Ghosts, Vampires and Zombies

Recently, the "researchers" Costas J. Efthimiou and Sohang Gandhi came out with a paper entitled Ghosts, Vampires and Zombies: Cinema Fiction vs Physics Reality where they tried to "prove" that none of these creatures could possibly exist. And catch this, they actually tried to do it using math and physics. What a joke!

Let's first dispense with their pathetic attempt to pre-empt my brilliant debunking.

Of course the paranormalist or occultist could claim that the Hollywood portrayal is a rather unsophisticated and inaccurate representation of their beliefs, and thus the discussion we give hear is moot.

Hey Professor! Learn to spell "here!" What a maroon.

There were three types of monsters covered in this "paper." I will go through and debunk their debunks one by one. The first monster is the ghost. Here's what the good professor had to say.

Ghosts are held to be able to walk about as they please, but they pass through walls and any attempt to pick up an object or affect their environment in any other way leads to material-less inefficacy — unless they are poltergeists, of course!
Let us examine the process of walking in detail. Now walking requires an interaction with the floor and such interactions are explained by Newton’s Laws of Motion.

blah, blah, blah ...

Thus the ghost has an affect on the physical universe. If this is so, then we can detect the ghost via physical observation. That is, the depiction of ghosts walking, contradicts the precept that ghosts are material-less.
So which is it? Are ghosts material or material-less? Maybe they are only material when it comes to walking.

Let's do a little experiment. What happens when you shine a polarized light beam on a pair of polarized glasses at different angles? Obviously, at one angle, the light passes through; at the other angle, the light is blocked. It's pretty obvious that ghosts are made of some form of meta-material that is polarized perpendicularly to the wave of gravitons that are virtually emitted from the center of the earth. That way the ghosts are blocked from passing through the floor, but can easily walk through walls. This also explains why if you throw a sheet over a ghost, it won't pass through the ghost and fall on the floor. Yet since the ghost's polarization only blocks up and down, the sheet is free to sweep to and fro through the ghost's body--almost as if it were hanging by a wire on a B-movie set. But when he raises his hands to say "Boo!" he is able to move the sheet. It's so obvious even a 5 year old can understand it.

The next ghoul on the list is the vampire. Since the paper's explanation included charts, tables and equations, let's look at the sumarry given in this article.

To disprove the existence of vampires, Efthimiou relied on a basic math principle known as geometric progression.

Efthimiou supposed that the first vampire arrived Jan. 1, 1600, when the human population was 536,870,911. Assuming that the vampire fed once a month and the victim turned into a vampire, there would be two vampires and 536,870,910 humans on Feb. 1. There would be four vampires on March 1 and eight on April 1. If this trend continued, all of the original humans would become vampires within two and a half years and the vampires' food source would disappear.

He's basing his entire calculation on the assumption that every vampire creates a new vampire every time it feeds. I think Dr. Efthimiou needs to go back to the source. The only way to create a new vampire is to drink the blood of the Prince of Darkness himself. Dracula is like the queen bee: the only member of the hive allowed to reproduce. So instead of a geometric progression, you get an arithmetic progression up until the Count decides the vampire population is just right for him, then it plateaus. Once again, math that a child would undersand.

The last of the spectres are zombies.

There exists a second sort of zombie legend which pops its head up throughout the western hemisphere — the legend of ‘voodoo zombiefication’. This myth is somewhat different from the one just described in that zombies do not multiply by feeding on humans but come about by a voodoo hex being placed by a sorcerer on one of his enemy. The myth presents an additional problem for us: one can witness for them self very convincing examples of zombiefication by traveling to Haiti or any number of other regions in the world where voodoo is practiced.

Gee perfesser, I thought you were trying to prove that movie monsters aren't physically possible. And so now you come out with a monster that you yourself admit is real. I don't even need to debunk here.

Obviously this paper fails at every attempt to disprove movie monsters, therefore they actually exist.

