P. After five or six days I stopped in at the park office. They hadn't heard from me since I arrived, and they were pondering sending a ranger up to Lost Horse to make sure I hadn't disappeared. The funny thing is, though, I had kind of disappeared. Something about the atmosphere of Joshua Tree had dissolved the blocks, burst the levees, purified my mind to the point where it was no longer separate from its environment. There was no more me; there was only the desert, and songs.

It was a four-day drive, by myself, from Austin to Joshua Tree. The first night I stopped at Balmorhea State Park, where I had a brief swim (just long enough to wash the East off) and lay down to sleep in my car, where through the back window I spotted the hugest shooting star I’ve ever seen. The second night I was at Chiricahua in southern Arizona, writing songs in the drizzle. The next day, after a hike, I drove across Arizona listening to David Sedaris. The fourth day, finally, I crossed the Colorado River and entered California.

My phone, as if on cue, freaked out. Vibrating uncontrollably, with strange garbled text on the screen. I still suspect that it was briefly possessed.

A few hours later I was by myself on the porch of the Lost Horse cabin in the heart of Joshua Tree National Park. This would be my home for three weeks. No one would particularly check on me. I was left to my own devices.

A guitar, a banjo, and books, to be precise. I had no internet connection or cell phone service at the cabin. Both were a thirty-minute drive away, in town.

I was terrified. I had never subjected myself to such solitude. I’d lived alone in Austin, and it had been a trial. In Myers-Briggs personality typology, I am emphatically an extrovert. Interpersonal interaction charges my batteries.

It all changed when I started writing the songs. The first morning I sat on a rock outside and read a few chapters of a strange novel about circus freaks. And I started to play guitar. That night, in the immense darkness, I sat in that little cabin and scratched out some enigmatic verses about owls, a sideways Twin Peaks reference. I felt immensely gratified. I felt a deep connection to music and music-making that I’d lost while working on my master’s degree.

I hadn’t planned to write songs at Joshua Tree. But the songs were there, waiting. All I had to do was write them down.

I did see people during the residency. I drove into town to check my email and buy groceries. The closest town was Joshua Tree itself, which is the smallest but most inviting of the three communities placed along Highway 62. Yucca Valley is where I’d go for groceries. Twentynine Palms is where I stopped first, where the park offices were located. There are about 25,000 people in Twentynine Palms. Just outside town there is a Marine Corps base with a population of about 8,000. This colors the whole community immensely. The huge military presence projected against the desert-rat vibe of Joshua Tree creates a unique melange.

The composer Lou Harrison took to this area late in his life. He purchased land near the village of Joshua Tree and constructed a straw bale house there. It is a landmark in the world of straw construction, with its striking archway and vaulted interior hall. The house is small, and the hall acoustically stunning. Light shifts through the windows from the otherworldly desert landscape outside. Harrison had only a year to enjoy his desert retreat. He wrote his last composition there. He passed away in 2003.

I was lucky enough to receive a tour of the house from its current caretaker, Eva Soltes. A longtime associate of Harrison’s, Eva has dedicated years to the creation of a comprehensive documentary film about the composer’s life and work. She runs an artist residency program and concert series at the house. When I visited, the film was still unfinished. Eva played me some footage and told stories of her work with now-legendary composers like Harrison and Conlon Nancarrow.

It turns out that Fared Shafinury, a terrific Persian classical musician who I met at the Ham Jam described in volume seven, is playing a concert at the Harrison House in a few days.

Back at the Lost Horse cabin, mostly I sat on the porch and wrote songs. They were deep and strange, pulling from mostly-forgotten childhood memories, high school camping trips, nights spent sitting by little lakes and sleeping in misty fields.

One of the last nights in the park, I made a fire out there and watched the daylight come down in patches. A group of climbers about half a mile up the road were packing up their gear. I could hear scraps of their conversation echoing through the dry air.

There is a place in Joshua Tree called the “Heart of Rocks.”

The trees themselves, Yucca brevifolia, deserve special mention. They are unusual, Seuss-like, and everywhere in evidence up in the Mojave. They live at higher elevations; in the national park they thrive in Lost Horse Valley, but disappear when you descend to the lower Colorado Desert. The name was coined by Mormon travelers in the mid-nineteenth century. The trees reminded them of the Biblical Joshua, raising his hands to the heavens.

P. In Celtic spirituality there is the idea of “thin places.” Evidently heaven and earth are only three feet apart, but in a thin place, they’re even closer. In these places the boundary between heaven and earth is translucent and the divine can be more easily apprehended.

It has been proposed by some string theorists that parallel universes exist right before our eyes, just micrometers away, but we can’t perceive them because they are shifted not across any of our familiar three dimensions, but across some other, much subtler dimension. They are just micrometers away, but micrometers in a direction we cannot see.

Music dramatizes time, makes us aware of the passing moment, makes us feel the seconds. Certain musical experiences might just shift us in one of those odd unseen directions, might lift the veil and create a thin place.

