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According to ancient Chinese mythology, humankind was created by the benevolent snake-goddess Nüwa (who is one of my very favorite divinities in any pantheon, by the way). But keen readers wonder: where did Nüwa come from?  Whence came the ocean and the earth and the sea and the winds and the heavens.  Oh, there is a story behind that too, but it is strange and troubling—sad and incomplete and beautiful like so much of Chinese mythology and folklore.


In the beginning there was nothing except for the universe egg—a vast perfect egg which contained everything.  Within the universe egg, yin and yang energies were mixed together so completely and perfectly that they were indistinguishable.  Then, through some unknown means, the egg changed—mayhap it became fertilized—and a being began to grow within it.  This was P’an Ku, the great primordial entity.  The yin and yang energy began to separate and build complex forms.  P’an Ku slowly grew and grew.  He started as something infinitely small but gradually he became larger and larger until eventually his vast arms came up against the sides of the everything egg.  The little embryo became a vast god. The walls of the egg became a prison.


Then P’an Ku grabbed an axe (which appeared from who knows where).  Using all of his gargantuan might, he smashed a great blow through the shell of the egg, which exploded. He was born—as was the universe.  Beside him, in the gushing yolk, the primordial magical beings came into being—the dragon, the tortoise, the phoenix, and the quilin. These special creatures helped the first deity as he began to separate chaos into order.  P’an Ku split the yin into darkness and the yang into light. He laid the foundation stones of the vault of the everlasting sky and filled the ocean with the waters of creation dripping from the shattered egg shell.


But as he built, a strange thing happened (though maybe not so strange to my fellow artists who can never quite craft their dreams into their works). The world he made became inimical to him. He aged. He suffered.  His creation was unfinished…and he died.  His breath became the clouds and the wind.  His body became the mountains and the plains of China. His eyes became the sun and the moon. The hair of his body and head became the plants and trees.


It was in this corpse-world that the creator deities moved: Nüwa, a child born of P’an Ku’s genitals…or an alien outsider? Who knows? Who can say? What is important is that eggs are important. In Chinese myth they are the source of everything.  The beginning of the universe.


Chinese mythology does not dwell on the end of the world quite the way other cosmologies do.  Our world is sad and broken enough that we don’t need to think about its ending. But there are ethereal hints from before the Chin emperor’s great purges which suggest that time is circular like an egg. Somehow, as we all began, so we will end back there again in the homogenized grey yolk of chaos.


Artist's Concept of WISE J224607.57-052635.0

Artist’s Concept of WISE J224607.57-052635.0

Ferrebeekeeper has featured some mind-bogglingly strange astronomic entities before—black holes, ultra-dense stellar remnants, hyper-giant stars with a million times the mass of the sun, colliding neutron stars—but today we move up to a vastly greater order of magnitude!  Astronomers have just discovered a new class of galaxy which emits energy at unimaginable levels.  Using NASA’s Wide-field Infrared Survey Explorer (WISE), scientists have discovered what are being tentatively called “extremely luminous infrared galaxies” (ELIRGs).

One of these galaxies (with the not-very-snappy designation “WISE J224607.57-052635.0”) is producing 10,000 times more energy than the Milky Way, despite being much smaller than our familiar home.  The newly discovered galaxy is putting out more energy than 10 trillion suns (or, more correctly, I should say it was putting out the energy of ten trillion main-sequence yellow stars). Scientists consider it the brightest known galaxy in the universe.

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WISE J224607.57-052635.0 is 12.5 billion light-years away.  Since the universe is 13.8 billion years old, what we are now seeing dates to a whole different era of galactic dynamics.  Today maybe WISE J224607.57-052635.0 is a burned-out remnant…or a perfectly respectable middle-aged galaxy like the Milky Way.  Who knows?  But twelve-and-a-half billion years ago it was releasing an inconceivable amount of energy—so much so that astronomers are having trouble adjusting their theories to it.  Perhaps some embryonic galaxies have black holes which gobble up stars at a much greater rate than initially thought or, alternately, some unknown set of circumstances has allowed the black hole (or holes?) at the center of WISE J224607.57-052635.0 to somehow surpass the theoretical threshold of black hole feeding.

