Νυνὶ δὲ Χριστὸσ ἐγήγερται...

The title of this post comes from Paul's first letter to the Corinthians, chapter 15 verse 20, "But now Christ has been raised from the dead..." where Paul points out how the Christian faith stands or falls on the historicity of the bodily resurrection of Jesus.

Apparently some among the early followers of the Way in Corinth were denying the possibility of resurection of the dead. Paul spends a good paragraph meticulously pointing out the logical consequences that flow from this premise, namely that Christianity itself is worthless and Christians are ἐλεεινότεροι πάντων ἀνθρώπων, of all men most to be pitied if Jesus was not, in fact, raised from the dead in the first place. The point is so important that he makes it twice in slightly different terms: if there is no resurrection from the dead, then Jesus hasn't been raised. If Jesus hasn't been raised, then your faith is κενὸν – empty, worthless, void of purpose. We might as well all be Epicureans. You can be a Christian if and only if (and I don't use that specific logical term lightly) you accept the fact of Jesus having been raised from the dead (the passive voice of that verb is a discussion for another time). If you don't accept the resurrection of the dead as a real possibility, you cannot consistently be a Christian because you destroy the whole foundation of your faith; and likewise if you accept the fact of Jesus' resurrection, you have no logically consistent choice but to accept Him for who He claimed to be.

"Νυνὶ δὲ Χριστὸσ ἐγήγερται..." And here Paul pulls a proof from contradiction out of the syllogisms of the preceding section: But since Christ has, in fact, been raised, we see that the premise that there is no resurrection of the dead leads to a false conclusion, and thus the premise itself must be false (to paraphrase slightly). As many people over the ages have investigated, found, and proclaimed, the Resurrection is one of the best-attested facts of history. "But since Christ has been raised, your faith is not worthless. It's not pointless. And that's just a taste of what's going to come." (Again paraphrasing.)

A hui hou everyone, and happy Easter! Remember He has been raised indeed.

Social Snakes

The other day I ran into an interesting blog run by a couple of people who work with rattlesnakes in Arizona. The name of the blog, like the title of this post, is Social Snakes.

Before I explain the reason for the name, I want to note that I consider myself fairly knowledgeable about snakes in general. I'm pretty sure they were my first favorite animal, and I've always loved their stream-lined sinuous shape. I'm familiar with many of the myths about snakes and also with the truth behind those myths.

But I was still taken completely by surprise by the snake behavior the authors of Social Snakes are documenting in the wild. What they are documenting appears to be social behavior in snakes, hence the title. This is pretty much counter to the general consensus about snakes, that they are mostly loners who prefer to be left alone except when mating or (for some species) hibernating for the winter.

Snakes are reptiles, after all, and the majority of reptiles are not especially good mothers. As far as I know, nearly all lizards and chelonians (turtles/tortoises) pretty much just abandon their eggs, and never interact with their offspring at all. On the other hand, the remaining reptiles actually make pretty good mothers; crocodilians are caring and nurturing mothers, building and guarding nests for their eggs, ferrying babies around in their mouths, and ferociously defending them from predators. There's evidence, too, the some dinosaurs at least took care of their egg and made good mothers.

So where do snakes fit in on this scale? Most snakes, or so the conventional wisdom goes, are with the lizards and chelonians; they lay eggs and leave the young to their own devices. The king cobra is currently the only species known to actually defend its eggs after laying them (as anyone familiar with Riki Tiki Tavi will remember), but the mothers abandon the nest right before the eggs hatch, leaving the hatchlings on their own.

However, there's an interesting loophole to this: not all snake are oviparous (egg-laying). Some, rattlesnakes in particular, are ovoviviparous, giving birth to live young. And it's here that the story gets interesting.

You see, the authors of Social Snakes (Melissa Amerello, Jeffrey Smith, and John Slone), have spent several years studying rattlesnakes in the wild, and they noticed some behavior not typically associated with snakes. Rattlesnake mothers were observed acting in ways more usually associated with mammals. The baby rattlesnakes would stick around with their mother for some time after birth, during which time she would actively watch over them and defend them against attack.

There are some tender and touching stories on that blog about rattlesnake mothers actively herding too-adventurous babies back into line with the rest, snakes going from placid and quiet to actively defending their babies and threatening intruders like a mama bear after giving birth, and even a case of one mother herding another mother's babies from going too far away, complex social behavior of a kind definitely unknown among snakes before. Mama and baby snakes would often be seen basking all together in one big pile of snake-y serenity, the darker parents perhaps soaking up extra solar radiation and making it available to their lighter-colored progeny.

Honestly, some of those stories of maternal care are quite touching, and at this point you should probably stop reading my attempts to explain and just go read the blog itself (it's not overly long, at this point).

Interestingly, one of the newer posts on the blog asks why, since people have been observing rattlesnakes for hundreds of years now, no one ever noticed this behavior before? The answer seems to be that, much like everything in science, your paradigm dictates what you will see. People had seen this behavior before, but no one could apparently bring themselves to accept that those repugnant reptiles might actually be showing maternal care for their children, and it was explained away in various manners. It was only by taking a fresh look and suspending previously held biases that these people were able to make sense of their observations and in the process get a glimpse into the secret family lives of vipers.