One night at the cabin in Joshua Tree, in the monolithic darkness, I sat listening to Julius Eastman’s Gay Guerrilla.

There has been a revival of interest in Eastman since the first commercial recording of his music appeared in 2005, a long fifteen years after he died alone in Buffalo, New York. In the early eighties he was known as a vibrant, controversial, politically engaged composer and performer in the new music scenes surrounding New York City and SUNY-Buffalo. He disappeared from the music scene around 1983. He evidently struggled with drug and alcohol abuse during the late eighties. Little has been published about this dark period of his life and what brought it on.

Rumors of his death had circulated more than once before, and it took eight months for an obituary to appear in the Village Voice. That article by Kyle Gann marks perhaps the moment when Eastman ceased to be a man and began his new life as a figure of myth.

His music remained forgotten, scraps of handwritten scores packed away in attics and trunks, until around 1998, when composer Mary Jane Leach set out to find an arresting multiple-cello piece she remembered from a concert in 1980. This search culminated in the 2005 release of the three-disc set that has subsequently introduced most of us to Eastman’s music.

The three multiple-piano pieces, Gay Guerrilla, Evil Nigger, and Crazy Nigger, lit my ears on fire when I heard them for the first time in September 2008. The music is strong, expansive, uncompromising. Each piece begins from a unitary idea and expands steadily outward in every direction to create immense spheres as encompassing as they are fundamentally geometrically simple.

The titles, though not as viscerally shocking now as they were in 1980, raise questions. Eastman was a black, gay, politically outspoken composer during the ‘60s and ‘70s, and ‘80s. Obviously it was important to him to reclaim certain contested linguistic terms.

He once said that Gay Guerrilla was about glorifying gay strength and resistance. It begins with patient repeated notes, like the steady forward paces of a silent army, an army of the geographically and politically dispersed. The range shifts lower, the dynamic increases. Single notes give way to repeated octaves. The pianos pulse away and toward one another, at one moment dissipating, at another collecting into edifices of unanimous rhythmic force.

At the apex, one by one, in a multitude of keys, the pianos break the stream of physical resistance represented by the unified rhythmic motive and leap into grand statements of the Lutheran hymn “A Mighty Fortress Is Our God.” 

It must be after the words of Gann’s obituary that everyone now refers to this moment as a reinterpretation of the hymn tune into a “powerful, wordless, gay manifesto.” It’s a clear suggestion, based on the title, Eastman’s words, and his political proclivities. But it’s also a dramatic enough musical moment that its power can exist free of any specific social referent.

Some associates blame Eastman’s frenetic and unreliable personality for the decline of his career and life. Others, including his brother, assertively place the blame upon a society systemically dedicated to the squelching of black genius.

It is only through the curatorial efforts of Gann, Leach, and others that we know Eastman’s music at all. Last year Jace Clayton, also known as DJ/rupture, released an album called The Julius Eastman Memory Depot. There is a complementary performance piece called, yet more poignantly, The Julius Eastman Memorial Dinner. Clayton envisioned an alternate universe in which Eastman is widely beloved, in which dozens of actors apply to impersonate him at special events. The music reinterprets Eastman’s, building from and around it, applying digital processes, stretching and twisting the original notes and structures.

“Reverence,” Clayton writes in the notes, “can be a form of forgetting.”

Many of Eastman’s scores were lost in the eighties when he was forcibly evicted from his New York City apartment. According to his mother, he wrote a symphony in his final years, but no one knows where it is.

P. One can lose a great deal of time on Wikipedia reading about Martian geography. It turns out that the planet’s northern hemisphere consists of relatively smooth plains, while the south features dramatic impact craters. One of these, the Hellas Planitia, resulted from an asteroid impact some four billion years ago. The crater is about 1,400 miles wide and 23,000 feet deep. Along Mars’ equator there is a canyon system, the Valles Marineris, that stretches over 2,500 miles from end to end. There is also a volcano, Olympus Mons, that stands fourteen miles high, about three times taller than Mount Everest.

Someplace in the northern hemisphere, in a transitional zone between the craters and the plains, sits a region that perhaps was coastal in some distant epoch, named Cydonia after an ancient Cretan city whose inhabitants were noted for their skill in archery.

NASA’s Viking 1 spacecraft reached Martian orbit on June 19, 1976. The ship’s lander decoupled and headed for the surface the following day. It landed in an area called Chryse Planitia (Greek for “Golden Plain”). It is a flat area largely devoid of geological interest, chosen for its relative safety. The lander took a series of dramatic photographs. In the first color image, sent on June 21, the volcanic landscape and its deep reds are undeniably reminiscent of the American Southwest.

Popular imagination has seized, though, upon another Viking 1 photograph, a picture of Cydonia taken from orbit. It captures a prominent mesa, roughly a mile in length, that bears an incredible resemblance to a humanoid face.

