we will visit the techno-industrial urban soundscape of Chicago, and finally the foggy netherworld of surrealistic Belgium, as we meet some of the other major composers in the ambient field.

Robert Rich, based in the San Francisco area, started out as a psychology student at Stanford University, but by the early '80s had switched over to experimental electronic and acoustic music. Robert Rich's Web site provides a comprehensive guide to his sonic universe. Rich continued his interest in psychological states by holding "sleep concerts," all-night events where the audience was invited to bring their sleeping bags to the concert hall and slumber through the night while Rich spun dream-music on his array of instruments. Some of this was recorded and was released in the late '90s on Rich's album INNER LANDSCAPES (1999). In 2001, Rich produced the audio DVD, SOMNIUM, which lasts 7 hours if played in its entirety, in an attempt to provide a "sleep concert" for any listener who wished to try it at home. All the albums I mention, as long as they are in print, are available from Rich's website.

Musically, Robert Rich has developed a highly individual sound, both as a multi-instrumentalist and a composer. An important component of this is his use of "just intonation," a pre-modern form of tuning in which all the notes and chords seem (to our ears, used to Western tuning) to be out of tune in a most eerie way. This mood of strangeness is enhanced by Rich's choice of instrumentation. One of his signature instruments is the steel guitar, familiar to country music, which he uses in an infinite-sustain, reverbed way to stretch and bend notes out into endless lengths. You will hear this weird wailing guitar winding its way through most of Rich's work; he also uses electric guitar (often played by guest instrumentalists, as much of his work is ensemble work) in a similar way. Rich makes great use of percussion, which he plays himself, as well as flutes, exotic stringed instruments, and violins. And of course there are Rich's electronic synthesizers, tuned to "just intonation" and providing backgrounds and harmonies ranging from the ethereal to the eldritch. He refers to his more watery synthesizer sounds as "glurp," an amphibian word he adopted when no other description quite defined the froggy plop he wanted to convey.

From his earliest musical days, Rich has been fascinated by Middle Eastern culture, not only its music with its quarter-tones and syncopated rhythms, but by Islamic philosophy and pattern-geometry. Many of his albums, such as his 1988/1991 GEOMETRY and his 1998 SEVEN VEILS, are directly inspired by this aural mysticism. Another main interest and theme of Rich's imagination is that of hidden or underground biology, especially that of bacteria, moss, and fungi. Like the avant-garde composer John Cage, Rich is a mycologist, or mushroom expert. Rich's musical interests also extend to the music of Southeast Asia and Indonesia, and you can hear the sound of the Indonesian gamelan in albums such as his fabulous 1989 album, RAINFOREST. In his 1991 GAUDI, which in my opinion is his best album so far, he unites the themes of sacred geometry, Islamic/Iberian mysticism, and microtonal harmonies in a gorgeous and yet understated synthesis.

Rich has collaborated with some of the very best in ambient music, both instrumentalists (such as the Chinese-American violinist Forrest Fang, to be profiled in a later chapter) and other electronic composers. In 1990 he worked with Steve Roach to produce STRATA, and in 1992, they returned with SOMA, which I regard as one of the greatest ambient albums of all time. Rich played his ghostly guitar on Roach's long piece "To the Threshold of Silence," the second CD of his 1992 WORLD'S EDGE album (described in the previous chapter). After that, however, they went in quite different directions. Rich has also produced albums of art-rock, under the artist title "Amoeba." He has continued to follow his path into musical images of water, darkness, microbiology, and dreams, with some very dark and terrifying passages like his three-CD live concert set, HUMIDITY (2000). His current work continues his explorations into non-Western tuning, Eastern instruments, and bizarre biology.

"Vir Unis"'s real name is John Strate-Hootman, and he's currently based in Chicago. As with all ambient musicians, he makes his music available through his Website.You have heard his name before in collaboration with Steve Roach, but "Unis" has never really been a part of the "school of Steve Roach." His style is heavily dependent on synthesizers and the use of fractals and other mathematical patterning to produce a gleaming and somewhat impersonal sound. If Roach is the voice of the vast open desert, and Rich the glurp of algae ponds and echoes of Islamic archways, then Vir Unis is the electric buzz of Midwestern powerplants, or the photon song of high-energy particles streaming from distant galaxies.

Vir Unis (which is fractured Latin for "one man") is a newer artist than Roach or Rich. During the '80s he was a drummer for experimental rock bands, but by the '90s he had moved into almost exclusively electronic music. He worked with Steve Roach in 1999 on the spectacular BODY ELECTRIC and later on BLOOD MACHINE. Unis' first major solo album was THE DRIFT INSIDE (1999), which as its title conveys, is a trancey passage of floating ambient with some percussion accents. In 2000, Unis released AEONIAN GLOW, which I regard not only as his best album, but up there with the other greats I've mentioned as an ambient masterpiece. AEONIAN GLOW, composed all electronically (with many altered sample sounds) takes its inspiration from the ancient religious philosophy of Gnosticism as well as from science fiction and modern physics. With my own spectrum of interests, I couldn't ask for anything more! It's made of all sustained notes, with no rhythm. It features dissonant and chilling microtonal harmonies, accented by "Gothic" tone-clusters, icy water sounds, electronic special effects, and near-subliminal samples of half-heard, altered radio broadcasts, with occasional somber bell sounds. One track is called "Particle Path," perhaps evoking the power of the particle beams at the Tevatron at Fermilab near Chicago. The most powerful track on AEONIAN, though, is the central piece titled "A Night of Passage," thirteen minutes of some of the most dramatic, mind-altering ambient ever composed. This is not for the faint-hearted!

In the years after AEONIAN GLOW, Unis has moved into a much more rhythm-oriented type of music, collaborating with fellow synthesist James Johnson in the PERIMETER series, whose track titles are taken from mathematics: "Cartesian Plane," "Singular Integral," "Geometry of Recursion," "Intersecting Planes." There are also references to Kabbalah and Western esotericism, in titles like "Mapping the Four Worlds," and "Spherical Archetypes." The music on these albums, as well as on Unis' own MERCURY AND PLASTIC (2002), tends towards the mechanical, chugging along in industrial rhythms with electric hums, sparks, crackles, buzzes, and roars reminiscent of Chicago's elevated transit system. Melodic elements are sustained by a droning, somewhat distorted electric guitar sound, that gives these pieces a hard edge more related to rock than ambient.

Just recently, Vir Unis has returned to the non-rhythmic, sustained ambient style he worked with in his earlier albums, with his short album, EVERYTHING SEEKS BALANCE (2004). In the last few years, he has also been busy with his own production company, AtmoWorks. AtmoWorks represents not only Unis' music but that of many other composers in different styles of ambient and electronic music. This creator of very esoteric music is not only helping his own cause, but putting himself directly into the effort to keep this music available and encourage the creativity and freedom of those who make it.

Vidna Obmana is the pseudonym of the Belgian ambient master, Dirk Serries."Vidna Obmana," as is stated on his website, means "optical illusion" in Serbo-Croatian, and like "Vir Unis'" pseudonym, allows him to make polymorphous music without his own personal identity getting in the way. Vidna Obmana has been working in the electronic and experimental music field for more than twenty years.

