• Did Isaac Newton slash the portrait of Robert Hooke?
• The Haunt of the Resurrection Men!
• Views of the dangers of masturbation for women,
• The weirdest weapons of history,
• and much more!

Many thanks to the hosts for an excellent carnival!  The next edition, the five-year anniversary of the carnival (has it really been that long?), will be hosted by The Renaissance Mathematicus.  As always, submissions can be sent to me, ThonyC, or the host blog — the latter two of which are the same this time!

I’m hoping to get back into some more gaming at my local game store, but I’m also planning to get back into painting fantasy miniatures.  For those unfamiliar, role-playing games and fantasy wargames can be played on tabletop with 25mm miniatures, and there is a vast collection of high-quality unpainted minis available for purchase.  Though I haven’t played games for quite some time, I’ve been painting on and off in the interim.

I thought I would share some images of my best paint jobs, with a little bit of a description to go with each one!  I should note that, being my best work, for every miniature you see here there are at least two more that didn’t turn out quite so well.  I should also note that these miniatures were painted for display, as opposed to being painted for gaming.  This means that I spent much more time on each paint job and used light coats to allow for finer detail.  Paint jobs for actual gaming are necessarily cruder and use thicker coats.

Without further ado, here are my best fantasy miniatures!

Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomèd mine—
Unweave a rainbow, as it erewhile made
The tender-person’d Lamia melt into a shade.

-John Keats, Lamia (1820)

Poet John Keats (1795-1821) once famously — and infamously — joked that Isaac Newton had destroyed the poetry of the rainbow by “reducing it to the prismatic colors.”  This statement has been quoted often whenever someone wants to argue that scientific knowledge dulls the beauty and poetry of nature.

Keats was being an idiot, though: a true understanding of the science behind a phenomenon  only adds to its beauty.  There are so many subtle aspects to even the simple optics of a rainbow that make it a fascinating and lovely subject of contemplation.  Once you get past the basic science of a rainbow, you are well-prepared to study more sophisticated and unusual phenomena such as this double rainbow that my wife and I saw from our house last July.

Double rainbow. It was, in fact, all the way.

I’ve had rainbows on my mind since I was recently asked to explain some of the optics by a journalist.  Surprisingly, standard optics textbooks such as Born and Wolf’s Principles of Optics and Hecht’s Optics have no discussion of the phenomenon.  This is likely due to the fact that most optical scientists have no need to understand rainbows in their research, but this does not mean they are not objects worthy of study.

So let me endeavor to explain all about rainbows: how they form, how double rainbows form, when fully circular rainbows form, and anything else I can think of.  This isn’t just trivia: a lack of knowledge of rainbows can lead to truly humiliating consequences.

Let’s start with the short explanation: a rainbow is formed when light from the sun hits falling rain, bounces around in the raindrops and gets directed back roughly the way it came.  Each color (wavelength) of light bounces a little differently in a raindrop and gets sent back in a slightly different direction; this results in us seeing different colors from different locations, giving us the beautiful multicolored bow.

Raindrops themselves can form in a range of different sizes, from 0.5 mm in diameter to 4.5 mm in diameter.  Drops larger than this end up splitting up into smaller droplets, so 4.5 mm is in fact an upper limit.  We’re concerned primarily with drops smaller than 1 mm which are, contrary to popular perception, spherical and not tear shaped.  For sizes on the order of a millimeter, we can safely ignore the wave properties of light and treat it as a collection of rays that suffer only reflection and refraction.  The standard picture to show how a rainbow forms is then given as follows.

The standard rainbow explanation picture.

A ray of light from the sun coming from the left hits the droplet.  It part of the light refracts  into the water drop, gets reflected once inside, and then gets refracted out of the drop roughly back in the direction it came, at an angle of roughly 42.5° relative to the incoming ray for red light.

This picture is accurate, but can actually be a little misleading: a cursory glance at it might suggest that we see a rainbow from each raindrop.  Each ray, however, returns at a slightly different angle, and therefore is seen at a different location.  This means that each color of the rainbow comes from a different group of drops, as illustrated crudely below.

This picture also demonstrates where a rainbow forms.  The rays of the sun come from directly behind the observer and reflect off the raindrops into the observer’s eyes; this means that the rainbow is centered on the shadow of the person’s head.  Because the sun is above us when rainbows form, our shadow ends up on the ground.  The result is that we typically can only see one fraction of the rainbow, with the remainder of it effectively “obscured by the ground.”  If one is high above the ground, however, it is possible to see a complete circular rainbow, as seen for example below.

A circular rainbow seen while skydiving over Illinois. Picture by Steve Kaufman, via Wikipedia.

So far so good, right? Well, there’s a bit of a problem with our simple “standard rainbow explanation picture” above: it shows only one ray coming in!  In fact, each droplet should have a collection of parallel rays hitting it, each of which gets reflected back in a different direction. This is shown for blue rays below.

At first glance, it seems like we should all colors spread out over all angles, and no rainbow at all!  In fact, this is partly true: the rays shown above, and the corresponding ones for the rest of the color spectrum, are spread out and appear in the interior of the rainbow as a bright region; this can be seen in my rainbow picture at the top of the post, reproduced below.

Note the bright region inside the primary rainbow.

So what distinguishes some of the rays and makes them a rainbow, where others just join into a “white noise” background?  Look carefully at the last two rays in the picture above — oh, heck, look at the same picture below with the rays drawn in red for clarity.