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Clearly astronomers are going to be sorting out what exactly happened out there for quite a while, but in the meantime, when you look up at the night sky remember you are looking at an invisible fountain of energy ten trillion times brighter than the sun. [Ooh, I made myself dizzy]


Eridanus is a large constellation which has been known since ancient times.   The constellation begins in the north (near Orion’s left foot) then winds south across the sky before snaking west towards Cetus the sea monster.  The river of stars which makes up Erdanus then doubles back east and eventually ends far to the south at the border with Hydrus, the water snake.  Because of its antiquity, there is some dispute as to where the name Eridanus came from:  second-century Greek astronomers believed the name indicated the sacred (mythical) river which Phaeton plummeted into after his unhappy attempt to drive the chariot of the sun.   Other etymologists, however, think that the name originated in ancient Mesopotamia where “the star of Eridu” was sacred to the primeval god Enki, lord of the abzu, a mythical abyss filled with all the fresh water in the world.  Eridu was the first known city of Earth, so the name may go back to the origin of civilization.

Enki in his watery home, the Abzu

Enki in his watery home, the Abzu

Whatever the origins of the name are, the constellation is the site of one of the strangest and most controversial objects in the heavens.  In 2007, astronomers using radio telescopes to survey the universe were astonished to discover nothing.  More specifically they discovered an immense and disconcerting amount of nothing—an enormous void in space time more than a billion light-years in diameter.  The Eridanus supervoid lies between six to 10 billion light-years away and its existence seems to be at odds with current cosmological models.

The Eridanus Supervoid (from an article by Bert Stevens)

The Eridanus Supervoid (from an article by Bert Stevens)

Cosmologists have several schools of thought concerning how the supervoid came into being and what its real nature is.  Because I am having trouble understanding any of these crazy theories, I have provided a rudimentary metaphor for each in blue (which would probably offend cosmologists, if they were reading my blog).

1)      Supporters of the standard model Big Bang theory say the region is colder because of dark energy, a hypothetical form of energy believed to permeate all of space.  If it exists, dark energy uniformly fills otherwise empty space yet interacts with none of the known forces in the universe (save gravity). The void is not empty but is filled with dark energy–which we do not yet understand: just like an empty room would seem empty to the Babylonians (despite being filled with air to us).

2)      A contrary theory proposes that the known universe orbits a supermassive black hole (in the same fashion that galaxies spiral around central black holes). This explanation would explain the “accelerating/expanding” universe as a sort of illusion: objects on the edge of the universe would be orbiting at a greater velocity than objects close to the black hole—a phenomenon which would affect their red shift relative to us.  Of course anything that got too close to the black hole in the void would be swallowed to an unknown doom into a black hole with the mass of another universe.  The universe is like an old vinyl record being spun around by a black hole in the center which is enormous beyond comprehension.  The expansion of the universe is an illusion caused by our limited perspective in such a scenario.   

3)      Laura Mersini-Houghton, a cosmologist who theorizes about the multiverse, believes that the supervoid is the imprint of another universe beyond our own.  Quantum entanglement has allowed us to see a shadow of this parallel universe in the form of the great empty spot located in Eridanus.  ??? Um, there are other universes out there which interact with our own in unknown ways which cause big holes (or maybe windows).

4)      Conservative astronomers speculate that the empty spot is an anomaly of the cosmic texture of the early universe.  Phase transition after the big bang resulted in heterogeneous distribution of matter. The universe is like a loaf of bread—sometimes it just has big holes in it because of the way it came into being.  

5)      The radiometric finding method by which the void was discovered is flawed.  The area only seems anomalously “cold” (in terms of EM emissions) because of a relatively hot ring of emissions surrounding it. The void doesn’t exist.  It was a mistake in observation.

6)      Something else entirely which we don’t yet comprehend and haven’t even imagined. Something else entirely which we don’t yet comprehend and haven’t even imagined.

