It's been a little bit quiet around here as I spent pretty much the last two weeks of July and the first week of August away, first back on the west coast for a family reunion then in Honolulu for a business trip. The triennial IAU (International Astronomical Union) conference was back in the U.S. for the first time in twenty-five years, and as a new organization EAO wanted to have a booth there to help get our name out. Which is why I got to spend a fun week in Honolulu talking to people about the JCMT!
Despite flying through the Honolulu airport twice a year on average for the past six years this was my first time actually outside the airport. It was a bit of a shock just how different it was from Hilo. O‘ahu has a lot of basically flat area, something that is in short supply on Hawai‘i, and it was discombobulating to drive for miles with essentially no elevation change. Though the half-mile walk to the convention center from my hotel was flat rather than uphill, so I'm not complaining.
Check out our nifty booth!
That fantastic diorama of the summit of Mauna Kea on the left there belongs to Subaru with whom we were sharing a booth, and boy, was it popular throughout the conference. It was really nice to be able to point out to people exactly where the JCMT (and everything else) on the summit was.
While I was there, I got to do something most people don't associate with Hawaii: ice skating! My co-worker and friend from college that I went over with, Will, suggested it, so one night after the convention was over we took the bus over the skating rink. I even took a really poor picture as proof!
Yeah, that picture didn't really come out well. I blame my slightly deranged expression on the fact that I was standing on ice skates and concentrating on not falling over. It was a lot of work, and there was much comedic flailing as I rounded the rink a few times, but at least I managed not to fall down over the course of the hour I spent on the ice. All in all, a fun experience. Look forward to some pictures from my time in Oregon soon!
Saturday, August 22, 2015
Saturday, August 8, 2015
Adding Cubits to your Lifespan
In my Bible-reading this morning I ran across Matthew 6:27 where Jesus says “And who of you by worrying can add a single πῆχυν to his ἡλικίαν?” This is an interesting verse to translate, because ἡλικίαν (pronounced heylikian, with the i's sounding like the i in machine) is usually translated as something like ‘lifespan,’ but πῆχυν (pronounced peychoon, where the ‘ch’ sounds like it does in German ‘Bach’ or Scottish ‘loch’) is a very straightforward word meaning ‘cubit.’
On the face of it, this doesn't make grammatical sense; how do you add a cubit to your lifespan? This has lead to two divergent translations I've seen: one involves translating πῆχυν as ‘hour’ (despite there being another definite word for hour, ὥρα [hora]), while the other translates ἡλικίαν as ‘height.’
Neither of these translations sound really good to my ear, so I when I came to the passage this morning I decided to go back to the literal meaning of both words and incorporate insights from relativity theory. Relativity tells us that time is simply another dimension like the three dimensions of space (which are inextricably linked in a four-dimensional spacetime), and that by using the speed of light as a conversion factor we can use units of measurement for space to measure time, and vice versa. What does a ‘second of distance’ mean? It's the distance light travels in one seconds, approximately 186,000 miles or 300,000 kilometers. And similarly, one ‘meter of time’ is the amount of time it takes light to travel one meter, approximately three nanoseconds.
A cubit, by the way, is very close to half a meter, so what Jesus is basically saying here is that you can't add even a nanosecond and a half to your life by worrying—so don't worry, because your Heavenly Father is in control. A hui hou!
On the face of it, this doesn't make grammatical sense; how do you add a cubit to your lifespan? This has lead to two divergent translations I've seen: one involves translating πῆχυν as ‘hour’ (despite there being another definite word for hour, ὥρα [hora]), while the other translates ἡλικίαν as ‘height.’
Neither of these translations sound really good to my ear, so I when I came to the passage this morning I decided to go back to the literal meaning of both words and incorporate insights from relativity theory. Relativity tells us that time is simply another dimension like the three dimensions of space (which are inextricably linked in a four-dimensional spacetime), and that by using the speed of light as a conversion factor we can use units of measurement for space to measure time, and vice versa. What does a ‘second of distance’ mean? It's the distance light travels in one seconds, approximately 186,000 miles or 300,000 kilometers. And similarly, one ‘meter of time’ is the amount of time it takes light to travel one meter, approximately three nanoseconds.
A cubit, by the way, is very close to half a meter, so what Jesus is basically saying here is that you can't add even a nanosecond and a half to your life by worrying—so don't worry, because your Heavenly Father is in control. A hui hou!
Sunday, July 26, 2015
Diagramming Noun Adjunct-Heavy Sentences
I learned to diagram sentences from my mother (a Linguistics major in college), but didn't appreciate it much at the time (to be fair, my mother didn't appreciate it either until she began teaching me and my sister). Until, that is, I ran across a sentence in the local newspaper that made me want to diagram it.
The sentence in question was “This is not an administrative license revocation matter.” (It has to do with the ongoing investigation into whether the mayor of Hilo inappropriately used government funds for personal benefit.) It's not particularly long—no complicated compound sentence or anything—it was merely the noun phrase in the predicate that attracted me. It took me quite a bit of research, though, to figure out what all those nouns near the end are.
The ending noun phrase “administrative license revocation matter” has what looks like a couple of nested noun adjuncts, which is where a noun modifies another noun the way an adjective normally would. “Administrative” is an adjective modifying “license,” which is itself serving as a noun adjunct modifying “revocation,” which entire phrase is modifying “matter” at the end.
And yet, nowhere could I find how to diagram something like that. One website helpfully told me that noun adjuncts are diagrammed like adjectives—on a diagonal line beneath the noun they modify—but I couldn't see any way to chain multiple noun adjuncts together.
After some time pondering the matter and scratching my head, I decided to
If any of you out there are more familiar with sentence diagramming and would like to point out how it should actually be done, feel free to sound off in the comments! A hui hou!
Wednesday, July 15, 2015
Why New Horizons Can See Pluto, and Hubble Can't
About a day ago the New Horizons space probe finally reached the end of its nine-year journey through space and accomplished its mission: a fly-by of Pluto, marking the first time humanity has gotten to see the surface of this mysterious minor planet.
And what a surface it is!