The Viking program’s chief scientist quickly dismissed the resemblance as a “trick of light and shadow.” But thirty-five orbits later, another photograph of the same region, shot with a different sun angle, shows the same face.

The face was seized upon by theorists of extraterrestrial life. It was just as immediately seized upon by scientific skeptics, who found it a pure example of human credulity.

More recent orbiters have given us higher-resolution photography that effectively dispels the idea of the Face on Mars. A beautifully shaded picture from the Mars Reconnaissance Orbiter, shot just a few years ago, offers a much clearer look at the mesa’s contours. It is just a Martian hill. And yet once you’ve seen the face, it is difficult to look at this photograph without seeing its outline below the surface details.

There is a word, “pareidolia,” taken from Greek roots meaning “wrong image.” Pareidolias are random packages of information within which the observer sees an image deemed to be significant. Our predilection for seeing human features in geological formations are the most common example. The countless spottings throughout history of Jesus, Mary, and other religious figures in trees, clouds, and grilled cheese sandwiches would also fall under this category.

Pareidolia describes specifically groundless images or sounds perceived. The more general term is “apophenia,” the experience of seeing meaningful patterns in random data -- the identification of meaning where, purportedly, no meaning exists.

Where, exactly, is significance? And what is an example of a mesa that means nothing?

In the Navajo Nation nearly every prominent geological feature, and many of the ostensibly insignificant ones, has some sacredness to it. They all play some role in that culture’s long and complicated creation story, a progression of four worlds, a steady pulsation of balance and imbalance. At the dawn of the current human era, a deity named Monster Slayer trekked from Navajo Mountain east to Mount Taylor, doing battle as he went with the alien gods that were terrorizing life on earth. Their fallen corpses ossified to become the dramatic rock formations of Monument Valley in Arizona.

It would be ridiculous to posit a face or other significant feature in such a mesa. We don’t need to look for significance. It is already there.

Aren't we excited about THIS: here, friends, is the first Grant Wallace Band music video, with animation by the fantastic Alex Mitchell.

And this here is our latest demo, "The Game of 58 Holes."

Our next show is December 5th at the Chicago Cultural Center, as part of their Loops and Variations series.

We're hard at work on our new mini-musical, Fo'c's'le, which we'll premiere with members of Ensemble Dal Niente at Constellation Chicago on January 5th.

And hey: here are the Wölfli Songs, a haunted set of folk carols that I wrote in Banff in February 2012. I've posted them before, but this is a brand new recording.

P. Austin, Texas is home to the world’s largest urban bat colony. Some one and a half million Mexican free-tailed bats live under the Congress Avenue bridge. Around dusk they come streaming out for their evening hunts, which result in the daily slaughter of innumerable mosquitos. A coterie of tourists and bat-lovers gather on the bridge nightly to view the proceedings.

The Texas state capitol rises to the north, a beautiful construction of limestone and sunset red granite. It was mostly built by convict labor. The grounds contain at least one example of every tree native to Texas.

The first night I spent there, we saw the bats and drove south on Congress to Amy’s Ice Cream. There was a drum circle going on in a vacant lot behind the store. It was May, and hot. The light bent around in the dusky heat. I was in love with Austin immediately. People frequently exposed to hippie culture seem to tire of it and grow skeptical. I grew up in a blue-collar community in Iowa, so I still find it refreshing, though I’ve generally partaken of it cautiously, dipping a toe or perhaps a foot rather than submerging myself fully disrobed.

When I think of Austin now, four years after moving away, I think of hot mornings drinking coffee with spicy breakfast tacos on a grubby patio someplace; I think of warm humid evenings with the party spilling into the backyard, rope lights and picking sessions; I think of walking the dark alleys by myself. I think of the last day I lived there, when I drove out into the hill country to a place called Krause Springs. We brought a guitar and a banjo and a cooler full of Lone Star. There was an achingly picturesque tire swing, up high so you could do a flip or two before you hit the water. It is actually a perfect swimming hole, hidden away in the vines and brush. It is near a town called Spicewood. I think Willy Nelson lives out there.

There is a thing in Austin called the Ham Jam.

Every first Monday of the month, a sixty-something bachelor named Daren opens his house to the city’s acoustic music community. Dozens of musicians attend, and from 9 p.m. until the mystical hours of the morning, music pours from every corner and out every window. People walk into the kitchen and grab a beer and some fresh baked ham (it’s not just a clever name), then join the old-time jazz session on the back porch or take their banjo upstairs to one of the bedrooms where songwriters swap their newest creations. A wildly bearded gent with an accordion sings Russian folk tunes on the stairs. Slim Richey, an old timer wearing a red suit and a fedora hat with a feather, lays down blues licks on the guitar and knows every single tune that is called. People have left their business cards on the kitchen counter. Slim Richey’s just says “Expert.”

