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I am extremely sorry that my posts have been so thin on the ground for the last fortnight.  I don’t have very good excuses for last week (although maybe the brain-melting heat wave which swept through the region provides some cover), but last night there was a blackout in Brooklyn, and there was no way I could write anything in the digital realm!  Being cast back in time made me reflect on the world before the internet and electricity.  Specifically I became fascinated by non-electrical lamps (which you never really think about until you need them).

Although I filled up my darkened house with LED tea candles and glowsticks, other peoples have not always had recourse to such safe options–like the Romans, who were forced to rely on candles, fires, torches, and their favorite night time standby, the oil lamp.  Ferrebeekeeper has touched on how the symbols and visual culture of Ancient Rome do not always make sense to us today…and indeed today’s post offers a powerful example of that.  Oil lamps came in all sorts of shapes and sizes (some of them seem to have been commemorative, or tourist trap items), but one of the absolute favorite lamp shapes was a foot.  These oil foot-lamps were sometimes bare and sometimes super ornate, but most often they are wearing handsome sandals.

So, why are these things shaped like feet?  Trying to research this question on Google resulted in me being whisked to various strange theological explanations of the Book of Romans by Dr. Lightfoot!  I was hoping that this was the foot of Mercury or something, but I never did get to the bottom of what is going on.  Speaking of which, the best hint I got was that the lamps may have been placed at the bottom of a mural so that the painting glittered in the darkness…which is to say these were the original and literal footlights.  This makes no sense to me, but it is sort of a modern English pun, I guess.  Perhaps it was a pun or a satisfying visual cue to the Romans as well.


Roman Foot Lamp with Sphinx Handle (Excavated in Libya, manufactured ca.1st century AD) Pottery

Whatever the case is, I love the feet!  These lamps are truly satisfying to look at, so maybe the Romans were on to something (they got roads and aqueducts right, after all).  If anybody wants to make a new old-style lamp company I am opened to that.  Also, if there are any classics majors out there who could explain this, please help us out in the comments!  I am unhappy with the “footlight” explanation and I long for a real understanding of what is going on with these charming feet!


Roman Imperial Foot-Lamp (Ca. 3RD-4TH Century A.D.) bronze


Exciting news from the world of mollusk research! Scientists have discovered new insights into how cuttlefish blend in so seamlessly with their underwater world.  Cuttlefish are chameleons of the undersea realm: they have the ability to change their color and texture in order to blend in with seaweed, coral, the ocean floor or whatever habitat they encounter.  Yet, even more remarkably, they can mimic the rough coloration and shape of other organisms, thereby fooling predators and prey by mimicking crabs and fish.


Cuttlefish copy the textures they find in their environment by means of small nodules known as papillae.  The cephalopods extend and retract these intricate bumps using muscles. They can become perfectly smooth in order to maximize their speed and maneuverability or they can take on the texture of rocks, coral, or even seaweed.  Scientists have discovered that the cuttlefish accomplishes this not by means of continuous concentration, but instead with muscles which can be locked in place by means of certain neurotransmitters (it pays not to contemplate the vivisection through which this knowledge was obtained).  If a cuttlefish takes on a certain texture and then promptly loses use of the relevant muscle nerve, the neurotransmitters remain active and it takes hours for the creature’s metabolism to return it to its neutral shape.


This may seem like a minor insight, but learning that cuttlefish (and presumably the squids and octopuses which use the same sort of papillae to alter their texture) are utilizing a muscle trick which is not unlike mechanism by which clams lock their shells in place is another step in unlocking the mysteries of these remarkable tentacled masters of disguise.


The Dwarf Planet Haumea

The Dwarf Planet Haumea

Haumea is a dwarf planet located in the Kuiper belt.  The little planetoid was discovered in December 2004 by a team of Caltech astronomers.  It is about a third the size of Pluto.  The team initially called it “Santa” but, in keeping with the IAU’s naming convention for Kuiper belt objects they eventually named the worldlet after a matronly fertility goddess from Hawaiian mythology.