I’ll be honest here.  Since I don’t have a radio telescope array or a degree in theoretical physics, these ideas are pretty hard to assay.  They are also wildly divergent.  I am therefore going to evaluate them aesthetically/emotionally (i.e. uselessly) in the following manner.  The first idea has the support of the astrophysics community, but is unsatisfactory until we have a more-than-theoretical understanding of dark energy (which could be forthcoming because of our discovery of the Higgs Bosun).  The second idea seems like it could be tested with mathematical modeling and astronomical observation (which so far seem to indicate there is no giant black hole in the middle of everything).  The third idea seems insane—and yet I have always intuitively felt that there are universes beyond this one (I’m sorry to be so guilty of such magical/hopeful thinking).  The fourth and fifth ideas seem quite plausible because they are boring (although why is the universe leavened like bread? Or why does it contain large relatively hot rings?).  The sixth idea is always applicable to everything.

Horses and Birds (M. C. Escher, 1949, wood engraving)

Horses and Birds (M. C. Escher, 1949, wood engraving)

Of course all this speculation may all be moot:  a more recent survey of the southern sky from a radio telescope in Australia suggests that there might be a much larger 3.5 billion light-year-wide void in the known universe.  That would certainly steer us back toward more conservative models of the universe, while at the same time leaving us with yet more questions.

The Atacama Desert (towards the Andes)

The Atacama Desert (towards the Andes)

The Atacama Desert of Chile is the driest place on Earth.  The desert is bounded in the west by the Chilean Coastal Range, which blocks moisture from the Pacific.  On the east of the Atacama run the mighty Andes Mountains which catch almost all the rainfall from the Amazon Basin.  Thus trapped between ranges, the desert receives 4 inches of rain every thousand years.  Because of the dryness, people are very sparse in the Atacama: they are found only at rare oases or as desiccated (but well preserved) mummies lying in pits.

The high altitude, dryness, and lack of nearby cities (with their lights and radio waves) make the Atacama a paradise for astronomers.  On a mountaintop 8000 feet up on the Atacama side of the Andes, engineers and scientists are working to put together one of the wonders of this age.


The Giant Magellan Telescope (hereafter the “GMT”) will be a miracle of engineering.   When it is completed in 2019 it will be larger than any telescope on Earth.  The scope is so giant that it will be mounted in a huge open, moving building (rather than the gun-turret-like buildings observatories are traditionally housed in).  No organization on Earth is capable of making a mirror large enough for the necessary purposes, so seven immense 8.4 meter mirrors are being used together to create a single optical surface with a collecting area of 24.5 meters (80 feet in diameter). The mirrors are the pinnacle of optics: if they were scaled up to the size of the continental United States, the difference between the highest and the lowest point would only be an inch.


The scope will be much more powerful than the Hubble telescope and take much clearer pictures despite being within the atmosphere of Earth.  In the past decade, telescope makers have used cutting edge engineering to compensate for atmospheric distortions.  To do so they fire multiple lasers grouped around the primary mirrors high into the atmosphere.  These beams of light excite sodium atoms in the sky which fluoresce—creating tiny “stars” of known wavelength, which serve as points of reference for the adaptive optics.  The official website of the GMT further explains the mechanism used to counteract atmospheric turbulence once these benchmarks are obtained:

The telescope’s secondary mirrors are actually flexible. Under each secondary mirror surface, there are hundreds of actuators that will constantly adjust the mirrors to counteract atmospheric turbulence. These actuators, controlled by advanced computers, will transform twinkling stars into clear steady points of light. It is in this way that the GMT will offer images that are 10 times sharper than the Hubble Space Telescope.

The telescope is designed to solve some of the fundamental mysteries about the universe. Scientists hope it will help them find out about the nature of dark matter and dark energy (which are thought to make up most of the mass of the universe).   Astronomers also hope to find out how the first galaxies formed and (perhaps) to ascertain the ultimate fate of the universe.  Most excitingly of all, the telescope should be large enough to peek at some of the exoplanets we are discovering by the thousands.  If life exists anywhere near us, the GMT should provide us with compelling evidence in the next twenty years.


