Of Years and Leap Years

So today is February 29th, the leap day. A day that only comes once every 4 years, with a few exceptions. In this post, I'll describe why we do this and why it's necessary.

Quick- how long is a year?
If you answered 365 days, you are mostly correct. In actuality, the Earth takes just a bit longer to go around the Sun- about 6 hours. In 4 years, this 6 hour difference amounts to 24 hours, or one day. Hence, the need to add an extra day every 4 years. However, the time is not exactly 6 hours, its more like 5 hours, 49 minutes, and some seconds. That means that if we keep adding leap days every 4 years, we'll eventually be too far forward. This is on why every year that's divisible by 100 a leap day is NOT included. But wait! If we never include those years we'll eventually lag behind. So years that are divisible by 400, even though they are also divisible by 100, are considered leap years and include a leap day. So 2000 was a leap year, but 1900 was not. Even that isn't perfect, but it's good enough. We should be fine for several thousand years or so with this system in place.

All of this applies to the Gregorian calendar, which is the most widely used calendar in the world. If you rely on alternative calendars, like the Chinese lunar calendar, the rules for leap days/months/years are different.

Why all the worry about how long the year is?
Note that in all this, we've been using the tropical or solar year which relies on the position of the Sun and the vernal equinox. There exists another definition of the year, the sidereal year, which relies on the position of distant stars and is a bit longer by about 20 minutes. More on this later.
What the solar year along with those leap years accomplishes is that the vernal equinox occurs at or very near March 21st. This ensures that the seasons remain synced with our calendar- northern hemisphere Summer, for example, is during June through August.

What is the vernal equinox?
This actually has two answers, both related. The first definition of the equinox is the location in the sky where the plane of the solar system (the ecliptic), or equivalently the path of the Sun, intersects the equator of the Earth as projected into space. It is currently located in the constellation Pisces. There is, equivalently, another equinox, the autumnal equinox where the same situation occurs. This one is near Virgo. These locations are also known as the first point of Aries / Libra, however, the precession of the Earth's axis has meant that these are no longer located in Aries and Libra.

The equinox is the point in space where the ecliptic and the celestial equator intersect. Credit: Dennis Nilsson, Creative Commons

The other definition of the equinox is the day in which the Sun spends an equal amount of time above and below the horizon. Basically, day and night are equal. This occurs when the Sun is physically located at or near the point defined above. In our year, this is about March 21 and September 21 and signals the onset of Spring and Fall. By making sure the equinoxes land near these days we ensure that the seasons occur at about the same time each year.
Note that we also have solstices where the amount of daylight is the shortest or longest in a year. These occur around December 21 and June 21 and correspond to the winter and summer solstices, respectively. These likewise corresponds to particular points in space: the first point of Cancer / Capricorn. Due to precession though (as I'll describe below) these are no longer located in Cancer and Capricorn but now are in the constellations Gemini and Sagittarius.

Why not use the sidereal year?
Using the sidereal year makes some sense, to me at least, since we're comparing to more distant and therefore fixed stars. The length of time of the sidereal year and the tropical year differ, however. An important consequence of this is that over time the constellations will drift throughout the year. For example, Orion is a very prominent constellation seen in the (northern) Winter months, like January. Over a period of 13,000 years or so you will no longer see it in Winter. Instead, you will see it in Summer, around July or so. This is because our calendar is synced to the seasons, not to the stars.

Another interesting and related consequence is that the location (but not the DATE) of the equinoxes will change. The vernal equinox, for example, is known as the first point of Aries because when it was defined the equinox was in the constellation Aries. Now, thousands of years later, the equinox is in Pisces, one constellation west of Aries. Do you know your astrological sign? If you look up on the newspaper they'll tell you so-and-so date corresponds to so-and-so sign. The reasoning is that the Sun would be in that constellation on those dates. However, these were defined thousands of years ago and, as I've just mentioned, the constellations have drifted. Hence, the sign you think you are is probably incorrect. That's one reason why you shouldn't be trusting astrological predictions.

Why don't the sidereal year and solar year match?
If you look at the figure of the Earth above, you'll notice that the line perpendicular to the ecliptic (the plane of the orbit) doesn't match the rotation axis of the Earth. The Earth's axis is tilted by about 23.5 degrees. The gravitational influence of the Sun and the Moon apply a small torque which causes the axis to precess like a spinning top over a period of about 26,000 years. That means the Earth axis won't always be pointed at the same location in space at all times and thus we won't always have a North Star.

The precession of the Earth's axis (yellow) causes the North Celestial Pole to trace out a circle in the sky (blue line). The track the vernal equinox covers is denoted in red. 

Let's consider an example: in the summer solstice the Earth's northern axis is pointed at the Sun and, say, background star X. Throughout the year the precession results in a slight change of the Earth's axis. The result is that a solar year later the axis points again at the Sun, but because of that slight change we need an additional 20 minutes or so for the axis to point to the same background star X. This would mark the sidereal year, but at that time the axis would no longer be pointing exactly at the Sun.

To summarize: we need a leap day so that our calendar remains synced to the seasons given that the year is slightly over 365 days long. Because of the tilt of the Earth's axis, however, we have two separate ways of defining a year. By focusing on keeping the seasons in line, when we see the constellations will drift across the year over a period of several thousand years.