Freaky Halloween

Last Sunday I went to the Mutter Museum. They were holding a special event(pdf) that I only found out about from a Minnesota based weblog; I really need to get out more. Since I went to see Gunther von Hagens' Bodyworlds exhibit a few moths back when it was in town, I thought I'd compare and contrast the two.

The first obvious difference is that the Bodyworlds specimens were specifically prepared for the exhibit. The Mutter specimens were created as study aids for medical students. The presentation at Bodyworlds was very impressive. I'm sure that if they had plastination back in the nineteenth century, many of the Mutter specimens would've been preserved in that manner. Finally, most (not all) of the Bodyworlds bodies were "normal." Very few Mutter specimens can be described with that word. "Freaks" might have been the more appropriate term in less politically correct times. For example, one display case had the colon of a man who died from constipation (at his autopsy, 40 pounds of feces were removed from him).

Obviously, my recollection of Bodyworlds is not as fresh as the Mutter, but I do remember it was interesting. However the Mutter was absolutely transfixing. Maybe it was the melding of history with science a la macabre that did it, but I'll be going back!

It starts out just like a more mundane medical museum. You are greeted by a portrait of B. Franklin and treated to some of his writings and correspondence about medicine. You get to see one of his pairs of bifocals (which he invented) as well as other medical instruments from that day. The museum moves on to others like Benjamin Rush (founder of the Philadelphia College of Physicians) and Thomas Mütter (founder of the museum) and a short history of medicine. Then you move to the specimen room. Wow! What a change.

From conjoined twins to the "soap woman," you get to see a veritable plethora of misshapen and deformed body parts. I stopped a little longer than usual to look at the skulls with microcephaly (not to be confused with the shrunken heads from South American tribes) because they reminded me of the conflict surrounding the Hobbit of Flores. So it was kind of a surprise to see some microcephalics featured in the movie they showed afterwards. It had nothing to do with the museum, but the subject matter was related. I was seated in an uncomfortable armless chair (they hadn't thought to stagger the rows so I got a really good view of the back of the head of the guy in front of me) watching an old grainy movie with horrendous sound quality.

There was also a movie with the Bodyworlds exhibit. It wasn't about the show either, but it was an IMAX movie about the human body. It was quite an impressive spectacle. There's no contest as to which movie was better. The movie they showed for Bodyworlds was the worst thing about the exhibit. The best part about it though, wasn't even the movie itself, but the Welcome to Philadelphia preview they showed beforehand (which I'm sure they show before all their shows). Seeing the skyscrapers of Center City from above then zooming in (all in IMAX) was cool!

The movie they showed at the Mutter was Tod Browning's 1932 cult classic Freaks. It was about a group of travelling circus "freaks" (carnies). It was originally billed as a horror flick, but I saw it more as a morality tale. The ugliest people in the film were the ones who were beautiful on the outside. Although there was one scene where all the freaks are crawling on the ground in the rain that reminded me of many modern horror movies.

Many of the afflictions I had just seen in the museum were featured in the movie. Besides the microcephalics, there were the conjoined twins Daisy and Violet Hilton--whom we shall call "the normal Hilton sisters." One of the most impressive scenes was watching the human torso, Prince Randian, light a match with one corner of his mouth will holding his cigarette in the other corner. At the Q & A after the movie, one of the emcees (a museum curator) mentioned that the scene before that was of him rolling the cigarette, but it got cut. Too bad that in 1932, the cutting room floor meant death. Another highlight (and a pretty good actor, actually) was the half-boy, Johnny Eck (check out his wesite). He had a twin brother who was normal (full body) and they got started in show biz doing vaudeville. Johnny's brother would play the part of a heckler during a magic act. The magician would respond by inviting him on stage to get sawed in half. When the audience was distracted, a switch would be made and the brother would be replaced by Johnny and a dwarf inside a pair of pants (that way the two halfs could run around the stage after the sawing was done).

All that almost makes me want to become one of them.

My personal faith

Although I have alluded to my religious inclinations in some previous posts, I've not actually come out and unequivocally averred my convictions. If you were curious, I've found this FAQ page that neatly sums up where I stand.