Of the ambient composers I've profiled so far, Vidna Obmana, in my opinion, is the darkest and most obscure. His harmonies are almost all dissonant, his characteristic intervals being minor seconds, minor ninths, and other edgy tonal choices. His "signature sound" is, like true ambient, slow, drifting, slowly cycling in long loops, contemplative, quiet, and often deeply melancholy. I tend to think that Vidna Obmana is so grim because he is not an American, and does not partake of the innocence, or the naivete, of any American composer. Hearing his music is like gazing at the grey, misty skyscape of Belgium, a land of near-perpetual rain and fog. When he finds a major chord, it is like a rare ray of sunlight over the Low Country landscape. This style is best heard in albums like THE SURREAL SANCTUARY (2000) and its companion album THE CONTEMPORARY NOCTURNE (also 2000). But these are only recent examples of a musical personality which has been in development for over 20 years.

Obmana is, like Robert Rich, a multi-instrumentalist. He plays not only synthesizers, but electric guitars, percussion, and varieties of a strange Eastern European flute called the fujara which provides not just one note, but a note and its overtones at the same time. It sounds more Southeast Asian than European. Obmana does mostly ambient drift, but he is capable of some compelling and complex electronic rhythms, as in his album CROSSING THE TRAIL (1998). Yet he depends more on harmony and chords to get his meaning across, rather than the special effects and trancing rhythms of other ambient composers.

Ambient music, the offspring of globalized technology, is an international field, and Vidna Obmana, like Steve Roach, has collaborated with other ambient composers from all over the world. It was Steve Roach who really put Vidna Obmana on the ambient map in America, with their ongoing series of collaborative albums. The Roach/Obmana duo released their first set, the 2-CD WELL OF SOULS, in 1995. This big long album contains some very scary, "out there" music, as well as lots of wall-shaking rhythms. They tightened up their structure in the single-CD album CAVERN OF SIRENS (1997), in my opinion the best of their collaborations. Full of unusual percussion and rhythms, this sonically fascinating album uses samples of many different voices, including a Tibetan monk chanting prayers, sirenlike female voices, gravel-voiced growls, and weird singing. Steve Roach himself provides the ecstatic vocals in the glorious, headlong motion of track 4, "The Current Below." Roach would re-work some of the ideas from this particular piece into his LIGHT FANTASTIC two years later. In 1998 they produced a sprawling 3-CD set called ASCENSION OF SHADOWS: Meditations for the Millennium. Their fourth album, INNERZONE (2002), returns to the land of creepiness, with underworld flute playing by Obmana. They have just released their fifth major collaboration, a record of a live concert called SPIRIT DOME (2004).

Obmana continues to be very active in Europe, not only in ambient music but in film, live concerts with other instrumentalists: jazz, rock, pipe organ, and even classical chamber groups. He has also done music for theater, opera, films, art installations, and even an aquarium (SOUNDTRACK FOR THE AQUARIUM, 2001). His voice is not as easy to appreciate as some of the other composers I've mentioned; his European gloom and Belgian surrealism go against our American fondness for clarity, energy, speed, and light. But Vidna Obmana's music is a rewarding experience for those who can appreciate a subtle world of grey tones and slowly shifting clouds.

Next: More ambient composers with fewer albums to their credit

Posted at 3:41 am | link

The brightest star in the ambient galaxy, in my opinion and many others' as well, is Steve Roach. Born and raised in Southern California, Roach moved to Tucson, Arizona in the late '80s and has been profoundly influenced by the desert environment. Roach has been working with electronic ambient music since the late '60s, and has moved through a number of phases in his career. His earliest published work was heavily influenced by the electronic rock of bands like the famous German group Tangerine Dream, and what is known as the "Berlin school" of electronic rock music, which depended heavily on synthesized rhythms and mechanically repeating sequences of notes programmed into that perennial synthesizer favorite, the "sequencer." But during the '80s Roach evolved his own unmistakable, and much-imitated, personal style.

He really came into his own with his landmark 1988 double album, DREAMTIME RETURN which is inspired by his stay in Australia and his contact with Aborigines and their music. The classic "Roach style" features elegant chords, often from jazz or rock origins, played on synthesizers and stretched out into sonic infinity by reverberation and other processing. Over these "floating chords" are many layers of percussion, special effects, samples, and acoustic instrument tones. This sounds like the recipe for "classic ambient" as I described it in the last post, and it is — because Roach is one of the people who invented classic ambient.

During the '90s, Roach moved into what might be called his "shamanic" period, where he was deeply influenced by the spirituality, rhythms, and music of Native and Aboriginal peoples, as well as his vision of what the music of prehistoric humans might have been. His monumental albums ORIGINS (1993) and ARTIFACTS (1994) are percussion-heavy journeys into a primal vision. They also feature the Australian aboriginal wind instrument known as the didgeridoo. He manages to avoid being either cute or colonialist, mainly by sheer musical devotion. During those years, he collaborated with other musicians such as Mexican percussionist Jorge Reyes and Spanish guitarist Suso Saiz on music influenced by ancient Mesoamerican civilizations. Some of these albums are FORGOTTEN GODS (1993) and EARTH ISLAND (1994).

At the same time, Roach was creating music which I like to call "desert space music." The finest example of this style, and definitely one of Roach's best works ever, is the 1992 2-CD set WORLD'S EDGE. While this uses plenty of rhythm, it is more expansive and futuristic, evoking images of vast skies and turbulent weather, desert landscapes and blazing sunlight, and the brilliant stars and space of an Arizona night. There's a kind of heroic quality to Roach's music, which is most evident here. It's also "American" in the best way, not explicitly patriotic or chauvinistic but built from the "American" ideals of optimism, invention, resourcefulness, perseverance, and courage in the wilderness. In a way, Roach is the Aaron Copland of ambient music. As a Southwestern desert visionary, he might also be considered the "Georgia O'Keefe" of ambient music.

But there's another side to Roach (actually, many sides). The second CD of the WORLD'S EDGE set, "To the Threshold of Silence," is an hour-long foray into "dark ambient," influenced by Tibetan Buddhist ritual music as well as shamanic drumming, all fading into the infinite dark spaces (made possible, as always, by that blessed digital reverb!). Roach goes even further into that dark energy in the 1996 album THE MAGNIFICENT VOID, which dispenses with percussion and consists almost entirely of long, sustained synthesizer notes in big, built-up layers, oscillating in a slow, pendulum-like rhythm. It's very spooky and cosmological.

I'm leaving out dozens of solo and collaborative works here, which can be found, along with sound samples, on Roach's discography page. Roach's creativity won't let him rest. He hates standing still stylistically just because he has once achieved a good combination of sounds. He has made explorations into things as diverse as cowboy music (DUST TO DUST, 1997), progressive rock (THE LEAVING TIME, 1988, with Michael Shrieve and David Torn, among others), and long-form "environmental" ambient, for instance THE DREAM CIRCLE (1994) and SLOW HEAT (1998). He's also collaborated with some of the other luminaries of ambient music such as Robert Rich, "Vidna Obmana," and "Vir Unis," who I'll be talking about in the next installment.