A handsome young man demonstrates Tuvan throat singing and plays doshpuluur in the hallway. This is Eliot Stone. Two of my Chicago friends had met Eliot while studying in Amsterdam during undergrad. He is one of those people who becomes interested in something and then attends to it with laserlike focus for a period of months. I befriended Eliot during my final months in Austin. He had lived there for some years after growing up in a small west-Texas border town. He is one of the characters you see haunting particular spots in Austin that give the city such vibrant human wallpaper. Eliot builds didgeridoos out of cactuses and plays them in the traditional Aboriginal style. He once hunted down an enigmatic instrument-maker in Switzerland to purchase a rare hand drum called a Hang, which looks like a flying saucer and sounds like a steel drum and evidently made him an unusually popular busker during South by Southwest.

I hung out with Eliot only a few times before we decided to go on a road trip to Big Bend. We stopped in Bracketville, his hometown, and drove a golf cart around the trails late at night until we got it stuck in a hollow and had to walk back. We made it to Big Bend on an uncharacteristically rainy night and shared a campsite with a colorful cohort of French Canadians. We hiked, sat in the hot springs, and attended a party on a pirate ship. I only saw Eliot another few times before I left Texas. He was living a ways off in west Austin, in a large house with a tremendous view and an infinity-shaped pool.

The day I left Austin I packed my one-bedroom apartment by myself and carried my possessions down four flights of stairs. It took about eleven hours and developed into one of the most emotionally harrowing days of my life. The first catharsis occurred when I unpacked my file cabinet and saw my life spread out across the floor, my old scores and papers, letters, concert programs. I was listening to my friend Eric Malmquist’s Symphony for Strings and Percussion. It was too much to bear, seeing my whole life on the floor like that.

The second catharsis happened as I carried objects down the stairs at around five o’clock in the afternoon. As the hot May sun began to relent, the evening became almost unjustly beautiful. The wind brushed the trees that rose above the windows of my apartment.

I felt they had a question for me.

I had loved Austin from first sight and moved there knowing absolutely no one. My first months there were lonely and difficult, my academic trials there had forced me into new self-conceptions. I had undergone baroque romantic turmoils there, made beautiful fascinating friends there, become myself there. I’d always felt I had a relationship with the city and not just its people, not just my Austin friends but Austin itself. I’d adored it with the affection a twenty-three-year-old might have more commonly reserved for a cute and mysterious young cellist.

Why are you leaving, Austin asked me. Where are you going. When are you coming back.

P. As a composer it is most terrifying to consider the piano trio (piano, violin, and viola). It’s difficult to balance these three instruments, the piano being so very large, and to make them equal partners. It is not at all like the string quartet, harmonious and egalitarian. In the piano trio there are dynamics to be negotiated, inequalities to be addressed.

Mozart and Beethoven wrote heaps of piano trios; the famously prolific Haydn wrote forty-five. I often find classical examples in the genre to be boring and practical. They sound like they were written as incidental music to passingly entertain people at a party, which is in fact often the case.

And then there is Maurice Ravel’s one entry. He wrote it in 1914, shortly after France entered World War I. He wrote it quickly so that he could volunteer for the army. 

Ravel was a fantastic orchestrator and a brilliant--possibly even underrated--melodist. What’s remarkable in the first movement is not merely the melody but how it is bent and shaped in time. The tempo is always changing, often slowing, with a floating, subaqueous result. The development section has some flash and fire, but it is brief, and then there we are in our little boat on the ocean again.

Everything in Ravel is exquisitely crafted. Stravinsky once compared him, somewhat chidingly, to a master Swiss watchmaker. No detail is left to chance. Every line is perfectly angled and every surface is sanded smooth. Each one is calibrated to the physics of the violin and cello bows. Time is measured in bow length and weight. Nothing extends past the changing of the bow. Like the sequences of up- and down-bows that constitute a violin line, Ravel’s music climbs and descends.

Ravel’s distinct personality operated within a traditional compositional paradigm. When he wrote this trio in 1914 he did so using a traditional four-movement model, with the opening movement in the classic Sonata form used for the opening movements of sonatas, symphonies, and major chamber works since the Classical era. 

The idea in Sonata form is that you get music (a primary theme), some other music (a secondary theme), and then things get complex and develop, and then you get back to the original music. ABA. But things change over time. The first time you hear that secondary theme, it is in a different, contrasting key. You don’t get to hear that music in the piece’s primary key until the recap at the end of the movement. If the piece starts in G Major, it’s probably going to go to D Major, and not return to G until that triumphant ending section.

You travel and visit places, and then you go home.

The first movement of Ravel’s trio begins in A Minor. The secondary theme is in A Minor. The development section proceeds. Then we hear the themes again, both in A Minor. He never transposes the second theme. We stay at home. Perhaps we gaze at other places through the window, or imagine them in the pages of a book. 