The National Science Foundation was initially going to contribute heavily to the telescope but, since the United States Government has become indifferent to science and knowledge, other institutions have been forced to pick up the slack.  The scope is being built by a cooperative effort between The University of Chicago, The University of Texas at Austin, The Australian National University, The Carnegie Institution for Science, Harvard University, The Korea Astronomy and Space Science Institute, the Smithsonian Institution, Texas A&M University, & The University of Arizona (so you can probably help out by donating to any of these institutions, particularly the lovable University of Chicago).



George Ellery Hale

George Ellery Hale

George Ellory Hale was the sickly (and only) child of a wealthy Chicago elevator magnate.  At an early age Hale showed an affinity for science and quickly began thinking of astronomy in much deeper terms than the mere cataloging and plotting of stars (which was the direction of the discipline when he began his career).  In 1889, as he was traveling on a Chicago streetcar, Hale had an epiphany about how to build a machine to photograph and analyze the sun.  He thereafter invented the spectroheliograph, which revolutionized stellar physics, and he operated the first spectroheliograph from his private observatory in his parents’ backyard. Hale was a master of studying light in order to understand the physical characteristics and chemical composition of stars, which made him one of the first (if not the first) people to be officially called an astrophysicist.

Because of his obsession with starlight, Hale was also obsessed with building telescopes.  His dual ties to the world of academic astronomy (he studied at MIT) and the world of business wealth gave him a unique ability to put together observatories and institutions.  Throughout the course of his life, Hale was instrumental in building four of the world’s largest telescopes (each telescope substantially outsizing the previous one).

Yerkes 40 inch Refracting Scope at Williams Bay, Wisconsin

Yerkes 40 inch Refracting Scope at Williams Bay, Wisconsin

Working as a professor and department head for the University of Chicago, he first spearheaded the creation of the Charles T. Yerkes Observatory at Lake Geneva, Wisconsin which featured a 40 inch refracting telescope (the largest refractor ever used for scientific discovery). When his plans outgrew the University of Chicago’s budgetary constraints, Hale joined forces with the Carnegie Institute to build a sixty inch reflecting telescope at Mt. Wilson Solar Observatory near Pasadena.  In 1908, this telescope, the largest in the world, was operational, but Hale was already building a 100 inch reflecting scope.  This larger scope became world famous when Edwin Hubble used it to demonstrate that the universe is expanding.   Hale was still not done: he laid plans and institutional groundwork for the 200 inch reflector at Mount Palomar.  Although Hale died before the Palomar scope was complete, the final observatory more than fulfilled his vision.  The Palomar telescope was the world’s most important observatory between 1948 and 1992.

 The 100 inch (2.5 m) Hooker telescope at Mount Wilson Observatory near Los Angeles, California

The 100 inch (2.5 m) Hooker telescope at Mount Wilson Observatory near Los Angeles, California

Because this is a short article I have glossed over the technical, scientific, and administrative hurdles faced by Hale in creating these telescopes, but, suffice to say the challenges were daunting.  Each scope was accompanied by breakthroughs in engineering, architecture, and material science.

The Mt. Wilson 60-inch design is a bent-Cassegrain reflector with a 60-inch diameter primary mirror

The Mt. Wilson 60-inch design is a bent-Cassegrain reflector with a 60-inch diameter primary mirror

Hale was not content to merely create 4 of the world’s largest telescopes.  He was also one of the founding trustees at California Institute of Technology.  Hale’s contacts and savvy were one of the fundamental reasons that Caltech so quickly moved to International prominence (and maintained its status as one of the world’s foremost scientific institutions).