At the end of the 1990s, Roach moved away from his "shamanic" period, and entered into yet another new world of musical inspiration. As it often happens, some of this was due to technical innovations. The application of computers and fractals to sound and rhythm generation brought forth a new way to add depth to electronic music. The main rhythmic beat can have endlessly changing layers of sub-beats inside each measure, and tone-colors can be made of shimmering textures rather than just individual notes. In 1999 Roach released his brilliant album LIGHT FANTASTIC which adds a cyber-dimension to his signature "desert spacemusic." His collaborations with "Vir Unis," such as BODY ELECTRIC (1999) and BLOOD MACHINE (2001) also feature this new computer-aided complexity.

His big solo album for 2001 was CORE, which I regard as a "retrospective" of 20 years of Roachmusic. Each track alludes to a style or theme he has explored over those years. CORE is also one of his most emotionally intense creations; this is definitely not "ambient" in the old sense of background mood music. Its frantic rhythms and dissonant harmonies no longer look back to a world of shamans and mystics but to the present and future world of uncertainty and terror.

Yet at the same time he was already working on his major release for 2003, a vast 4-CD set named MYSTIC CHORDS AND SACRED SPACES. There are nearly 5 hours of music on this set; it's as long as Wagner's PARSIFAL if you play it all at once (do not listen while driving or operating heavy machinery). Like his earlier MAGNIFICENT VOID, MYSTIC CHORDS is composed exclusively of long sustained notes in multiple, slowly shifting layers. There's no wild drumming, no fractal rhythms and no hot special effects. In this set, Roach is influenced not by Aboriginal music or rock or jazz, but by the Late Romantic composers of the 19th and 20th century such as Alexander Scriabin, whose grand mystical chord made of a "spiral of fourths" inspired some of the harmonies in MYSTIC CHORDS. Though this is one of Roach's finest efforts so far, MYSTIC CHORDS is also one of his less "accessible" works. It isn't something that automatically lights up your audiosphere. You have to approach it by learning its "language" of slow chord changes and long spaces. MYSTIC CHORDS is esoteric; I would even call it "initiatory," as it is explicitly music for an inner journey.

All these albums can be found by going to the Roach website, though some of them are out of print. The site has sound-samples available, though they are best if you have a cable modem or DSL (broadband) net access. Roach has his own private label, "Timeroom Editions," and sells his albums, from all labels, from the website.

The reason, in my opinion, why Roach can carry so many styles, and be so prolific without losing quality, is that he is the most "musical" of ambient/electronic composers. That is, he chooses chords, harmonies, rhythms, textures, and tone-colors which are innovative and make musical sense no matter what the genre is, and he knows how to pace an album so that there is never too much of the same thing. (This doesn't apply to his minimalist "environment" works, which are meant to be the same thing all the way through.) Because his style is so characteristic, Roach is easily imitated, but you can immediately hear the difference between Roach and his imitators. He has inspired what I call the "school of Steve Roach" among a whole generation of ambient musicians in the US and Europe. He has worked with some of them directly as producer and mentor; others just hear his work and imitate him. Some of them, such as Biff Johnson and the Spanish Max Corbacho are quite good in their own right. Others, not to be named here, range from "generic Roach" to slavish imitation. But while these guys are still making music like Roach in the '90s, Roach has raced on ahead into the 21st century.

Next: other first-magnitude stars of the ambient firmament.

Math and physics: I'm still working with vector problems. Pythagoras is godlike. How can so many different quantities be related by such a deceptively simple proportional formula? If I listen to Roach and try to do math at the same time, I feel like I'm on the astral plane.

Posted at 5:38 pm | link

The first example of true "ambient" electronic music was probably SONIC SEASONINGS by Wendy Carlos (1972). She blended electronic, acoustic, and recorded environmental sounds like birds, thunder, howling wolves, and rain into a set of four pieces which were meant to evoke the mood of each season. SONIC SEASONINGS has stylistic features which would eventually be standard for ambient music: sustained electronic tones, environmental sounds, modified acoustic instruments, and electronic special effects. The basic idea was not to create a "concert" piece which had to be played as an object of full attention, but a background of sound which would evoke a mood, a landscape, a feeling: an audible ecosystem.

Another composer who is more widely considered a founder of ambient is Brian Eno, specifically with his 1978 album MUSIC FOR AIRPORTS. Again, this album defines the language for ambient music, as well as its quiet mood. Its synthesizer tones may sound a bit dated nowadays, but you can hear echoes of this album in more than twenty-five years of imitations, up to the present time. Two years later, Eno collaborated with avant-garde jazz pianist Harold Budd to create the exquisite PLATEAUX OF MIRRORS album (1980). Both are still currently active though they've worked in many other styles than ambient.

By the late '70s, then, the characteristics of the ambient genre were pretty much settled, and they've remained the same, with some important variants, since then. Here are some of the characteristic qualities of ambient music:
1. Slow pace. Much of ambient moves much slower than other music, whether pop or classical. In fact, some "ambient" composers have adapted the slower movements of some classical pieces, sensing a common quality. Whether it be rhythm or melody or pacing or the rate of chord changes, true ambient goes slowly. It also tends to be soft, rather than loud like rock, opera, or big band jazz. This is deliberate, because ambient music, above all, is the music of contemplation, just as jazz or dance music or dramatic classical music is the music of action.
2. Sustained notes, whether on synthesizer or an acoustic instrument.. Ambient won't use 100 notes when one or two will do. Synthesizers, like conventional organs, lend themselves naturally to long, sustained notes while instruments like flutes, pianos, or guitars produce notes of limited length. An important invention for ambient is digital reverberation which allows any sound, even an acoustic one, to be stretched out into near-infinity. Ambient music would be nowhere without such techniques of sound-extension and blending, which have given Eno and Budd and all their successors that vast and mystical sound. There is no such thing as "ambient unplugged."
3. Limited melody and minimalism.During the era when the first ambient composers were doing their work, the "classical" field was also undergoing the trend towards "minimalism" in music. The musical celebrity Philip Glass led the way with his frenetic repetitions and slowly phasing melody and texture changes. Another influential figure for ambient is Steve Reich who was already doing tape loop and repetition pieces in the '60s. And yes, the ambient composers, though not part of the academic "contemporary classical" music scene, were listening closely to people like Glass and Reich. Ambient pieces are almost by definition minimalistic, whether they use rhythm or not. Minimalism is hardly a modern trend; in fact it is an essential part of the sounds used by humans throughout the ages to alter one's state of consciousness. Ambient music has from the beginning (as I mentioned earlier) been connected with the mind-explorations of the psychedelic '60s and the pop mysticism of the "New Age." More about this later.
4.Use of "environmental" and other sampled sounds.As with Carlos' SONIC SEASONINGS, a large proportion of the ambient pieces I know use recordings from nature, as well as human voices, seemingly random bits of radio broadcasts, Native or Aboriginal chanting, industrial sounds, and anything else that fits the composer's purpose. This has its origins in the very earliest tape music, musique concrete which might be translated as "conglomeration music" made exclusively from cut-ups and modification of recorded sound. Usually these samples are added as accents to music made by synthesizers and acoustic instruments. There are plenty of human voices in ambient, but they are usually wordless singing, unrecognizable whispers or garbles, or word-bytes. It's rather rare to find actual coherent "songs" with words in ambient pieces, though they do occur. Spoken word, modified or not, is more common.

