Happy Leap Day!

Happy February 29th, everyone! As this is the first leap year since I started my blog I thought I would give a quick overview of the Gregorian calendar system that brings it about.

Any such discussion should begin, however, with the introduction of the Julian system which the Gregorian system replaced. The Julian calendar was a modification of the Roman calendar put in place by Julius Caesar, taking effect in 45 BC. It was an attempt to keep the calendar in sync with the seasons, which is necessitated by the fact that the Earth does not take an integer number of days to orbit the Sun. The sidereal year, the amount of time it takes for the Sun to return to the same apparent location in the sky relative to the background stars, is about 365.25636 days. While this is not too complicated, we also have to account for the fact that the direction of the Earth's rotational axis is not constant with time, but rather wobbles very, very, slowly like a top. This cycle takes a long time to complete \(-\) about 24,000 years \(-\) but it does produce noticeable results, such as the fact that the time between successive equinoxes or solstices (called a tropical or solar year) is about 365.24237 days \(-\) about 20 minutes shorter than a sidereal year. It's also more important for purposes of agriculture, because the seasons are tied to the solar year rather than the sidereal year.

Anyway, because the year is not an integer number of days, any attempt to use an integer number of days in a calendar will lead to a slow drifting of seasons. Given enough time (and at \(\sim{}\)1 day every 4 years, it wouldn't take too much time) the seasons would drift slowly backwards through the year. Spring, summer, fall, and winter would all begin earlier and earlier. While this might not sound too bad in theory, it can play havoc if you're a farmer wanting to use the calendar to know when you should be planting or harvesting your crops \(-\) and in a pre-industrial society, that could mean the difference between surviving through the winter or starving to death.

Prior to Julius Caesar the Romans tried to fix this situation by the random inclusion of extra (intercalary) months. And I do mean random, the Roman officials in charge for the year were in charge of determining if they needed an extra month, and since these officials served for "a year", there could be quite the temptation to increase the length of one's rule or deny a rival extra time in office. Julius Caesar decided to come up with a system that would be independent and self-correcting after a stint in Egypt, where a system of adding 1 day every 4 years had been proposed, but not carried through. His mathematical advisors came up with the same idea, and in 46 BC he mandated the adoption of the Julian calendar.

Now, the Julian calendar was quite the improvement over the previous chaos, to be sure. It was good enough, in fact, that some countries continued to use it up into the 20th century. It kept the dates of equinoxes and seasons much better than any previous attempts, and only gained 1 day every 128 years. Given the length the Roman empire lasted after the adoption of the calendar, the few days gained weren't that big a deal. However, by the Middle Ages, the seasons were definitely out of sync. By AD 1582 the equinoxes were happening about 10 days earlier than they should (March 11 instead of March 21). Pope Gregory XIII decided to fix this state of affairs, and asked the finest mathematical minds in Europe to come up with a better system, which eventually came to bear his name.

The difference between the Julian and Gregorian system isn't very big. Under the Julian system, the calendar gains about 3 days every 400 years, i.e., in 400 years there are 100 leap days in the Julian system. The Gregorian system fixes this by taking away 3 of those leap days, for a total of 97 leap days ever 400 years. The way this was accomplished was by decreeing that years ending in 00 would not be leap years (like they ordinarily would) unless they were also divisible by 400. So the 2000 was actually rather special: it wouldn't be a leap year except for the fact that it is divisible by 400. Likewise, the year 2100 will not be a leap year, even though it is halfway between two leap years.

Such a simple, tiny change, yet what a big difference it makes! In the Julian system, over a period of 4 centuries there are \[100\times366+300\times365=146,100\,\text{days}\] while in the Gregorian system there are \[97\times366+303\times365=146,097\,\text{days}\]
That doesn't seem like a big difference, yet the Julian system is accurate to 1 day every 128 years, while the Gregorian system is accurate to 1 day every 7,700 years, over 60 times as accurate. Pretty neat, huh? Happy Leap Day!

Cheese!

After my post yesterday looking at some of the deep mysteries of physics and our universe, I wanted to do something a little lighter today, so I decided to take a closer look at one of my favorite cheeses: Brie.

A tasty slice of Brie.