For a more math-related discussion, check out the Bad Astronomer's take on leap days

Update: Check out these two short videos to learn more about the leap year:
Minute Physics (with a shout-out to the UCLA Galactic Center group!) and CGPGrey

Chilean Anti-Sunset: 2/27/2012

Here is today's anti-sunset picture:

As I've mentioned before, my view faces East so I can't really see the setting Sun. What I see is the Sun illuminating the Andes and the clouds in the sky. One of these days I'll show you a sunrise, that should be far cooler. I'll probably wait until winter, though, so I don't have to wake up as early the mountains are snow covered. In the meantime, enjoy the anti-sunset.

Supernova 1987A

Very massive stars, those that are at least 8 times the mass of the Sun, explode as supernova when they die. Note that the Sun WILL NOT do this, nor will most of the stars of the Galaxy. Only the rare, massive stars go supernova. The mechanics of how supernova work is still an active area of research and has to deal with the physics going on in the core of the star.

The remnant of SN 1987A. Credit: ESA/Hubble, NASA (link)

One particularly famous supernova is SN 1987A, so named because it was the first (A) supernova (SN) observed in the year 1987. This is the brightest and closest supernova to go off in modern times. The event went off in the Large Magellanic Cloud, our nearby satellite galaxy which is visible from the Southern Hemisphere. The distance is approximately 51.4 kiloparsecs from Earth or 168,000 light-years (remember your distance units?). It was close enough, and in a well studied region, that we have identified the progenitor star before it went supernova- it was a blue supergiant star.

At that time, neutrino detectors had recently been constructed on Earth and this is the first, and thus far only, time in which neutrinos have been detected from an astronomical source other than the Sun. About 2 dozen neutrinos were detected from SN 1987A and, from what I understand, these have resulted in hundreds of papers concerning neutrino and supernova astronomy. This makes SN 1987A one of the most famously studied supernova of all times.

But what are neutrinos? Neutrinos are extremely tiny, electrically neutral particles that barely interact with anything- trillions of neutrinos pass through your body each second and yet none of them interact or affect your body in any way! These elusive particles are produced in nuclear processes such as radioactive decay and nuclear fusion. Well, fusion is exactly what's going on inside of stars that allows them to shine and hold them up against their own gravity. Neutrinos are also a natural by-product of supernova and its expected that the energy carried by neutrinos exceeds the energy the supernova emits as light (approximately all the light the Sun will produce over its entire lifetime!) by a factor of 100 or so.

Why all this talk about SN 1987A? The Astronomy Picture of the Day (APOD) has been putting up cool images on SN1987A for the past few days. The first is depicted at the beginning of this post. Here is the second:

Animation of the core of SN1987A from 1994 to 2009. Credit: Hubble Space Telescope, NASA, ESA; Video compilation: Mark McDonald (link)

This very cool animation depicts how the central source has dimmed and, more importantly, how material from that source has reached and impacted the ring of material around the source and caused it to glow. The origin of the ring, this small one (whose diameter is about 1.3 lightyears) and the larger figure-8 pattern on the other image, still remains a mystery. These rings existed BEFORE the supernova and have been lit-up by the light and particles that have reached them.

I'm no supernova astronomer, but even I think SN 1987A is cool and I'm glad these really neat images are out there for the public (and scientists) to enjoy.

Suvudu Cage Match 2012: Initial Thoughts

For the past few years, Suvudu has run a tournament pitting memorable characters from science fiction and fantasy against each other to find out who is the Cage Match Champion. This year is no different and they've just announced the lineup for the coming competitions. I encourage you to take a look. Voting begins March 5th!

One of the cool things about these cage matches, which is obviously their intent, is that you get introduced to characters you've never heard before and encouraged to read about them. I can honestly say that this resulted in The Name of the Wind and The Malazan Book of the Fallen moving up higher on my to-read list (last year Quick Ben of Malazan won and the prior year Kvothe ended up third). Characters from those two books/series are back again- Bast and Anomander Rake. Anomander is absolutely awesome in Malazan (at least up to book 3, where I'm currently at), so I (and many others) will definitely be cheering him on. This year, I must check out Peter V. Brett's The Warded Man (the cover for the sequel, The Desert Spear, initially drew me in). His character, Jardir, is facing off against Lady Jessica of Dune. Apparently, Jardir is also a desert warrior so the organizers were very excited for it. I'm also happy that I've read the first book of Brent Weeks' Night Angel Trilogy as I now know who Kylar Stern is (he's facing Gimli of The Lord of the Rings).
Some other characters to watch out for, in my opinion, include: Moiraine Damodred from The Wheel of Time, Kelsier from Mistborn, Tyrion Lannister from A Song of Ice and Fire (aka Game of Thrones), Richard Rahl of The Sword of Truth, and Mr. Wednesday from American Gods.

The cage matches are not just about voting on some online poll. Many authors sign up to write up what they think will happen so you get to see some very cool 'fan fiction' as characters from completely different series clash against each other (I still remember how Jaime Lannister threw Hermione Granger out a window). They've also asked fans to draw art for the characters. That should also be very cool.

So be sure to follow along on Suvudu's website for the news and vote for your favorite characters. May Anomander Rake the strongest one win!

Book Review: The Dreaming Void by Peter F. Hamilton

A friend of mine had recommended books by Peter F. Hamilton and encouraged me to read the Void trilogy claiming it was the more 'fantastical' of the lot. As I do prefer fantasy in general, I gave it a shot. My initial impression was very negative, but by the end I was enthralled by the story. Apparently, the book is part of a much arger universe, but I had no problem staring with it.