Though the above characteristics sound limited, ambient actually has quite a variety to it. Despite what I said about slow, soft, sustained notes, there is a whole style of ambient which uses rhythms. Here's yet another list of some of the different styles of ambient.

1."Classic" ambient. This is the stuff I've described above, with its "synthesizer washes" and drifting, dreamlike mood. Believe me, there's acres of it out there, and I've trekked across lots of them. It's the easiest material to produce. With a few synthesizers and sound-modifying computers, a digital reverb device, and basic recording studio technology, anyone who can afford the price of, say, an SUV, can create his own electronic recording studio. You have to sort through a lot of this soundage to find what's good. A subset of this is dark ambient which is meant to have a creepy, spooky, cavernous, nightmarish, even disturbing quality. I love this stuff but sometimes it's not for the faint-hearted.
2. "Techno-ambient." This is ambient with rhythm. The rhythms can be made with real drums and other percussion, or they can be synthesized, or they can be made with clever looping of otherwise unpercussive sounds. It can go quite fast, and can be loud—and yet it's still considered ambient, because of its trance-inducing quality. I tend to like this type the best, especially when the composer varies his/her output between the dreamlike soft stuff and the harder drumming.
3. "Tribal" ambient. This is rhythmic ambient in which the percussion element is taken from drums and other percussion associated with Native or aboriginal peoples. It will also involve Native chanting or more likely, imitations of Native chanting. This music often attempts to reproduce shamanic drumming, or at least evoke it. But "tribal" ambient, for me, brings up unsettling issues of Western exploitation of Native musics outside their proper context, even when the "tribal" element is well-done. Some composers, especially those who have had actual contact with Native musicians in order to learn from them, can pull this off with respect and rise above the "colonialism" much as other Western artists and musicians have used African or Oriental material in their work. But the field is also full of tacky tracks where just because someone plays the bongos, it is called "tribal."
4. Avant-garde, minimalism, drone, and "glitch." These are the most extreme types of ambient. With avant-garde, you get a fragmented, sometimes noisy and toneless, rambling flow of sound, whether from instruments or environment or both, which defies interpretation or sense; it's the personal expression of its maker and often nothing but that. Minimalist ambient is minimalism squared—one long note or environment or chord or effect for a whole hour. Why listen? The answer is not to listen, but to keep it in the background. It can actually be rather pleasant, because it's meant to be a kind of "audible incense" for other activities. "Drone" is, as it sounds, composed of very long single or multiple notes, with no melody and little change until a new effect appears. Like the minimalist stuff, it's meant to be kept in the background, but it's usually not as pleasant. "Glitch" dispenses with note and melody altogether, and uses sounds like static, scratchy vinyl records, malfunctioning electronics, bugs, and other nasty little noises. This kind of stuff is for special tastes only.

A classical music purist (and there are still plenty of them) would say, at this point, "But this isn't really music, because nothing happens! What's the point of this? It just rambles, without any structure or development! It uses a few recognizable notes here or there, but then goes on and on and on endlessly until the listener just nods off or trances out!" And my reply is, "Well, yeah."

Ambient music simply does not follow the aesthetic canons of conventional music, whether "classical" or popular. It has something else in mind. Nevertheless, ambient has already entered the realm of "classical" music played in orchestra halls. Pieces like Gyorgi Ligeti's LUX AETERNA (1966) and the very slow, mysterious string and orchestral work of Estonian composer Arvo Part can be considered ambient without electronic elements. And more significantly, a piece that I would consider "ambient" won the Pulitzer Prize in 2003, namely "On the Transmigration of Souls" by John Adams. This piece, which was commissioned by the New York Philharmonic in memory of those who died in the September 11, 2001 terrorist attacks, has many of the characteristics of ambient that I described above: electronic sampling of voices, long sustained notes, slow pace, contemplative mood, and limited or hidden melodies.

At its best, ambient music is meant to provide a mind-expanding experience, without drugs. Some ambient composers deliberately intend to express spirituality in their music. Ambient music, unlike dance or pop electronica or so many other types of non-classical music, is quite serious. It is not shallow entertainment. Though that classical music purist might maintain that only classical music can truly be "serious," i.e. deal with matters of deep and complex philosophical or spiritual interest, ambient is one of the non-classical Western musics where the creators work in a sense of "seriousness." (Other types might be folk, gospel, or blues, which hardly ever intersect with ambient.) What began as an exploration of electronic and environmental sound has become, in the hands of creative people working with the best in modern musical technology, a genre of music that can carry more meaning than it appears to.

In my next installment, I'll talk about some of the important ambient composers of our era, and refer you to their Websites so that you can encounter their work for yourself.

Posted at 4:04 am | link

It would take far more space than what I have here to give even a short history of electronic music. Instead, I refer you to some sites on the all-seeing all-knowing Web which can give you a fair idea of it. Dartmouth University's Electro-Acoustic Music program has this information-packed timeline on the use of mechanical, electronic, and computer technology in music. And this Finnish music site provides a rich selection of links which will give a fine introduction to electronic music in general, both in the "serious" and pop fields.

Musical creativity has always been inspired by technical and material advances. This started with the first time some caveperson realized that they could get a sound out of a hollow bone or reed, and it hasn't stopped since. In the 19th century, for instance, developments in piano technology impelled Beethoven to write some of his later, great piano sonatas. The first electronic musical instruments started showing up in the 1920s, and were immediately used in both concert and film music. Pop music didn't start using electronics widely until the 1960s. An electronic milestone was the Beach Boys hit song "Good Vibrations" (1966) which used the sound of a theremin (see the Dartmouth site). This had been used in countless cheesy horror films in the '50s but here it was on a rock song heard by millions. The psychedelic era of the late'60s and the '70s witnessed a proliferation of electronic sounds in both popular and "serious" music. This sound explosion was generated by the invention of the small portable synthesizers which I talked about in the previous entry. Now any rock band or university electronic music studio could afford to make this kind of music.

Now here we are in 2004, the 21st century. It's the FUTURE and our music sounds futuristic! We wear pink and silver spandex suits and drive around in flying cars. Oops, wrong future. Well, at least we have electronic music—everywhere. Our sound-environment, wherever we turn, whether public or private spaces, is shaped by electronic devices. Even if you think you're listening to "acoustic" music, it's mediated by many layers of electronics, not only in reproduction but in processing before it ever gets played on the sound system. Most of the time, electronic sounds are mixed in with more "conventional" sounds played on familiar instruments (which may however be modified electronically). You can't escape it, unless you were to play your guitar or harmonica in your own private acoustic parlor or porch.