Brie is a soft cheese that originated in the Brie region in France. That white rind you see is actually a mold, typically either Penicillium candidum or Penicillium camemberti. (Although these molds are in the Penicillium genus, they are not closely enough related to Penicillium chrysogenum [the commercial source of penicillin] to actually be of use in warding off infection.)

Fungi are pretty cool organism, because of their saprotrophic nature, although that's also one reason I generally prefer to avoid eating them. Saprotrophic basically means that an organism digests its food outside of its cells (unlike bacteria, protozoa, or plants) by secreting various digestive enzymes, then absorbing the simpler products into its cells. Given that this is something typically associated with fungi and the decomposition of dead things, I was shocked while researching it to discover that this is essentially the same way that vertebrates, including people, digest their food. There really is almost no difference, though, if you think about it: in humans, the food in enclosed in the small intestine, but it's still outside the cells (mathematically, humans are homeomorphic with donuts) which secrete various digestive enzymes that break it down before the smaller simpler products are absorbed into the bloodstream for transport throughout the body. It's one of the reasons fungi are considered more closely related to animals than to plants. Fascinating, really. Next time you have a big meal, ponder the fact that you share the same basic idea behind your digestion with fungi of all shapes and flavors!

Superluminosity Redux

Remember that story from last September, about the startling report by a group of physicists at the OPERA neutrino detector in Italy and how they'd apparently been measuring neutrinos traveling superluminally? The paper said that, on average, neutrinos were making the trip in about 60 nanoseconds less than it would take light to make the trip. The paper generated some major waves in the science community, as it appeared to go against everything we thought we knew about relativity. However, despite the startling (and frankly, alluring) possibilities faster-than-light travel would open up, most people (myself included) remained highly skeptical, given that relativity has always been correct every single time it's been tested.

Now, it appears that the answer to the question may be as simple as a loose cable connection. Scientists at OPERA have said that they found a loose connection in a fiber optic cable that brings signals from GPS satellites to OPERA and its main detector. When the cable was tightened and re-tested, data was found to arrive around 60 nanoseconds faster than previously thought...which is just about the time discrepancy seen in the experiment. The paper claimed a time accuracy of \(\pm10\) nanoseconds, so if the 60 nanosecond systematic error is removed, it's quite possible (and most likely) that the neutrinos are traveling just a bit slower than light \(-\) although not by much, certainly.

There's another interesting tidbit lurking here, though: according to the scientists, there may be another error in the setup, involving a piece of equipment that time-stamps the neutrino arrivals \(-\) but this error might actually increase the speed of the neutrinos over what was claimed previously. I haven't found any estimates of the time increment this might have, and it remains to be seen if it actually exists, but rest assured I will keep you informed when I find anything.

In all likelihood, this is how it will end up. The timing error by a loose cable will be found to account for the discrepancy, and relativity will stand triumphant once again. I'll be the first to admit it would be pretty interesting for the opposite to be true, and for the neutrinos to actually be moving superluminally \(-\) but that's how science works. It's a search for the truth (or at least it should be), not what you want to be true. And, really, relativity is already pretty incredible as it is. I mean, the very fabric of spacetime fluidly adjusting itself so that light in a vacuum always moves at a particular speed relative to an observer? Time actually slowing down in a gravitational potential well? Space being something that curves and deforms based on the presence of mass-energy (which are really just two aspects of the same thing)? How impossibly cool is that??

Mauna Kea Snow.

This week while working up at the Vis on Mauna Kea, I was called in early Tuesday morning (about 7:30) because the road to the summit needed to be closed to visitors. At that point, although there was a large mass of clouds off to the east, the weather was actually pretty nice, not raining or blowing, blue sky off to the east, not overly cold for the altitude and time of day. Fifteen minutes later, it was snowing pretty good. Since I can count the number of times I've experienced snow falling from the sky on two hands, this was a pretty big experience for me. (Thankfully I was sitting inside an idling vehicle blocking the summit road, not actually out in the snow.)

Getting snow down at the level of the Visitor Information Station, at 9,200 feet, is really quite rare. It snowed for perhaps 20 to 30 minutes before turning to a frigid rain that lasted the entire remainder of the day without pause. The snow all melted up to maybe 11,000 feet within 3 hours, but it was real pretty while it lasted. I even managed to get some pictures of it:

Looking up the summit access road, from my vantage point parked half across it.

More of the mountain slope above the Hale Pōhaku area.