Just look at all those surface features! There's a large icy vaguely heart-shaped region in the middle (which reminds me of Antarctica for some reason). It's flanked on two sides by extremely dark patches. On the right side of the picture long shadows betray the presence of fierce mountain ranges jutting from the smooth plains around them. What looks like a long canyon sits on the left side of the image, while vast smooth plains fill the top half. Speaking of which, there's a noticeable dearth of obvious impact craters—I can spot a few, but it's nothing like, say, Mercury, or our Moon.
When I was growing up in the 90's, from as early as I could remember I was fascinated by other planets. This was the beginning of my lifelong journey to become an astronomer, as I devoured every bit of reading material I could get my hands on pertaining to the solar system. This was right after the two Voyager probes had completed their missions to the outer planets (Voyager 2 flew by Neptune the year I was born, 1989), so there was an eclectic mixture of information in the books I read, depending on how old they were and how up-to-date their information was. (Looking back, I realize this was excellent training for my young self in sifting multiple conflicting sources of information and piecing together a coherent narrative from them. Huh.)
The newer books had pictures of the outer planets and their moons from the Voyager probes that were of resoundingly better quality than the ones before it. Those two probes taught us so much about the planets that we simply couldn't see from our vantage point on Earth. The point to this rather rambling divergence is that I know now what people must have felt like when those first pictures of each new planet were coming back. If you're not familiar with our previous best images of Pluto, let me show you one (courtesy of the Hubble Space Telescope):
To be clear, the actual photos of Pluto are those two small pictures at the top; the larger ones are computer models extrapolating from those pictures. These were among the best images of Pluto we had until yesterday. And yes, that's a photo from 1996, but we didn't really get any better ones in the intervening time period; here's another one from 2012:
The letters WFC3 at the top of this image stand for Wide Field Camera 3, the last and most technologically advanced camera installed on the Hubble Space Telescope, so this is as good it's possible for Hubble to get. With that in mind it's easier to appreciate just how amazing the pictures from New Horizons are.
“But hang on,” you may be saying, “why can't Hubble get better pictures of Pluto? It gets all those amazing pictures of galaxies, and they're a lot further away than Pluto is!”
If you're asking this, then you're in luck, because I asked myself the same thing driving home from work today. The apparent discrepancy comes about due to us humans not having a good intuitive sense about sizes and distances so far outside our everyday experiences. To really get a feel for why things are the way they are, we need to use math.
My idea for this was find the diameters and distances to Pluto and a nice galaxy that Hubble had photographed, take their ratios, and see just how much bigger the galaxy would appear on the sky. Then while researching these bits of information in order to write this post I discovered that an astronomer named Emily Lakdawalla had already done exactly that. So rather than write up another post that would say pretty much the exact same thing, you get to go read her blog post. (She also already has an excellent image showing the relative sizes of a lot of Pluto-sized bodies in the solar system using the newest images of Pluto and Charon!)
I had an idea to take a picture of a galaxy and a picture of Pluto and shrink the Pluto picture down and stick it on the galaxy picture to see how they compare, but I did a quick back-of-the-envelope calculation with a galaxy picture I picked out and discovered that Pluto would be about two pixels across (which agrees quite well with the conclusion in Emily's blog post that Pluto would theoretically cover less than two pixels of Hubble's WFC3). I tried sticking a little 2×2 bright green square into the image, and could barely make it out at 100% resolution even knowing where to look. So I figured it wouldn't be especially interesting to show given that putting the picture up on this blog would further shrink it. Sorry.
But to come back to the point I was trying to convey originally, this is a historic day (well, yesterday technically) for planetary science, unmanned space probes, and Pluto. If you come across any of the doubtlessly many more images to come back from New Horizons I hope you now better appreciate them for just what a huge leap forward they represent for our understanding of this fascinating little ice-and-rock-ball out on the outskirts of our solar system. A hui hou!
P.S. Also, New Horizons' mission isn't quite as over as made it sound in the opening sentence. It will continue to observe Pluto and its moons for about another month or so as it whips on past, and will probably continue to send back observations about anything else it can see way out there for a long time to come after that. Exciting!
And what a surface it is!
![]() |
| Pluto, as imaged by New Horizons. Credit: NASA/JHUAPL/SWRI |
When I was growing up in the 90's, from as early as I could remember I was fascinated by other planets. This was the beginning of my lifelong journey to become an astronomer, as I devoured every bit of reading material I could get my hands on pertaining to the solar system. This was right after the two Voyager probes had completed their missions to the outer planets (Voyager 2 flew by Neptune the year I was born, 1989), so there was an eclectic mixture of information in the books I read, depending on how old they were and how up-to-date their information was. (Looking back, I realize this was excellent training for my young self in sifting multiple conflicting sources of information and piecing together a coherent narrative from them. Huh.)
The newer books had pictures of the outer planets and their moons from the Voyager probes that were of resoundingly better quality than the ones before it. Those two probes taught us so much about the planets that we simply couldn't see from our vantage point on Earth. The point to this rather rambling divergence is that I know now what people must have felt like when those first pictures of each new planet were coming back. If you're not familiar with our previous best images of Pluto, let me show you one (courtesy of the Hubble Space Telescope):
![]() |
| Credit: NASA/STScI |
![]() |
| Credit: NASA/STScI |
“But hang on,” you may be saying, “why can't Hubble get better pictures of Pluto? It gets all those amazing pictures of galaxies, and they're a lot further away than Pluto is!”
If you're asking this, then you're in luck, because I asked myself the same thing driving home from work today. The apparent discrepancy comes about due to us humans not having a good intuitive sense about sizes and distances so far outside our everyday experiences. To really get a feel for why things are the way they are, we need to use math.
My idea for this was find the diameters and distances to Pluto and a nice galaxy that Hubble had photographed, take their ratios, and see just how much bigger the galaxy would appear on the sky. Then while researching these bits of information in order to write this post I discovered that an astronomer named Emily Lakdawalla had already done exactly that. So rather than write up another post that would say pretty much the exact same thing, you get to go read her blog post. (She also already has an excellent image showing the relative sizes of a lot of Pluto-sized bodies in the solar system using the newest images of Pluto and Charon!)
