MATH AS ART

just as math and music are inextricably intertwined, so too are math and art. case in point: the mandelbrot set, a set of points on the complex plane, the boundary of which forms a fractal, a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole, an instance of self-similarity or feedback based on recursion.

for my purposes, the math behind the musings of benoit mandelbrot and others is interesting, but not nearly as much as the jaw-dropping visual representations of the formulae. these visuals have entered the popular consciousness, as presented in books, calendars and other collections of art.

can a visual depiction of a mathematical formula really be considered as art? absolutely. if art is the deliberate arrangement of visual elements in a way that appeals to the senses or emotions, then fractals are art every bit as much as are the works of michaelangelo, picasso, or pollack, each of whom created controversy by stretching the boundaries of our understanding of aesthetics and visual expression.

behold, and see for yourself (click to enlarge). please be sure to click on the links above for "mandelbrot set" and "fractal", and check out the animated illustrations !!

MANDELBROT SET

















JULIA SET

HALLOWEEN CANCELLED

for most of my adult life, i enjoyed the annual parade of children in costume that appeared at my door seeking treats on halloween. all that changed nineteen years ago today. on halloween eve, 1990, i was riding my silver wing on a busy traffic artery in suburban philadelphia, on my way to a job interview, when a little old lady in a big ol' cadillac in the oncoming lane made an illegal left turn, right in front of me. i was boxed in by traffic, and barely had time to hit the brakes before impact.














the collision sent me flying across two lanes of traffic, to land on my back, unconscious, on the sidewalk. when i came to, bystanders were gathered around, the other driver was claiming loudly that she "didn't even see him" (me), and the ambulance crew had just arrived. what followed was a nightmare. i was strapped onto a wooden backboard, my helmet still on, and taken to the nearest ER. every part of my body seemed to hurt, especially my neck, back and left shoulder. i spent the next eight hours on that backboard, without benefit of pain medication, until all x-rays and MRIs had been taken. the board itself became a torture device beyond description, digging into my vertebrae, shoulders and tailbone. after an eternity, blessed morphine.

long story short, i'd suffered a broken clavicle and separated left shoulder. they could find no evidence of damage to my back or neck, though the full-face helmet probably saved my life -- the portion protecting my chin and lower face was cracked in two. i spent many weeks in pain, wearing a sling to immobilize my left shoulder as it healed. i even was successful in landing a different job. and, since the other driver was cited, i eventually won a modest medical settlement.






















but i never got to pass out treats that halloween, and each subsequent year has found me experiencing PTSD symptoms as halloween approaches. i associate the holiday with horrific pain. intellectually i understand the connection, emotionally i cannot escape it. so i've sadly become one of those who turn down their lights on the festive night, trying to mentally numb myself through the evening. such a shame.

that was my second near-fatal motorcycle accident, the first having occurred in tucson five years earlier, under nearly identical conditions -- major street, little old lady in a big ol' oldsmobile pulls in front of me. i'm an extremely safe and cautious rider, but the simple facts are that (a) the smaller size of motorcycles and bicycles doesn't fit the search image of "traffic" for most drivers, and (b) many drivers should not be allowed behind the wheel. i've long been an advocate of including both a practical driving test and a written test for EVERY driver EVERY time he/she renews their license. there are too many inept, inattentive, or just plain idiotic people who are allowed to pilot those missiles on wheels that we call cars. and don't even get me started on those who use cell phones or texting behind the wheel.

still, i haven't lost my love for motorcycles. i would love to have another full-dress touring bike, perhaps a BMW. the freedom of a bike is the closest one can come to the sensation of flying without leaving the ground. you're travelling in three dimensions, not two, and all your senses are alive and heightened. just keep me away from little old ladies in big ol' sedans !!