Again, to catalog how electronic music is used in films, rock, and pop culture would be far more than what I could do here. But you already have heard it, for instance the endlessly re-played soundtrack, by the Greek-French composer Vangelis, to CHARIOTS OF FIRE (1981). Ads for luxury products on TV, for instance perfume, jewelry, or fancy cars, like to use electronic sound, and of course it continues to be a staple of science fiction culture everywhere except the retro-music of John Williams in the STAR WARS series.

The obnoxious thumping bass which you hear from the SUV or sports car stopped next to you at the red light is electronic music. It's generated by a bass machine, not some guy actually playing the bass. Same with the drum rhythms and the repetitious but listenable hooks of "urban"music and rap, and the insistent beats of techno and dance music that you might hear in a fashion store. Just about any pop song now will have some electronic element in it. Another electronic innovation which has formed a large amount of the pop sound we currently hear is "sampling," in which snippets of any sound imaginable are digitized and made available for manipulation. In the old days of horse-drawn tape recorders, we did this by actually cutting up tape and splicing it back together. We also got our tape samples to repeat by splicing our tape into a loop and playing it through the machine. Nowadays the loop-repeating of samples is done completely digitally. Any DJ , or any amateur with a minimum of equipment, can do this.

Electronic music is still being done in the "serious" music field, but it's really obscure. To find it, you'd have to go to academic venues like Dartmouth (see above), University of Illinois at Champaign-Urbana, or Indiana University at Bloomington. The Brandeis Electro-Acoustic Music Studio where my father and I put in so much time in the late '60s is still going strong. Nevertheless, you're probably not going to hear this music anywhere unless you make the pilgrimage to these places or to avant-garde theater and art spaces, usually found only in college towns or big cities.

There is, however, a whole other field of electronic music which is neither "pop" nor "serious." It has a wide variety of sounds, but has been classified unfortunately as "new age music" which turns most listeners away. Yes, back in the 1980s when this music first appeared, it was associated with altering consciousness, bodywork and massage, Yoga, meditation, "channeled" drivel, crystals, angels, rainbows, and other holdovers from the '60s. Some of it still is. But human creativity is an irresistible force, and since the '60s, forms of electronic music which are neither academic avantguardia nor commercial pop nor sticky karmic twaddle have emerged. This music defies classification, so naturally I'm going to classify it. The general term for it is ambient because it originated in attempts to create an audible "environment" for contemplative listening. In my next installment, I'll talk about ambient and its varieties, and lead you to some of its best practitioners.

Don't worry, I'm still doing math and physics

I feel as though I have finally made some progress and am moving ahead, with both magnitude and direction. Having learned enough trigonometry to solve triangles, I can now solve vector problems (An airplane is moving at 600 km/hour on course at 75 degrees, with a wind of 40 km/hour blowing from 240 degrees…). I need to solve, and solve, and solve, until I acquire familiarity with it. Not that I'm going to be flying anywhere; every problem I solve actually solves nothing in the "real" world.

Posted at 1:46 am | link

The sine wave, or the sine curve: for a kid back in the '60s, when I was growing up, this was a classic symbol of the Mystery of Science. The shimmering wave showed up in the ominous opening to the old TV series (1963-1965) THE OUTER LIMITS, where the disembodied voice intoned:

"There is nothing wrong with your television set. Do not attempt to adjust the picture. We are controlling transmission… We will control the horizontal. We will control the vertical… you are about to participate in a great adventure. You are about to experience the awe and mystery which reaches from the inner mind to… the outer limits."

The spooky science fiction series reinforced in my impressionable mind (and probably many others) the connection between scariness, weirdness, sine waves, and Science in general. Science was something that was done by odd men (never women) dressed in odd clothing, and it usually brought about horrific effects, monsters, and disasters.

The sine curve on the screen brings back, for those of a certain age, Sputnik images of science, where guys with very short hair and white shirts, and the famous pens and pencils in the plastic pocket protectors, stared into oscillator screens, slide rules at the ready. They were fighting the Commies with science and brains, they were rocket heroes under the sign of the sine and the atom.

It never occurred to me that I would, or could be one of them. Not only didn't girls do this, but in my own artistic and academic family, none of us did it. And yet now that I attend to sines and cosines and their wavy graphs, I remember those early images of sines and scientists.

A few years after THE OUTER LIMITS, in the late '60s, I found myself looking with wonder at those same glowing green sine waves, not because I was in a science lab, but because I was working with electronic sound generators. That same curve which introduced the "Outer Limits" was also a picture of a sound, which you heard at the beginning of the program: the sine tone. For electronic music, it was the sweet song of the sine siren, the most basic of sounds.

While my peers in 1968 and 1969 were doing drugs, marching in protest marches, and "expressing their biological ascendancy" (euphemism), I was in a gadget-packed room creating electronic music. My father, professor of music at Brandeis University, was the director of the electronic music studio there and I had free run of the place when the students weren't using it. I was a teenage nerdgirl having fun with big reels of shiny brown tape and what were then state-of-the-art music synthesizers. We used the Buchla modular synthesizer and later the Arp synthesizer as well. Later on (1973) I worked a summer as tester and sound designer for Moog Synthesizers.

You can read about my adventures in electronic music here, in my "Growing up with Electronic Music" series:

Part One: From Forbidden Planet to Brandeis University

Part Two: The Electronic Music Studios of Europe

Part Three: Minnies and Pollies: My work at Moog Music, Inc.

All of this is an introduction to the other main topic of this Electron Blue Weblog: music, especially electronic music. In the next few entries I'll be talking about what makes electronic music tick (or beep), the different styles it comes in, and electronic composers I particularly like.

I also plan to say quite a lot about classical, or "serious" music, which is the music I was brought up with. My favorite "classical" music is that of the 20th century, though I listen to music from all eras.

Posted at 1:42 am | link

I don't have a "Theory of Everything." I won't ever have, or even attempt to devise, a "Theory of Everything." But lots of other people do, and they often present their crankery on the Web and send long manuscripts Proving It to professional physicists. I am constantly surfing physics sites and one of my favorites is the website of Gerard 't Hooft, a Nederlander who won the Nobel Prize for physics in 1999. As you can see from this website, Dr. 't Hooft has a wry sense of humor as well as a genuine desire to explain his work to interested non-professionals. And the non-professionals write back to him. Recently, he added a new section to his Website, called How to become a GOOD theoretical physicist. He introduces it thusly:

It so often happens that I receive mail - well-intended but totally useless - by amateur physicists who believe to have solved the world. They believe this, only because they understand totally nothing about the real way  problems are solved in Modern Physics. If you really want to contribute to our theoretical understanding of physical laws - and it is an exciting experience if you succeed! - there are many things you need to know. First of all, be serious about it. All necessary science courses are taught at Universities, so, naturally, the first thing you should do is have yourself admitted at a University and absorb everything you can. But what if you are still young, at School, and before being admitted at a University, you have to endure the childish anecdotes that they call science there? What if you are older, and you are not at all looking forward to join those noisy crowds of young students?