Crystal Lava

This last week, The Geological Society of America held its annual meeting in my home town of Philadelphia. There were all sorts of presentations, workshops, seminars and other events. Naturally I didn't attend any of it since I had more mundane things to do, like thermal analysis. I did follow most of the highlights from the meeting though, on ScienceDaily. Yet the geological story that really caught my attention wasn't from the meeting at all, but from a September issue of Nature. In Decompression-driven Crystallization Warms Pathway for Volcanic Eruptions, Dr. Katharine Cashman of the University of Oregon argues that rapid crystallization of magma causes it to heat up by as much as 100°C.

The reason may be counter-intuitive, but the more magma crystallizes, the hotter it gets and the more likely a volcano will erupt, according to a team of scientists that includes a University of Oregon geologist. The knowledge likely will aid monitoring of conditions at Mount St. Helens and other volcanic hot spots around the world.

It certainly does seem counter-intuitive: decompression generally causes cooling. That's the basis for how refrigeration works. In the diagram on the right (thanks to Wikipedia), the two places where there are pressure chages are the Compressor and the Expansion Valve. The Compressor increases the pressure and superheats the refrigerant. The Expansion Valve causes decompression and auto-refrigeration. This is how most materials behave.

I remember when I was a kid, my grandfather let me shoot his 22 caliber rifle at a spent aerosol can. The can still had pressure in it, because when I hit it (we'll just pretend it was on my first shot), the rapid decompression caused the can to fly (and the momentum from the bullet probably helped out there too). When we recovered the can, it was covered with frost and very cold to the touch.

Why then does magma behave so counter-intuitively? The answer lies in a process called fractional crystallization. From wikipedia:

Fractional crystallization is one of the most important geochemical and physical processes operating within the Earth's crust and mantle. Fractional crystallization is the removal and segregation from a melt of mineral precipitates, which changes the composition of the melt.

Fractional crystallization in silicate melts (magmas) is a very complex process compared to chemical systems in the laboratory because it is affected by a wide variety of phenomena. Prime amongst these is the composition, temperature and pressure of a magma during its cooling. The partial pressure of vapor phases in silicate melts is also of prime importance, especially in near-solidus crystallization of granites.

In the case of the above study, water seems to be the key. At the pressures existent deep in the Earth, water is dissolved in the magma preventing crystallization. Think about a glass of salt water. The salt isn't crystalline because of the presence of water keeps it in solution. However, if you leave the glass on the counter for the water to evaporate, you'll see the salt begin to crystallize out. A similar process appears to happen to the magma as it moves up towards the surface of the Earth. About 2 kilometers from the surface, decompression causes the pressure to drop enough that the trapped water is able to turn to steam and escape the magma. As a result, certain minerals in the magma begin to crystallize. But shouldn't the escaping steam cool the magma? How does the crystallization cause it to heat up?

The short answer is that crystallization is exothermic. This means that it produces heat. Melting and vaporization are endothermic; they require heat. Another example of an exotherm is an oxidation reaction, such as combustion. Since both exothermic and endothermic things are happening to the magma, the exotherms must be winning. The tool of choice for measuring exotherms and endotherms is the Differential Scanning Calorimeter (DSC).

The basic idea of the DSC is to measure the difference in heat flow between a sample and a reference standard. The set-up is pretty simple. Two identical sample pans are placed side by side over two very sensitive temperature probes (thermocouples). One pan contains a sample of the material to analyze, and the other is empty and acts as the standard. This whole set-up is inside an oven (or a chiller) where the temperature can be carefully controlled. As the temperature inside the instrument changes, the thermocouples detect any difference in heat-flow between the two pans.

If an endothermic event (like a melt) occurs, then the sample will absorb some of the heat it is being given for the melt process, while the standard will continue to use all its heat for temperature increase. The thermocouples will detect the temporary slight difference in temperature and send it to the computer. On the DSC chart, this will show as a downward facing peak.

If an exothermic event (like crystallization) occurs, then the sample will heat up and the thermocouples will detect it. If the exothermic event is encountered during a cool down, then the sample either briefly stops cooling, momentarily heats up a tad, or just cools at a slower pace than the standard. On the DSC chart, this will show as an upward facing peak.