RADIO DAYS

i grew up in rural northern montana, as one of the very earliest baby boomers. the times were simpler, slower, more meditative. family entertainment centered around the radio -- television was in its birthing years, and we didn't get our first black-and-white tv until i was ten or so. by then, the inner life of imagination fostered by radio and by reading had already imprinted on my thinking, and on my perception of the world.

close your eyes for a moment and imagine gathering at the kitchen table after supper, turning on the radio (AM only, with an analog dial -- FM radio and digital displays were in the distant future) for the evening's entertainment. i have vivid memories of the sonorous voices and imaginative sound effects on dramas like Gunsmoke, The Lone Ranger, Rin-Tin-Tin, Sergeant Preston of the Royal Canadian Mounted Police, comedies like Amos and Andy, Edgar Bergen and Charley McCarthy, Arthur Godfrey and The Art Linkletter Show, and spooky mystery shows like Inner Sanctum. i can still tell you the names of characters, the actors who voiced them, even the names of their horses.

and i can tell you exactly where i was, and the visions and feelings that ran through me, during particularly vivid episodes. those visions and feelings continue to nourish me today. even given the quality of tv shows such as Sesame Street or Mr. Rogers, the fact remains that while visual images do provide windows onto other places, other peoples, they have a dampening effect on one's imagination. is it coincidence that the generations raised on tv have a harder time grasping abstract concepts in school? you be the judge.

READING GROUP

as part of my determination to become more active socially, i've joined a reading group facilitated by one of the staff at my nearby barnes & noble. last night was the first meeting i attended. by coincidence, the group is reaching the end of its current focus, i.e. pulitzer prize-winning fiction. the book being discussed was The Surrounded, by d'arcy mcnickle. since i've been an avid reader of books by and/or about native americans for decades, the social issues presented weren't new to my awareness. i was struck, however, by the author's careful, graceful pacing of thoughts and events -- perhaps a reflection of the times (it was published in 1936).

just as relevant for me was being part of an intellectual discussion with thoughtful, intelligent people. as a single retired man, it can be too easy to isolate myself in the comforts of routine at home. good to be out, good to be interacting. it gives me hope for a next possible step: finding a writer's support group. until then, it's all good.

HUBBLE SPACE TELESCOPE

it's hard to believe that next year will mark 20 years since the launch of the hubble space telescope into earth orbit. this extraordinary piece of hardware has provided many thousands of visual images, from our solar system to deepest space. the data returned by hubble have been instrumental in refining with great precision the distances between objects in space, helping to refine estimates of the age of the universe. it also confirmed the theory that the vast majority of galaxies have black holes at their center, mapped small patches of sky that are the deepest (i.e. most distant) ever obtained at visual wavelengths (see image below, click to enlarge -- the majority of objects you see are not individual stars, but entire galaxies), and recorded the collision of fragments of comet shoemaker-levy 9 with jupiter in 1994, all with jaw-dropping visual clarity. the hubble space telescope ranks among the most prolific and useful tools ever devised by human ingenuity.

VAMPIRES AND OTHER MYTHS

i just love it when someone shines a bright scientific light on irrationality or superstition. for all you halloweeners, wiccans, religious literalists, and other "belief without benefit of proof" souls out there, check out this article on the physics of vampires, and see if it doesn't stimulate a few sleepy brain cells. if not, you'll probably at least find it amusing. now you must excuse me while i go file my canine teeth to a finer point.

SOLARY SYSTEM DEBRIS FIELDS

most people aren't that familiar with our own planet's neighborhood, the solar system. ask random friends to name the planets in order from the sun outward, and you'll see what i mean. of those who can, when the notion of debris fields is mentioned, their automatic response will be the asteroid belt which lies between the orbits of mars and jupiter. a smaller number will recall that far, far outside the orbits of the major planets exists a sphere of billions of asteroid-sized objects known collectively as the oort cloud, long thought to be the source area for the comets which periodically are pulled by the sun's gravity into a monumental elliptical orbit which invades the inner solar system, e.g. halley's comet or the recent comet hale-bopp.

it turns out that most comets probably originate in debris fields which lie much closer than the oort cloud. these fields are differentiated by their position relative to the orbit of our outermost planet, neptune. (yes, my children, pluto has been demoted from planet to dwarf planet status, and small wonder -- as it were.)

follow along. inside neptune's orbit are cis-neptunian objects, residing between the orbits of neptune and jupiter.

outside neptune's orbit are layered torus- or cloud-like gatherings called trans-neptunian objects, arranged in outward order as follows -- the kuiper belt, scattered disk objects, a few smaller assortments, and finally our old friend the oort cloud. it all makes for a much more complicated collection of objects which orbit our sun than most people ever imagined. following are illustrations of these complex assemblies, from inner to outer. as always, click on any image to enlarge it.