I had an idea to take a picture of a galaxy and a picture of Pluto and shrink the Pluto picture down and stick it on the galaxy picture to see how they compare, but I did a quick back-of-the-envelope calculation with a galaxy picture I picked out and discovered that Pluto would be about two pixels across (which agrees quite well with the conclusion in Emily's blog post that Pluto would theoretically cover less than two pixels of Hubble's WFC3). I tried sticking a little 2×2 bright green square into the image, and could barely make it out at 100% resolution even knowing where to look. So I figured it wouldn't be especially interesting to show given that putting the picture up on this blog would further shrink it. Sorry.
But to come back to the point I was trying to convey originally, this is a historic day (well, yesterday technically) for planetary science, unmanned space probes, and Pluto. If you come across any of the doubtlessly many more images to come back from New Horizons I hope you now better appreciate them for just what a huge leap forward they represent for our understanding of this fascinating little ice-and-rock-ball out on the outskirts of our solar system. A hui hou!
P.S. Also, New Horizons' mission isn't quite as over as made it sound in the opening sentence. It will continue to observe Pluto and its moons for about another month or so as it whips on past, and will probably continue to send back observations about anything else it can see way out there for a long time to come after that. Exciting!
Monday, July 13, 2015
Close Encounters with the Katydid Kind
Today at work, during our morning tea time, I spotted something in the hall which at first glance I somehow thought was a giant green spider, but which on a second look turned out to be a fairly normal-sized katydid.
I've never seen a katydid here in Hawaii before, so I had to check with my co-workers that it wasn't some invasive species that should be killed on sight. Once I'd ascertained that it was not, I undertook to return “Katy” to the outdoors. I don't really have any experience with katydids; I only really know what to expect from their relatives, grasshoppers and crickets. I wasn't sure if she would prove flighty and try to jump away, so I very carefully and slowly put one hand in front and one hand behind her to see if I could carry her out slowly without the entire affair devolving into me frantically trying to catch her as she hopped equally frantically away.
To my surprise, she took a calculating look at my approaching hand and calmly and sedately climbed aboard with basically no encouragement on my part. Katydids are herbivorous and harmless to humans, so while she was on my hand and so obligingly demure I took the chance to study her up close as I took her back through the break room (and my coworkers there) on my way outside.
Katy seemed to be about as interested in me as I was in her, returning my curious stare with a frank and thoughtful one. She looked as if she were mulling something over as her miniature mouth parts and antennae slowly waved to and fro. Thus I was caught completely unprepared when she suddenly leaped directly at my face!
I'm pretty sure I let out a startled squawk – I know I jumped, to the great amusement of my coworkers I'm sure. My eyes had reflexively slammed shut due to, y'know, something jumping at my face, and as I carefully pried them open again it was to find Katy calmly hanging out on my nose.
Now, if you read this blog you're probably aware that I don't take pictures of myself lightly or often, but I couldn't pass up the golden opportunity to see what I looked like with a katydid on my nose. To my great sorrow, while I was pulling out my camera Katy decided she didn't like my nose after all and jumped down onto my arm, where I had to be content with the picture above. After a few more pictures (most of poor quality sadly) I took her outside and let her off on one of bushes near the door.
All in all, it was fun. It's not everyday you get startled half to death at an office job by the insect equivalent of a cow, after all. A hui hou!
![]() |
| This katydid, in fact. Let's call her “Katy” for simplicity. That's my arm, for scale. |
I've never seen a katydid here in Hawaii before, so I had to check with my co-workers that it wasn't some invasive species that should be killed on sight. Once I'd ascertained that it was not, I undertook to return “Katy” to the outdoors. I don't really have any experience with katydids; I only really know what to expect from their relatives, grasshoppers and crickets. I wasn't sure if she would prove flighty and try to jump away, so I very carefully and slowly put one hand in front and one hand behind her to see if I could carry her out slowly without the entire affair devolving into me frantically trying to catch her as she hopped equally frantically away.
To my surprise, she took a calculating look at my approaching hand and calmly and sedately climbed aboard with basically no encouragement on my part. Katydids are herbivorous and harmless to humans, so while she was on my hand and so obligingly demure I took the chance to study her up close as I took her back through the break room (and my coworkers there) on my way outside.
Katy seemed to be about as interested in me as I was in her, returning my curious stare with a frank and thoughtful one. She looked as if she were mulling something over as her miniature mouth parts and antennae slowly waved to and fro. Thus I was caught completely unprepared when she suddenly leaped directly at my face!
I'm pretty sure I let out a startled squawk – I know I jumped, to the great amusement of my coworkers I'm sure. My eyes had reflexively slammed shut due to, y'know, something jumping at my face, and as I carefully pried them open again it was to find Katy calmly hanging out on my nose.
Now, if you read this blog you're probably aware that I don't take pictures of myself lightly or often, but I couldn't pass up the golden opportunity to see what I looked like with a katydid on my nose. To my great sorrow, while I was pulling out my camera Katy decided she didn't like my nose after all and jumped down onto my arm, where I had to be content with the picture above. After a few more pictures (most of poor quality sadly) I took her outside and let her off on one of bushes near the door.
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| Katy, back in her natural habitat. |
Tuesday, June 30, 2015
Belated Tau Day
I realize I missed it by two days, but happy belated Tau Day everyone! What's Tau Day, you ask? It's like Pi Day (3/14), but for Tau (6/28). "But what's tau," you're probably asking.
Simply put, tau is twice pi, or \(\tau=2\pi\). Like pi, tau is irrational and transcendental. But what's so special about \(2\pi\)? Why not \(3\pi\), or \(4\pi\), or any other integer multiple?
The reason has to do with circles, geometry, and the ancient Greeks. Everyone who's taken geometry is familiar with the formula for the circumference of a circle, \(C=2\pi r\), where C is the circumference and r is the radius. This, however, is the modern formulation. The ancient Greek geometers who first came up with the concept were thinking in slightly different terms: namely, that two times the radius of a circle equals its diameter. Thus, to them, the formula would be expressed as \(C=\pi d\) where d is the diameter (\(d=2r\)).
That formulation looks nice and compact, just four symbols total (although that itself is a modern artifact, as symbolic algebra as we know it wasn't invented until the Middle Ages). However, it's not quite as fundamental as it could be, because the diameter of a circle is a less fundamental concept than its radius. A circle can be—indeed is—defined as the set of all points whose distance from a single central point is exactly equal to the radius. There's no such simple way to define a circle using a diameter other than to cut it in two and use the radius anyway. Hence, the modern formulation uses radius rather than diameter.