What follows is an extensive curriculum plan, starting from beginning mathematics and moving into calculus, topology, classical mechanics, thermodynamics, relativity, quantum mechanics, advanced mechanics, and lots more. It goes on for pages.

I am pretty sure that 't Hooft created this section partly as an intimidation strategy for the cranks, in other words, "so you think you know physics, well, learn THIS before you bother me again." But I believe he is mostly sincere and that he is influenced by the MIT internet-based courses which have recently been made available. He has attached Internet and web resources for all of the sections he mentions, and stresses that this curriculum section is only at its beginning. The words which attracted me are the ones about someone who is older and not looking forward to joining crowds of young college students. That describes me. I don't know whether I will go back to university at some point in this quest, but right now I think it's unlikely. 't Hooft says:

This is a site for ambitious people. I am sure that anyone can do this, if one is gifted with a certain amount of intelligence, interest and determination.

Well, I think I have all three of those qualities, especially the last two. But we will see. 't Hooft continues:

Now, here begins the serious stuff. Don't complain that it looks like being a lot. You won't get your Nobel Prize for free, and remember, all of this together takes our students at least 5 years of intense study.

Five years?? In my case, it will probably take at least 10! When I am learning my elementary math and physics, I often feel as though I am mowing a lawn with a scissors. Nevertheless, I still want to mow the lawn. When it comes to Dr. 't Hooft's curriculum, I am only at the beginning of page 1. Fortunately, I am already an English speaker and I already know the Greek alphabet.

In gratitude for his Web curriculum efforts, I dared to write Dr. 't Hooft an e-mail explaining what I was doing and inviting him to look at my own Website. To my astonishment, he promptly sent me a reply! He commented positively on my site, and reminded me that his curriculum section was only at the beginning stages. Yes, this busy elite scientist took the time to send a reply back to a beginning student. This is a class act. I would call it nobelprize oblige.

Vector Detectors

The Red Spine Book's section on vectors proved to be confusing and poorly laid out graphically. It was about the same level of clarity as the old manual for Microsoft Word for Windows 2.0 (for those ancients who remember this). So I had to resort to Ruritania again, where our little fantasy royal courtiers were happy to take me on a balloon ride over some rivers, and explain vectors in fairly clear diagrams and text.

My Friendly Mathematicians and Scientists are always telling me how valuable diagrams are. But I often find them confusing, because as an artist I see them as pictures or renderings of "reality" rather than symbolic representations. I have to remember that a vector diagram is not a rendering nor even a blueprint, and that the length and direction of a vector arrow is not meant to describe a three-dimensional reality like a trajectory or a piece of architecture. It is a symbol. I can only too easily over-visualize whatever I am diagramming, turning a simple rectangle into an elevation or a plaza, or a curve into a landscape. Just as with my synesthetic number-colors, I have to turn down my imagination in order to work with the basic elements. Perhaps later on, when I am further into Gerard 't Hooft's realm of theoretical physics, I can allow my imagination back in.

Posted at 11:04 pm | link

Every so often in my math path I encounter an area which is full of formulas or processes which I have to memorize. Much of the "math and physics teaching" I read doesn't approve of just memorizing formulas, and discourages such rote learning, but there are some places where I find that it is necessary. Otherwise I have to "re-invent" the entire thing every time I work with it, which gets tedious. Examples of this are the quadratic formula on how to solve quadratic equations, and the trigonometric identities which I was working with last week. Now that I have enough trigonometry to resume my work in learning basic mechanics in physics, the same holds true for those formulas about vectors, and vertical, horizontal, and curved trajectories of projectiles in ideal space.

When I'm faced with these formulas, as well as the mathematical processes which were used to derive them, I can get stuck in the grinding gears. I try in vain to visualize the different lengths on the graph or in a triangle which are then combined and recombined to make trigonometric relationships. Drawing diagrams only helps in the short run; after the basic sines and cosines, verticals and horizontals, things get too complex for me to visualize. And yet I have to know these things and become familiar with them in order to proceed.

What I have done throughout my work is to create a "calligraphed" page which shows the formula and its derivation, and some uses it is put to. Despite doing signs professionally, I am not really a calligrapher, and my lettering styles are limited. For these pages I mostly use what might be called "architect's capitals" or "graphic design block letters," familiar to those who work with architectural drawings. I include whatever I think will help me to remember how the formula works, and what the components are. I may use different colors, but usually I don't add any extra drawing or art, which would distract from the austere purpose of the written page.

What I have found is that the act of writing it down formally, helps me fix it in my mind. I can remember it not only by referring back to the page I have drawn, but by remembering the page in my mind's eye. I also find that the handwork of carefully making up the page adds strength to the memorizing process. That's why doing it on the computer wouldn't be as effective. I have done pages on polynomials, on conic sections, on formulas for describing acceleration, and on trigonometry. Here is an image of my latest page showing the formula for the trajectory of a projectile fired at an angle. The arrangement is mine, but the sequence of information comes from one of my trigonometry books. I keep all the pages I have done in looseleaf notebooks, where I can return to review what I need. Looking at the pages brings back not only the mathematics, but the memory of when I did the work, along with the mood, circumstances, and events of the time when I was writing it.

Posted at 3:17 am | link

Last year I read a fascinating and fanciful article in SCIENTIFIC AMERICAN called simply PARALLEL UNIVERSES (Scientific American, May 2003). If you've been following this Weblog so far, you'll remember Lee Smolin's ideas about parallel, or multiple, universes emerging from black holes in our own universe. The author of this article takes it even further, and describes how not only could there be an infinite number of parallel universes, but by the laws of logic and probability, there is a universe "somewhere" where there is an exact duplicate of you and me, doing exactly what you and I are doing.

Though the author swears that the physics of this whole setup are possible, the article reads more like science fiction than science. It is at any rate a brilliant piece of creative thinking, something to make us wonder and speculate rather than go searching for ways to prove it. This imaginative author is named Max Tegmark.

The name sounds like it should belong to an action hero — Max Tegmark, master of cosmic rays! But he's a bona fide cosmologist and astrophysicist who teaches at the University of Pennsylvania in Philadelphia. He is of Swedish origin, now only in his mid-thirties, already the author or co-author of dozens of professional papers as well as popular science articles.

Naturally, he has a Website. It is one of the least stodgy, most personal scientist's Websites I've ever seen. The homepage is graced not only with a picture of smiling Max but of his two adorable little sons Philip and Alexander. There are links to loads of photos of Max and his family, including his Brazilian wife Angelica, who is also a cosmologist (they tend to marry within the tribe), his relatives, her relatives, his travels, his childhood pictures, important moments in their lives, places they've been, and famous and less-famous scientists they know, including John Wheeler, Martin Rees, and Stephen Hawking.