But the key changes at the end. At last we get warm C Major and hear threads of that primary theme, like waves at night lapping against a beach you cannot see.

P. The puzzle runs like this:

As I was going to St. Ives,
I met a man with seven wives.
Every wife had seven sacks,
Every sack had seven cats,
Every cat had seven kits;
Kittens, cats, sacks, and wives,
How many were going to St. Ives?

If you do the math that’s seven wives, 49 sacks, 343 cats, and 2401 kittens--surely the recipe for an adorable, scratchy, and highly contentious trip to St. Ives. The full complement is 2800, plus the happy husband himself.

Are we to count the narrator, who is also going to St. Ives? Then the number is 2801, again assuming that we aren’t intended to count the polygamous, feline-loving patriarch of the operation. The grammar seems to indicate that we are only to count the kittens, cats, sacks, and wives--so I suppose the narrator should be left out, unless she herself is a wife (or, it bears suggesting, a cat). There is no way of determining this information, which makes the puzzle fundamentally undecidable.

The situation becomes yet more tenuous when you consider that the narrator is going to St. Ives, but the party he “meets” may in fact be coming the other direction. Which would make the number of kittens, cats, sacks, and wives proceeding down the St. Ives highway either zero or one, depending again on the identity of our mysterious narrator.

As a mathematical puzzle it is simple and not basically interesting. As a grammatical puzzle, it charms with its ambiguities.

P. Rugby, North Dakota is the geographical center of North America. Amtrak’s Empire Builder train stops there once daily, in the morning, as it passes along highway 2 from Minot, North Dakota toward Montana and Glacier National Park.

The railroad created Rugby. At first it was to be called “Rugby Junction,” after a famous railroad station in England. The ploy was evidently to attract English settlers to the area. The English settlers were not convinced. As of the 2000 census the community still identified 50% German and 40% Norwegian. About three thousand people live in Rugby.

A large cairn in town marks Rugby’s geographical claim to fame. According to the U.S. Geological Survey, it stands about fifteen miles from the actual center of the continent. This is not so many miles, in this part of the country. Rugby is 67 miles from the nearest major city of Minot, North Dakota. It is 223 miles from Fargo, 458 from Minneapolis, 838 from Denver, and 1332 from Seattle.

Much closer is the Canadian border, only 45 miles north. This is the site of the International Peace Garden, a 2,339-acre botanical garden lying along the world’s longest unfortified border. The park can be visited without passing through customs.

Just south of Rugby is another attraction, the Northern Lights Tower. This 88-foot steel sculpture is lit at night to pay homage to the beauty of the aurora borealis. It is a somewhat unusual monument in that it seeks to honor not just a region or political area, but the whole continent at whose center it stands. The tower is currently under construction to improve the lighting.

The train doesn’t stop for long in Rugby. A few passengers disembark, a few board the train, and you roll on toward Montana. As you enter the trees on the west side of town, a sign on the back of the S&S Laundry building reads, “Rugby Says Hi.”

P. As the train pulled out of Rugby I was listening to Horatiu Radulescu’s Fourth String Quartet, which may have contributed to the moment’s atmosphere of subtle menace.

Radulescu, who died in 2008 a fine Romanian mystic composer and impeccable kook, wrote using spectral techniques of composition. This is one of those musical terms almost universally disavowed by those most associated with it. It has to do with basing musical decisions on the physical, harmonic properties of tones. The result is often a shimmering, overwhelming, waving sort of sonic texture.

As a student Radulescu named a piece after the Polynesian god Taaroa. His teachers didn’t like this because they thought it was “mystical” and “imperialistic.” In the early seventies Olivier Messiaen said he was “one of the most original young musicians of our time.” Many of his fellow students disagreed.

My favorite thing about Radulescu is his invention of the “sound icon,” which is a concert grand piano retuned to his own spectral schema, turned on its side, and then bowed. He would write a piece for 16 or 17 of these sound icons. Sometimes there would be also, say, a viola. He once wrote a piece for forty flutes. Often these go on for an hour or so. The effect is immersive, psychedelic. Or rather, I’d assume it is, as like most people I’ve never heard Radulescu’s music live. Most concert presenters are loath indeed to convert their fine pianos even temporarily into sound icons.

So the Fourth String Quartet is actually scored for nine quartets. Typically (if anything regarding Radulescu’s music can be considered typical) it is performed by one live quartet with the remaining eight pre-recorded. This group of eight quartets features instruments retuned dramatically and enthusiastically such that no two strings are tuned to the same pitch. Radulescu imagined them collectively as “an imaginary viola da gamba with 128 strings.” The central, live quartet plays in a traditional tuning adjusted slightly lower than is conventional.