Overall Impression
One of the things I don't like about some science fiction novels is how they really want to convince you everything is futuristic. Instead of developing unique characters, an interesting plot, or subtly revealing the world, they smash technology right into your face. I have no problem with a high-technology setting, but I've seen many sci-fi books that seem far too focused on that and that alone. The Dreaming Void, unfortunately, starts that way. You have to really focus to peer behind the veil of technology and see the characters acting out their story. It doesn't help that the characters aren't initially very interesting at all. This is a bad start to the book, and I'm sad to say I was actually thinking about how much more fun it would be to read something else. However, I persevered and about 50 or so pages into the book, the characters and the story starts to pick up. By then, things are fine. There's still more high-technology coming at you, but you take it for what it is- magic. The book cycles between the normal world and what's going on in the Dream (ie, inside the Void). I actually preferred the Dream parts and would have gladly skipped most of the rest of the book just to get to those parts. While the Dream itself isn't terribly original, everything there, characters, setting, etc, are just so much better developed than in the normal world. That alone made me want to finish the book and look to the rest of the trilogy.

Characters
A multitude of characters is introduced very early in the book, but none of them really stand out. Even in epic fantasy tales with dozens of characters you still have an idea of who is important and can differentiate the characters. I did not get this at first. Once we reach Edeard I finally felt we had reached a real character and yet he's only part of the Dream. One of the first characters we see is, in my opinion, one of the weakest developed. He has all these super powerful skills, but no memories of his past and no desire to find out why. He just carries out his mission, which even he doesn't know what it is. I'll admit that's a clever idea, but I kept wondering: who is this man? what does he want? why does he want it? He does develop eventually, but in my opinion he is still incomplete by the end of the story. Similar things are true for the rest of the characters. After a while, though, the plot gets interesting enough that you ignore these character quirks and can appreciate the story.

Like I mentioned before, the Dream parts of the story are my favorite and I felt the characters there were far better developed than those in the actual story. One potential problem may have been that all the characters start out very separated. Hence, there is very little connection between them and less room to develop them with meaningful interactions. I've seen that on other books, but these tend to have all the characters converge near the end in a really satisfying fashion. This does not happen in this book. It looks like it might do so eventually, but perhaps that will happen in the subsequent books. It feels like most of the time the viewpoint character is alone in a spaceship struggling with his/her thoughts or in conversation with a single other character. In contrast, within the Dream the characters are all together in the same village and interact with one another.

Plot
This is one of the better apects of this book. There is an unaccessible region of space, the Void, in the center of our Galaxy, which has defied explanation. Mysteriously, one man has dreams which come from the Void and he shares them with the rest of humanity. A religion emerges from it and the story opens with their plans to undergo a Pilgrimage to the Void. Unfortunately, doing so could cause the Void to expand and devour the Galaxy so naturally alien species are opposed to that. There are also factions among humanity that oppose, favor, or just wish to take advantage of this movement. Thus, there are plenty of interesting plot lines going on. Some center on finding the Second Dreamer, a second person who has begun having Void dreams and could lead, or halt, the Pilgrimage.

Within the Void, the story follows Edeard's life. He is a supremely talented young man, orphaned when bandits killed his parents. The setting and pace are very different here from the rest of the book. We get to see much simpler activities in his daily life. There is some technology- the characters can use telekinesis and telepathy, there are genetically engineered animals, and they know they came to the planet from elsewhere. Despite this, these abilities are used more like magic and so the world seems almost medieval. The plot, while simple, is very engaging and the Dream ending was extremely satisfying.

Setting / World Building
The Dreaming Void takes places very far into the future. Humans can be either normal, like you an me; Advancer, with genetic modifications to make them better in various ways; or Higher, with lots of bionics that make them nearly god-like in their abilities. There are also humans who have downloaded themselves into a vast quantum-computer-space-collective intelligence (Advanced Neural Activity, ANA), which effectively makes them immortal, and there are other humans who have split their consciousness into multiple bodies. The variety among humanity is interesting, but it takes a while for the reader to appreciate this. There are also several alien species, though the main ones we hear about are the Ocisen Empire and the Raiel. The Raiel are interesting as they have been studying the Void for millenia and possess very advanced technology. There also mention of post-physical aliens and it's possible that Higher culture along with ANA is a step in humanity achieving some existence beyond the physical realm.

In the Dream, while there is advanced technology, it is more internal and appears more like magic. Hence, the society is more medieval with some isolated villages and some bigger cities like the famous Makkathran. Loudtalk, third-hands, farsight are all mental abilities that everyone uses there to some degree or other. Edeard belongs to the Eggshaper Guild which basically works using these mental abilities to genetically engineer monkeys, cats, eagles, and other animals so they can be readily used to do whatever task is necessary.

Final Thoughts
The book starts off a bit slow with characters that take a while to get to know and like. If you persevere, however, you are rewarded with a surprisingly rich universe and a good plot. The Dream part of the story is, in my opinion, the best part of the book. While I'm not immediately going to get the second book, if and when I do it will be firstly to continue the Dream arc story and secondly to see how the rest of the plot in the normal universe develops.

What's next for me? I'm not 100% sure. I have the third book of the Malazan Book of the Fallen: Memories of Ice, which I am very keen to read. I also have a set of short stories from Tor which could be a nice change of pace and I also bought Neverwhere by Neil Gaiman since it was just $2.99 on the Kindle a few days ago. I try not to let good offers like that pass by!

Distance Units in Astronomy

Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space. 

- Douglas Adams, The Hitchhiker's Guide to the Galaxy

I've had a few posts already concerning astronomy. Before I go on with more astronomy posts, I figure I'd have a sort of introductory post were I describe the different distance scales and units we use in astronomy. Not only should this be an informative post, it should also serve as a useful thing to link back to whenever I mention some of the terminology.