The chart below is a DSC scan I ran of a material known as a plastic crystal. Plastic crystals are a class of compounds that store and release heat through a reversible solid-solid transition from an ordered crystal to a less ordered plastic state. The phase transition of a plastic crystal involves more energy than the heat of fusion. Plastic crystals are therefore very useful in industry for heat storage; they are sort of like heat capacitors. This is why I thought it would make a good example. Obviously whatever is crystallizing out of the magma must also have a high crystallization enthalpy in order to counteract the endotherms associated with decompression and still raise the temperature by 100°.

Allow me to explain what is happening in the above chart. I tested the plastic crystal sample starting at 20°C, then slowly ramped the temperature up to 120°C, then let it cool back down to 20°C. That is why the curve doubles back on itself--the x-axis of the chart is increasing temperature. The scan begins at the left (the lower curve) and moves towards the right. The first event is an endotherm around 80°C. This corresponds with the sample going from a crystalline to a plastic phase. Unlike the material in the example chart on the wikipedia page (which offers a very good explanation if you're still scratching your head after reading me), the plastic crystal is crystalline at room temperature and becomes amorphous before melting (I didn't take it up that high, but if I had, you would see that the melt endotherm was much smaller than the decrystallization endotherm). This happens because when the material hits about 80°C, it begins to absorb heat in order to break up the crystals--heat that would otherwise be used to raise the temperature. The standard (empty pan) undergoes no such transition, and the instrument detects the difference.

The next event happens at around 120°C when the curve doubles back to the left. This is where the temperature begins to drop back down. No "heat event" happens here. The final event begins at about 70°C. This is the exotherm of crystallization. Here the sample begins to heat up faster than the standard as it crystallizes. I'm not exactly sure why there is a 10°K (It is customary in thermal chemistry to use kelvins when talking about change in temperature. An increase of 1°K is equal to that of 1°C.) discrepancy between the crystallization and decrystallization temperatures, but that kind of thing is not unusual.

So what appears to be happening in a volcano is that first the magma decompresses (and cools some) as it flows towards the surface and nears the dome of the volcano. Second, the decompression allows trapped water to escape the magma (and cool it some) in the form of steam. This should manifest itself to the observer as a series of minor "steam heavy" eruptions from the mountain. Third, the loss of water allows minerals in the magma to undergo crystallization. This crystallization, like that of the plastic crystal, is highly exothermic and overpowers the previous endotherms raising the temperature of the magma by up to 100°K. :-) Fourth, this exotherm greatly increases the energy of the magma just as it's getting near the dome of the volcano. This makes for a very explosive situation.

And so with that, I shall leave you with a bang! (courtesy of Exploring the Environment)

Mt. St. Helens 1980 eruption animation

Friggatriskaidekaphobia

Last night I went to the Freethought Society of Greater Philadelphia's annual Friday the thirteenth Anti-Superstition Party. Preceding the party was a lecture (sponsored by the Philadelphia Association for Critical Thinking) from none other than Mr. Skeptic himself, Michael Shermer. Unfortunately, I missed the begining of his talk as I was getting into my costume (yes, I volunteered). But I was able to catch most of it and he was quite good. I also bought a copy of his latest book Why Darwin Matters. Here's a few highlights from the speech.

1. He told the story of how his transition from fundamentalist Christianity to atheism began at Pepperdine University. He enrolled with the intention of studying Theology, but decided to study science instead because he was pretty good with numbers methodology. Then he started to slowly take a critical look at his own beliefs.

2. He laments that the word skeptic has the negative connotation of being against something rather than being for anything. In fact, skepticism is not a philosophy but a methodology, and should properly be interchangable with the word science.

3. He stressed the importance of approach when dealing with fundamentalists. If you start off by telling someone that their beliefs are ridiculous and nonsensical, you're going to lose that person. It is irrational to alienate someone you're trying to woo over to your side.