The two rays exiting at the lowest point in the drop — the topmost two rays entering the drop — are nearly parallel to each other, whereas all the other rays have significantly different directions.  By a curious quirk of geometry and optics, we have an entire group of rays (clustered around roughly 42.5°) that are all going in the same direction.  More rays equals more light intensity, and we therefore have an unusually bright “beam” of light leaving the droplet at those special angles.  These collection of parallel rays form the rainbow that we see.

You’ll notice that the size of the droplet plays no role in the direction that light goes on exiting; provided a droplet is spherical, it will create a rainbow in the same direction regardless of size.  This of course makes sense, because we can’t expect a rain shower to consist of a collection of raindrops of exactly the same size!

One important question has remained unanswered: what causes different colors of light to refract differently within the raindrop?  The short answer is that the speed of light in water (and, in fact, in all matter) depends on the wavelength (color) of light in a process called dispersion.  Because refraction depends on the speed of light, every color takes a slightly different path in the droplet.  Dispersion has been most famously visualized in the classic Pink Floyd album cover for Dark Side of the Moon, using Isaac Newton’s classic experiment with prisms as inspiration.

But this explanation is sort of a “punt”: we explain the rainbow by punting to “dispersion,”  but what actually causes dispersion?  The answer is fortuitously related to a recent post I did on Chladni patterns and the phenomenon of resonance.  A simple example of resonance is making a child’s swing move by pumping your legs at just the right frequency: when your motion matches the natural oscillation frequency of the swing, your movements add up over multiple swings to create one big swinging motion.  You have made the swing move by driving it at its natural, or resonant, frequency.

Atoms have their own natural frequencies associated with them that arise (very roughly speaking) from the orbit of electrons around the nucleus*.  A diagram of the Bohr atom may help here.

The Bohr atom. Electrons can only exist stably in discrete orbits, and typically absorb/emit light by making transitions between these discrete orbits.

Thanks to the laws of quantum mechanics, electrons can only orbit in certain special orbits, labeled in the picture of a simple hydrogen atom above by the index n.  Each of these orbits has its own natural frequency of motion, kind of like all the planets in the solar system each have their own length of year.  When an atom is illuminated by light, the light drives the atom much like a child makes a swing move.  The response of the atom depends crucially on the relationship between the frequency of the light and the natural frequencies of the atom.  This is the origin of dispersion: this interplay between the natural oscillations of the atoms and the oscillations of the light wave that drive them.

Putting together all that we’ve learned so far, we now have a pretty substantial explanation of the rainbow!  This means we can turn to that magical and elusive phenomenon, the double rainbow.  In fact, a double rainbow is relatively easy to understand with what we’ve learned; it arises from rays of light that reflect twice inside of raindrops.

The rays from the double rainbow come back at a more extreme angle than those of the primary rainbow: by my calculation, they make an angle of about 50° with respect to the incoming ray.  This means that the double rainbow lies outside of the primary rainbow, as one can see from experience.  The colors will also be reversed, as we can see by posting the primary rainbow figure right next to the comparable double rainbow figure.

The double rainbow will be naturally dimmer than the primary rainbow.  Every time light is reflected inside the drop, part of it “leaks” out of the droplet and is lost.  The more times it bounces around inside, the more light is lost.

With that in mind, we can ask: are there higher rainbows?  In fact, it is possible on rare occasions to see the tertiary and quaternary (3rd and 4th) rainbows, caused by light bouncing around 3 and 4 times within the rain droplet, respectively!  However, these bounces cause the light to exit the drop traveling roughly in the same direction that it entered.  This means that the tertiary and quaternary rainbows can only be seen when the raindrops are between the sun and the observer.

This process can be repeated in the right laboratory conditions.  In 1998, researchers observed rainbows** up to an amazing 200th order by the use of a high-powered laser and a pendant water drop hanging from the bottom of a glass dropper of diameter roughly 2.5 mm.

So what does all of this information gain us?  As I have noted, there isn’t really a practical application for rainbow optics, to my knowledge.  However, learning about how rainbows work demonstrates that even such a simple effect has hidden complexity to it.  This complexity, in my opinion, adds another layer of beauty, giving me, I daresay, a stronger connection to the science of rainbows and to nature in general.

***

* I should point out here, lest I be accused of oversimplifying, that electrons do not actually “orbit” the nucleus.  At the atomic scale, the wave properties of electrons are dominant, and the electron can more accurately be described as a “cloud” around the nucleus.  However, this electron cloud still had natural frequencies of vibration associated with it.

** P. H. Ng, M. Y. Tse, and W. K. Lee, “Observation of high-order rainbows formed by a pendant drop,” J. Opt. Soc. Am. B 15 (1998), 2782.

The 1950s and 1960s must have been a wonderful time to be a science fiction writer.  Not only was the genre at the height of its popularity, but its novels were readily tapped for screen adaptations.  Growing up, I was completely unaware that many of the films I watched on Sunday afternoon “Creature Features” were based on novels, but now I find it fascinating to go back and see how the movies compare to their original inspirations.

One of these that I believe almost everyone on the planet must have heard of at one point or another is Jack Finney’s The Body Snatchers (1955), later revised to Invasion of the Body Snatchers.

First edition cover via Wikipedia, which actually accurately depicts a scene in the book.

Finney’s book was an immediate sensation, and was quickly turned into the instant classic 1956 film Invasion of the Body Snatchers.  Three other adaptations followed, in 1978, 1993 and 2007.  But what of the original novel, and how does it compare to the films?  Let’s take a look!