THE MARS-JUPITER ASTEROID FIELD

TRANS-NEPTUNIAN OBJECTS (TNOs)

SIZE COMPARISONS FOR LARGEST TNOs

THE OORT CLOUD

POTPOURRI

potpourri, as in a few random quickie topics, just for fun --

~~ The Goosenecks of the San Juan -- a deep oxbow series of meanders on the san juan river in southern utah. i had the great good fortune to be introduced to the goosenecks from river level, during a five day rafting/kayaking trip orchestrated by my old and dear friend irene. she was in her avon raft, and i was in a kayak borrowed from the university of arizona kayaking club. the san juan is a sweet little river, ranging from class I to III on the international scale of whitewater difficulty, just right for a then-beginner like me. a unique feature -- sand waves. the river bottom is sandy, and the current under certain conditions will sculpt rollercoaster-like waves on the substrate, which in turn generate a series of waves at the water surface. they appear, persist for a few minutes, then vanish. magical. oh yes, the goosenecks are featured prominently at the end of the movie "Thelma and Louise", though the location is mistakenly identified by one character as the Grand Canyon. (click on image to enlarge)

~~ wake turbulence -- disturbance of the air through which an airplane passes. at busy major airports, avoidance of wake turbulence is one factor which determines the spacing between arriving or departing aircraft, as well as following distance and relative position in the air. the primary forms are jet wash and wingtip vortices. vortex turbulence isn't limited to jets. small private aircraft generate it too, and design features like tapered or elliptical wings and wingtip mounted winglets are intended to minimize induced drag on the aircraft, and interference with following aircraft.

~~ Jackie Robinson -- the first African American baseball player to break the color barrier, when he started with the Brooklyn Dodgers in 1947 (the year of my birth) at Ebbets Field. he endured much racist abuse from fans and other players, but persisted in his career, helping the Dodgers win the 1955 World Series. Robinson was one of the early heroes in the desegregation movement, and remains an iconic figure in baseball history in his own right -- he was the first player of any race to win the Rookie of the Year Award, he played in six World Series, he was selected to play in six consecutive All Star Games, and was the first black player to receive the National League Most Valuable Player award, in 1949.

and th-th-th-that's all, folks !

PHOTOGRAPHY - NEUTRAL DENSITY

from wikipedia -- "this photo of strickland falls in tasmania, australia, was taken using a neutral density filter. ND filters reduce light of all colors or wavelengths equally, allowing an increase in aperture and a decrease in shutter speed without overexposing the image. to create the motion blur seen here, the shutter must be kept open for a relatively long time, making it necessary to reduce the amount of light coming through the lens." [NOTE: for motion blur of flowing water, a shutter speed of 1/8 second works well. click on the image to enlarge for a much better view.]

AFRICAN WILDLIFE

on 12 october i posted a description of christian the lion, who was adopted as a cub in london, and successfully returned to the wild in kenya. the video of christian's reunion with his onetime owners and lifelong friends, widely circulted on youtube, continues to resonate on the web.

christian's adaptation to the wild was overseen by renowned conservationist george adamson, who spent his life preserving africa's fauna and habitat, and who later was murdered by poachers. his work is carried on by his protege and partner tony fitzjohn. i refer you to their website, WildlifeNOW, a source for information on a number of projects, including an update on christian. i've since read the most recent edition rendall and bourke's book A Lion Called Christian, and recommend it highly.

PHEASANT HUNTER 1, GRIZZLY 0

some events just leave me speechless at the unutterable stupidity of humans. as described in an article in the choteau, mt, acantha, a party of four men were hunting pheasant in an area of dense undergrowth on the prairie just east of the rocky mountain front. this region is home to a population of grizzly bears, which are listed as a threatened species under the endangered species act. it was not an idle fancy which prompted taxonomists to give the grizzly the species name ursa arctos horribilis -- grizzlies are notoriously temperamental and violent in defending their territory and their young.

the prime directive for any hunter is to know your prey, including its territory, habits, preferred diet, and also the animals which share its habitat -- particularly large omnivores which might pose a threat to the hunter. of the hunting party in question, two were from alaska, and two were montana residents. all four knew (or should have known) better than to seek pheasants (which can easily be found along the edges of wheatfields and in hedgerows) in a dense grove of trees, shrubs and berry bushes that grew well over the hunters' heads, limiting their view. this is a recipe for predictable, avoidable disaster, and disaster is what ensued.

one of the alaska hunters, a 68-year old retired dentist, "surprised a radio collared female grizzly who was bedded down for the day with her three cubs." about 22 feet separated the man from the grizzly. defending her cubs, she charged the intruder, who was armed with a 5-shot semiautomatic 20-gauge shotgun. he managed to pump three rounds into her before she feel dead at his feet.

