Building a Pyramid

I promised my little brothers that I would put some pictures of the pyramid I built in Minecraft up on my blog, so here they are.

View of the pyramid from the south, along the entrance causeway.

This pyramid was actually a pretty interesting learning experience. Minecraft takes place in a world of blocks, which are usually taken to be one meter on a side. When I decided to build a pyramid, I first thought of building a replica of the Great Pyramid of Giza, which is 230.4 meters (755.9 feet) on a side at the base and would have stood 146.5 meters (480.6 feet) tall when it was built. Given the constrictions of Minecraft my pyramid would need to have a 45\(^\circ\) angle rather than the 51\(^\circ\) 50' 40" of the actual one (and thus only 115 meters high), and a quick calculation showed that it would require on the order of 2,054,360 blocks to build an entire pyramid.

Edit (6/14/13): The calculation is simple; it's just
\[N=\sum_{n=1}^{115}(2n)^2\] which can be solved in four lines of Python code, viz:
>>> N = 0
>>> for n in range(1, 116):
...    N += (2 * n)**2
>>> print(N)

View of the pyramid from the south-east corner. Ignore the flying castle in the background.

I also quickly learned that the area I wanted to build it in was much too small, so I decided to scale down and build a smaller pyramid 100 meters on a side. The same calculation showed that such a pyramid would still require 171,700 blocks (same calculation as before with different upper limit), and since I was going to have to gather every single block myself, I decided to cheat and take advantage of Minecraft physics (or lack thereof) to build a hollow pyramid consisting of only an outer shell.

View from atop the black obsidian pyramidion. Some previous work can be seen, the Library building to the left and the floating Sky Castle to the right.

This scheme still required a total of 10,000 blocks of sandstone, which I methodically went about gathering. (Edit (6/14/13): To arrive at that number, imagine the pyramid as a series of concentric square rings, since it's hollow. You can imagine collapsing them down into each other, until you have nothing but a square patch of sandstone a hundred meters on a side. Simply square that number, and you arrive at 10,000.) The entire process of gathering materials and building the pyramid probably took me a good ten hours over a period of several days, and really put into perspective what it must have taken to build an actual, solid pyramid over twice as large as the one I finally completed.

The Sun rising behind the pyramid in the east. It is very impressive in-game.

R.I.P. Neil Armstrong

In case you haven't yet heard, Neil Armstrong, the first man to walk on the surface of another world, passed away Saturday at the age of 82.

According to people that knew him well, Armstrong was a humble man who never let fame go to his head. After becoming the first man to walk on the Moon he continued to work in the aerospace industry in various capacities, even taking a position at the University of Cincinnati's engineering department. His contributions to spaceflight stretch far beyond what he was most famous for. Armstrong was a big proponent of returning to the Moon, and expressed himself rather eloquently on the subject in 2010:

“Some question why America should return to the moon. ‘After all,’ they say, ‘we have already been there.’ I find that mystifying. It would be as if 16th-century monarchs proclaimed that ‘we need not go to the New World, we have already been there.’”

Here's hoping that the wishes of this great American hero will be realized before too many more years have passed.

Deoxyribonucleic Acid

Today on Astronomy Picture of the Day I found this amazing video visualizing the DNA molecules that exist in every one of the trillions of cells that make up your body. It's seriously incredible. Fearfully and wonderfully made indeed. The video explains it better than I can, so I'll stop talking and show it:

Globular Cluster Photo Series (Part 21): M19

Today I've got a picture of the globular cluster Messier 19. Much like M9 that I showcased last time, M19 is one of the globular clusters closest to the galactic core. It is about 28,000 light-years from Earth, and about 5,200 light-years from the core, narrowly beating M9 (at 5,500 light-years) for closest globular cluster to the core that I've showcased so far. M19 is the most elliptical globular cluster known (though it is only slightly noticeable in this picture), and is about 140 light-years across the long way. This is a good 50% bigger than M9, so since they are about the same distance away M19 looks a lot bigger on the sky at 17.0 arcminutes to M9's 12.0. (The full Moon for comparison is about 30 arcminutes across.)

Messier 19 in Ophiuchus.

Other than its great ellipticity (which may actually be a visual effect due to intervening dust extincting the light on one side), M19 is a fairly standard globular cluster with little to say about it despite its great size. It contains a rather small number of variable stars and was one of the earlier objects that Charles Messier observed. And other than that I really can't find much more interesting information about it. A hui hou!

VLBA Tour: With Pictures Edition!

As mentioned in my last post, Tuesday I had the opportunity to take a tour of the Very Long Baseline Array (VLBA) radio telescope located on Mauna Kea. It was a great experience, very interesting, and I definitely learned a lot. I brought my camera with me intending to take lots of pictures, only to realize after taking one that my camera battery was drained.

So, I switched over to using the camera in my cell phone, which is where all of these pictures come from.

The VLBA, as I mentioned previously, is the world's largest interferometer, meaning that the 10 radio telescopes in it all work together to give the sharpest views of any telescope ever. In a single night of observing each telescope can accumulate over 15 terabytes of data – so much data, in fact, that it's cheaper to send the physical hard drive to the headquarters in New Mexico by Fedex than to send it over the Internet. This interferometer is so sensitive that they can actually use it to measure how fast continental plates are drifting apart over time, and GPS satellites are kept updated using the information it provides.