Well. I didn't intend for this post to end up in a discussion of the philosophy of science, but there you go. If you haven't yet, go and read Social Snakes. If some of those stories don't warm your heart at least a smidgen, well...I'd say you were cold-blooded, but...

Python Practice Results

Well, the Python training course last week was a bit tiring (three eight-hour days in a row at a fast-and-furious pace), but also quite interesting. I definitely learned a lot of new stuff from it.

Some of the exercises we did had us creating graphs or plots, and while they don't mean much in and of themselves, I thought I'd show one or two of them off.

This picture is hard to see at the size it shows up, but it represents a noisy data set to which various lines have been fitted. This was quite inspiring for me because I've actually tried a few times in the past to fit lines using NumPy and hadn't been able to do so on my own.

(If you can't read the legend, the gray dots are points from the original curve with some random noise added, the blue, green, and red lines are various order polynomial fits [linear, quadratic, and cubic, respectively], the dashed line is a least-squares fit, and the gray line at the bottom is the residuals between the least-squares fit and the original line.)

This second picture below is interesting because it represents some real-world data. The spiky black line is readings from the water vapor meter (WVM) on the James Clerk Maxwell Telescope for a period of one night a few weeks ago, taken every 1.2 seconds. It measures the amount of precipitable water vapor in the atmosphere in the direction it (and the telescope) is pointing. (Lower is better, as water is extremely efficient at intercepting the sub-millimeter wavelength light that the JCMT collects.) The extremely thin red, blue, and green lines are again polynomial fits of various orders (and possibly a least-squares fit, I didn't get time to add a legend before we had to move on since this was actual data and not an exercise).

Anyway, just thought I'd share some of what we did. I'm really looking forward to being able to put some of this new knowledge to work in the future, and I'm especially excited to be able to do my own fits to data.

Python Programming Programme

The first three days of this week we're having a Python training course at my work, which I've been attending. Having no formal training in Python (or any computer language for that matter), I've been looking forward to this. While the first day was mainly an introduction to Python itself (and thus covered a lot of what I've learned myself), I still learned several new things, including some that have been mysteries to me for years.

Today we dove into efficient numerical processing with the NumPy package, something I don't really have much experience in (although much of the morning was spent working with the matplotlib graphing package, which I have been working [and struggling] with extensively for the last three weeks). I was quite excited at the end of the day when I managed to read a FITS image and display it, with a crude image stretch, entirely with Python code. It was quite exhilarating. It was cool to discover that our instructor was also an amateur astronomer, and used code he'd written to help process his images.

Tomorrow we're supposed to jump into the SciPy suite of scientific tools. I've at least used NumPy a little bit from time to time, but I haven't ever really found a need to use SciPy before so this should be very informative.

Pi Day!

So it turns out that Pi Day was this past week (3/14), and I forgot all about it as usual. However, entirely by chance, I actually engaged in some appropriately pi-involving activities that day, and thought I'd put it up here.

It started with me and some coworkers at tea-time in the break room, where there was a newspaper-insert advertising a set of nine miniature pizzas for sale. One of my coworkers jokingly said that it was a ploy by the pizza company to sell half the pizza for the same cost.

There was a pause of a few seconds during which I could practically see the wheels turning in his head. I'm sure I looked the same way, as we both mulled over the implications of what he had said. “Actually...”

We both dived for calculation tools, and began scribbling figures and formulae. The result was interesting enough that I thought I'd share it.

First of all, assume the following picture (representing an idealized pizza in a box):

This pizza has an area of \(\pi r^2\). Now, take a look at the following picture, representing nine miniature idealized pizzas in a box of the same size:

The radius of each of these mini-pizzas is \(1/3\) that of the original pizza, or \(r/3\). Thus, the total area of the pizzas is \(9\times\pi(r/3)^2=9\times\pi(r^2/9)=\pi r^2\). Which is exactly the same as the original, single pizza! So the nine mini-pizzas actually give you just as much bang for your buck as the single large one. (In reality I've ignored some details, such as the fact that the nine pizzas have twice the circumference as the single one so you're getting twice as much crust, which means that the actual area covered by condiments will be slightly smaller than the single pizza.).

I noticed something else interesting about this. Let's imagine an arbitrary number of little circles packed into a square in a regular grid, such as that shown in the picture above. We'll let \(n\) stand for the number of circles on a side. Then the area of the pizzas is \(n^2\times\pi\times (r/n)^2=\pi r^2\). The circumference, however, is \(n^2\times2\pi\times(r/n)=2n\pi r\). So if we take the limit as n goes to infinity – if we imagine squashing more and more smaller and smaller circles into the square – the area stays constant, but the circumference goes to infinity. Yet the area of the circles remains \(2\pi r^2\). So if we imagine throwing darts randomly at the whole area, we would always have the same change of hitting the underlying square. (The area of the square is \(4r^2\), the circle area is \(2\pi r^2\), so the ratio of their areas is \(4r^2/\pi r^2=4/\pi\approx1.2732\). Thus the chance of hitting the square rather than one of the circles remains a constant \(1-(1/1.2732)\approx0.2146=21.46\%\).) So even though there could be an infinite number of circles, with an infinitely long cumulative circumference, you'd still have exactly the same chance of hitting one (78.54%) as you would if there were just one circle.