Unfortunately, using the radius introduces that factor of two into the picture. You see, the modern formulation goes only halfway. The ancient Greeks liked their version because it was clean and simple: take any line segment to be the diameter of a circle, multiply it by this one single, simple constant (\(\pi\)), and boom, you have the circumference. And you can see the simplicity there that all mathematicians strive for.
So let's say we want to remake the modern formulation to get rid of that ugly extra 2 in there. We can simply multiply pi by it and get tau, to make our new formula \(C=\tau r\). It's simple, elegant, and—importantly—more fundamental than using pi. Take any line segment as the radius of a circle, multiply by tau, and bam—you've got your circumference.
Pi was a good first attempt at getting a very important number in math and physics, the circle constant that shows up everywhere cyclical processes are involved. It's just the wrong constant. It's the ratio of the circumference to the diameter, when the more fundamental constant is the ratio of the circumference to the radius—tau.
It's getting late and I should wrap this post up, so I will end by providing a link to The Tau Manifesto for anyone who's still interested. It's where I first encountered the idea of using tau instead of pi, and shows in detail how tau simply makes more sense to use in many areas of math and physics. I was reflexively against the idea when I first read it, but over time I've come to see how much sense it makes—to the point I'm even writing about it here on my blog. Funny how these things happen. A hui hou!
Simply put, tau is twice pi, or \(\tau=2\pi\). Like pi, tau is irrational and transcendental. But what's so special about \(2\pi\)? Why not \(3\pi\), or \(4\pi\), or any other integer multiple?
The reason has to do with circles, geometry, and the ancient Greeks. Everyone who's taken geometry is familiar with the formula for the circumference of a circle, \(C=2\pi r\), where C is the circumference and r is the radius. This, however, is the modern formulation. The ancient Greek geometers who first came up with the concept were thinking in slightly different terms: namely, that two times the radius of a circle equals its diameter. Thus, to them, the formula would be expressed as \(C=\pi d\) where d is the diameter (\(d=2r\)).
That formulation looks nice and compact, just four symbols total (although that itself is a modern artifact, as symbolic algebra as we know it wasn't invented until the Middle Ages). However, it's not quite as fundamental as it could be, because the diameter of a circle is a less fundamental concept than its radius. A circle can be—indeed is—defined as the set of all points whose distance from a single central point is exactly equal to the radius. There's no such simple way to define a circle using a diameter other than to cut it in two and use the radius anyway. Hence, the modern formulation uses radius rather than diameter.
Unfortunately, using the radius introduces that factor of two into the picture. You see, the modern formulation goes only halfway. The ancient Greeks liked their version because it was clean and simple: take any line segment to be the diameter of a circle, multiply it by this one single, simple constant (\(\pi\)), and boom, you have the circumference. And you can see the simplicity there that all mathematicians strive for.
So let's say we want to remake the modern formulation to get rid of that ugly extra 2 in there. We can simply multiply pi by it and get tau, to make our new formula \(C=\tau r\). It's simple, elegant, and—importantly—more fundamental than using pi. Take any line segment as the radius of a circle, multiply by tau, and bam—you've got your circumference.
Pi was a good first attempt at getting a very important number in math and physics, the circle constant that shows up everywhere cyclical processes are involved. It's just the wrong constant. It's the ratio of the circumference to the diameter, when the more fundamental constant is the ratio of the circumference to the radius—tau.
It's getting late and I should wrap this post up, so I will end by providing a link to The Tau Manifesto for anyone who's still interested. It's where I first encountered the idea of using tau instead of pi, and shows in detail how tau simply makes more sense to use in many areas of math and physics. I was reflexively against the idea when I first read it, but over time I've come to see how much sense it makes—to the point I'm even writing about it here on my blog. Funny how these things happen. A hui hou!
Wednesday, June 17, 2015
Panorama Extravaganza
In my outings and explorations, I often find myself drawn to taking pictures with an eye to stitching them together into a panorama after getting home. I don't know why; I never really set out with the intention of making one, the muse just comes sometimes. The problem is that after spending time carefully hand-stitching the resulting panorama together and admiring the result they go off to live on my hard drive because it's hard to find a good way to show an image that's much wider than it is tall.
Last year I realized that with my dual-monitor setup I actually have a pretty good way to display some of my panoramas: as wallpaper for my 3,840-by-1,200 desktop. I created a wallpaper from some pictures of Polulū Valley which has adorned my desktop until today. However, I didn't get around to making more wallpapers from my old panoramas until today when I went through and created a few more from those that would stand it, then took pictures of them so I can show them off.
Some panoramas just didn't work, being much too wide (although I just realized I could probably cut those into pieces and make wallpapers from them). None of them fit perfectly, of course, and all required a little cropping, but I found another four that were close enough in aspect ratio to make work with minimal cropping.
A lovely view from Laupāhoehoe Point. I love the dynamism of the waves coming in and the poignantly deep sapphire blue of the ocean.
A beautiful sunset from Pu‘u Kalepeamoa, near Hale Pōhaku, with Mauna Loa (left) and Hualalai (just visible through the clouds right of the sun).
A tranquil vista of Lake Waiau (minus the northernmost bit). This is the wallpaper I have right now, as it's just so...irenic. Idyllic, even.
I was a bit surprised to find that some of my older panoramas were actually too small to be made a proper wallpaper at this resolution, as they were too short either vertically or horizontally. I used to take photos with smaller resolutions back before I had a terabyte of hard drive space to store them on, and it definitely shows (my lovely Crater Lake panorama wasn't wide enough to cover both screens). I was equally surprised to find one of my oldest panoramas was big enough to use:
This panorama, from sometime early 2008, is a not-particularly clear shot of the lower tall of Tall El-Hammam, an archaeological site in Jordan north-east of the Dead Sea that I had the pleasure of excavating at for parts of two seasons in 2007 and 2008. It's beyond doubt the site of Sodom from the Early Bronze through Middle Bronze periods, then several other cities through Iron, Roman, and (I think) even Byzantine periods (it may be the site of the Roman-period city Livias, mentioned in texts, but whose location was otherwise unknown). As you can see, the soil in the plain of the Jordan down in the Dead Sea Valley is quite fertile and the lower tall had a lot of crops being grown on it at that time. I know they've excavating quite a lot in the lower tall in the years since I went so I don't know what it looks like now, though I hear this coming season (next January) they'll be going back to the upper tall where I dug and where this panorama was taken from.