Anyway, here's a shot of the Mauna Kea telescope, with some people in the foreground for scale. Each dish is 25 meters across (82 feet), and the whole array is about ten stories high when pointed straight up as in this picture.

The Mauna Kea node of the VLBA.

See that part at the bottom of the dish? That's a room. A room that we got to visit. A small cylindrical room that immediately brought to mind spaceships from every B-grade science fiction movie in the last century.

The room just beneath the center of the radio dish.

The guy in the middle facing the camera was our guide Tony, one of the two employees of this telescope that do the majority of the maintenance.

After that, we climbed up the ladder in the picture to another smaller room where all the instruments were kept. From there, we were able to exit a small door and find ourselves on the mirror itself!

The dish, with the door we came out of visible at the bottom.

Standing on the dish was amazing. Absolutely incredible. As mentioned it's over 80 feet across, all curving in a gently parabolic arc, and so blindingly white I was wishing I had my sunglasses. (The picture doesn't convey it very well, but wow, the white paint on the dish reflected so much light it was like a minor form of snow blindness until my eyes adjusted.)

We were even allowed to climb up the steeply sloping outer edge to where we could look back down to the parking lot almost ten stories below. It was intense. Taking the picture below was difficult, as I was trying to hold on to the dish edge with one hand so as not to slide back down while taking a picture with the other on a phone without a dedicated camera button.

Don't look down!

Pretty amazing view, no? Here's another panorama of the dish taken from the same location by turning around:

As mentioned earlier, the thing in the center that looks like a space capsule is the instrument room where the various detectors are stored. There are quite a few different receivers covering a much, much thicker band of the electromagnetic spectrum than the visible light we can see, and the brown object near the top of the picture is actually a parabolic ellipsoid mirror that can direct the radio waves the telescope receives into any of the various instruments.

It also looks pretty neat with a bit of lens flair behind it.

So, there you have it. Pictures from my VLBA tour. All in all it was a great experience, the two guys who run it were great to talk to, happy to show off and talk about their telescope. You could tell they loved what they did. Anyway, that's it for tonight, a hui hou!

P.S. This telescope is located at about 11,000 feet on Mauna Kea, nearly 3,000 feet below the summit, so none of the hills you see in these pictures is the summit peak. Just local cinder cones.

VLBA Tour

Today I had the great privilege of being able to go on a tour of the Very Long Baseline Array (VLBA) radio telescope located on Mauna Kea. To be more precise, the VLBA is a set of ten radio telescopes stretching from Mauna Kea to St. Croix in the Virgin Islands that operate as the world's largest interferometer, which means that they observe together to give the sharpest views of any telescope ever (though in radio frequencies, not visible light).

Anyway, this post is simply advance notice for a more full and detailed review which will come in the next few days. It was a really great experience, and I don't have time to write a review to do it justice at the moment. A hui hou!

Globular Cluster Photo Series (Part 20): M14

Today I have a picture of the globular cluster Messier 14 in Ophiuchus. M14 is a rather large cluster around 100 light-years across, and at a respectable distance of about 30,300 light-years. The cluster's large physical size gives it a size of 11.0 arcminutes on the sky, about a third the width of the full Moon. The entire cluster shines about 400,000 times as bright as the Sun, but is just below naked-eye visibility at its distance.

Messier 14 in Ophiuchus.

M14 is known to contain 70 variable stars, quite a decent number for a globular cluster. In 1938 a nova went off in the cluster, but this fact was not discovered for 28 years until photos of the cluster taken in 1938 were examined in 1964. It's estimated from these photos that the nova reached a peak brightness over 5 times that of the brightest non-nova stars in the cluster. This is only the second nova known to have appeared in a globular cluster (and the first was in 1860, before it could be photographed).

Globular Cluster Photo Series (Part 19): M9

The last globular cluster I showed a picture of, Messier 64, was quite far away from the galactic center. Today I'm going to go in the opposite direction with a picture of Messier 9. This cluster is moderately far from Earth at a distance of about 25,800 light-years, but that's because it happens to be one of the closest globular clusters to the galactic core. The distance between M9 and the core is only about 5,500 light-years, which is pretty small when you remember that the Galaxy is about 100,000 light-years across. (For comparison, our Solar System is about 23,000 light-years from the core.) M9 is a average-sized cluster about 90 light-years across, which at its distance translates to a size of about 12.0 arcminutes (about a third as large as the full Moon).

Messier 9 in Ophiuchus.

Partly as a result of being so close to the center of the Galaxy Messier 9 is retreating from us quite quickly, at a rate of 224 kilometers per second (just a hair over half a million miles per hour). It is also located close to the dark nebula Barnard 64, which you can see as the region to the upper-left of the cluster that appears to be devoid of stars. This dark molecular cloud (made up of interstellar gas and dust) is probably something like what the Orion Nebula and the Lagoon Nebula would look like from the other side.