4. He spoke about how Intelligent Design is essentially like giving up on the search for knowledge.

5. When he spoke about the grandeur of the Universe, he quoted extensively from the late Carl Sagan. This was especially moving as I consider Sagan to be one of the greatest Poets of Reason.

6. After the lecture, at the party, Dr. Shermer told me that despite his busy schedule, he still gets in about ten hours of bicycling per week. One more reason for me to be skeptical of all you who say "I'm too busy to exercise."



Someone should tell the guy in the Leprechaun costume that you're supposed to cross your suspenders in the back. No wonder they kept slipping off. Doh!

Cirque du Lune

October 6th was the Harvest Moon. The Harvest Moon is the full moon that falls nearest the autumnal equinox. It happens right around harvest time, and since the Harvest Moon-rise is in near synchronicity with the sunset, it has given ancient cultures an extra few hours of light to work with. But there's more to the Harvest Moon than just antiquated superstition and primeval pragmatism. The HM steals colors. A recent NASA article explains it best.

Moonlight steals color from whatever it touches. Regard a rose. In full moonlight, the flower is brightly lit and even casts a shadow, but the red is gone, replaced by shades of gray. In fact, the whole landscape is that way. It's a bit like seeing the world through an old black and white TV set.

The reason for this lies in the human retina. We have two basic kinds of light receptors: rods and cones (we have three kinds of cones--but more on that later). The rods are sensitive to faint light, and the cones can differentiate colors. During the day, our cones supply enough information to the brain for it to build a color model of the world we see. But in the moonlight, rods are king. Our cones just cannot generate enough data for us to see a technicolor world.



The above photoshopped image is my attempt to simulate the effect. It is a blend of 15% moonlight color (see below) and 85% grayscale. But this is not the only way the Moon steals color from us. Besides being fainter, moonlight has a different spectrum than sunlight. It doesn't reflect 100% percent of the Sun's light, it absorbs some--and not all wavelengths are absorbed equally. Furthermore, the Harvest Moon is renowned as being an Orange Moon. There are two reasons for this: at this time of year the Moon stays lower on the horizon, and there is more dust in the atmosphere during the HM. Put together, it means that moonlight must pass through a much thicker and denser atmospheric dust filter during HM than at other times of the year. As a result, blue wavelengths get filterted out preferentially. It turns out that the sky is blue for the same reason that the Sun and Moon appear yellow/orange when near the horizon.

This got me thinking that if I were to do an extended exposure where the "cones" got to see the HM moonlight, I should see different colors (less blue). The picture below is the result of that experiment. Besides the apparent yellowing of the painting, the long exposure reveals a moon-glare that was invisible to my diurnal human eyes.



But obviously all this talk of the Moon "stealing colors" is metaphoric. Of course the colors are still there; we just can't see them because of the light. Well, actually no. If you can't see the colors, then they don't exist. Let me say that again: colors you don't see, don't exist.

"What kind of solipsistic nonsense is that?" you ask. Or perhaps you're asking "What is 'solipsistic'?"

Solipsism is a group of varied philosophic tendencies that state that "the self" or "the mind" is the truest (or only true) reality: Cogito Ergo Sum. The most extreme case--metaphysical solipsism--claims that nothing outside of the mind is real. My introduction to solipsistic thinking was the paradox of Schrödinger's cat. This thought experiment is an extension of the observed and reproducible phenomenon from Quantum Mechanics that a quantum entity which can exist in one of two quantum states, exists in neither and exists in both (quantum superposition), until the moment it is observed. In the experiment, a cat in an opaque box is set to be killed if an atomic nucleus (with a 50% chance of decaying) decays. After the prescribed period, until someone looks into the box and observes, the cat is neither dead nor alive. It is in quantum superposition of being both dead and alive. In other words, the definite fate of the cat (which happened in the past) does not exist until it is realized by the mind of an observer. We can call this Quantum Solipsism.


Naturally, I rejected this and decided that solipsists were either clowns or lunatics. It would be years later (I was still in high school) before I learned about epistemological solipsism, so I shall come back to it later.