The story is narrated by Dr. Miles Bennell, a doctor in the small town of Mill Valley, California.  Set in the late 1970s (at that time the far future), Bennell struggles to describe and explain the events that quietly devastated the town some time past.

I warn you that what you’re starting to read is full of loose ends and unanswered questions.  It will not be neatly tied up at the end, everything resolved and satisfactorily explained.  Not by me it won’t, anyway.  Because I can’t say I really know exactly what happened, or why, or just how it began, how it ended, or if it has ended; and I’ve been right in the thick of it.

The trouble begins with a seemingly small event of no major significance.  Becky Driscoll, an old high school crush, visits Bennell’s office.  It is not a social call, however; Becky is terribly worried about her cousin Wilma.  Wilma has become convinced that her Uncle Ira — who she has been living with for years — is not her uncle at all.  She cannot explain exactly what is wrong with him, as his physical characteristics are unchanged and his personality is the same, but Wilma is certain it is not him.

Becky and Miles visit Wilma, and can find nothing wrong with Ira.  Miles refers Wilma for psychiatric counseling and thinks nothing more about it.  However, the very next day he has another visitor: a woman who is convinced her husband is not her husband.  Within a week, he has referred five more patients with similar fears to the same psychiatrist.

Things come to a head, however, when Jack Belicec interrupts a dinner date between Miles and Becky and insists that they accompany him to his house.  Lying in Jack’s basement is a naked corpse, horrifyingly unformed but bearing a distinct resemblance to Jack himself.  They soon discover that the town of Mill Valley is being taken over by an extraterrestrial force, one that can almost perfectly duplicate a living creature and disintegrate the original when he or she sleeps.  When it becomes clear that Miles, Becky, Jack and his wife are the only remaining true humans in town, they must discover a way to expose or defeat the alien threat before it spreads and consumes the entire earth.

The novel is wonderfully fast-paced; once I began reading it, I could hardly put it down.  The sense of fear and paranoia in the book is palpable: from the beginning, Miles is at an almost complete disadvantage, and the odds worsen against him every day.

Perhaps my favorite part of the book is the explanation, by the pod people themselves, of their origins and goals.  The pods are not themselves sentient: they are lifeforms that have been pressed by the forces of evolution into a nomadic, parasitic existence.  Those people duplicated (with their human sentience) understand this very well, and can explain it with a horrifying bluntness.  The pods are carried from world to world by radiation pressure of stars, like spores drifting on the wind, and they subsume any organisms they find at their destination.  Like many parasites, they will eventually move on: the duplication process is imperfect and all duplicates will die within five years, leaving a dead world behind as the pods depart.

The novel originally appeared in serialized form in 1954 in Colliers Magazine, and clearly captured the public’s interest and imagination.  However, many science fiction writers were less impressed with the material.  As Wikipedia notes, in 1967 the author Damon Knight wrote a critique of the book in which he blasted both its science and its plot.  Of the science, Knight wrote

The seed pods, says Finney, drifted across interstellar space to Earth, propelled by light pressure. This echoes a familiar notion, the spore theory of Arrhenius. But the spores referred to are among the smallest living things – small enough to be knocked around by hydrogen molecules…In confusing these minute particles with three-foot seed pods, Finney invalidates his whole argument – and makes ludicrous nonsense of the final scene in which the pods, defeated, float up into the sky to hunt another planet.

Personally, I think that Knight is being too hard on Finney.  The “light pressure” referred to here is the inherent momentum, or “kick”, of light, something I’ve discussed on this blog several times (e.g. here and here).  The pressure of light is so weak that it can typically only be used to manipulate microscopic particles; however, it is now known that it can also effect the behavior of relatively large objects like asteroids!

This is somewhat beyond the point, however: Finney was clearly trying to plant the image of an organism that drifts from place to place like seeds on the wind, and to me it works very well.  By griping about the little details, Knight is missing what readers love about the book, a phenomenon that a recent article summarized very well.

Knight also blasts the plot details:

Almost from the beginning, the characters follow the author’s logic rather than their own. Bennell and his friends, intelligent and capable people, exhibit an invincible stupidity whenever normal intelligence would allow them to get ahead with the mystery too fast. When they have four undeveloped seed pods on their hands, for instance, they do none of the obvious things — make no tests, take no photographs, display the objects to no witnesses. Bennell, a practicing physician, never thinks of X-raying the pods.

Here again I am much more forgiving than Knight!  The characters have been put into a situation of unspeakable horror, and it is not a shock to see them react out of panic rather than reason.  The seed pods that Knight refers to are found in the basement of the protagonists’ refuge, clearly placed there to replace them!  It seems quite in human nature for the characters to want to destroy the pods immediately rather than study them with a Vulcan-like indifference.

It is tempting to look at The Body Snatchers as an allegory about communism, or the decline of civilization, or a general agoraphobic fear of the mass of humanity.  However, apparently Finney himself, as well as the creators of the 1956 movie adaptation, did not intend the story to be an allegory.

That is perhaps the strength and staying power of The Body Snatchers; it is a tabula rasa upon which the reader (or viewer) can write his own fears.  Recently, I wrote an introduction to John Blackburn’s The Face of the Lion, a horror thriller that anticipated many modern “zombie stories.”  In that introduction, I noted that zombie stories are likely successful because they can be used to portray and confront many different ideas in horror.  Upon further reflection, it seems that The Body Snatchers could in fact be an early “proto-zombie” story itself: human beings are slowly being turned into dangerous, emotionless shells of themselves, and actively seek to spread the contagion to others.  The pod people story could be seen as another anticipation of the modern zombie craze, which perhaps makes it not coincidental that the most recent movie adaptation came out at its height, in 2007.