It's so nice to finally have a place to show off my panoramas rather than letting them languish on my hard drive, and I hope you enjoyed seeing so many in one post. A hui hou!
Last year I realized that with my dual-monitor setup I actually have a pretty good way to display some of my panoramas: as wallpaper for my 3,840-by-1,200 desktop. I created a wallpaper from some pictures of Polulū Valley which has adorned my desktop until today. However, I didn't get around to making more wallpapers from my old panoramas until today when I went through and created a few more from those that would stand it, then took pictures of them so I can show them off.
![]() |
| My Pololū Valley wallpaper. |
A lovely view from Laupāhoehoe Point. I love the dynamism of the waves coming in and the poignantly deep sapphire blue of the ocean.
A beautiful sunset from Pu‘u Kalepeamoa, near Hale Pōhaku, with Mauna Loa (left) and Hualalai (just visible through the clouds right of the sun).
A tranquil vista of Lake Waiau (minus the northernmost bit). This is the wallpaper I have right now, as it's just so...irenic. Idyllic, even.
I was a bit surprised to find that some of my older panoramas were actually too small to be made a proper wallpaper at this resolution, as they were too short either vertically or horizontally. I used to take photos with smaller resolutions back before I had a terabyte of hard drive space to store them on, and it definitely shows (my lovely Crater Lake panorama wasn't wide enough to cover both screens). I was equally surprised to find one of my oldest panoramas was big enough to use:
This panorama, from sometime early 2008, is a not-particularly clear shot of the lower tall of Tall El-Hammam, an archaeological site in Jordan north-east of the Dead Sea that I had the pleasure of excavating at for parts of two seasons in 2007 and 2008. It's beyond doubt the site of Sodom from the Early Bronze through Middle Bronze periods, then several other cities through Iron, Roman, and (I think) even Byzantine periods (it may be the site of the Roman-period city Livias, mentioned in texts, but whose location was otherwise unknown). As you can see, the soil in the plain of the Jordan down in the Dead Sea Valley is quite fertile and the lower tall had a lot of crops being grown on it at that time. I know they've excavating quite a lot in the lower tall in the years since I went so I don't know what it looks like now, though I hear this coming season (next January) they'll be going back to the upper tall where I dug and where this panorama was taken from.
It's so nice to finally have a place to show off my panoramas rather than letting them languish on my hard drive, and I hope you enjoyed seeing so many in one post. A hui hou!
Thursday, May 28, 2015
Puzzling Matrices
A coworker of mine brought a puzzle into the staff lounge/dining area at work a few weeks ago. Since then a couple of us have worked on it on and off, and so far we've got...
…the frame, and a smattering of connected fragments. It's decidedly not an easy puzzle.
Progress on this puzzle, since we completed the outside frame, is typically in the range of 0–2 connections made per person, per day. It's a thousand-piece puzzle, fifty pieces wide by twenty tall. Yesterday as I managed to get a connection more by chance than skill, I wondered just how many connections there were in the puzzle.
It's not a very difficult problem, once we realize that the puzzle pieces are arranged in an essentially regular rectangular grid. This allows us to simplify the problem immensely (in true physicist fashion) by imagining the puzzle as a matrix of \(m=50\) and \(n=20\). The problem thus becomes a question of how many “edges” there are between all the pieces of a regular matrix.
We can start to break the problem down by looking at special cases: first of all, there are four corner pieces, each of which have only two connections. Then, there are a number of edge pieces, each of which will have three connections. Finally, the remainder of the pieces are interior pieces which have four connections each.
If we call the length and height of the puzzle m and n, then the number of edge pieces is going to be \(2\cdot[(m-2)+(n-2)]\). (The picture below may help you picture the various areas involved; the edge pieces are the areas in green, the corners are blue.)
The number of interior pieces is simpler, it's simply \((m-2)\cdot(n-2)\). Now that we have the number of each type of piece, it's a simple matter to multiply them by the number of connections they have and divide by two since every connection is getting counted twice. This gives us a formula for a function:
\begin{align}f(m,n)&=\frac{1}{2}\Bigl[2\cdot4+3\cdot2\cdot\bigl[(m-2)+(n-2)\bigr]+4\cdot\bigl[(m-2)\cdot(n-2)\bigr]\Bigr]\\
&=\frac{1}{2}\Bigl[8+3(2m+2n-8)+4(mn-2m-2n+4)\Bigr]\\
&=\frac{1}{2}\bigl[8+6m+6n-24+4mn-8m-8n+16\bigr]\\
&=\frac{1}{2}[4mn-2m-2n]\\
&=2mn-(m+n)\end{align}
Phew! That's a lot friendlier looking. Funny, I remember when I used to hate algebra with a passion, but that was kinda fun. Absence really does make the heart grow fonder, I guess.
Anyway, we've got our function, but we should probably test it with easy cases. Let's take the cases where \(m=n=2\) and \(m=n=3\):
Here we have some (extremely simple) puzzles. For the first one, on the left, it's easy to see that there are four connections between the four pieces. Plugging 2 in for m and n in our function gives: \[f(2,2)=2\cdot2\cdot2-(2+2)=8-4=4\] So that works. The second puzzle is larger, but it's still easy to count twelve connections between the nine pieces. Plugging 3 in for m and n gives us: \[f(3,3)=2\cdot3\cdot3-(3+3)=18-6=12\] So it appears to hold water. Going back to the puzzle at work, which had \(m=50\) and \(n=20\), we have: \[f(50,20)=2\cdot50\cdot20-(50+20)=2000-70=1930\]Which is a lot of connections! Anyway, my curiosity is sated, and you now have a simple formula to use for party tricks or whatever in the future. A hui hou!
…the frame, and a smattering of connected fragments. It's decidedly not an easy puzzle.