The first thing I noticed about this website is how dazzlingly beautiful both Max and Angelica are. This is not fair. No one should be this beautiful and brilliant at the same time. But once I got past grumbling at fate, I immersed myself in the exuberant world that Max and his wife have created online. Max's personality shines through everywhere. It's a sunny, outgoing character filled with enthusiasm and optimism and good humor. It seems, in the best way, innocent, untouched by the irony, tragedy, and darkness of the harsh world. Perhaps it's almost improbably innocent, motivated by love of his subject and confidence in himself. He chooses to share pictures of himself and his folk in all sorts of situations, at the beach, hiking in the mountains, pondering and adventuring, as if he were inviting us cold websloggers to be part of his extended family.

Some of this site is hilarious, especially his "bloopers page," his silly poetry and his "bottom 95 percent pointless" web icon. The guy obviously has a great sense of humor. But if you want his serious side, there is plenty of cosmology, starting right on the front page. He invites us to read about his work in gravitational lensing, cosmic background radiation, supernovae, dark matter, dark energy, gamma-ray bursts, and other fascinating cosmic stuff. He's not just a scientist who actually has a life, he's a life which does science.

Now it's your turn to be enchanted by Max. Visit the Max Tegmark Website and see for yourself.

As for me at the Electron, I need to disenchant myself. I need to avoid the distractions of beautiful scientist people and stories of science heroes, as well as exciting cosmology and physics far in advance of what I can currently comprehend. I need to get back to what I am doing today, and tomorrow, and tomorrow: my slow progress through the fundamental simple grammar of mathematics, trigonometry, vectors, forces, and basic mechanics. I need to keep my head down, lest I be too enthralled by the shining stars to do the hard groundwork.

Posted at 1:56 am | link

I am using three trigonometry textbooks in my trip through trig. They are: TEACH YOURSELF TRIGONOMETRY, by P. Abbott, revised by Hugh Neill, which I refer to as the "BritBook" because it is of British origin, SCHAUM'S OUTLINES: TRIGONOMETRY Third Edition, by Robert Moyer and Frank Ayres, Jr., which I refer to as "Red Spine" because of the colorful design of the cover, and TRIGONOMETRY: THE EASY WAY by Douglas Downing, PhD, published by Barron's Educational Series. All three are available at Borders Books, which is where I got them.

I use the BritBook as my main text. This is because the BritBook is smaller and lighter than the other ones, and thus I can put it in my briefcase and carry it around and on trips without adding extra weight. Also, it seems to be clearer and more concise than the others. It has a kind of stiff-upper-lip impersonal quality to it, with measurements in centimeters and meters, and British spelling of words. The problem sets put me into a landscape of hillocks, towers, flagpoles, swampy areas, chimney stacks, windswept coastlines, church steeples, rivers, and bridges, all eminences casting shadows in the pale northern sunlight. One problem is set in wartime and asks (using given data) how far a soldier can go along a road A without being in range of enemy gunners, and what length of the road is within range. The BritBook's conciseness means that I do the intermediate steps of solving their examples, and so I have added quite a lot of notes in coloured pencil on the pages.

"Red Spine," an American production (McGraw Hill Schaum's Outline series, over 30 million sold), is on the other hand, obsessively helpful. It prints work-throughs for all of its example problems, and puts the answers to the problems right alongside the problem. Thus to keep myself from seeing it, I must cover the answer with a sheet of thick paper as I work down the page. Despite the large (11" x 8") size of the book, Red Spine's printing is rather small and difficult for my aging eyes to read. I am currently using Red Spine for my introduction to vectors, since the Brits don't cover it in their book.

"Ruritania" is my least favorite of the three. Despite its title, it is not an "easy way" and they assume that some accessible teacher is working along with the student using the book. It also assumes that the student already knows many basic concepts which this student (i.e. me) may not know. It has several problems involving creating abstract formulas from other already proven abstract formulas. This is something I am not much good at; I do much better when I'm dealing with concrete and specific number values rather than just general letter stand-ins. The most annoying thing about "Ruritania," which is why I give it that name, is that it is presented as a fantasy story featuring various characters in a somewhat 19th-century-style kingdom. They are depicted in cartoons and their story involves having them "discover" trigonometry and what it is all about. There's a king, a lady Professor, a sad-sack accountant standing in for the student, a friendly giant, an inventor/adventurer, a builder, a mischievous gremlin, and other stock figures. This may sound charming, but it's not, and I keep feeling sorry for these fantasy folk who were created solely for the purpose of serving as mathematical illustrations. (Set them free! Let them live their own lives!) This same crew is also featured in Barron's study books for algebra and calculus. I will have to spend a bit more time with them in Ruritania, because Barron's trigonometry text has a fairly good section on vectors. I am going slowly, as usual, so my vector arrow isn't very long.

There are many Websites devoted to trigonometry, mercifully free of fantasy characters. One of my favorites is Fergus Murray's trigonometry page which has beautiful colors and designs. Dave's Short Course in Trigonometry from David Joyce at Clark University is also good and the applets are fun to play with.

Posted at 4:45 am | link

There are a lot of popular books out now about the amazing scene of modern physics, for instance Brian Greene's best-selling THE ELEGANT UNIVERSE or the various Stephen Hawking productions like A BRIEF HISTORY OF TIME or THE UNIVERSE IN A NUTSHELL. I have often heard professional physicists admonish beginning students like me to remember that though the authors make these exotic physics concepts look exciting, these books are about stuff far more advanced than anything I will ever study at least soon. And I should attend to learning my basic high-school physics and not trouble my head about string theory or D-branes or quantum gravity. OK, granted I am still struggling with things that the authors of these books learned before they were ten years old, but still, some of these popular science books are wonderful.

My favorite one so far is THE LIFE OF THE COSMOS by Lee Smolin. It's available at Amazon.com, of course. Lee Smolin is currently a theoretical physicist at an avant-garde physics think tank near Ottawa, Canada (more about that later) and is also a participant in the very classy science and philosophy website The Edge . He also has the cover story in the recent January 2004 issue of SCIENTIFIC AMERICAN, on "Loop Quantum Gravity."

THE LIFE OF THE COSMOS was published in 1997 and it is filled with wonderful ideas about how black holes are formed, why and how the laws of physics are the way they are in this universe, and whether there are other universes, spawned through black holes. Smolin eventually describes an "ecology" of zillions of possible universes each having a different set of physical parameters, and each having a different "evolution." And each has a level of "fertility" as it produces offspring universes through black holes. Some universes are more "viable" than others, and ours is one of them. Not only biological life, but the origin and persistence of entire universes, may depend on principles of "self-organization." The main problem is that this question is hard to resolve through experiment, as there's currently no way to detect any of these parallel universes. But they'll think of some way, I'm sure.