Artist's conception of Haumea and its pink spot

Artist’s conception of Haumea and its pink spot

Although Haumea is typical of other dwarf planets in the Oort cloud in that it is a hunk of rock covered with ice, there are a couple of very unique things about the body.  Most notably Haumea is shaped like a lozenge (as opposed to being mostly spherical like other planets).   Astronomers believe that Haumea has sufficient gravity to overcome the compressive strength of its material.  In other words it chould be approximately spherical, however the planet is rotating with such velocity that it has become spindle shaped—like a water balloon thrown in a rifling spiral.


The extreme rapidity of Haumea’s rotation is its other defining characteristic.  It rotates more rapidly than any planetlike object with a diameter greater than 100 kilometers.   Haumea rotates completely every 3.9 hours so days there are incredibly short (although its huge orbit takes 283 years to complete—so years are long).  It is believed that Haumea’s breakneck spin comes from a titanic collision with some other Oort belt object.  Haumea’s two dinky moons were probably also created by the impact.  Haumea has a large red spot on it–perhaps because of the presence of minerals–or the fractured perturbance left by an impact.

A Quincunx

Continuing Q week, we come to the quincunx, a geometric pattern in which five units are arranged in an x shape.  That concept may have sounded complicated because there were too many letter-based phrases in the sentence, but the quincunx will be instantly familiar as the side of a standard six-sided playing die with five spots on it.  The quincunx takes its distinctive name from an ancient coin of the Roman Republic from the second century BC.  The little coin was worth 5/12th of an “as”–the standard bronze Republican coin of the time (which makes me glad I did not have to make change for buyers of that period).

The quincunx shape was popular with the Romans, who were inclined to numerological superstition, and subsequently, during the middle-ages, the shape found its way into many heraldic representations.

Five Fig Leaves in a Quincunx Pattern (known as "Saltire" in Heradlry)

Beyond its use in money, logos, and coats-of-arms, the quincunx shape has long been used for fruit orchards. To quote the Hegarty Webber Partnership, a website created by British garden designers with an eye for history:

Thomas Browne, in his Garden of Cyrus of 1658, claimed that the Persian King Cyrus was the first to plant trees in a quincunx. He also claimed to have discovered that it also appeared in the Hanging Gardens of Babylon. Seventeenth century diarist and garden guru Sir John Evelyn also thought it was the best way to lay out apple and pear trees.

The classical Persian precedent may be doubtful, but the quincunx is a wonderful way to lay out trees. As can be seen in the illustration below, such a staggered arrangement not only creates regular parallel rows (as would a normal four by four arrangement) but additionally creates regular diagonal rows.  A visitor to such an orchard would see a regular row whichever way she looked.  Such layouts create the illusion of more space (since we are used to rows which are perpendicular to each other) but they make it easy for orchard-goers to mistakenly turn down diagonal rows and become lost.

Finally, and most bafflingly, the quincunx is the underlying concept for a 2 dimensional square projection of a 3 dimensional spherical space.  Since a sphere represents an entire 3 dimensional frame of vision for a viewer in the center, such quincuncial projections show all aspects of a scene: above, below, side-to-side, in-front, and behind. An entire field of vision can thereby be distorted into a square. To better illustrate this concept, here is a quincuncial projections of the unusual octagonal (gothic!) crossing of Ely Cathedral in Cambridgeshire, England.

Gah! A Full Field Panorama of the Octagonal Crossing at Ely Cathedral (a quincuncial projection)

A stained glass sky-light window is immediately above the viewer and thus at the center of the composition.  The floor is the grey border around the edges.  The entrance door is at the top of the composition (upside down) while the central knave stretches upward from the bottom of the picture.  The north and south trancepts stretch off to the left and right. Finally, since Ely cathedral is octagonal, there are 4 additional doors  running along the diagonals of the composition.  There! I’m glad to have cleared that up, now I’m going to go have a drink and clear my head.  If you are really ready to go on a dimension warping trip into the world of panoramic photography, here is a link to other quincuncial projections.  Good luck on the other side of the looking glass!

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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