![]() |
| Yes, that's the picture on the puzzle. |
It's not a very difficult problem, once we realize that the puzzle pieces are arranged in an essentially regular rectangular grid. This allows us to simplify the problem immensely (in true physicist fashion) by imagining the puzzle as a matrix of \(m=50\) and \(n=20\). The problem thus becomes a question of how many “edges” there are between all the pieces of a regular matrix.
We can start to break the problem down by looking at special cases: first of all, there are four corner pieces, each of which have only two connections. Then, there are a number of edge pieces, each of which will have three connections. Finally, the remainder of the pieces are interior pieces which have four connections each.
If we call the length and height of the puzzle m and n, then the number of edge pieces is going to be \(2\cdot[(m-2)+(n-2)]\). (The picture below may help you picture the various areas involved; the edge pieces are the areas in green, the corners are blue.)
The number of interior pieces is simpler, it's simply \((m-2)\cdot(n-2)\). Now that we have the number of each type of piece, it's a simple matter to multiply them by the number of connections they have and divide by two since every connection is getting counted twice. This gives us a formula for a function:
\begin{align}f(m,n)&=\frac{1}{2}\Bigl[2\cdot4+3\cdot2\cdot\bigl[(m-2)+(n-2)\bigr]+4\cdot\bigl[(m-2)\cdot(n-2)\bigr]\Bigr]\\
&=\frac{1}{2}\Bigl[8+3(2m+2n-8)+4(mn-2m-2n+4)\Bigr]\\
&=\frac{1}{2}\bigl[8+6m+6n-24+4mn-8m-8n+16\bigr]\\
&=\frac{1}{2}[4mn-2m-2n]\\
&=2mn-(m+n)\end{align}
Phew! That's a lot friendlier looking. Funny, I remember when I used to hate algebra with a passion, but that was kinda fun. Absence really does make the heart grow fonder, I guess.
Anyway, we've got our function, but we should probably test it with easy cases. Let's take the cases where \(m=n=2\) and \(m=n=3\):
Here we have some (extremely simple) puzzles. For the first one, on the left, it's easy to see that there are four connections between the four pieces. Plugging 2 in for m and n in our function gives: \[f(2,2)=2\cdot2\cdot2-(2+2)=8-4=4\] So that works. The second puzzle is larger, but it's still easy to count twelve connections between the nine pieces. Plugging 3 in for m and n gives us: \[f(3,3)=2\cdot3\cdot3-(3+3)=18-6=12\] So it appears to hold water. Going back to the puzzle at work, which had \(m=50\) and \(n=20\), we have: \[f(50,20)=2\cdot50\cdot20-(50+20)=2000-70=1930\]Which is a lot of connections! Anyway, my curiosity is sated, and you now have a simple formula to use for party tricks or whatever in the future. A hui hou!
Monday, May 25, 2015
Kīlauea Lava Lake
Two weeks ago my friend Graham and I took a trip out to Volcanoes National Park to see the Kīlauea lava lake. (This isn't the trip I posted about before, which didn't actually materialize.) We also stopped at a nearby bird sanctuary and took a neat drive up the side of Mauna Loa, though in pretty much reverse order to how I just listed things.
We spent forty-five minutes sitting in the line of cars waiting to get to the viewing overlook at the Jagger Museum so it was after sunset by the time we got there, the visibility not improved by a light drizzle. Due to that I'm afraid I wasn't able to get any pictures worth sharing, but thankfully Graham was a bit more prepared and managed to get some video with his DSLR. He'd also been two weeks earlier when the lava lake first rose into view and took footage then too, which I had the idea of compositing together to give a comparison of the activity levels at both times.
When we went the lake was a bit more active than it had been when he'd first gone, with one side constantly slowly boiling like a pot on the stove, periodically throwing a spray of incandescent rock into the air to fall as molten rain as giant bubbles of gas burst unceasingly from the depths of the earth. In the dark it's hard to get a sense of scale, but when you watch the video below keep in mind that that lava lake is eight acres in size. I've taken the footage from both trips and played them one after the other, sped up by 4x to keep the video shorter. (Apologies for the lack of sound; the original audio is just a babble of tourists and doesn't add anything so I muted it, and since this is pretty much my first video compositing experience I was more focused on getting it working than adding audio.)
Only a few days after this trip the lava lake level lowered to where it once again couldn't be seen from the overlook and so far as I know hasn't risen again, so it looks like I caught it just in time. Who knows, though, this is the apparently the first time it's been visible from the overlook in something like thirty years, so perhaps it indicates that the eruption activity center is moving back to the summit and away from the flank. Only time will tell.
Oh, I mentioned going on a scenic drive up the flank of Mauna Loa. The day was intermittently rainy and sunny, with rain clouds rolling in waves across the landscape, so while it was pretty it again wasn't very conducive to photography.
What was (surprisingly) conducive to photography were some of the birds we saw as we drove up. I was driving along on the one-lane road and noticed a solitary francolin standing on the left side of the road. It was standing on one leg in what looked like a fresh dirt-bath dirt patch, and continued to stand there as the car got closer…and closer…and closer, until I had pulled up directly beside it. It seemed completely unfazed as rolled down my window and sat staring at it in stupefaction, mere feet from where I sat.
(If I may digress; francolins are in the same family as chickens [though never domesticated], and I grew up around a lot of chickens. Other than chicks that were incubated and raised primarily around humans, I've never seen a chicken-like bird this unafraid of people, especially a wild one. I couldn't [and to a degree still can't] get over just how unruffled this bird was. I guess this must have been what it felt like landing on Mauritius and encountering the dodos for the first time.)
Anyway, after picking my jaw up off the floor, I was able to get some extreme close-ups of the francolin thanks to its complete coöperation, such as this one:
After what felt like a few minutes staring in wonder at this fearless bird as it stared dispassionately back, we left it where it was and continued up the road. Not much further we ran into a flock of five francolins in the process of slowly crossing the road, whom we interrupted just as they had a bird directly on each side of the road. Once again they weren't inclined to move even as we drove directly between them, mere feet away from a francolin on either side. Given the behavior of the francolins I've seen on Mauna Kea it was, frankly, a bit surreal. I don't know why these francolins so far up Mauna Loa are so fearless – perhaps the isolation and lack of experience with humans? – but it was a really amazing experience.