It reminds me a bit of the Koch Snowflake, a geometrical figure with an infinitely long perimeter that encloses a finite area.

In Search of Platyhelminths

"What on Earth is a platyhelminth?", I hear you ask.

A platyhelminth is a flatworm, from the Greek roots πλατύ- (platy) meaning "flat" and ἑλμνθ- (helminth) meaning "worm." Platyhelminths are pretty amazing creatures that lack some of the features we multi-cellular animals find pretty important, such as a digestive system. And a respiratory system.

Now, there are many other creatures out there lacking those systems that make their livings as parasites, and while it's true that there are a lot of parasitic platyhelmithes, there are also a decent number of them out making a living for themselves just fine without these trivial systems that we might consider indispensable. They do it by having a very simple body plan. It has to be, because the only way for oxygen and nutrients to reach all their cells is by diffusion, which has practical limits on how far it can work.

Within the platyhelminths, there is an order called Tricladida, whose members are commonly known as planarians. They have some remarkable regeneration abilities; some of them reproduce by simply leaving their tails behind, which then grow into a whole new planarian! In fact, cutting them into pieces merely causes all the various pieces to regrow into new flatworms. There have even been experiments performed where people cut a planarian's head in half longitudinally, and both halves regrew into new complete heads, leaving a two-headed planarian! (I have never heard if anyone ever took this to the logical next step and created a nine-headed hydra planarian.)

Planarians, like the rest of the platyhelminths, are mostly very small creatures, a few inches long at the most. This is due to their simple body plan as mentioned above. But there is one species, Bipalium kewense, that grows much longer than that, reaching up to 60 cm (about 2 feet) in length! What's even more interesting is that this particular species lives on land rather than in water...and it lives in Hawai‘i. (They also live in many other parts of the world besides Hawai‘i, having been inadvertently introduced around the globe by humans. They are believed to be native to Southeast Asia, however.)

Often while walking in the early morning I would see these strange, worm-like creatures sliding along across the sidewalk without knowing what they were. Recently though, I learned that B. kewense was the largest known planarian in the world and realized that was what I had seen all those times, at which point I thought it would be neat to get some pictures or maybe a video of one of them.

With that goal in mind, I got up early one morning this past week and set out to look for them before going to work. After a lovely early-morning walk of twenty minutes' duration along the sidewalk next to the uncleared jungle on the UH campus, I found what I was looking for, a B. kewense a good eight inches long out for an early-morning squirm.

Bipalium kewense on a sidewalk in Hawai‘i.

I realize that picture doesn't give you much sense of scale, so here's another one with my hand in it for comparison:

(I discovered that it's really difficult to hold a phone in one hand to take pictures while trying to position your other hand and an oblivious piece of wildlife in a nicely framed photograph taken by that same phone.)

You may be wondering about the shovel-shaped appendage on one end of this particular flatworm. That's its head, and it contributes to their endearing common name of "hammerhead slug," despite them not being related to slugs at all (other than both of them being in the kingdom Animalia). Here's a closeup if you want to see it better:

Close-up of the head of B. kewense, also called the "hammerhead slug."

(Apologies if you did not, in fact, want to see it better.)

I don't think the reason for the head's peculiar shape is exactly known, but since they are known to eat earthworms, it may serve as a method to increase the area of their sensory apparatuses, allowing them to better find and follow earthworm tracks.

Finally, if you'd like to see one of these strange creatures in glorious motion, you're in luck! I took a video (if you don't care enough about the planarian to watch the video, there's also some nice early-morning birdsong recorded in it):

All in all, planarians are fascinating creatures, and I think it's really neat to be able find them in the wild around here.

Snow Chains and Volunteering

Though thankfully unrelated.

Last Friday I had some Snow Chain Installation Training, which was interesting because I've never installed snow chains before, never having lived any place where they would actually be necessary. Having said that, I was under the impression that it involved driving the vehicle to be snow-chained over and onto the chains with which to snow-chain said vehicle. However, the chains we have (at least for some of the vehicles) are a different design that simply engulfs the wheel like a hungry starfish engulfing a tasty bivalve. No driving involved, other than simply driving off afterwards with snow chains attached.

All of it which underscored by the fact that I have no official reasons to go up to the summit in an official vehicle as part of my job at the moment, and would be extremely unlikely to do so on a day which was snowy enough to require chains if I ever did. But at least it was interesting.

Also, tonight I went up and volunteered at the Visitor Information Station for the first time since I've been back. I could tell I needed to build up my high-altitude tolerance again! It was a beautifully clear night, though the biting wind drove most people away after a few hours (I also need to build up my cold tolerance again). An enjoyable evening altogether, though, and I got a chance to catch up on what the sky's been doing the last few months (which is hard to do with all the clouds in Hilo). I'm hoping to get back into the astrophotography scene soon as well. Anyway, I should get to bed to be ready for work tomorrow. A hui hou!