the acantha article is factual, noting that the hunter (rather lamely) noted, "i was just in the wrong place at the wrong time." gee, ya think? blundering around in known grizzly habitat in autumn, when females with cubs are feeding in preparation for winter hibernation. i submit one glaring observation -- these morons should not have been in that situation in the first place. it sickens me. now a grizzly is dead for no good reason, three cubs are orphaned, and a mighty hunter is thinking, "whew, what a close call." indeed. my only regret is that he did not turn his 20-gauge on himself, rather than on the bear. it would certainly be one small step in the direction of correcting human overpopulation, the root of nearly all our planet's ecological, social and economic ills. SUPPORT YOUR RIGHT TO ARM BEARS !!

NATIVE AMERICAN WRITERS

i have a lifelong hunger for understanding the experience of other ethnic, social or gender groups, including native americans. by coincidence, the book reading club i am about to join will be discussing The Surrounded by D'Arcy McNickle, a Salish writer. i've read dozens of books by or about different indian nations and individuals over the years, and while my natural affinity is for the northern plains tribes, the perspectives of writers from all regions are important.

i was pleasantly surprised to find an extensive list of native american writers at wikipedia. my own short list includes (but is not limited to):

James Welch -- Fools Crow

Sherman Alexie -- The Lone Ranger and Tonto Fistfight in Heaven

Vine Deloria, Jr. -- Custer Died For Your Sins

Dennis Banks -- Ojibwa Warrior

Russell Means -- Where White Men Fear To Tread

Woody Kipp -- Viet Cong at Wounded Knee

Dee Brown -- Bury My Heart at Wounded Knee

Mari Sandoz -- Crazy Horse, The Strange Man of the Oglalas

Stanley David Lyman -- Wounded Knee 1973

please note that while the last three authors are non-indian, their meticulous research and willingness to set their own cultural biases aside produced valuable windows into the lives of their subjects, and into the conflict between indian and white cultures. please note also that i am not one of those whites who romanticizes indian culture beyond all recognition of reality. every culture has its strengths and shortcomings, its heroes and scoundrels and just plain folk. still, for me it is an undeniable truth that indigenous peoples, especially those threatened or oppressed by a powerful colonizing culture, deserve to be understood and respected on their own terms. as do we all. (click on map to enlarge)

ORANGE

(from wikipedia) -- "the orange is a hybrid of ancient cultivated origin, possibly between pomelo and tangerine ..... the plant originated in southeast asia. the name is thought to ultimately derive from possibly the telugu naannja or or tamil naram, the names of the tree in the respective languages." [perhaps the language origin explains why we have no words that rhyme with orange?] click on images to enlarge.

RADIO MARGINAL 98.1

thank you, martina !! my facebook swedish friend who lives in portugal, sent me this link to a terrific portuguese radio station, Radio Marginal at 98.1 FM. click on it, and you can listen a nice mix of latin and smooth jazz on your computer. ain't technology grand?

GLOBAL WARMING

no, this will not be a rant on the human excesses that have led to global warming, species extinctions, habitat destruction, or other insults to the planet perpetrated by us bipedal, opposable-thumbed, large-brained, myopic humans. these are all measurable effects, and for this writer, not in dispute.

but there do remain those who contest the degree, the cause, even the existence of global warming as a critical issue. every paradigm shift in human history, be it in the arts, the sciences, religion, or any other activity, has generated controversy, sometimes heated, sometimes violent or repressive. good science requires that we examine the validity of all hypotheses, weighing each fairly, and then making up our own minds. toward that end, prompted by a recent exchange with someone whose intellect i respect, i have provided the three links above, so that you can, at your leisure, read and consider both data and interpretations, and arrive at your own conclusions (hopefully tentative ones, since all positions are subject to revision as new facts become available).

THE MILLION MAN MARCH

on this day in 1995, organizers led by nation of islam head louis farrahkan successfully orchestrated a mass gathering of black men on the capitol mall in washington, dc. proclaimed as the million man march (though an official poll counted just over 800,000 participants), the gathering's intent was to (a) call political attention to racial and urban issues; (b) present to the world an image of the african-american male that countered racial stereotypes; and (c) encourage solidarity among the black community, especially among black men who felt disempowered by racist laws and policies.

the gathering was the result of a nationwide grassroots effort, and was partially successful in achieving its goals, though the permanence of that achievement was to some degree overshadowed by controversy surrounding farrahkan, and by society's lethargy when it comes to making substantive positive change for its own sake. for a window into what the event was like for those traveling to it, as well as a vivid depiction of issues within the black community, i highly recommend viewing director spike lee's insightful film Get On The Bus.