At the end of the road, about 6,000 feet up, one of the trails to the summit of Mauna Loa begins. It's a long hike, about three or four days, with cabins to stay at along the way. The end of the road also offered an amazing view down to Kīlauea caldera, which we were able to catch glimpses of in between the clouds rolling through. We also took a short hike to where some Mauna Loa silverswords had been planted as part of a reintroduction program. It was interesting to see the differences between them and their Mauna Kea brethren.
The Mauna Loa silverswords, as seen above, seem to have their leaves initially green only to turn silver later, while the Mauana Kea ones appear to be silver from the get-go. All the ones we saw were pretty small; that was one of the largest ones, and it's only about the size of a large cabbage. Of course, that may just be due to age differences between the two populations (both of them human-planted, coincidentally). The Mauna Loa silverswords, additionally, seemed to have only a single rosette, in contrast to the Mauna Kea ones that often have multiple rosettes in one plant. (I've heard this is the result of a genetic bottleneck; the single-rosette form is the standard, the multi-rosette is due to a mutation, but it just so happened that when they were collecting what few silverswords remained on Mauna Kea for breeding the few they got had this mutation so the ones that have been re-introduced do as well.)
Also between the drive and the volcano we stopped a bird sanctuary, which I don't have much to say about other than that it was a nice mile-long hike in the gathering dusk, trying to make out lots of little bird flitting about in the trees. And there were some neat kalij pheasants in the undergrowth that were pretty fearless around us too, though not quite to the extent the francolins were. All in all, a nice trip.
We spent forty-five minutes sitting in the line of cars waiting to get to the viewing overlook at the Jagger Museum so it was after sunset by the time we got there, the visibility not improved by a light drizzle. Due to that I'm afraid I wasn't able to get any pictures worth sharing, but thankfully Graham was a bit more prepared and managed to get some video with his DSLR. He'd also been two weeks earlier when the lava lake first rose into view and took footage then too, which I had the idea of compositing together to give a comparison of the activity levels at both times.
When we went the lake was a bit more active than it had been when he'd first gone, with one side constantly slowly boiling like a pot on the stove, periodically throwing a spray of incandescent rock into the air to fall as molten rain as giant bubbles of gas burst unceasingly from the depths of the earth. In the dark it's hard to get a sense of scale, but when you watch the video below keep in mind that that lava lake is eight acres in size. I've taken the footage from both trips and played them one after the other, sped up by 4x to keep the video shorter. (Apologies for the lack of sound; the original audio is just a babble of tourists and doesn't add anything so I muted it, and since this is pretty much my first video compositing experience I was more focused on getting it working than adding audio.)
Only a few days after this trip the lava lake level lowered to where it once again couldn't be seen from the overlook and so far as I know hasn't risen again, so it looks like I caught it just in time. Who knows, though, this is the apparently the first time it's been visible from the overlook in something like thirty years, so perhaps it indicates that the eruption activity center is moving back to the summit and away from the flank. Only time will tell.
Oh, I mentioned going on a scenic drive up the flank of Mauna Loa. The day was intermittently rainy and sunny, with rain clouds rolling in waves across the landscape, so while it was pretty it again wasn't very conducive to photography.
What was (surprisingly) conducive to photography were some of the birds we saw as we drove up. I was driving along on the one-lane road and noticed a solitary francolin standing on the left side of the road. It was standing on one leg in what looked like a fresh dirt-bath dirt patch, and continued to stand there as the car got closer…and closer…and closer, until I had pulled up directly beside it. It seemed completely unfazed as rolled down my window and sat staring at it in stupefaction, mere feet from where I sat.
(If I may digress; francolins are in the same family as chickens [though never domesticated], and I grew up around a lot of chickens. Other than chicks that were incubated and raised primarily around humans, I've never seen a chicken-like bird this unafraid of people, especially a wild one. I couldn't [and to a degree still can't] get over just how unruffled this bird was. I guess this must have been what it felt like landing on Mauritius and encountering the dodos for the first time.)
Anyway, after picking my jaw up off the floor, I was able to get some extreme close-ups of the francolin thanks to its complete coöperation, such as this one:
![]() |
| "What, never seen a francolin before?" |
After what felt like a few minutes staring in wonder at this fearless bird as it stared dispassionately back, we left it where it was and continued up the road. Not much further we ran into a flock of five francolins in the process of slowly crossing the road, whom we interrupted just as they had a bird directly on each side of the road. Once again they weren't inclined to move even as we drove directly between them, mere feet away from a francolin on either side. Given the behavior of the francolins I've seen on Mauna Kea it was, frankly, a bit surreal. I don't know why these francolins so far up Mauna Loa are so fearless – perhaps the isolation and lack of experience with humans? – but it was a really amazing experience.
At the end of the road, about 6,000 feet up, one of the trails to the summit of Mauna Loa begins. It's a long hike, about three or four days, with cabins to stay at along the way. The end of the road also offered an amazing view down to Kīlauea caldera, which we were able to catch glimpses of in between the clouds rolling through. We also took a short hike to where some Mauna Loa silverswords had been planted as part of a reintroduction program. It was interesting to see the differences between them and their Mauna Kea brethren.
The Mauna Loa silverswords, as seen above, seem to have their leaves initially green only to turn silver later, while the Mauana Kea ones appear to be silver from the get-go. All the ones we saw were pretty small; that was one of the largest ones, and it's only about the size of a large cabbage. Of course, that may just be due to age differences between the two populations (both of them human-planted, coincidentally). The Mauna Loa silverswords, additionally, seemed to have only a single rosette, in contrast to the Mauna Kea ones that often have multiple rosettes in one plant. (I've heard this is the result of a genetic bottleneck; the single-rosette form is the standard, the multi-rosette is due to a mutation, but it just so happened that when they were collecting what few silverswords remained on Mauna Kea for breeding the few they got had this mutation so the ones that have been re-introduced do as well.)
Also between the drive and the volcano we stopped a bird sanctuary, which I don't have much to say about other than that it was a nice mile-long hike in the gathering dusk, trying to make out lots of little bird flitting about in the trees. And there were some neat kalij pheasants in the undergrowth that were pretty fearless around us too, though not quite to the extent the francolins were. All in all, a nice trip.