I must say, snow's not so bad when sea level and warmth is just 45 minutes' drive away. I certainly wouldn't want to live with the stuff for any appreciable length of time, though.

Building and Tree

Up at the altitude of the Visitor Information Station at 9,200 feet (2,800 meters), the only trees growing are primarily hardy māmane trees (Sophora chrysophylla). In the spring they bloom with beautiful vibrant yellow flowers, and I can already see some early bloomers bursting into flower. I hope to get a good picture of them at the height of their flowering season this year, because it's really quite gorgeous. But what I really wanted to talk about today was one particular māmane sapling I came across on Thursday. This sapling was a bit unusual, because it was growing out of the side of a building.

One adventurous young māmane sapling.

To give you a sense of scale, that skirting through which the tree is growing goes up to about my shoulders. (This is Ranger Cabin C, by the way, if you're familiar with the area.) I took a peek inside, and discovered that the tree's base is a good two feet back from the base of the building, and not only that, but there were several other, smaller shoots growing up from the base as well. While I can understand how these neodendrons are getting their light, I'm left scratching my head as to where they're getting their water from. The side they're on – the south side – is the downhill (or ma kai – “ocean-wards”) side, so I can't imagine that the slight amounts of rain at this elevation is running under the building. I suppose the tree must simply have long roots now, but that still leaves me wondering how it fared as a seedling. Quite mysterious.

As to the fate of the tree (and building): while I'm sure that normally no one would think twice about lopping off the offending branches, māmane trees at this elevation are a protected species as they are the only food source of the endemic palila, a critically endangered species of Hawaiian honeycreeper now found exclusively on the upper slopes of Mauna Kea. So I don't know what the eventual fate of the tree (and building) will be.

Fax by Internet

The other day I ran into the need to send a fax while I was at home and without access to one of those archaic machines. Being of limited mobility to actually go out and find a fax machine I could use, I was inwardly bemoaning the fact that in this modern age I couldn't just email the required documents (since they were all on my computer already anyway) when I happened to stumble across a very useful website.

FaxZero is a website that lets you send faxes over the Internet. All you have to do is fill in some basic information about yourself and the recipient, attach the files you wish to send, and away they go! There are two different modes: you can send up to five free faxes a day, as long as they're three pages or less and you don't mind an ad appearing on the cover page. Or, you can pay $1.99 for an ad-free (or non-existent) cover page, plus the ability to fax up to fifteen pages at a time. All in all, quite the handy website if you need to send the occasional fax but don't have easy access to a fax machine. It helps if you're faxing documents that are already digitized, otherwise you'll have to scan them or something similar, but it works very well. You can attach files with extensions .DOX, .DOCX, and .PDF, which ought to cover most of your faxing needs.

Forays in Innovative Picture Combination

About two weeks ago as I was on my way up to work in the morning, we stopped briefly on Saddle Road to snap some shots of Mauna Kea. Since I didn't have my camera along that day, I decided to try out the camera on my new phone. The aspect ratio on my phone is 5:3 which results in somewhat thinner pictures than I'm used to with my camera (which is much closer to 3:2). Because of this, I went ahead and took two different pictures of the mountain, in landscape and portrait mode, then had the idea to combine them into a single, cross-shaped image. Sort of a semi-panorama, if you will. The early morning sky was beautifully cloud-free, and allowed me to get this image:

Mauna Kea, 'midst Heaven and Earth, 'twixt Sea and Sky, etc., etc.

I think that from an artistic point of view this is an interesting image, because you have two orthogonal axes that draw the eye. Vertically, it gives you a sense both of the height of the mountain (13,796 feet above sea level), and of the infinite vault of heaven stretching endlessly above it. And yet for all its height, Mauna Kea is extraordinarily flat, and the horizontal axis gives you a sense of it receding off into the distance on either side. And in the middle, where the axes meet, is the Heart of the Moutain, a large crater that appears heart-shaped from this direction (it's a little on the small side here, but you can make it out). All in all, a very interesting picture I think. If you found it interesting or thought-provoking, let me know in the comments!

Lunar Vistas

Monday night was extremely quiet up at the Vis and I'd run out of stuff to do, so I took the opportunity to do a little astrophotography. Monday night was also the day before the Full Moon, however, and it was a bit too late to feasibly bring out the imaging telescope, so I decided to try something I'd never done before: connecting my camera directly to a telescope and taking pictures with it.