JOAN BAEZ

last night the PBS series American Masters broadcast a tribute to activist and singer Joan Baez, titled "How Sweet The Sound". we can view the entire program online, from 15 october through 10 december. it was a spellbinding 90 minutes for me (summarized in text here). she was raised by quaker values of non-violence and bearing witness to wrong-doing, and she has spent her entire life being true to those values. her activism has included speaking out publicly for civil rights, against the vietnam war, against violence perpetrated on women, against violence in places as disparate as northern ireland and south africa, and against the proliferation of nuclear weapons. she joined non-violent civil demonstrations often, and was no stranger to being jailed for speaking her conscience. her resolve never wavered, and her voice remained true. it continues to do so to this day. she is one of my enduring heroes.

THE SPEED OF SOUND

on this day in 1947 (my birth year), test pilot chuck yeager became the first human to break the sound barrier, flying in an experimental rocket-powered Bell X-1 aircraft (shown below) at an altitude of 45,000 feet. surpassing the speed of sound (about 768 mph, or one mile every five seconds) had long eluded pilots and aircraft builders. some considered it to be a near-solid barrier, impossible to penetrate. aircraft buffeting increases exponentially as one approaches the critical speed, due to the accumulation and compression of air directly in front of the aircraft. but once that speed is exceeded, smooth flying returns.

yeager's extraordinary feat is described in tom wolfe's book The Right Stuff, and also in the movie of the same name. yeager himself appears briefly in the film, playing a bartender at the legendary desert pilots' bar owned and run by woman pilot pancho barnes.

below is a u.s. navy F-18 Hornet at the instant of surpassing the speed of sound.

A VISUAL MUSICAL TREAT

this morning i was browsing classical music on youtube, and by happy fortune came across a presentation i'd never seen before. in an orchestra, individual musicians play from their instrument's score (like a blueprint or set of instructions on which notes to play when, how loud and for how long). the orchestra's conductor directs from a master or full score, a complex assembly of all the individual instruments' parts. as you learn to read musical notation, it becomes as second nature as reading written language in a book, so much so that eventually you will be able to sight-read, i.e. glance at a score and know immediately what the notes, chords and intervals will sound like.






















what i discovered is a variation on a conductor's master score. it is a video presentation, an intricate, dynamic musical animation of the delightful second movement of beethoven's symphony no. 2, the allegretto. what you will see is not notes, but rather a set of lines scrolling across the screen (not unlike a heart monitor), color-coded to each instrument in the orchestra -- in this case flutes, oboes, clarinets, bassoons, french horns (my instrument!!), trumpets, tympani and strings. each instrument's line ascends or descends with pitch, just like a the notes printed on a musical score do, and each line disappears when there is a rest (silence) for that instrument. the very cool thing is that you don't have to know a thing about musical notation to quickly learn how to read what is being played, and in fact to predict what is coming next. the presentation is straightforward and intuitive, and a lot of fun. you can close your eyes and sink into the music (i recomment this), or you can turn down the volume and imagine what is being played, then turn it up to see if your instinct is accurate. most instructive is to have both on, and simply enjoy.

try it -- you'll be amazed at how quickly your understanding of the interplay of voices is enhanced. the music comes alive to both your ears and your eyes. you'll be dazzled by the musical genius that created this tapestry of interweaving voices. beethoven was one of a small number of transformational giants in music history. he is one of the reasons that classical music has survived over the course of centuries, while less sophisticated forms appear and disappear like wraiths in the mist.

so -- sound turned up? at long last, here is the visual and audio performance of the exquisite second movement of his symphony no. 2, a piece i've listened to for decades, and of which i never tire.

CHRISTIAN THE LION

bought in a department store as a cub in 1969, christian the lion bonded with his two young australian owners, john rendall and anthony burke, then living in london. after it became apparent that christian had grown too large and mature to continue a domestic life, he was successfully reintroduced to the african wild by conservationist george adamson (best known for his movie Born Free). the two former owners journeyed to africa in 1972 to visit christian, not knowing whether he would remember them, or be too wild too approach. the resulting reunion was captured on film and circulated globally on video, via the internet and tv shows such as "The View". it is guaranteed to bring tears to the eyes of the most stoic viewer. click here to view and enjoy.