There is a coherent mathematical foundation to all of this, to the intonational decisions being made. When people say music sounds mathematical, the subtext is not generally one of pleasure. We have developed a linguistic fissure between the mathematical and the sensuous that simply doesn’t make sense in music. All music is of course mathematical, as it concerns waves of different frequencies related by different ratios. I suppose what some listeners dislike is when the construction of the music, its formal manifestation, sounds mathematical--or perhaps the more precise word is mechanical. And mechanism is clearly not among Radulescu’s sins. This music as it unfolds is exactly as mechanical as a wolf spider crawling across a window. The music creeps along at a rate it appears to have chosen, stopping when it will, hesitating, looking back, glancing left and right. Its forward motion is not balanced or decisive in a manner that suggests premeditation. It is deeply organic. That word is overused, with vague referent, by composers and critics of new music. I use it to mean that this music sounds distinctly, terrifyingly, alive. Also large. And perhaps completely beyond our control.

Radulescu built the music, sculpted this sonic construction, to reflect individual spiritual questing. The mode is one of ever-growing ascents with intermediate descents. A final, triumphant ascent crowns the fifty-minute form.

He worked on the piece for eleven years before it was premiered in 1987.

The subtitle of the quartet, obliquely enough, is “infinite to be cannot be infinite, infinite anti-be could be infinite.” Radulescu was very much into the writings of Lao Tzu. The subtitle is “hommage á Leonardo da Vinci.” The analogy to the great inventor, a man whose imagination knew no boundary, is an evocative one.

P. The Penrose steps, also known as the impossible staircase, make four ninety-degree turns in two dimensions to loop back onto themselves. They thus climb continuously, such that a person could ascend or descend them forever without getting anywhere at all.

It’s a variation of the same geometric principle exhibited by the Penrose triangle, the classic “impossible object,” which was made famous by the mathematician and physicist Roger Penrose in the 1950s. Its three bars appear to cross behind and back in front of each other. Penrose called the triangle “impossibility in its purest form.” The eye accepts it as a valid construction. It is only when we consider the object, imagine it projected into our own beloved three-dimensional space, that we deem it impossible.

The Penrose stairs were first discussed in a paper Penrose wrote with his father in 1959, but made immortal the following year in M.C. Escher’s lithograph Ascending and Descending, which features faceless figures passing each other as they travel up and down an impossible staircase.

Escher had previously depicted geometrically challenging staircases in House of Stairs and Relativity, both of which featured stairs in multiple directions moving toward and away from the viewer. But the simple looping staircase in Ascending and Descending has a special elegance, paired with the strange mystery of the monkish people utilizing it.

There are twenty-five figures on the steps, walking in both directions. One story below, a lone figure stands on a balcony, gazing up at the stair-climbers. 

Two stories below him there is another, sitting pensively on what must be, nominally, the front steps of the house, gazing across the featureless ground upon which the house sits, away off the frame of the drawing. Below the steps, a stairway opens down into a lower level. Near the top of this staircase, a few tiny emblems are carved into the wall.

Escher’s Waterfall, printed in 1961, explores similar territory. Water falls through a wheel and flows, apparently downhill, along a zig-zagged aqueduct reminiscent of two Penrose triangles stitched together--and then reaches again the top of the waterfall. The water always flows back into itself. Escher, like Radulescu, was a “mathematical” artist.

Again my attention is pulled to the interior rooms, the lower balconies. Two figures are represented in Waterfall. One admires the cascade, leaning back on the wall. Another casually hangs clothes from a line. I wonder about these peoples’ lives, about the rooms seen through all those windows. I wonder about the strange whimsical plants below the mill, the trees and ramparts and structures seen in the background. I imagine the fictional engineer who built this city. I wonder who designed the polyhedral capitals that crown the aqueduct’s two grand columns.

In medieval Eurasian churches there is not infrequently seen the symbol of the three hares. They chase each other in a circle, their ears pointing to the center. But each animal shares its ears, one each with its pursuer and its pursued, so that only three ears are actually depicted.

No primary documentation has been found to explain this design’s symbolic meanings. As seen in Christian churches it is generally assumed, perhaps facilely, to be symbolic of the Trinity; yet it originated in sixth century cave temples in China, and was a popular Buddhist emblem before it was adopted by medieval Christians. 

The symbol’s meaning seems to shift based on its context.

Emerging from pagan cultures the emblem seems to reflect fertility and the moon cycle, as the hare was traditionally associated with lunar deities. Many cultures have gazed at the moon and seen the shape of a rabbit in its distant hills and craters; and of course, the rabbit is a famously fertile beast. Female hares can carry two distinct litters of offspring at one time. The fertile rabbit, along with its patron Germanic goddess Eostre, gave us the Easter Bunny--still a popular fertility symbol surrounding the Vernal Equinox, although we don’t much culturally recognize it as such.

The Christian significance of the holiday is akin, and resurrection is clearly a powerful symbol for that time of year. At some point it evidently became dangerous for the church to admit that the principle of rebirth applies metaphorically to all of us and to the earth, and not solely literally to Jesus of Nazareth.

The equinox, of course, is the time when day and night are of equal length everywhere on the planet.