Here on Earth we use two main systems to measure distances. We have the English systems (inches, feet, miles) used in the United States, and the metric system (centimeters, meters, kilometers) used everywhere else. The English system is archaic, with odd conversions: 12 inches is one feet, but 5280 feet is one mile. The metric system is more modern and based on factors of ten, so you can always convert units quite easily, 1 meter = 100 centimeters = 1000 millimeters, etc. I grew up with the English system, but I like the simplicity of the metric and that's what we generally use in the sciences. However, things in astronomy tend to be very far apart and so we've ended up making some odd units.

The Astronomical Unit
When measuring scales in the solar system (or other planetary systems) it is best to use astronomical units (AU). The astronomical unit is defined as the average distance between the Earth and the Sun and corresponds to about 150 million kilometers (93 million miles). Now, we still use kilometers in some cases. For example, the distance between the Earth and the Moon is only about 384,000 kilometers or 0.00257 AU. Such 'small' distances are best kept in kilometers. Note that even though I say small, that's actually a considerable distance: the Earth's radius is about 6,731 km (more on this later).
Planetary distances in our solar system (and others) are best expressed in AU. For example, Mars is at about 1.5 AU and Jupiter is at about 5 AU. The outermost planet in our solar system, Neptune, is at about 30 AU. The gas and dust disk surrounding the nearby young star V4046 Sgr extends out to a radius of 370 AU, more than 10 times the distance between the Sun and Neptune.

The Lightyear
A lightyear is the distance that light travels in one year. Unfortunately, because it has 'year' in the name, most people think it is a unit of time. Light travels at a constant speed of 300,000 kilometers each second (186,000 miles a second). This is extremely fast and is the fastest speed that can be attained in our universe. You can calculate how much distance light would cover in one year and use that as a natural unit of distance. This corresponds to about 9,460,730,472,581 km (nearly 6 trillion miles). This is a huge distance, but stars are even farther than that: the nearest star, Proxima Centauri, is about 40,000,000,000,000 km (25 trillion miles), or more easily: 4.2 lightyears. The Galaxy itself spans 100,000 lightyears. The lightyear is then one of the more natural units to consider when talking about interstellar distances. However, there is another widely used unit to consider.

The Parsec
While the lightyear is easy to grasp among the general public, astronomers tend to prefer the parsec. It's definition involves the concept of parallax. When you look at something, you are using both eyes to perceive it and judge its distance. If you alternate closing one eye and opening the other, you will see the object appear to shift. How great the shift is depends on the distance between you and the object. We can apply this to astronomy as well. However, stars are so distant we have to use a wider baseline- our eyes are not separated widely enough. What we actually use in astronomy is the orbit of the Earth. In the simplest case, we take two images spaced half a year apart and compare them. Nearby stars will have shifted with respect to more distant background stars. Half of this angle is the parallax angle and is actually used to determine distances with simple geometry. One of my friends runs another astronomy blog tackling a single word in astronomy per week; you can check out his explanation of parallax here.

You can express angles in two ways: radians, as in 2pi radians in a circle, or degrees, as in 360 degrees in a circle. When you make the approximation that tan x or sin x is approximately x (for small values of x), you are assuming that x is expressed in radians. Parallax angles are small in astronomy, so this is perfectly valid, however we prefer to use arcseconds (1/3600 of a degree). How many arcseconds are there in 1 radian? Easy: 3600 times 360/2pi, or  206,265. So if we want a distance that corresponds to a parallax angle of 1 arcsecond as measured from the Earth, whose orbit is 1 AU, this distance must be 206,265 AU. This is the definition of the parsec, or pc: one parsec is 206,265 AU.

The parsec is widely used in stellar astronomy. The nearest star is about 1.3 parsecs, so this is a slightly more natural unit for stellar distances than the light year (1pc = 3.26 light-years). For one of my research projects, I set an outer limit of 100 pc and for another, 150 pc. However, the parsec is sometimes not enough to express distances so we turn to kiloparsecs (kpc) and megaparsecs (Mpc) for even larger distances. These are, as they sound, equivalent to 1,000 and 1,000,000 parsecs, respectively. The kiloparsec is useful for measuring large scales within our own galaxy; for example, the center of our galaxy is just 8 kpc away. Megaparsecs are more useful for distant galaxies; however, for very distant galaxies we tend to use another way to express distances- redshift.

Redshift
Okay, so redshift isn't truly a unit of distance, but I'll describe it here. Hot gas emits lights at very particular wavelengths, depending on what gas it is. When it's cold, it absorbs light at exactly those wavelengths, too. When we look at stars and galaxies we see emission or absorption features corresponding to the gases present. However, sometimes these features are not at the right wavelengths. The phenomenon behind this is Doppler shift: when something is moving towards (or away from) you, the sound or light will get shifted in frequency. This works on the Earth as well, for example when you hear sirens speed past you- the pitch of the siren changes. The same is true for light in astronomy. Stars and galaxies moving towards us have gas features, known as spectral lines, shifted to shorter, or bluer wavelengths. The opposite is true for objects moving away from us- the lines are shifted to the red, or redshifted.