What started me on my road to giving solipsism a second look was my study of Neoplatonism, Middle Platonism and Plato. (That's right. I studied them in reverse order)

Neoplatonism is epitomized in the figure of Augustine of Hippo. Augustine believed that the sensible realm (the world we know) is transitory in nature, and that abiding realities could only be found in the intelligible realm, with God as its source. I really had trouble swallowing that circus act.

Middle Platonism is exemplified by Philo of Alexandria. Philo's Platonic reading of the Jewish scriptures, along with the transcendence of God and the abasing of the physical body, layed the groundwork for the future theological fondations of Christianity. Who are the crazies? I decided to check out the source.

Plato deserves much more attention than I can give him here, so forgive me if my summary is a bit curt. Plato seems to have also believed in the dichotomy of the sensible and intelligible. The intelligible is where the ideal exists and the sensible is but a poor imitation. This can be seen in his example of the chair.

He thought that everything had a sort of ideal form, like the idea of a chair, and then an actual chair was a sort of poor imitation of the ideal chair that exists only in your mind.

The trouble with this is that the mind (ie. - the brain) itself is fluid and not invariable. Today's ideal chair need not be tomorrow's, and mine (an EZ recliner) is surely not yours. Plato had it backwards: the "form" that exists in the mind is a contrived model based on incomplete sensory input. And this applies to all the "reality" that we know. As an example, let's re-examine the issue of color.

While it's true that some materials preferentially absorb or reflect certain wavelengths of electromagnetic energy, the "colors" that you and I are so familiar with are constructed in the brain. They do not exist outside of our awareness! Take a look at the retina (since rods and cones are types of neurons, I feel safe calling the retina part of the brain). Below is a graph showing wavelength sensitivity of the three types of cones in the human retina.



Each type of cone detects a different range of wavelengths. The peak of each curve represents the wavelength that gives the strongest signal for that cone type. Each type of cone reports only the intensity of the signal it receives. It cannot differentiate between a weak signal close to its "peak" wavelength and a strong signal further off on a tail of the curve. By having different cone types with overlapping sensitivities, the brain is able to put the information together and construct a color.

You may notice in the above graph two of the cone types (in the "red" region of the spectrum) are very close together. This means that our brains can more precisely discriminate between wavelengths in this neighborhood of the spectrum. To explain this, we need a quick review of evolutionary history. Most non-mammalian vertebrates--including birds--have four types of cones.

Some time ago, the ancestor of all mammals lost two of those cones. This is most likely because this animal was nocturnal and so wasn't well served by such fantastic color vision. Today, non-primate mammals only have two cone types. Which brings us to primates and their three. There are two ways this could have happened. If the "lost cones" were in fact just dormant, they could've been reactivated. This was not the case. Instead, a new cone type was created by a process called duplication. First, a copying error caused there to be an extra copy of the gene for "red" cone. Later, mutations caused the duplicate cone to become sensitive to somewhat different wavelengths. This is why their sensitivities are so close. Although there is a theory that this evolved as a way to better distinguish pinks--an indicator of fertility and emotion in primates. I'm all flush just thinking about it.

The thing to remember here is that the brain is not seeing wavelengths. It is getting sensory signals and constructing colors from them. A combination of different wavelengths of light that activated the cones in the same manner as a single pure wavelength would be seen as the exact same color. In the Scientific American article What Birds See, Tim Goldsmith tells of an experiment he did with birds . He trained birds to react to a certain wavelength of violet light and not others. He then demonstrated the the right blend of (92%) blue and (8%) UV light was indistinguishable from the training light to the birds. We would naturally be able to tell the difference because we don't have UV cones; we would see blue or violet. But for most of the spectrum, birds have a broader range of colors than we do.

It's not that the brain is being fooled into seeing the wrong color. Color is a creation of the brain. It's not out there in nature. It's only in the mind. When you take in all the leaves on the autumn trees, remember that those colors aren't actally there: they only exist in your head! When you're brought to joyful tears by the blushing pinks on your baby's cheeks, remember that those colors aren't actually there: they only exist in your head! And while you're marvelling at the magnificent works of art at the local museum, remember that those colors aren't actually there: they only exist in your head!