So what can we say about the movie versions?  Talking about the movies and a comparison to the book necessarily requires spoilers, which I put below the break for those interested.

***

A movie adaptation of a horror story often has a happier ending than the book, as studios pressure the writers and director to make the film appeal to the broadest audience possible.  It is rather remarkable that the opposite is true in the case of The Body Snatchers.

In the book, Becky, Miles, Jack and his wife all survive the invasion, which ends unexpectedly as the pods flee into space, deciding that humanity is too defiant to truly conquer.  The remaining pod people end up living out their remaining truncated lives as ordinary humans.

In the 1956 film adaptation, Miles is the only survivor.  He flees in terror to a local highway, pleading with someone, anyone, to listen to him about the threat.  The ending is an undeniable classic, in large part thanks to the amazing performance by Kevin McCarthy.

The movie ends on an ambiguous but semi-optimistic note, as a fortuitous crash of a truck laden with pods convinces the FBI to listen to Miles’ story.  This twist was the result of studio intervention, however; the director and screenwriter wanted the movie to end as the clip above shows.

Nobody stopped the makers of the 1978 film from making it apocalyptic.  In the climactic scene, Matthew Bennell (played by Donald Sutherland) destroys a pod growing facility, mirroring the finale of the original book.  We next see him walking in public again, seemingly disguising his emotions to blend into the pod crowd.  When Nancy, another survivor, waves and smiles at him, Matthew points and screams — he was converted to a pod person after all.

In the 1993 version Body Snatchers, the pod people have taken over a military base.  A helicopter pilot manages to destroy a series of outgoing pod-laden trucks with explosives, but the ending narration suggests that this effort is too late, and that the pods have spread too far to be stopped.  This film is considered the best of the adaptations by none other than Roger Ebert.

In the 2007 film The Invasion the pods have been replaced with an alien fungus that infects the human brain and seizes control of it.  This movie has the most optimistic ending of them all, as a cure is found for the fungus and the invasion is ended, with all of the infected people being returned to their normal selves.  In a perhaps related observation, this film is considered the worst of the adaptations by critics.  Roger Ebert seems to have noticed the zombie connection that I mentioned, saying in his review:

And the aliens themselves are a flop. Just like zombies, they’re pushovers: easy to spot, slow-moving, not too bright, can be shot dead or otherwise disposed of.

I suspect that we’re by no means done with body snatching!  With major movie adaptations coming roughly every 15-20 years, we’re due for another invasion before too long.

The demonstration of a couple of Chladni patterns are shown in the video below.  A metal plate, supported by a post in its center, is vibrated at a single frequency by use of a mechanical driver.  For most frequencies, nothing at all happens; when certain special frequencies are hit, however, standing waves appear on the plate, driving the sand away from the points of large vibration to the points of no vibration.  By varying the frequency of oscillation, we can find a large number of the so-called resonance frequencies and their accompanying patterns, which become increasingly complex and beautiful as we up the rate of oscillation.

Chladni figures are a lovely examples of resonance, an important concept in almost all branches of physics, including vibration.  Rigid and semi-rigid bodies possess an (in principle) infinite number of natural frequencies of vibration at which the object “wants” to move.  In this post we look at resonance, as illustrated by Chladni’s demonstration, and the role it plays in numerous phenomena.

You likely took advantage of resonance at a very young age, though you likely didn’t know it!  A child’s swing is in essence a pendulum, and has a natural frequency at which it likes to swing.  To get the swing going, you pump your legs and arms in time with this natural frequency, allowing the motion to build up over each period of swing.  In doing so, you are driving the swing at its resonance frequency.  If you were to drive the swing at any other frequency, you would find that your motions tend to work against the swing as much as with it, resulting in very little motion.

A pendulum or swing is the most simple example of a system that can be driven at resonance; most objects have multiple resonance frequencies, indeed an infinite number of them.  The next example in order of complexity is a vibrating string which is fixed at both end, like those on a guitar or a clothesline.  If we were to mechanically drive this string, we would find that it has a lowest (fundamental) frequency, which we will call f, and then higher-order frequencies (harmonics) at 2f, 3f, 4f, and on to infinity.  The vibrations on the string (which we call modes) look different for each harmonic, as illustrated below.

Strings of different lengths, thicknesses and tensions will have different fundamental frequencies, but they will all follow the same pattern: higher-order resonant frequencies will all be integer multiples of the fundamental.  So what is the origin of this pattern?  The picture above actually provides the answer, if you look at it carefully: The fundamental and harmonic modes are those for which one round trip of waves on the string is a single wavelength.  A single cycle of a wave, the size of a wavelength, is one for which the wave has completed one complete up/down motion, as shown below.

The fundamental mode in the picture above is only a half-wavelength; a full round trip of the wave back and forth across the string constitutes a complete wavelength.  When we drive the string at one of these fundamental frequencies, we are always adding to the vibration of the string in the same way at the same point in the string’s cycle, much like a child on a swing always pumps it at the same point in the motion to move it higher.

Looking again at the mode pictures above, it is to be noted that the higher harmonics each have points where the string amplitude is zero: there is no motion of the string at these points, which are called nodes.  We could in principle put a finger on the string at those points, blocking its motion there, and not affect the harmonic mode at all; this technique is used in guitar playing and is known as a pinch harmonic.  The waves themselves don’t move or change shape at all, except to move up or down; they essentially “stand in place.” Because of this, they are known as standing waves.