Within our Galaxy, this can be used to track the velocity of stars, but in general it doesn't tell us anything about distance. However, the situation is different for far away galaxies. It turns out that all but the closest galaxies are moving away from us. And when you measure distances through other ways (perhaps I'll describe these on some future post), you realize that the farther the galaxy, the greater the redshift or in other words- the faster it is moving away from us. Using these sorts of measurements, astronomers have determined that the universe is expanding in all directions. The result of that is exactly what we expect: galaxies are moving away from each other and the farther away a galaxy is, the faster it is moving. This is Hubble's law, which can be used to estimate distances:

d = cz/H0

Here z is the redshift, c is the speed of light, and H0 is the Hubble constant, which has a value of about 72 km/s/Mpc. The units of H0 are weird, but if you look closely the km/s cancels out from the speed of light and, since redshift has no units, all that's left is Mpc (megaparsecs). Because the speed of light and the Hubble constant are just conversion factors, one can just use redshift to describe distances to other galaxies. Things are a bit trickier in actual practice because of cosmological effects, but this is enough to get a handle on what astronomers mean when they refer to the redshift of galaxies.

Other Distance Units
The AU, the lightyear, and the parsec are the most commonly used distance estimates in stellar astronomy and redshifts are almost mandatory when dealing with other galaxies. However, you can still create useful units by comparing objects that we know in a lot of detail. Here are a few that are commonly used in stellar and planetary astrophysics.

Solar & Jupiter Radii
When measuring other stars it is sometimes useful to have a good comparison. In general, we use the Sun for all such comparisons. The Sun's radius is 695,500 km (432,450 miles). Sometimes, solar radii are useful in describing binary systems. For example, the binary system V4046 Sgr is comprised of two sun-like star that are just 9 solar radii apart. That's really close! Note that 1 AU is about 215 solar radii. For extrasolar planets or very low mass stars we use the radius of Jupiter (69,173 km) as a comparison. Note that this is about 1/10th the radius of the Sun. By using these units we get an easy to understand comparison between objects we know about.

Earth Radii
Remember I mentioned the separation between the Earth and the Moon is on average 384,000 km? One way to express this is to make use of Earth radius (6,731 km) as a unit. This means the separation between Earth and the Moon is on average about 63 Earth radii. Planetary radii (usually either Earth or Jupiter) are useful when studying extrasolar planets, as they give us a readily comparable size estimate. For reference, 1 solar radii ~ 10 Jupiter radii ~ 100 Earth radii. That's a nice relationship to keep in mind.

FloridaTech... 6 years later

Nearly 6 years ago, I received my Bachelor of Science degree in Astronomy (technically, it was Space Sciences, option in Astronomy & Astrophysics) from Florida Institute of Technology. I bumped into one of my old professors, Dr. Terry Oswalt, the head of the department, at AAS this January and he encouraged me to stop by and give a talk. I agreed, after all, right now in February we are in summer recess at the Universidad de Chile and I intended to travel a bit.

So I made my way to campus and got there an hour before my talk. It was raining and cloudy and I was super tired- I had arrived just that morning in Orlando from a long flight. Fortunately, my brother was driving so I could sleep part of the way. I wanted to walk around campus, but decided to first go to the Physical Sciences building as it was still raining. Already I could see new buildings on the Southern side of campus; there's even a swimming pool now. It looks like things are looking up for FIT.

Upon entering the department, I was pleasantly surprised:

My talk was being advertised on TV monitors! I think this is a first for me. They also had the more traditional paper advertisements, but this was so cool.

I went in and chatted with the Department Head about FIT, the changes, and what's new with me. When I was an undergrad I took his introductory astronomy classes, but other than that we hadn't interacted much. Now I was drinking an expresso (alas, he could only offer me decaf) in his office and talking science. I felt like I was now practically an equal, a point that became more evident after I gave my talk.

My talk started at 4pm in one of the classrooms I had used. I remember once giving there a brief 10-minute presentation on some research I had done as part of a Research Experience for Undergrads program (at UCLA), so it wasn't the first time I had been up in that room talking to people. A bunch of my old professors showed up and shook hands with me. That included Matt Wood, who taught the advanced astrophysics classes and was glad to see one of his students come back with a PhD; Ming Zhang, who I worked with modeling the Earth's magnetosphere; and Marcus Hohlmann, which, although a physicist, was my advisor at FIT.

The talk, Identifying & Studying Nearby, Young, Low-Mass Stars, went very well. It was a bit longer than other times I've given it, clocking in at about 55 minutes, but that may be because I stopped to explain a few basic concepts since I know that many there would be physicist or undergrads and may not know any of the astronomy slang. I had a diagram for describing UVW space velocities (as well as some gestures that went along with it) and a very basic explanation for visibilities when talking about radio astronomy. There were a handful of good questions at the end, which I think I addressed properly, and a student came up later to talk about how the SARA telescopes could be used to do related science.

It felt nice to revisit my old campus. While heading out I bumped into Hamid Rassoul, the Dean of the College of Science. He was always a cool and enthusiastic professor. He couldn't make it to my talk, but we chatted for a bit. He said it would be nice if I came back to work here as faculty- they would like to have new professors and researchers that were educated at FIT. I think I've made a good impression on my old teachers. I felt like an equal among them. Before, when I was an undergrad, I was a bit intimidated by how smart these people were. Now I realize that I am one of them and can join them in discussing science and the future.

A last look at the Olin Physical Sciences Building (the one with the dome)

Book Review: The Kingdom of Gods by N.K. Jemisin

This is the third and final book in the Inheritance Trilogy by N.K. Jemisin. The first book, The Hundred Thousand Kingdoms, was very cool, particularly for the concept- this is a world with gods and men, but with a twist: men have chained the gods to do their bidding and have used them as weapons. What a way to turn upside-down a familiar genre trope!