THAT OLD PARADOX

all my life i have searched for the perfect balance between nature and culture. cities offer fine dining, museums, live theater, music, dance, cultural diversity -- yet they are also polluted, overcrowded, noisy, and sometimes dangerous. wilderness offers peace, comfortable solitude, clean air, the delight of watching wild animals, birds and plants -- yet it is also socially isolating, short on access to the arts, and sometimes hard work. where is the middle ground?

for a time, in my early 30s, i found it in some measure. i was caretaker at a nature conservancy preserve in southern arizona, and made frequent trips into tucson, 65 miles away. but my marriage came apart, and i aspired to return to school for my degree (ecology & evolutionary biology), so i moved back to tucson to attend the university of arizona.

now, after a lifetime of colorful jobs in far-flung places, i'm retired, and thinking about where i'd like to live more permanently. both the southwest and the pacific northwest have their appeal, in that they are known quantities with familiar attractions. but might i want to try someplace i've never lived before? i vascillate. the familiar: portland, oregon, or tucson, arizona? someplace new: santa fe, new mexico, or san luis obispo, california? what about overseas? spain, ireland, costa rica, tanzania, new zealand? so many possibilities, cultures, climates. i welcome suggestions.

THE DOZENS

also known as crackin', snappin' or dissin', the dozens is an improvised competition of trash talk, usually in good fun but sometimes turning serious, featuring insults aimed at the other person's mama, family, appearance, intelligence, hygiene, or a long list of other attributes. this article from wikipedia sums up the cultural origins and variations on both the name and the contest. one intense variant is a rap battle, as portrayed in the movie 8 Mile, an autobiographical portrayal of rapper Eminem's coming up.

i looked on google and youtube, and mostly found only descriptions, not many examples besides some old videos from the tv show "In Living Color". if you come across any, please leave the link using the "comments" tab at the bottom of this post. thanks !

2009 NOBEL PEACE PRIZE

president barack obama appeared to be as surprised as everyone else when it was announced that he is the 2009 receipient of the nobel peace prize, joining the ranks of such illustrious winners as jane addams, cordell hull, george marshall, linus pauling, martin luther king, jr., anwar al-sadat, menachim begin, mother teresa, desmond tutu, elie wiesel, the dalai lama, nelson mandela, jimmy carter and al gore. the nobel committee cited obama "for his extraordinary efforts to strengthen international diplomacy and cooperation between peoples."

as much as i have supported obama from the beginning, and continue to do so, at first blush it seems premature to bestow the peace prize to him after only nine months in office. still, he started actively promoting civilized discourse and conflict resolution among the nations of the world long before he took office. perhaps, after so many years of u.s. militancy and cultural condescension under the bush administration, the world is simply ready for a breath of fresh air, not to mention mutual respect. to that extent, i do not begrudge him this moment in history.

DEMOGRAPHICS

thinking of moving? curious about what life is like in other parts of the united states? here is an online resource for discovering the cultural, economic, geographic, climate, and community structure for hundreds of cities, easily found on the user-friendly map. just plain fun to explore.

NGC 1672

no political rants, no elucidatory elocution, just the most gorgeous photo i've ever seen of a spiral galaxy, NGC 1672. click to enlarge, and prepare to catch your jaw as it drops.....

SATURN'S RINGS

today NASA announced that its spitzer telescope had detected the presence of a faint "super-sized" ring around the planet saturn, tilted 27 degrees from saturn's equatorial plane (and that of the other rings). the ring extends from 128 to 207 times the radius of saturn, and is about 20 times as thick as the diameter of the planet. the ring's particles are presumed to originate from impacts on saturn's moon phoebe, and they share phoebe's retrograde orbit. (click on image to enlarge)

it is a strange and wondrous universe out there -- and we're still just getting to know our own tiny neighborhood, the solar system. i live for discoveries like this.

SCIENCE ONLINE

here are three of many science resources for stimulating your neurons, and perhaps inducing actual cogitative activity:

~~ Science 2.0 - a lively and very well-informed blog by hank campbell.

~~ Science Codex - a news source on a wide range of topics within science.