The 200-inch (5.1 m) Hale Telescope (f/3.3)

The 200-inch (5.1 m) Hale Telescope (f/3.3)

Hale was an indefatigable scientist, administrator, and thinker who accomplished a huge amount in his life.  His far-sighted observatories and his pioneering work in astrophysics laid the groundwork for humankind’s most profound discoveries about the actual nature of the universe.  However Hale suffered terribly from neurological and psychological problems.  He was sometimes incapacitated by headaches, insomnia, and a horrible ringing noise. Throughout his adult life he consulted with an elf or demon which appeared to him when the ringing in his head reached an unbearable pitch.  Psychologists and biographers have argued that this visitation was not actually a hallucination but rather a sort of allegorical figure used by Hale to personify his manic-depression.  Hale’s writings (and the accounts of those around him) cast doubt upon this interpretation.  He spent increasing amounts of time in sanitariums and he was fully institutionalized for the last years of his life.  Many biographers add this detail as a sort of embarrassing footnote to an otherwise glorious life of innovation and discovery.  Perhaps it should not be a dismissive footnote—Hale’s madness and his greatness went together.  Lesser men—or saner ones—could probably not have built huge eyes with which humankind stared into the darkness of deep space.


Years ago, when I first moved to New York and was a bright optimistic young person, I would travel around the city via subway.  Every day I entered and left the same entrance to the same underground train stop.  One day somebody dropped a bag of cheap glitter stars right by the exit.  These stars were different colors and different shapes.  They started as a glittering clump at the top of the stairs but thanks to foot traffic and weather, they quickly got everywhere.   Blocks away one would come upon glistening stars dotted along the sidewalk.

Then the stars began to fade and deteriorate.  Their shininess wore off in the rain. Their arms broke as people walked on them, but every once in a while you would see one that had caught in a protected location and survived.  Eventually there were no glitter stars left at all, but I suppose that the stuff they are made out of—bits of plastic and metal foil—is still out there in a landfill, or running down through drains into the ocean, or just blowing in the wind.

I mention all of this because it is a poignant metaphor for the currently projected fate of the expanding universe.  The ultimate destiny of the universe was once a problem relegated to theologians and mystics (and crazy people).  However, when cosmologists fathomed how the universe began–with the big bang 13 plus billion years ago–the question of how the universe would end became a legitimate scientific topic.   Edwin Hubble’s discovery that the universe was expanding provided an ominous hint as to the ending.

The way the universe will end is contingent on whether the momentum of the universe’s expansion is greater than the force of gravity (which in turn depends on the amount of matter in the universe and the density of that matter).  The current scientific consensus–based on carefully considered estimates of the universe’s mass density and on the most recently observed rate of cosmic expansion—is that the universe will continue to expand indefinitely.

Physicists, astronomers, and cosmologists therefore now project a rather glum fate for everything that exists. The death of the universe is divided into 4 stages summarized below:

Stelliferous: (Now to 100 trillion years into the future) This is an era teaming with stars: great masses of matter coalesce together into stellar masses and begin fusing together and releasing all sorts of energy as they do so.  Bit by bit though the brightest stars will wink out and only long-lived red dwarfs will remain.

Degenerate (100 trillion to 1037 years in the future) After even the red dwarfs fade into darkness, most of the universe’s mass will remain in the dying husks of stars, or in the remains of more exotic stellar death (black holes left by the destruction of super massive stars,  neutron stars, and white dwarfs). Electromagnetic energy in the Degenerate era will be generated by particle annihilation and proton decay rather than stellar fusion.

Black Hole Era (1038 to 10100 years into the future) After protons all decay away from the universe, the only large objects creating energy will be black holes which will themselves slowly evaporate into exotic matter over a vast expanse of empty time.

Dark Era (10100 years into the future to eternity) Protons and black holes will be gone and only the effluvia radiation from their passing will still exists in the universe.  All that remains will be photons of immense wavelength, neutrinos, positrons, and electrons–sad burned-out remnants which lack any order or meaning.  The universe will be incredibly vast, a horrible dark cold broken thing and it will remain that way forever.

So there you have it.  The fate of the universe is to slowly freeze and decay over trillions and trillions of years and then dissipate away into dark nothingness over eternity.

Of course 10100 years is a very long time indeed.  There is still plenty of time for beach parties and flower gardening, but this is not the end I would have wanted for anything I esteem as much as the universe. There isn’t much I can do about it though, except to hope that some unknown aspect of the cosmos provides a more spectacular and fiery end or that Vishnu intervenes.  Or maybe there is a multiverse in which our cosmos floats like an abstract bubble:  in the past, every time we thought we understood the universe it turned out that we were only looking at a small part of a greater whole.  It wouldn’t surprise me if something still eludes us.