Overall Impression
A great end to the Inheritance Trilogy. We get to see much more of Sieh, the Trickster, and learn a lot about the god's hierarchies and how the world works. Like the other books in the series, I actually care more about the story and politics going on the background than the personal stories that the characters are going through. I think that's just part of how I approach books though, and the story is interesting in either case. I was worried that the Glossary wouldn't show up well in the Kindle version, as I had heard good things on the author's blog, but I'm happy to say it looks fine. There's also a short story at the end that wraps up something from Book 2.

Plot
The plot was a bit unpredictable and the main character appears somewhat removed from it. This also happened on the other books: basically a lot of Big Things are going on and the main character is ill-equipped or ill-placed to handle all of them. He or she, though, is central to the story as is revealed at the end as everything comes together. Thus, it can be a bit hard reading through the book and wondering what's important. That makes it hard to care about things like the rebellion against the Arameri and the impending war, which I thought are key, but the point is that those things aren't central to the story. This is the story of Sieh and his relationship to Shahar and Deka. It's a personal tale told with an impressive story taking place in the background. I sugget you just take it easy and enjoy the ride. The author does a good job of foreshadowing so the ending is satisfying when you get to it. I could have done without the coda at very end, though.

Characters
The story is told through Sieh's point of view. This is the firstborn godling, the offspring of Nahadoth and Enefa, the son of chaos and death, god of childhood and mischief. I was a bit hesitant at first because I worry about the main point-of-view character being a god. I mean if a god knows everything, can do anything, etc, etc, how could you possibly tell a good story? Fortunately, N.K. Jemisin has created gods that adhere to a rational set of rules. In a sense, they are not that different from us mortals (except when they are) so it wasn't too hard to connect to the characters. While Sieh's story is, effectively, alien to us, there are still parts of it we can identify with.

The Arameri siblings Shahar and Dekarta are also important characters and play key roles both in Sieh's personal story and the underlying story arc. We don't get to see too much of the Three gods, but when we do it's satisfying. Those guys/girls are cool.

Setting / World Building
Sky, Shadow, Echo; the world and the relationship between gods and mortals makes the setting unique. As I mentioned before, one of the reasons I read the first book was its unique play on the familiar 'gods in fantasy' genre trope. Gods here can be chained and, as we see in Book 2 (The Broken Kingdoms), killed by mortals. This book reveals the variety of godlings (niwwah, elontid, mnasat) which is quite interesting.

The author also reveals some more about the creation mythology in her work. The Maelstrom, from which the Three main gods (Nahadoth, Enefa, and Itempas) sprung forth, is mentioned throughout the story. The relationship between the Three is very interesting, but sometimes shocking. You have to remember that although we call them 'gods', that doesn't mean they are male (or female). Hence you get offspring from the combination Naha+Enefa, Itempas+Enefa, and Naha+Itempas as well as any of the Three with their respective offspring. Seeing the Nightlord go from male to female is a bit disturbing, as is the male to male or female to female pairings between gods (and between mortals, too). Our society is becoming more open to that sort of thing and N.K. Jemisin is not the first fantasy author I've seen to include such elements in their work.

One thing I've found interesting (which is really more relevant to the first book) is the fact that in Book 1, the Arameri are ruthlessly ruling in the name of Bright Itempas and the Nightlord Nahadoth is chained. If you assume light=good, dark=bad (again, a common genre trope), you realize that you've basically won. Except that things are terrible. It reminds me of an old Final Fantasy game I played once. While in the game you are part of the Warriors of Light meant to banish the terrible darkness, but you learn that in the past there were also Warriors of Darkness to banish the terrible light. Too much of one thing, be it light or dark, is bad. The Inheritance Trilogy pivots on the importance of Balance.

Final Thoughts
This is a fitting conclusion to the Inheritance Trilogy. I'm not 100% sure of why it's called that, though. It makes sense for the first book, but less so for the subsequent ones. The same thing holds true for the little text blurb on the cover: "Gods and Mortals. Power and Love. Death and Revenge. She will Inherit/Unleash/Destroy Them All". It's really cool, but again makes more sense for Book 1.
While the focus was on the characters, the underlying plot is interesting and the setting is quite cool. If you've read book 1 and 2, you should go ahead and finish it. If you haven't read book 1 and 2, I recommend reading book 1 and if you like it keep going (the author provides free sample chapters if you want to have preview). This are the author's first published books and they are well written. I will probably be checking out her Dreamblood Duology when it comes out.

Next up is back to science fiction. A friend keeps recommending Peter F. Hamilton, so here we go with The Dreaming Void.

Science Education Standards in America

I recently read a very interesting, and alarming, Scientific American article on statewide science standards in the US. This picture says it all:

Credit: The State of State Science Standards 2012

The figure comes from a report from the Thomas B. Fordham Institute on the standards for K-12 education used in the various states. The overall conclusion is that the science standards for the majority of the States are mediocre to awful.
These standards are what's used to build curricula through the various states and grade levels. For example, I looked up the science standards for California and browsed through to the astronomy related ones. For sixth grade, here's what it has to say:

The solar system consists of planets and other bodies that orbit the Sun in predict­able paths. As a basis for understanding this concept:
  a. Students know the Sun, an average star, is the central and largest body in the solar
system and is composed primarily of hydrogen and helium.
  b. Students know the solar system includes the planet Earth, the Moon, the Sun,
eight other planets and their satellites, and smaller objects, such as asteroids and
comets.
  c. Students know the path of a planet around the Sun is due to the gravitational
attraction between the Sun and the planet.