This sort of mechanical resonance has had unexpected and devastating consequences in the past.  As I’ve noted on my other blog, suspension bridges have been brought down when soldiers marched across them in formation, inadvertently driving the bridges at the resonance frequency until they collapsed.  The most horrifying accident of this sort was the  collapse of the Anger Bridge in France in 1850.  A battalion of soldiers were crossing during a thunderstorm; although they knew not to march in formation, the swaying of the bridge caused them to unconsciously match its motion.  226 people were killed in the disaster.

The collapse of the Angers Bridge, via Wikipedia.

A string can only vibrate along its length; when we consider objects that have length and width, we can get correspondingly more complicated resonance phenomena.  This was what German physicist Ernst Chladni (1756-1827) demonstrated using the clever technique that now bears his name.  A rigid plate will have a set of natural resonance frequencies just like a string, and when the plate is excited at one of these frequencies, it will form a standing wave with fixed nodes.  These nodes will form lines on the plate, in contrast to points on the string.  Chladni realized that sand sprinkled on the top of the plate would be pushed away from the vibrating regions and settle into these nodes, allowing the node patterns to be seen.

From William Henry Stone (1879) Elementary Lessons on Sound, via Wikipedia.

Chladni excited these resonant vibrations by drawing a violin bow across its edge, as shown above.  Today, however, we can mechanically drive the plate from below with a mechanical driver — essentially a speaker hooked up to a frequency generator!  I purchased a commercial mechanical driver and Chladni plate, but it is possible to build one yourself by cannibalizing a speaker.

The patterns that result are beautiful, and increasingly complicated as the frequency is increased.  Those patterns that I’ve found are shown in the slideshow below.

We can compare my patterns with those sketched by Chladni himself, in his 1809 book Traité d’Acoustique.  Similarities between my modern version and Chladni’s can be readily seen.

So can we learn from the existence of resonance vibrations, each occurring at a discrete isolated frequency?  In fact, similar mathematics describes the energy levels of electrons in atoms and many other systems!

The era of quantum mechanics really took off in 1913 when Niels Bohr speculated that the curious properties of light emitted by atoms was the result of electrons only being allowed to exist stably in certain specific, discrete, orbits, each with its own discrete energy.  What Bohr could not explain is why electrons could only maintain these discrete orbits.  This question was answered in 1924 when Louis de Broglie postulated that electrons themselves have wavelike properties.  Just like waves on a string, then, an electron wave has certain natural modes of oscillation, and these are the stable states of the atom.  Some of these probability waves are illustrated below, via Wikipedia.

Laser cavities also demonstrate special modes of resonance.  In a rectangular laser cavity, a laser can be induced to output one of multiple so-called Hermite-Gauss modes (named after the mathematical functions used to describe them).

The first few Hermite-Gauss modes, via Wikipedia.

These modes are a little different from those described earlier, as they are not distinguished by their energy (or frequency), but rather by their momentum.  Nevertheless, the principle remains the same.  If one uses a circularly symmetric cavity, one can produce the so-called Laguerre-Gauss laser modes, some of which are shown below.

Some of the Laguerre-Gauss laser modes, via Wikipedia.

If we use a circular Chladni plate, we can also get a new set of patterns, as Chladni himself demonstrated in his book.  These patterns are strikingly similar to those of a circular laser cavity.

So by studying the vibrations of a metal plate, we can gain insight into everything from light to atoms!  Not a bad outcome from an experiment that was first done in the early 1800s!

Update: I thought I’d mention the specific tools I used for my Chladni setup, as following the “official” requirements through an online science store can be expensive!  I ordered a vibration generator and Chladni plate from DrMass.com for about $250.  Instead of purchasing a very expensive signal generator to drive the system, I purchased a stereo receiver from Radio Shack for $100.  To generate the frequencies, I downloaded a free tone generator app to my iPhone!  All told, I spent quite a bit of money to get my system running, though as I noted above it is possible to build your own driver for much cheaper.

The principle behind one of these cloaks is illustrated below, taken from the original paper by Pendry, Schurig and Smith.   The cloak guides light around the central region and sending it along its original path, like water flowing around a boulder in a stream.  The lines in the illustration represent rays of light being deflected and returned to their original trajectories.

The device is passive; it “works its magic” by virtue of the materials it is built out of, and guides light around the hidden region by what amounts to refraction.

It is fun to talk about the unusual implications of optical invisibility, but it is hard to show it!  Cloaks are complicated, and there are relatively few experimental realizations to date — and those that do exist are not easily reproducible without a lot of resources.

Fortunately, there exists a simple trick, suggested by my colleagues*, that can be used to demonstrate the principle of cloaking in a striking way!  I assembled a version of this trick myself for use in a recent popular talk on invisibility physics that I gave; a short video of it is shown below.

A finger placed behind the device is readily visible, but a finger placed within the cloak vanishes!

For about $50, you too can make your own “cloaking device”, albeit an oversimplified and crude one!  Let’s take a look at how it is done.

The device is constructed out of eight glass right-angle prisms arranged as shown in the top-down photograph below.

The operation of the cloak is really simple to explain.  Suppose we look through the device from the bottom up; light coming from above bounces through the system as shown in the following image.  (Rays have been color-coded to clearly show path of travel.)