"Vishnu, you out there buddy? Some help?"

This past April, I announced with some fanfare (or at least with bold letters) that Ferrebeekeeper was going to expand to feature a digital gallery of my paintings and other artworks.  In retrospect, perhaps I should not have made that statement on April Fool’s Day (although that is the day I started blogging).  Circumstances have indeed made a fool of me, and my projected site expansion has been delayed again and again. More than a season has gone by and still there is no art gallery.  Fortunately, I am now confident that my gallery launch really is just around the corner! To give you a little teaser until the final version is launched, here are two of my miniature allegorical paintings from a series which I started more than a year ago.

Donut Universe with Centaur and Mummy (Wayne Ferrebee, 2010, oil on panel)


Torus with Spearman, Bagpipes and Barnacle (Wayne Ferrebee, 2011, oil on panel)

Here’s the story behind the genesis of these works: when I was cleaning my pockets before doing a load of laundry I found a sketch of a centaur, a clock, and a snail trapped in a miniature torus-shaped universe.  Although I’m not sure what prompted that initial sketch, I have since made several tiny paintings based around toruses which, as explained here are elegant metaphors for insular universes.  Indeed some cosmologists and topologists feel that the actual universe might well be torus-shaped (or more precisely, shaped like a triple torus) an idea which appeals to my inner gourmand. The paintings are obviously echoes of each other.  Both feature huge predatory animals lurking under pastries floating in outer space.  The splendid toadfish (Sanopus splendidus) in the first painting and the gharial (Gavialis gangeticus) in the second are even facing the same way as if both waiting in ambush. Each panel also has an invertebrate, a galactic backdrop, and ancient beings brandishing hand weapons.  However the cast and the props are quite different–a bold Assyrian warrior takes the place of the desiccated mummy while the gothic clock sunk in icing is replaced by a mournful bagpipe floating in space.  A yellow lipped sea krait seems intent on escaping the entire scene.

What does all of this mean?  Well, as Socrates surmised, artists don’t know what their works mean. Like everyone else we have to guess, but the reoccurrence of similar roles in the two paintings—even as the setting and the circumstances change–suggest to me the circular nature of interaction between living things.  This theme is highlighted by the circular nature of the main subject, the torus. And of course there is something obviously and purposefully missing from both paintings, a physical and metaphysical emptiness exemplified by the famous hole in the donut, and the void of the universe. Whether this additionally reflects the hunger of the animals, the soundlessness of the bagpipe, the lifelessness of the mummy, and the timelessness of the stopped clock is an open question.

Saul with his Servants at the Fortune-teller of Endor (Rembrandt van Rijn, 1657, bistre ink on paper)

I wrote earlier about sepia ink, the beautiful drawing and writing medium used in the Mediterranean for thousands of years which was obtained from the ink sacks of cuttlefish.  Was sepia ink also used by the great northern masters for their sketches? Not at all: there was an altogether different source of the beautiful smoky brown inks used by Brueghel, Durer, Lorraine, and Rembrandt (as well as most other German, French, Flemish, Dutch, and English artists) when they sketched from life. The name of the transparent shadowy brown pigment with yellow undertones was bistre and its source was not a mollusk but rather a tree.  Bistre was made with the soot left over from burning beechwood.  The beechwood ash was boiled with water to produce a cheap and superior drawing pigment. Although steel and copper nibs certainly existed, most masters probably sketched with simple reed pens or goose quills (waterfowl were generally agreed to provide the best drawing quills and geese were most readily available).