So, a sixth grade teacher would be using these guides to make lessons that teach these concepts. I think those are pretty key concepts that everyone, even non-astronomers, should know. What the study presented is that some states have very clear and well-thought out guidelines. California is one such state and is graded 'A'. The report for Colorado follows and it's ranked at 'D'. Here's what I found for the science standards for Colorado (I'm looking at the eight grade Earth Science standards):

1. Weather is a result of complex interactions of Earth's atmosphere, land
and water, that are driven by energy from the sun, and can be
predicted and described through complex models
2. Earth has a variety of climates defined by average temperature,
precipitation, humidity, air pressure, and wind that have changed over
time in a particular location
3. The solar system is comprised of various objects that orbit the Sun
and are classified based on their characteristics
4. The relative positions and motions of Earth, Moon, and Sun can be
used to explain observable effects such as seasons, eclipses, and Moon
phases

Compare, in particular, point 3 from Colorado to point b from California. Both are talking about the same thing, but one is much more vague. This vagueness in what exactly constitutes a valid lesson in the various states is one of the points the report raises. Unclear guidelines are basically meaningless and useless when defining a curriculum or trying to assess a student's understanding. You may argue that they give the instructors greater flexibility in what they teach, but really- there are some basic facts that students should learn and this should be made explicitly clear.

Another thing mentioned in the article and the report is the undermining of evolution. You've probably heard about this on various news sources. This is part of a growing trend in the US to make laws that prevent the teaching of evolution or enforce teaching intelligent design, creationism, or other alternatives. One troubling example is recent changes in New Hampshire: teachers are required to provide alternatives to any lesson if a parent dislikes it. This means that a high school student could in principle graduate having avoided learning about evolution, the Holocaust, contraception, or even gravity, all because his or her parents thought those were touchy subjects.

While there is a religious undercurrent to this, I think it's more of a misunderstanding of science and a fear of the change it can drive. I went to a private, religious high school in Puerto Rico and I learned about evolution my science classes, as it should be. I don't doubt that there are many schools out there that have no problem with teaching evolution, regardless of whether or not they are religious schools. The problem, I think, is that most people, and the politicians in charge, have no idea what evolution is and think that scientists are somehow out to get them and shatter their beliefs. Not teaching, or undermining, evolution just reinforces this idea and makes things worse.

All this talk against science makes me think Americans want to believe, not to know or understand. Science and mathematics give us tools we can use to understand the world around us and figure out things on our own. While you may not think this negligence regarding science education is a big issue, in the long run, it will be. If this continues on the same trend, less and less emphasis will be given to providing a meaningful science and mathematical education to the following generations. Student's will still graduate, but what they will require for that degree will be ever less. All of the advances of technology we enjoy, like cars, iPods, the Internet, satellite television, all come about thanks to our understanding of science. When I see such attacks against eduction (or these poor science standards), I have to wonder: why don't the people in power want us to continue to advance in technology and in our understanding of the universe? Are they afraid of what we might learn, or what we might do if we can think for ourselves?

GJ 667Cc: A Potential Life-Supporting Planet

Exoplanet surveys have been discovering planet after planet. With over 700 confirmed planets and thousands of candidates, it's sometimes difficult to get excited over another one. But then, when you least expect it, some team announces a brand new planet that either challenges the norm or is just outright cool.

The latest announcement making the headlines is for GJ 667Cc. The claim is that this is the 4th extrasolar planet found in another star's habitable zone.

The GJ 667 System

First, a breakdown of the name. GJ stands for the Gliese & Jahreiß Catalog of Nearby Stars. This is the 667th star in that catalog. The uppercase C refers to the fact that this star is in a triple system: there's GJ 667A, GJ 667B, and GJ667C. And finally, the lowercase c refers to the second planet discovered in the system (the first would be GJ 667Cb, there is no 'a' planet).

GJ 667, located about 22 light-years away, is a triple system formed by a pair of closely separated K stars and a more distant M-type companion. K and M are spectral types and indicate the effective temperature at the surface of these stars, this in turn is modulated by a star's mass and age. The M star (GJ 667C) is the least massive of them all and is at least 230 astronomical units (AU, the distance between the Earth and the Sun) away from the closer pair. I had recently mentioned how binaries and multiples can hinder planet formation (see here), this is yet another example of the case where the separation between the stars is large enough that planets can still form.

One other interesting observation is that the system is 'metal poor'. What this means is that, compared to the Sun, the system has far less heavy elements (oxygen, carbon, iron, etc). These are the building blocks of planets and you expect to see more planets when you have more of these elements.

The Habitable Zone

A key concept in extrasolar planet research is that of the habitable zone. The idea is that if we are to search for life, we should search for the conditions that permitted life to develop on Earth. The most important thing for life on Earth is liquid water. Hence, all we have to do is look for systems that can host liquid water. This is why so much emphasis is given to the exploration of Mars and Europa. Both of these worlds in our own solar system may have liquid water beneath their surfaces.

For extrasolar planets, however, the situation is trickier. We don't know the characteristics of the planet, and the atmosphere is of utmost importance in determining the surface temperature. For example, Venus could be argued to be in the habitable zone, but with a surface temperature of 460 °C (860 °F), it clearly cannot have liquid water on its surface. One easy approximation, though, is to assume that the planet has an atmosphere comparable to that of the Earth's. If the Earth were moved closer to the Sun, the surface temperature would be higher and, eventually, all water would evaporate. In the opposite case, if we move Earth farther from the Sun, the temperature drops until all the water freezes. The region where the water can be liquid on the surface defines the habitable zone. The edges are rather fuzzy, since atmospheric physics plays an role in controlling the temperature.