Now, I've taken pictures through a telescope with my camera before, but not the same way. Before, I put the camera to the lens of the eyepiece and took a picture, but Monday night I used a special connecting piece to attach my camera directly in place of the eyepiece, which has several advantages. For one thing, it's one fewer set of lenses for the light to pass through and attenuate before reaching the CCD chip, and for another, it allows me to take much longer images because I no longer have to worry about holding the camera steady because it's attached to the telescope.

Anyway, since the Moon was out and nearly full, I decided to turn my new camera-with-extremely-powerful-zoom-lens assembly on it and take some pictures. Once I figured out the correct exposure, the resulting images blew me away with their clarity and detail. I couldn't see the entire Moon due to the narrow field of view of the camera + telescope setup, so I had the idea to do one of the things I do well and put together a panorama of the Moon's surface. I took pictures all over the Moon's disk, then stitched them together by hand to get the picture that you see below.

Our glorious Moon. Click on the picture to see a larger version.

North in this picture is roughly to the upper-right, so this picture represents what you would typically see from the northern hemisphere. The slight bulge at the bottom-right is an unavoidable side-effect of the fact that I only got a few pictures of that region, and they contained subtly different perspectives. I was able to fix such perspective problems on the rest of the disk by using multiple photos, but that section by chance only had one or two photos covering it. Altogether this picture is composed of 10 separate exposures.

You can't see many shadows in this picture due to it being lunar high noon on the side facing us but if you look at the upper-left side you can see just a hint of shading, evidence that the Moon was still a day from being full.

Finally, I'd just like to note that this is the first time I've actually connected my camera (a Nikon DSLR) to a telescope and used it for astrophotography in the six years since I got it. That was one of the original reasons I got a DSLR in the first place, instead of just a point-and-shoot, so I was gratified that I was finally able to fulfill one of the purposes I had in mind for it when I got it.

Slice of the Earth

Working up at 9,200 feet (2,800 meters) on Mauna Kea the other day I gained a new perspective on just what a thin shell humanity inhabits on this great giant globe of ours. At that elevation anything more strenuous that a walk becomes noticeably more exerting, due to the fact that you're working in about 70% of normal atmospheric pressure. This led me to ponder just how thin a volume people really live in, compared to the size of the Earth. As an astronomer I'm always interested in a new perspective, and being the visual sort of chap I am I decided to make something visual to explain.

I ended up creating the picture below, which attempts to show a slice though the Earth down to the core and compare it to a few other things, namely the heights of Mt. Everest and Mauna Kea and the depth of the Marianas trench. I decided to create it with a scale of one kilometer per pixel. Since the mean radius of the Earth is 6,371 kilometers, this is a BIG picture. It's so big I decided to just write my commentary in, rather than write a bunch more and have you scroll through a large boring picture. The reason I chose that scale is so that details at the surface could actually be made out, since the Earth turns out to be smoother than a pool ball if you compare them.

I also learned, upon trying to upload my finished masterpiece, that Blogger apparently has a maximum filesize limit (whether data-size or pixel-size I don't know, but frustrating either way). It cheerfully uploaded my picture without telling me anything was wrong, only for it to show up at about a quarter size, completely unreadable. I therefore remedied the problem by chopping my work into quarters (which hurt, artistically) which you see below. It's not quite as pretty as it is in its entirety (saving at lower quality to decrease the file size didn't help either), but I think it manages to get the idea across. Enjoy!

Edit (2/8/12): Today I went back, changed some of the text around, and split the picture into six pieces, each of which I saved as a PNG file, so the overall quality is much better. Check out the new and improved version below.

 

 

 

Final thoughts: this picture was a beast to put together. It took me the first five of Beethoven's symphonies plus I-don't-even-remember-how-many Vivaldi concerti. There are 4,122,000 pixels in the (original) picture, spread over 48 different layers (mostly because almost every bit of text automatically makes its own layer). It was tough, but I think the results are worth it.

Edit: Sometime after making this picture I learned that I'd drawn the Marianas Trench completely wrong. In actuality, it would look more like an inverted version of Mauna Kea—rather than a steep-sided canyon, it's more of a very gently-sloping depression in the ocean floor. The depth is still correct, but just imagine it being a very gentle depression sloping out at a very low angle.