The gray edifices of Escher’s lithographs and mathematical purity of Penrose’s formations fail to suggest fertility like the pastel colors of Easter eggs. They do convey, in a forceful, visceral manner, the existence of endless cycles.

P. Rogers Park is on the far north side of Chicago, all the way north and all the way east. It’s above the northern terminus of Lake Shore Drive, so most of the blocks end in beaches. It’s the most ethnically diverse neighborhood in Chicago, with large groups that are white, black, Mexican, Jewish, and African. The neighborhood is rough around the edges in a way that makes it colorful and only occasionally dangerous. It still has a fairly foul reputation amongst young Chicagoans who live in posher, whiter neighborhoods.

There are a whole ton of great Ethiopian restaurants, which all have good coffee and injera and saucy meats. There is one little Korean diner, right by the el tracks, that will make you a kimchee omelet on the cheap. There is the Heartland Cafe, a scruffy and inconsistent but somehow lovable left-wing cafe in a huge old house with a giant screen porch. There’s barely anyone ever in there and you’re always wondering how they stay open.

Clark Street is full of pawn shops, Mexican restaurants, some of which stay open late, and traffic.

Loyola Park stretches along the lakefront north of its eponymous university for nearly a mile. These are some of the largest and least occupied beaches in the city. You can sit out there at night and watch the planes come in from over Lake Michigan. One by one they emerge, first static like little sky candles, then growing and becoming mobile.

Rogers Park was once the confluence of two Native American trails, the paths of which are now traced by Rogers Avenue and Ridge Boulevard. It is named for one of the original white settlers of the area, Phillip Rogers, who worked as a trader there beginning in the 1830s. Like many of the outlying neighborhoods, it was a village that gradually became encompassed during the immense growth of Chicago in the mid-nineteenth century. The city officially annexed Rogers Park in 1893--the same year as the famous world’s fair that brought international attention and energy to a Chicago still rebuilding from the devastating fire of 1871.

Chicago is built on an extremely consistent grid. Roads like North Avenue run straight west from the lakefront to the Fox River in the far western suburbs. Many of them continue on as state highways--North Avenue, in the form of highway 64, travels west to the Mississippi River and on into Iowa. This makes the few diagonal roads in the city, like Ridge, extremely off-putting. Many of these diagonals are major thoroughfares--Milwaukee, Elston, Clark. Where they hit major north-south-east-west intersections, a strange thing happens to one’s spatial perception. After traveling on a grid with strict adherence to the four cardinal directions, suddenly a panoply of options opens.

There is a certain, subtle Midwestern warmth to Chicago underlying a basically cold, prickly, urban character. The winter is long, gray, anesthetic. We’re all in it together. And yet even on the crisp autumn days when everything appears to be perfect, I can’t deny feeling a sense of sadness just beneath the surface. It bubbles up in the faces of the strangers I see on the street, the old-timers who have never lived anywhere else, the twenty-somethings who consign themselves to the dream of upward mobility.

Each red line train traverses the city from the industrial wastes of the far south side past Chinatown, underground as it crosses through the heart of the loop, back above ground to the historic, comely and well-kept houses of Lincoln Park, past Wrigley Field and alongside the border of an enormous graveyard, past the Green Mill jazz club where Al Capone was a frequent customer, through the Vietnamese community of Uptown and the rapidly gentrifying Edgewater neighborhood up again to Rogers Park.

Mayne Stage is right off the train stop at Morse Avenue. They host rock shows, comedians. They project Bears games on a big screen; I was in a packed house there to hear Vijay Iyer’s trio. Once a year or so, they host Chicago contemporary-music darlings Ensemble Dal Niente to play some strange new sounds.

P. We decided to sit in the front row, and Professor Bad Trip was loud.

Fausto Romitelli had composer-cred. He studied with Franco Donatoni and Gerard Grisey and spent a bunch of time at IRCAM in Paris. He was also interested, in some manner or another, in rave culture and psychedelic rock. Professor Bad Trip has been compared to Miles Davis’ 1970s music and The Doors. To those unacquainted with the names mentioned to begin this paragraph: these comparisons are unusual for a European composer of modernist pretensions.

Perhaps this explains the piece’s somewhat controversial reputation among composers and performers of new music. I don’t think everyone at the concert loved it, but we sure were ready to talk about it when the show was over, I’ll tell you that much.

Romitelli wrote the piece in 1998-2000. He died in 2004 after a long battle with cancer. He was only 41. Professor Bad Trip was his magnum opus. It is in three movements, which he titled as “Lessons.” Ensemble Dal Niente performed the three lessons separately, with short intermissions and interlude pieces in between.

You can hear the whole piece on Youtube, if you want, but it isn’t the same. Hearing it live was less a musical experience and more a sort of initiation.

So we were in the front row, and the sound was intense, and shortly after the music began, I closed my eyes and began to see things.