Labels:
birds,
francolins,
Kīlauea,
lava,
Mauna Loa,
photos,
silverswords,
volcanoes
Thursday, May 7, 2015
Kīlauea Topography
Later today I'll be taking a trip to Hawai‘i Volcanoes National Park to see the lava lake in Kīlauea caldera. In case you haven't heard: Kīlauea has had a lava lake in its summit caldera constantly since it began its current eruption on January 3, 1983, however, the level of the lake has fluctuated over time, and for most of its existence has been very low – too low for tourists to see from safety, and only visible with cameras set up on the very rim of the crater. Just recently, within the last two weeks, the level of the lake has risen dramatically, making it easily visible.
But wait – I'm using terms like caldera and crater willy-nilly here without definition. Kīlauea the volcano has a slightly complicated summit, and there are several names bandied about when talking about it. This post is as much for my sake as it is for yours, but I'm going to try to map out exactly where all the various names refer to. First of all, have a Google Maps view of the area:
This is a satellite photo of the area around the summit caldera of Kīlauea. This picture is mostly for reference. For actually pointing out the various parts, I've created the following picture with various regions colored in for clarity:
Here's the summit region again, with significant features colored it. Shown in red is Kīlauea Caldera. Calderas are a common feature at the summit of volcanoes, and are formed when the summit of a volcano collapses after a particularly strong eruption – the magma in the magma chamber has been erupted and can no longer provide support to the overlying rock. It's likely that Kīlauea Caldera was formed over several centuries, and may have attained its current form after a particularly violent eruption in 1790. I'm not 100% sure of these boundaries, as the walls of the caldera steadily diminish to the southwest where lave has spilled out, and there may be a small lobe to the northeast that I haven't included, but the outline is close enough.
The smaller green area within the caldera is Halema‘uma‘u Crater. (Remember my tips for pronouncing long Hawaiian words with reduplication! It's Hale·ma‘u·ma‘u.) Halema‘uma‘u Crater is a smaller pit crater within the larger caldera, and has been the location of most of the volcanic activity at the summit for quite a while (though not all of it; directly to the east of the caldera in the picture above you can see the pit of Kīlauea Iki where an eruption happened in 1959 that created some of the tallest lava fountains ever recorded).
Finally, within Halema‘uma‘u crater, colored in blue, is Overlook Crater, named for…I'm not really sure, actually. I guess the fact that it can be seen from the overlook at the nearby Thomas A. Jagger Museum. This is the actual volcanic vent, and has in the past taken the form of a yet smaller crater within Halema‘uma‘u crater. This is where the lava lake I talked about has actually been residing, usually far enough below the surface as to be unseen from the overlook.
However, starting on April 24th, the lava lake inside the vent rose almost to its lip (at the floor of Halema‘uma‘u crater), the highest it had ever come since the vent opened. As of April 29th the lava has actually risen enough to spill onto the crater floor, and has since fluctuated around the level of the floor of the crater floor. It's clearly visible from the overlook, and a lot of people are going out to take a look, including myself. If all goes well I hope to have some pictures of it soon, and with this post under your belt you'll be able to follow what I'm talking about when I casually throw out names like “Halema‘uma‘u crater.” A hui hou!
Edit: Well, maybe this'll teach me to announce things ahead of time. Turns out, due to unforeseen circumstances, several of the people I was planning on going with couldn't make it today, so we're postponing to a later date yet to be determined. I'll be sure to write about it when it does happen, though.
But wait – I'm using terms like caldera and crater willy-nilly here without definition. Kīlauea the volcano has a slightly complicated summit, and there are several names bandied about when talking about it. This post is as much for my sake as it is for yours, but I'm going to try to map out exactly where all the various names refer to. First of all, have a Google Maps view of the area:
This is a satellite photo of the area around the summit caldera of Kīlauea. This picture is mostly for reference. For actually pointing out the various parts, I've created the following picture with various regions colored in for clarity:
Here's the summit region again, with significant features colored it. Shown in red is Kīlauea Caldera. Calderas are a common feature at the summit of volcanoes, and are formed when the summit of a volcano collapses after a particularly strong eruption – the magma in the magma chamber has been erupted and can no longer provide support to the overlying rock. It's likely that Kīlauea Caldera was formed over several centuries, and may have attained its current form after a particularly violent eruption in 1790. I'm not 100% sure of these boundaries, as the walls of the caldera steadily diminish to the southwest where lave has spilled out, and there may be a small lobe to the northeast that I haven't included, but the outline is close enough.
The smaller green area within the caldera is Halema‘uma‘u Crater. (Remember my tips for pronouncing long Hawaiian words with reduplication! It's Hale·ma‘u·ma‘u.) Halema‘uma‘u Crater is a smaller pit crater within the larger caldera, and has been the location of most of the volcanic activity at the summit for quite a while (though not all of it; directly to the east of the caldera in the picture above you can see the pit of Kīlauea Iki where an eruption happened in 1959 that created some of the tallest lava fountains ever recorded).
Finally, within Halema‘uma‘u crater, colored in blue, is Overlook Crater, named for…I'm not really sure, actually. I guess the fact that it can be seen from the overlook at the nearby Thomas A. Jagger Museum. This is the actual volcanic vent, and has in the past taken the form of a yet smaller crater within Halema‘uma‘u crater. This is where the lava lake I talked about has actually been residing, usually far enough below the surface as to be unseen from the overlook.
However, starting on April 24th, the lava lake inside the vent rose almost to its lip (at the floor of Halema‘uma‘u crater), the highest it had ever come since the vent opened. As of April 29th the lava has actually risen enough to spill onto the crater floor, and has since fluctuated around the level of the floor of the crater floor. It's clearly visible from the overlook, and a lot of people are going out to take a look, including myself. If all goes well I hope to have some pictures of it soon, and with this post under your belt you'll be able to follow what I'm talking about when I casually throw out names like “Halema‘uma‘u crater.” A hui hou!
Edit: Well, maybe this'll teach me to announce things ahead of time. Turns out, due to unforeseen circumstances, several of the people I was planning on going with couldn't make it today, so we're postponing to a later date yet to be determined. I'll be sure to write about it when it does happen, though.
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