Not only does LIFE OF THE COSMOS deal with the fantastic multiverse, it also has some of the best explanations of relativity and quantum mechanics for the non-professional reader, that I have ever read. These are chapters 16 through 19, in section four, "Einstein's Legacy." Early in chapter 16, Smolin introduces the question of what "space" really is with this amusing passage:

"We may begin very simply, by asking how we talk about where things are. One way is to describe their position relative to me: my left shoe is on my foot, my computer is in front of me, my guitar is on my favorite chair which is ten feet to my left, my cat is on my head. This suffices for most purposes, but it seems not completely satisfactory, for where am I?" (Smolin, page 214)

It's like a rather surrealistic but serene interior scene by Belgian surrealist Rene Magritte, as the physicist ponders the relativistic universe with a cat (of course, it's Schrodinger's) on his head.

Smolin is a long-term researcher at an amazing place, the Perimeter Institute for Theoretical Physics in Waterloo, Canada, outside of Ottawa. I can't resist thinking of Harry Potter's "Hogwarts School of Witchcraft and Wizardry" when I visit the Perimeter Institute website. To read their lecture topics is to peruse a world far from our mundane "muggle"existence. Perimeter is funded by the people who made a fortune off the "Blackberry" portable telecom devices, as well as the Canadian government and other donors. It is currently constructing a slick new building for its headquarters. Unlike Hogwarts, which seems to exist in a kind of perpetual early 1900s, Perimeter is resolutely 21st century. If they ever find out how to prove those parallel universes, it might just be here.

Meanwhile, I'm back walking on the long single-lane dirt road, a thousand miles away from string theory and loop quantum gravity. I've finished my introduction to trigonometric identities, and will now encounter vectors, and graphs of trigonometric functions.

Posted at 3:23 am | link

In a recent e-mail conversation with one of my "Friendly Mathematicians," who will hereafter be named "Professor B.," he reports that he has heard that "someone whom I respect told me that good mathematicians tend to think of math kinesthetically rather than visually. I think this might be true of physicists also."

I find this is true of my approach to math as well. I just didn't quite know the word for it (kinesthetically). That is, mathematical work and concepts relate to physical body movement and tactile experiences. Some of this is predictable: when I encounter an acute angle in geometry, I "feel" its sharpness (perhaps because my plastic drafting triangle actually does have sharp edges and points). But then angles are also paths traveled, as if I were driving my Electron car along the line-roads of geometry. An acute turn angle will cause more pressure on the driver than a gentler obtuse angle, and a sharp curve will exert more g-force on me than a wider curve. Just because I am not actually traveling these paths doesn't mean that I don't have some much more attenuated equivalent of it in my mind.

Similarly, when doing circle geometry or working with the trigonometric "unit circle," I literally feel as if I were going around in circles. I can even get dizzy if I stare at a circle for too long. The trigonometric "unit circle" also feels like a spinning wheel or an old-fashioned "tether ball" or a weight on a cord, which I am holding and spinning in a circle to demonstrate "centrifugal force."

And all this without leaving my chair!

As for color, I am mildly synesthetic, which means that I see numbers as colors. This peculiar perception is probably much more common than people think, and there are now some very good studies on the phenomenon, especially those of Richard Cytowic. Richard Cytowic's Website has a wealth of links to material on synesthesia.

I am certainly not as synesthetic as most of the people whom Cytowic has studied, but it is definitely noticeable for me. I know musicians who see different keys as colors, and another friend recently mentioned to me that she sees the different months of the year as colors.

My number colors are as follows: Zero: clear or transparent. One: white. Two: brown. Three: pale yellow, the color of the background of a New Jersey license plate. Four: rich orange. Five: dark blue, sometimes dark green. Six: pale blue, a color sometimes known as "periwinkle." Seven: Purple. Eight: golden yellow. Nine: black. For numbers with more than one digit, they are neither individual colors nor a mixture of the colors of each digit; they are a mosaic or a tiling of the different colors, except for number 11, which for some reason appears to me as beige. I can guarantee that your "number colors" will be quite different from mine; there seems to be no pattern to individual perceptions of synesthetic number colors.

In algebra, I perceive the variables a, b, and c as colors as well as x, y, and z. A is red, B is blue, and C is light blue (not yellow, as might be expected from primary colors). X is metallic gold, Y is bronze, and Z is black. These number and letter colors have been a distraction to me while working with math, and I've had to train myself not to see them when I am doing the work. Outside of mathwork, I enjoy seeing the mosaic of different combinations.

I am pleased to note that I am in good company; the famous physicist Richard Feynman was also synesthetic and saw numbers and other concepts as colors.

Posted at 8:02 pm | link

Greetings, Electronic readers!

This is the first installment of "Electron Blue," my Weblog. My own voice now joins the urban rush of virtual sound that makes up what has been called the "Blogosphere." As my logo caption explains, I am an artist who has been captivated by mathematics and physics, and who is determined to learn these things, to the best of my ability and as long as I am able to do so. I do not know how far I will go, but I do know that these endeavors have no end and that whatever I learn, there is always more. I am doing this by myself, from books and Internet, rather than taking courses in any classroom.

You can read the longer story of my adventure up to now by clicking on the links at the "Mathematics and Physics" section of my Pyracantha website. As it is, I start my Webjournal here in medias res ; I am now in my third year of studying mathematics.

In these electronic pages you will read about my studies, and struggles, with mathematics, physics, geology, and whatever other scientific matters catch my attention. I also intend to talk about my own work as an artist and as a connoisseur of classical and electronic music. I hope to bring you interesting notes about music and composers you may have never heard of.

Since I am also much involved with religion and philosophy, I will be talking about those subjects as well, hopefully in a calm and contemplative way. However, it is likely that I will also post some rants, whether about gender, language, culture, or current events. You may find these rants entertaining; but you also are welcome to skip over them.

One thing you will never find in this Weblog is politics. I vote in almost all the elections I can, and I probably have political views, but I don't want to talk about them. Too many other bloggers are only too happy to go on about politics, so why add more verbiage to that stewpot. No politics here.

More than one scientist has told me that the perspective of an artist, with its visual and nonlinear outlook, will be valuable in the study of math and science. I don't know whether this is true yet. I also don't know whether the much-mentioned connection between music and mathematics is true. So far they are just things I have heard about, without much evidence in my own experience.

In my quest for learning mathematics and physics I have encountered many professional mathematicians and scientists who have encouraged me and given me help and advice. I thank all of these "Friendly Mathematicians and Scientists" at the very beginning, and hope that I can remain their friend throughout my journey. And even more thanks go to Amanda Walker, the "Net Goddess," the Webmistress without whose patient help and generosity this entire site would not exist.

Current Math Work

I have been working my way through Trigonometry in the last quarter of 2003 and first half of 2004. Currently I am working on Trigonometric Identities, about the sines, cosines, and tangents of compound angles, sin(A+B), cos(A+B), as well as the (A - B) and tangents of those. After that I have been working with multiple angles, and solving equations involving all of the identities mentioned above. Seems like the key method here is to keep substituting one mathematical expression for its equivalent until something works. I find this section of trigonometry rather dry and formulaic, especially without context, but I know it will be very important for my later studies in calculus and physics. My motto when faced with tough math that I have to learn abstractly is, "The Application will be Revealed to me Later." A kind of mathematical eschatology.

Posted at 1:01 am | link