The illusion is obviously not perfect — looking at the “cloak” from any direction other than directly in front of one of the flat faces will not provide any effect, other than a highly distorted image.  This is not exactly a flaw, as more recent cloaking investigations have focused on such “directional” cloaks as a way to simplify the design requirements.

But an interesting question arises: the prisms are made of clear glass: why doesn’t some of the light passing through the system just go right through the side of the prism and into the  diamond-shaped cloaked region?  For that matter, why doesn’t some of the light escape out through the sides of the cloak as it bounces around?  The answer is that the light is totally internally reflected at the glass interfaces, and none escapes until it hits the exit surface head on.

What is total internal reflection?  As discussed in my “basics” post on refraction, when light crosses a flat interface between two media, it changes direction: this is the phenomenon of refraction.  When light goes from a rarer medium (like air) to a denser medium (like glass), the ray gets bent towards the line perpendicular to the surface.  When it goes the other way, from a denser medium to a rarer medium, it gets bent away from the perpendicular; this is illustrated below.

Refraction satisfies Snell’s law, which says that the angles of the rays and the refractive indices (labelled by n) satisfy the relation:

.

We won’t worry about Snell’s law in detail right now, but the important thing to note is that  light coming from glass to air exits the interface at a bigger angle than it hit the interface.  But this means that there is some critical angle at which the light is refracted parallel to the surface!

This means that any light hitting the interface at greater than the critical angle will not be refracted at all: in fact, it will be completely reflected inside the glass, and no light will escape.  This is total internal reflection, and it is also, loosely speaking, how fiber optic cables can transmit light over long distances with little loss.  The light is trapped inside the glass cable and cannot escape except at the ends.

A crude illustration of how fiber optics works.

A glass with a refractive index of n = 1.5 will have a critical angle of 41.8°, meaning that any light hitting the interface with an angle larger than this will be totally reflected.  In our prism cloak, light is hitting the boundary at 45°, so all the light is funneled from one side of the cloak to the other without escaping.

Though this device is not even close to a perfect cloak and is certainly not invisible, it does demonstrate two important aspects of the original invisibility cloak design.  First, it guides light around a hidden region, as a perfect cloak would be expected to do.  Second, it hides the interior region by total internal reflection, and this is essentially what happens in a perfect cloak as well.  In fact, a perfect cloak in principle would have a refractive index of zero on the interior edge, meaning that all rays of light, regardless of angle, must be trapped within.

The effect is also good enough to impress people and convey that invisibility is scientifically feasible, if not possible — yet!

A finger behind the prism cloak — readily visible with little distortion.

A finger inside the prism cloak — not visible!

* A special thanks to Mike Fiddy and Robert Ingel of UNC Charlotte for suggesting this idea.

Written in 1976, The Face of the Lion is a rather unusual novel — it can be considered an early novel that contemplates the possibility of a “zombie apocalypse,” so popular in horror fiction today.

When a remote region of the Scottish Highlands is cordoned off by mercenaries working for the laird James Frasier Clyde, the British government suspects that Clyde is planning to test a home-made atomic bomb in a bid for Scottish independence.  It becomes quickly clear, however, that Clyde is not seeking to keep people out as much as keep something in: a horrible disease is spreading among the people of the area, turning them into mindless raging beasts that can spread their contagion with a touch.  As the infection spreads beyond the restricted region, bacteriologist Sir Marcus Levin and Colonel Lawrence of the Internal Security Service race to understand and contain it before the entire country, if not the world, is devastated.

The Face of the Lion is very much a classic style of Blackburn novel: part horror and part mystery.  There is a sinister and complicated force behind the plague, and discovering its origin is just as much a part of the plot as is stopping it.  True to all of Blackburn’s fiction, the story contains many twists and turns, all the way up to its final shocking revelations.

This is not one of Blackburn’s strongest novels: by 1976, he had been writing horror — and about plagues in particular — for nearly 20 years, and the story doesn’t “click” as much as his earlier works.  In fact, the story is reminiscent of even his first novel, A Scent of New-Mown Hay, in which a sinister disease threatens to wipe out the world.  Nevertheless, The Face of the Lion is well-crafted and works well as an introduction to Blackburn’s work, which was hugely popular in his time and had a significant influence on later British horror authors.

I had a lot of fun with the introduction to this book, trying to fit it into the broader genre of “zombie apocalypse” novels.  This gave me the opportunity to present a short history of such novels, stretching back hundreds of years to the first “last man” story in 1805.  The Face of the Lion was very much ahead of its time and I think readers will be fascinated to see how much Blackburn anticipated future developments in the genre.

It’s also worth noting that I had a small part in the design of the cover of this edition!  I provided the basic structure of the lion and biohazard sign and Valancourt crafted it into the excellent cover that is pictured above.  Hopefully it gives the right feeling of sophisticated menace that John Blackburn’s books so rightly deserve.

One that caught my eye was J.B. Priestley‘s short 1927 novel Benighted.

Cover of the Valancourt edition, reproduced from the original.

This was the second novel of J.B. Priestley (1894-1984), a prolific author who published 26 novels during his lifetime.  It was with his third novel, The Good Companions, that Priestley achieved major success, but Benighted was significant in its own right, being made into the 1932 film The Old Dark House, starring the iconic Boris Karloff.

What is it about?  The movie title is rather perfect, as the story is of a genre of what may be called “old dark house” stories.  In such stories, a group of people are gathered by design or fate in a old sinister house, are trapped within it together by circumstance and subjected to unspeakable horrors.