I experienced powerful visions throughout the evening. I’d report them to my friends between movements. Breaks in the music, even stepping outside the hall did not interfere. When the music began again, I’d drop back into the space.

During the first lesson I was driving through the Middle Park valley of Colorado. I was somewhere along highway 40, following the Colorado River, somewhere west of Byers Canyon and east of Kremmling. The valley is wide open, there, and as I drove it began to fill with sand that steadily streamed from the sky like I was in the bowl of an immense hourglass. Then the valley was full of sand and I was walking on the dunes. I came across a buried house. The chimney was sticking up out of the sand. I could see inside that the house was filled from floor to ceiling with hardcover books.

During the second lesson I was in Carlsbad Caverns in New Mexico. The lights went out, and I was alone. In the darkness I found that when I touched the rock formations they would glow a bluish green from within, and where I touched them, lichens and mosses began to grow.

During the third lesson I saw an old mansion on a small hillside, and then I saw a tunnel in the ground below the mansion. The tunnel filled with rushing blood, which came up into the house; and then from outside the house, away down the hill, I saw the windows burst and blood come spraying from every window and door.

P. In Homer’s telling, Daedalus’ labyrinth consisted of a single path to the middle. It was a dancing path for Ariadne, the daughter of King Minos. Evidently prehistoric labyrinths were built as paths for ritual dances. In this version, Daedalus’ labyrinth was simply a winding trail, not a building.

Only in later versions of the story did the labyrinth become a tremendous edifice, a maze with multiple forking paths and dead ends. Ovid wrote that Daedalus constructed the labyrinth so cunningly that even he could barely find the exit. Today “labyrinth” and “maze” are often used synonymously. Traditionally, though, a labyrinth is more specific. A labyrinth has one path in and the same path out.

Eventually Daedalus’ story evolved to include the imprisonment of the Minotaur and its death at the hand of Theseus, who solved the puzzle of the labyrinth simply: Ariadne gave him a ball of thread, which he used to trace his path through the maze. The two then fled from Crete.

Daedalus has come to represent the archetypal skilled artisan. He focuses on his craft and not its ends. The labyrinth was built so meticulously that defeating its monstrous occupant became a difficult task indeed. The same moral is illustrated more dramatically by the later tale of Daedalus and his son Icarus. Enraged at the failure of the labyrinth and the elopement of his daughter, King Minos imprisoned Daedalus and Icarus. Daedalus built two sets of wings and the two escaped, but Icarus flew too close to the sun, melted his wings, and fell to his death in the ocean.

For Argentinian author Jorge Luis Borges, labyrinths were a complex metaphor that reflected the inscrutable mysteries of the world and of divinity as well as the human impulse to construct ever more complex artifice to reflect or even surpass that mystery. In his story Two Kings and Two Labyrinths the Babylonian king builds a tremendously complex maze and tempts the Arabian king to lose himself within it, which he swiftly does. The Arabian king responds by conquering Babylonia and leaving the defeated king to die in the desert, explaining that his labyrinth “has no stairways to climb, nor walls to impede thy passage.” God has created the largest and strangest labyrinth of all.

One of Borges’ most famous stories, “The Garden of Forking Paths,” imagines a Chinese scholar named Ts’ui Pên who left a successful political career to write a deeply complex novel and simultaneously construct an equally complex labyrinth. He was murdered soon thereafter, leaving behind only an “indeterminate heap of contradictory drafts” that constituted both the novel and the maze, which used time as its medium and created a panoply of forking pathways from event to event.

In the medieval period hundreds of labyrinths and turf mazes were built in Europe. In Scandinavia they are often found in fishing villages on the coast. It is thought that they were built to trap malevolent winds, spirits, or trolls that might interfere in a successful fishing trip. It was not until later that labyrinths took on their current association with contemplation and prayer. The modern mystic walks the labyrinth to achieve a quiet mind and close association with the present moment.

In the Hyde Park neighborhood of Austin, Texas there is a labyrinth in the yard behind a Unitarian church. I used to find it on my runs, jog the path to the center and back, and then continue down the roads and alleys of the neighborhood.

Daedalus escaped Crete, surviving the flight that claimed Icarus. He found asylum in Sicily, where he built a great temple to Apollo. He displayed his wings in the temple as an offering to the god. King Minos came searching for Daedalus, traveling from town to town with a riddle he knew only the great craftsman could solve. He carried a spiral seashell and asked that a string be run through its apertures. Daedalus solved the puzzle easily, tying a string to an ant which then walked through the interior paths of the seashell. Once again, a thin thread defeats the complex maze--this time a labyrinth of nature’s creation.

Minos demanded Daedalus be handed over. King Cocalus, who had been the craftsman’s patron, insisted that Minos first have a bath and enjoy his hospitality. Minos did not survive this bath. Depending on the story, he was killed either by Cocalus’ daughters or by Daedalus himself.