Since I have a great fondness for both beech trees, reeds, and geese, it cheers me to think that the great drawings of the old masters were produced with such humble materials. Unfortunately there is no way to set out any sort of comprehensive collection of bistre drawings: the medium was more universally used then anything other than carbon black.  Even a little sampler would involve a wildly eclectic mixture of works from all sorts of drafstmen from wildly different ages and schools. So, instead I am showing three little Rembrandt drawings to represent bistre. I don’t write as much about Rembrandt as I do about other lesser artists (i.e. the rest) because my feelings about his ineffable works are hard to characterize.  The “Lines and Color” blogs summarizes the scope of Rembrandt’s drawings:

Over 1,400 of his drawings survive, conservatively estimated at less than half of what he produced. (For most great artists we’re lucky to have a few dozen. For Vermeer and Franz Hals we have none.) Also unlike most of the great masters, the majority of Rembrandt’s drawings were not done as preparation for paintings, and very few were signed as pieces to be presented to friends or patrons. Most of his enormous outpouring of drawings were apparently done for himself, as visual record of his life and experience or simply for the joy in the act of drawing.

The multitude of subjects encompassed in 1,400 drawings provides a comprehensive overview of life in seventeenth century Holland (which was one of the focal points of the first wave of true globalism).  Out of the murky brown ink washes emerge an endless parade of long-vanished people, places, and things. The figures work, play, and struggle in cities manufactured of hasty brown lines under brown clouds beside an ink wash ocean (over which inky ships carried the spices of the old world and the furs from the new). Magicians scheme, children squall, and captive lions recline.  It is my favorite alchemy. Rembrandt gives us an entire world crafted out of water and beechwood ash.

Lion Resting, Turned to the Left (Rembrandt van Rijn, c. 1650-52, ink on paper)

Today, Ferrebeekeeper ventures far far beyond my comfort zone into that most esoteric and pure realm of thought, mathematics.  But don’t worry, we are concentrating on topology and geometry only for long enough to introduce a beautiful, intriguing shape, the torus, and then it is straight back to the real world for us…  Well, hopefully that will prove to be the case–the torus is anything but straight.  It is, in fact, very circular indeed, and, as we all know, it has at least one big hole in it….

Wikipedia defines a torus as “a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle.” That’s hard for me to wrap by head around but the meaning becomes much more comprehensible in the following illustration.

So a torus is a circle wrapped around in a circular path.  You can find a variety of other ways of mathematically representing the torus here, but the simple definition suits our purpose.

One ring toroid them all....

I admire torus shapes because I think they are very beautiful.  Just as the golden ratio and the Fibonacci sequence are aesthetically appealing, there is a pleasure to merely beholding or touching a torus: ask anyone who has contemplated a ring, a golden diadem, or a cinnamon donut.  Talk to an indolent adolescent sprawled on an inner-tube bobbing on the surf, and you will immediately grasp the hold that toroids have on humankind.

And beyond humankind....

In addition to its obvious aesthetic merits, however, there is a mysterious aspect to the torus, a hint at hidden dimensions, negative space, and infinity.  Kindly contemplate the old eighties video game Asteroid (you can play the game here if you are too young to remember: amusingly, your ship is an “A” which reminds me of Petrus Christus’ enigmatic painting).  If you pilot your ship to the far left of the screen you emerge on the right side of the screen: the flat screen represents a cylinder. However, to quote Bryan Clare from Strange Horizons, “the bottom of the screen is connected to the top as well. This has the same effect as if the screen were rolled into a cylinder, and then bent again to glue the two circular ends together, forming the familiar donut shape.” So, when you play asteroids you are trapped in a miniature toroid universe which appears 2-dimensional. Try to blast your way out of that!

The following famous math problem further illustrates the nature of the torus.  Three utility companies need to connect their respective lines (gas, water, and electric) to three different houses without ever crossing the lines.

Connect each utility to each house. Don't cross the lines.

The problem is impossible on a two-dimensional Euclidean plain and even on a sphere, however topologists realized that if you poke a hole through the plane or the sphere (thereby making it a torus) the lines can be connected.

To finish the article here is a movie of a torus being punctured and turned inside out. The result is a torus of the same dimensions but with reversed latitude and longitude.  It’s hard not to love such a funny shape.  But it is hard for me to wrap my mind around the larger implications.  I think I’m going to stop trying and head off for some donuts.

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