In Benighted, Philip and Margaret Waverton and cynical acquaintance Roger Penderel are traveling through a remote section of Wales when a savage storm forces them to seek shelter.  The only place available is an ancient mansion owned by the bizarre and decadent Femm family, together with their monstrous servant Morgan.

The Femms are clearly afraid of something, and very hesitant to allow guests even for the night.  Nevertheless, there is nowhere else to go, so the Wavertons and Penderel take up a spot near the ground-floor fireplace.  While there, they probe deeper into the mysteries of the house as well as their own fears and secrets.  As the storm intensifies outside, the danger grows within.  Before the night ends, the inhabitants of the house — visitor and resident alike — will find themselves struggling to survive.

Benighted is much more than a spooky thriller — it is also a character study.  We learn about the Wavertons and Penderel (and others) as the story progresses, and gain sympathy for even the seemingly most reprehensible of them.  That is not to say that the story is not creepy or thrilling — it is!  At a mere 152 pages, it has no unnecessary filler and moves briskly, though it does not feel rushed.

The Valancourt edition has an excellent introduction by Orrin Grey, who like me has a love of the macabre, creepy and supernatural in fiction.  He talks about his involvement in Benighted here, which he in fact recommended to Valancourt.

It was a good recommendation on Grey’s part, because Benighted is an excellent novel worth reading for its characters and ideas as well as for its creepy atmosphere.

• cosmonauts who had to survive the Siberian forest after surviving space,
• fixing astronomical equipment with earwax,
• Victorian issues with masturbation,
• Margaret Thatcher’s dubious connection with soft-serve ice cream,
• and much more!

Many thanks to Mike Finn and Jenn Wallis for putting together an excellent carnival!

The next edition of The Giant’s Shoulders will appear at the Something by Virtue of Nothing blog on 16th May 2013.  Posts are due for submission by May 15, and can be submitted directly to the host, to  ThonyC at The Renaissance Mathematicus or to me right here!

The island of Sumbawa, with Mount Tambora clearly seen. Via Wikipedia.

The eruption of Tambora is a troubling reminder of the powerful forces that lie sleeping within the Earth.  When the mountain blew, it ejected an estimated 160 cubic kilometers of material, with an eruption column some 43 kilometers high.  Before the eruption, the mountain was 14,100 feet tall, and one of the tallest in Indonesia; afterwards, only 9,354 ft of its height remained.  Ash was distributed throughout the upper atmosphere worldwide, resulting in significant climate effects, as we will note below.

The death toll from the eruption was horrific: some 12,000 people were killed as a direct result of the eruption, with even more dying in the aftermath from famine and disease.  The most modern estimate suggests 71,000 people died in total.

In that era, worldwide communication was still slow and unreliable.  There are not many detailed reports of the eruption itself, and its aftermath.  On this grim anniversary, I thought I would share some of the original first-hand accounts of the event and the devastation.

The best source of information on the Tambora eruption comes from Sir Thomas Stamford Raffles (1781-1826), who was at the time the Lieutenant Governor of Java, Indonesia.  Though Java had long been a Dutch colony, the Netherlands was annexed by Napoleon into the French Empire in 1811.  With Java now a French holding, it was seized by British forces (including Raffles) that same year.  Raffles was appointed Lieutenant Governor and maintained that post until the end of 1815, when control of the colony returned to the Dutch.  In the aftermath of the eruption, Raffles requested eyewitness accounts from residents of his districts, and these were combined into a “Narrative of the effects of the Eruption from the Tomboro Mountain in the Island of Sambawa on the 11th and 12th of April 1815,” which was finished in September of that same year.

The eruption formally began on April 5th, and the loud booms from the mountain were heard hundreds of miles away and first interpreted as cannon fire. Ships and military expeditions were actually sent from various settlements to respond to what was thought to be citizens under attack. Ash began to fall on the 6th, however, leaving no doubt as to the cause of the sounds.  From here, we turn to extracts from different (relatively distant) parts of Java for accounts.

An extract of a letter from Grissie (presumably Gresik):

I woke in the morning of the 12th, after what seemed to be a very long night, and taking my watch to the lamp found it to be half past eight o’clock, I immediately went out and found a cloud of ashes descending; at 9 o’clock no day light-the layer of ashes on the terrace before my door at the Kradenan measures one line in thickness; ten A. M.-a faint glimmering of light can now be perceived overhead: half past 10- can distinguish objects 50 yards distant: 11 A. M .-Breakfasted by candle-light, the birds begin to chirrup as at the approach of day: half past 11-can discover the situation of the sun through a thick cloud of ashes; 1 P.M. found the layer of ashes one line and a half thick, and measured in several places with the same results; 3 P. M. the ashes have increased one eighth of a line more; 5 P. M it is now lighter, but still I can neither read nor write without Candles. In travelling through the district on the 13th, the appearances were described with very little variation from my account, and I am universally told that no one remembers, nor does their tradition record, so tremendous an Eruption – some look upon it as typical of a change, of the re-establishment of the former Government; others account for it in an easy way by reference to the superstitious notions of their legendary tales, and say that the celebrated Nyai Luroh Kidul has been marrying one of her children, on which occasion she has been firing salutes from her supernatural Artillery. They call the ashes the dregs of her Ammunition.

It is interesting to note that many locals considered the eruption a sign of impending change; in Simon Winchester’s book Krakatoa, he suggests that the later eruption led to the end of Dutch colonial rule, as the Indonesians took the event as a sign of displeasure from the gods.