~~ the Science portal at Wikipedia - ditto.

there are, of course, many such resources. feel free to recommend your own favorites, using the "comments" tag below. thanks.

BOBBY McFERRIN

just for fun, here are three videos of performances by bobby mcferrin, the virtuoso singer and improviser. the first is a medley from "The Wizard of Oz," the second is a song called "drive," and the third is an ethereal improvisation with jazz bass guitarist richard bona. settle back, and enjoy.

THIS IS YOUR BRAIN ON MUSIC

i am only partway through daniel j. levitin's eye-opening book This Is Your Brain on Music: The Science of a Human Obsession. levitin is a former rock musician turned neuroscientist. in the book, he explores the connection between music -- its performances, its composition, how we listen to it, why we enjoy it -- and the human brain. he reveals how composers exploit the way our brains make sense of the world, why we emotionally attach to music we listen to as teenagers, why 10,000 hours of practice (not talent) makes virtuosos, and how insidious jingles (a.k.a. ear worms) get stuck in our heads. he argues that music is fundamental to our species, perhaps even more so than language.

here is a brief summary of the fundamental defining qualities of music (borrowing heavily from the book):

pitch -- a purely psychological construct, related both to the actual frequency of a particular tone, and to its relative position in the musical scale.

rhythm -- refers to the durations of a series of notes, and to the way that they group together into units.

tempo -- the overall speed or pace of the piece.

contour -- describes the overall shape of a melody, taking into account only the pattern of up and down movement of notes.

timbre -- (rhymes with amber) a kind of tonal color produced in part by overtones from a given instrument's vibrations, distinguishing it from the sound of other instruments.

loudness -- how much energy an instrument creates, or how much air it displaces. the amplitude of a tone.

reverberation -- the perception of how distant the source is from us, in combination with how large a room or hall the music is in.

when these basic elements combine and form relationships with one another in a meaningful way, they give rise to higher-order concepts such as:

meter -- refers to the way in which tones are grouped with one another across time, extracted from rhythm and loudness cues. (a waltz meter organizes tones into groups of three, a march into groups of two or four.)

key -- a hierarchy of importance that exists between tones in a musical piece, existing not in the world but in our minds.

melody -- the main theme of a musical piece, i.e. the succession of notes that are most salient in the mind of the listener.

harmony -- relationships between the pitches of different tones. this can mean simply a parallel melody to the primary one, or it can refer to a chord progression.

with these definitions as backdrop, levitin explores any number of assumptions we make about music, in particular how recognition of music occurs in the human brain. he asks:

"how are memories of music different from other memories? why can music trigger memories in us that otherwise seem buried or lost? and how does expectation lead to the experience of emotion in music? how do we recognize songs we have heard before?

"tune recognition involves a number of complex neural computations interacting with memory. it requires that our brains ignore certain features while we focus on features that are invariant from one listening to the next -- and in this way, extract invariant properties of a song. that is, the brains computational system must be able to separate the aspects of a song that remain the same each time we hear it, from those that are one-time-only variations, or from those that are peculiar to a particular presentation. if the brain didn't do this, each time we heard a song at a different volume, we'd experience it as an entirely different song!! and volume isn't the only parameter that potentially changes without affecting the underlying identity of the song. instrumentation, tempo and pitch can be considered irrelevant from a tune-recognition standpoint. in the process of abstracting out the features that are essential to a song's identity, changes to these features must be set aside."

to demonstrate, you will find below links to three different performances of j.s. bach's "Air on the G String" -- the first a vocal performance by bobby mcferrin; the second a violin performance by sarah chang; and the third a classical guitar performance by peo kindren. please note how our dry, academic definitions of musical qualities come alive, varying from one performance to the next, and yet the essential, identifiable piece is immediately recognizable by our brains. levitin's book explores these and many other ideas which can only broaden our understanding and enjoyment of that ephemeral experience we call music.

THE NATIONAL PARKS

last night i watched the final episode of historian/filmmaker ken burns' newest PBS series "The National Parks: America's Best Idea." i'm a huge fan of all of burns' work, including "The Civil War" and "The War" (WWII) -- but for me, this is his masterpiece to date. combining little-known historical and political backgrounds, interviews, information on the ecology, geology and natural history of each area, and matchless cinematography, this documentar is required viewing for any citizen. and here's a shameless plug -- to order any of his works, or other PBS DVDs, simply click here.