Everything that you know as reality is a construct of your brain. You cannot directly know the reality outside of your own awareness. That's not to say that reality is just an elaborate simulation, Occam's razor makes that quite remote. We just don't "know" any more about the outside reality other than it correlates well enough with our own realities that we can satisfactorily interact with it. This philosophy is otherwise known as epistemological solipsism.

Perhaps it's time for me to join the circus.

Remember ... walking in the sand.

My sister (the same one from the Katrina video) took this picture on her recent vacation in Georgia. I thought it was so cool; I just knew that I had to blog about it. Unfortunately, I know next to nothing about starfish--but that's never stopped me before.

This is actually a really good picture. The composition and the lighting are perfect. And you can make out the starfish's tracks quite well. Looking at the picture, the ocean is off to the upper left. So the starfish started to briefly head off away from the water, then he banged-u and headed on home. Shortly after the picture was taken, my sister picked him up and gently tossed him into the ocean (which was quite a ways away and still receding).

The next thing that pops out at you about the picture is that the starfish left exactly three whole body prints in the sand. Was he making sand angels? I'm not sure what he was "thinking," but these were surely spots where he stopped and began to sink in due to the soft, wet sand. These couldn't have been caused by waves crashing in around him, as these would've erased the record of his past travels. By that same token, the first whole body print must represent where our friend was resting when the tide first receded. Also, the possiblity that he didn't slow down but hit some unusually soft patches of sand seems unlikely to me. There's nothing in the sand around those three spots to indicate that such soft spots are there. These were almost certainly pit-stops.

The initial impression is the shallowest of the three, and the second print--which lies so close to the first as to overlap it--is the deepest. My guess is that shortly after the tide began to recede, our starfish friend moved to a more "comfortable" position in the sand and stayed there a while longer. Then he began his trek.

The third impression is the most interesting to me. This represents his turn back towards the ocean. It would be too easy to anthropomorphise our spineless, pentapodal friend and say that this was where he realized that he was heading in the wrong direction and stopped to get his bearings straight. He pulled the beach map out of his glovebox, all the while his wife was nagging him about how "I told you that wasn't the ocean exit!" In truth, I don't know a thing about how starfish navigate. I did some looking on the internets (including wikipedia) and came up empty. I even asked my sister what she thought the starfish was thinking. Her unhelpful reply was "Damn! I was right there with him and I totally forgot to ask him." That leaves me no choice but to stick with my lost traveler metaphor.

The other interesting thing about that third impression is the difference in the track marks leading to it and away from it. In the tracks leading away from the third impression, you can clearly see where the hind appendages were dragged through the sand. The tracks to the impression seem more evenly dispersed. It's like the difference between tracks left by a sled (with rails) and a toboggan. My extemporaneous expertise tells me there are two possible explanations for this. Perhaps he was in a bigger rush after changing direction (this fits in nicely with my lost traveler metaphor). Or maybe it was just the difference between moving with or against the grain (in the sand, the "grain" would be created by the receding tide).

All this made me curious as to how starfish actually do move. Here's a good explanation from Jonathan Dale's website.

The underside of the starfish is covered with hundreds of tube feet, which it uses for walking around, for attaching tightly to rocks, and for holding on to prey. To move, each tube foot swings like a leg, lifting up and swinging forward, then planting itself on the ground and pushing back. At the tip of each tube foot (in most species) is a suction cup. These aren't used when walking on level ground, but can be used when walking up sheer surfaces.

Here's a nice close-up photo of the tube feet from Wikipedia:




Here's a cool time-lapse video of some starfish moving around an aquarium from Jan Ellenberg's site.



And finally, take a look at this "creepy" YouTube video of a brittle star walking along the bottom of a tank. It actually moves its limbs like an octopus. Unfortunately, it has three few limbs to get PZ all excited.



My sister tells me that she has entered the photograph in a "nature photo" contest on the internets. I sure hope she wins!

UPDATE: The picture is now up on National Geographic! Hurray!!!