From Sumanap, which is now spelled Sumenep:

On the evening of the 10th the explosions became very loud, one in particular shook the Town, and they were excessively quick, resembling a heavy cannonade. Towards evening next day the atmosphere thickened so much, that by  4- o’clock it was necessary to light candles. At about 7 P. M. of the 11th, the tide being about ebb, a rush of water from the Bay occasioned the River to rise four feet. and it subsided again in about 4 minutes; the Bay was much agitated about this time, and was illuminated from a Northerly direction. On the Island of Sahotic, fire was seen distinctly at a short distance to the South-east. The uncommon darkness of this night did not break till 10 and 11 A M. of the 12th, and it could hardly be called day light all day. Volcanic ash fell in abundance, and covered the earth about two inches thick, the trees also were loaded with them.

The “rush of water” from the Bay was certainly one of several relatively small tsunamis that was created by the explosion of Tambora.

From Baniowangie, now Banyuwangi, we get the report:

At 10 P.M. of the 1st April we heard a noise resembling a cannonade, which lasted at intervals till 9 o’clock next day, it continued at times loud, at others resembling distant thunder-but on the night of the 10th the explosions became truly tremendous. frequently shaking the Earth and Sea violently; towards morning they again slackened, and continued to lessen gradually till the 14th, when they ceased altogether-on the morning of the 3d April, ashes began to fall like fine snow., and in the course of the day they  were half an inch deep on the ground; from that time, till the 11th the air was constantly impregnated with them, to such a degree that it was unpleasant to stir out of doors- on the morning of the 11th the opposite shore of Bali was completely obscured in a dense cloud, which gradually approached the Java shore and was dreary and terrific -by 1 P. M. candles were necessary, by 4 P. M. it was pitch dark, and so it continued until 2 o’clock of the afternoon of the 12th, ashes continuing to fall abundantly: they were 8 inches in depth at this time. After 2 o’clock it began to clear up, but the sun was not visible till the 14th, and during this time it was extremely cold-the ashes continued to fall, but less violently, and the greatest depth, on the 15th of April, was 9 inches.

Comparing the reports as we get closer to the mountain, it can be clearly seen that the effects get appreciably worse.  Nothing could compare to the experiences of the Rajah of Saugur and his neighbors, whose home village was right at the foot of the mountain itself (communicated to Raffles by Lieutenant Owen Phillips):

About 7 P.M. on the 10th of April, three distinct columns of flame burst forth near the top of Tomboro Mountain, all of them apparently within the verge of the crater, and after ascending separately to a very great height, their tops united in the air in a troubled confused manner. In a short time the whole Mountain next Saugur appeared like a body of liquid fire extending itself in every direction.

The fire and columns of flame continued to rage with unabated fury until the darkness, . caused by the quantity of falling matter, obscured it at about 8 P.M.  Stones at this time fell very thick at Saugur-some of them as large as two fists, but generally not larger than walnuts; between 9 and 10 P. M. ashes began to fall, and soon after a violent whirlwind ensued, which blew down nearly every house in the village of Saugur, carrying the tops and light parts away with it; In the part of Saugur adjoining Tomboro, its effects were much more violent, tearing up by the roots the largest trees, and carrying them into the air together with men, houses,  cattle, and whatever else came within its influence, (this will account for the immense number of floating trees seen at sea.) The sea rose nearly 12 feet higher than it had ever been known to be before, and completely spoiled the only small spots of rice lands in Saugur-sweeping away houses and every thing within its reach.

The whirlwind lasted about an hour, no explosions were heard till the whirlwind had ceased, at about 11 A. M.  From midnight till the evening of the 11th, they continued without intermission, after that time their violence moderated, and they were only heard at intervals, but the explosions did not cease entirely until the 15th of July. The mountain still throws out immense volumes of smoke, and the Natives are apprehensive of another Eruption during the ensuing rainy season.

I cannot even imagine the terror of the people as this monstrous eruption began right on their doorstep.  As I have said, some 12,000 people are estimated to have been killed by the eruption directly, through volcanic activity and the tsunamis that resulted.

The caldera of Mount Tambora today, via Wikipedia.

Tambora’s eruption had even more far-reaching influences.  1816 became known as the “Year Without a Summer“, as ash and sulfuric acid from the blast spread worldwide through the upper atmosphere, blocking solar radiation from reaching the Earth.  Snow and freezing temperatures still occurred on the East Coast of the U.S. in June, and people would hang clothes out to dry only to find them frozen to the line later in the day.  The year was also known with grim humor as “Eighteen hundred and froze to death.”

Mount Tambora also likely had at least one major impact on culture.  The cold rain ended up ruining a June 1816 outing in Switzerland for Mary Shelley, Percy Shelley, Lord Byron and John Polidori, and the group ended up staying indoors.  The grim weather inspired grim talk of ghost stories and bringing the dead to life through electricity (via the newly-discovered galvanism).  Lord Byron challenged each member of the group to write his or her own supernatural story.   The outcome of this challenge led to two major literary figures in horror.  John Polidori wrote The Vampyre, which would later inspire Bram Stoker’s Dracula. Mary Shelley, of course, would end up writing Frankenstein.

]]> http://skullsinthestars.com/2013/04/10/april-10-1815-mount-tambora-blows-up/feed/ 3 skullsinthestars The island of Sumbawa, with Mount Tambora clearly seen. Via Wikipedia. stamfordraffles gressie sumanap baniowangie The caldera of Mount Tambora today, via Wikipedia. frankenstein