We can apply the same criteria to other star systems. In this case, though, we have to take into considering the type of star. Hot stars will emit more light and have more distant (and broader) habitable zones. Cool stars, like GJ 667C, will have habitable zones that are closer and narrower than the Sun's. The estimated habitable zone for GJ 667C extends from 0.11 to 0.23 AU. For comparison, Mercury's orbit around the Sun is about 0.3 AU.

Habitable zone comparison for stars of different luminosities.

GJ 667Cc

An international team led by Guillem Anglada-Escude of the Carnegie Institution of Washington just recently put out a Letter on the Astrophysical Journal regarding their results (you can check out the paper here). I remember seeing the paper this morning, but didn't read the author list. Now I realize one of my colleagues here at Universidad de Chile is among the authors. There's also a pair of authors from the Pontificia Universidad Catolica de Chile, so it's no surprise that it's all over the news in Chile (for example here and here).

The study involved using a new set of software to re-analyze some radial velocities. Most planets discovered to date have used the fact that a planet will cause the star to shift back and forth relative to us. This will induce a small variation in the radial velocity of the star that we can detect. The bigger the planet and the closer to the star, the greater the variation and the easier we can detect it. 

With this technique, the team finds planets orbiting with periods of 7.2 and 28.15 days. There's also a suggestion of a third planet (at 75 days) and a linear trend that could suggest a giant planet in a much larger orbit. 

GJ 667Cc is the 28-day planet. For this system, that corresponds to a distance from the star of about 0.123 AU. As mentioned above, this is within 0.11 to 0.23 AU, the habitable zone for this star. The planet is considered a 'super-Earth'. This is because the estimated mass is about 4.5 Earth masses. This is much larger than the Earth's and presumably the atmosphere will be a lot thicker. This can pose some problems, but we don't actually know any details of the atmosphere. Even if the planet itself is problematic, you can't rule out moons in orbit around it. These would also be in the habitable zone (though they could be too small to have an atmosphere and liquid water).

Orbital configuration of the GJ 667C planet system in comparison to our Sun's. The habitable zone, and it's possible extent, is illustrated. Note the different distance scales for both systems. Credit: Guillem Anglada-Escude et al. (2012)

Can the planet truly have life? Unfortunately, we are in no place to answer that question. We still need to pin down the parameters of the system and we would still have no idea on the atmospheric properties of the planet. In addition, I had previously mentioned that low mass stars are notorious in producing large flares of high-energy radiation that can be detrimental to life (see here). The activity level of the star is not mentioned in the paper, but, if I recall correctly, planet searches tend to focus on the more quiescent stars. Even if it's quiet now, it may have been more active in the past when it was younger (the system is at least 2 billion years old).

Other Habitable Worlds

The other candidate habitable worlds being listed in these press releases are GJ 581d, HD 85512 b, and Kepler 22b. GJ 581 has a controversial planet (g) that lies neatly in the habitable zone, but different researchers argue whether the planet actually even exists. The d planet, however, is not disputed and lies just inside the outer edges of the habitable zone. All of these planets are super-Earths. That is, they are several times the mass of the Earth. This is not surprising as the more massive a planet is the easier it is to detect. I'm sure that as our methods improve we will find smaller, more Earth-like, planets.

Book Review: Anathem by Neal Stephenson

I read this book after a recommendation from an astronomer colleague of mine. However, I already had it in my list of books to check out. I am glad I did, my only regret is not reading this sooner.

Overall Impression
This was an excellent book. It's a bit heavy (figuratively, as I was reading on the Kindle) and takes a while to develop. There is a lot of science-y discussion, including topics from quantum mechanics, consciousness, chemistry, and some philosophy as well, most notably Plato's allegory of the cave (ie, the theory of forms). While one doesn't need to understand these things, they are part of the story and can slow down the uninitiated reader. That aside, though, the book was a great read. The plot and characters aren't too outstanding, but the setting for the story is fascinating. Stephenson creates a world that seems similar to ours, but also very much different. The terminology and history drive that point home. That alone makes it one of my favorite books thus far this year (which isn't saying a lot since we just started the year).

Plot
The plot takes a while to take off. You need to get about 200 pages into the book to start seeing important events take place. Of course, the first 200 pages are supremely important in developing the setting, the characters, and foreshadowing some of the events, so don't even think about skipping through! In a sense, it's a bit like epic fantasy in that it suffers from the 'flaw' of requiring quit a bit of time to fully comprehend the world. Like good epic fantasy, though, the book manages to make it interesting and does have some action and interesting dialog all throughout. It may seem a bit slow at first, but enjoy it for what it's worth and you'll be rewarded.

Once the plot gets going, it becomes a bit of a detective story with the characters trying to figure out why certain things happened. This leads to even more mysteries, which drives along the plot. At first the characters are all in their math but slowly they get summoned extramuros to face the challenges the world is facing and that drive the mystery of the plot. The reader is constantly playing catch up to try to understand why things are happening, particularly when philosophy is being discussed. It makes the book a bit hard to put down, though!

Characters
The story is told from the point of view of the main character- Fraa Erasmas. The fraa indicates he is a male avout in Arbre's terminology (see below). While he is very smart, as is practically everyone of important in the book, he isn't the brightest. In fact, he seems pretty ordinary and down to Earth (or should I say, down to Arbre?), which helps the reader identify with him. We also have other cool characters, though, like Cord, Yul, the ita Samman, and other avout like Lio, Jad, etc. Seeing how many of the characters are scientists, a couple of themes resonate such as science vs religion and science education in our society.

One of the coolest things, in my opinion, about the characters, is that many of them are astronomers (or in their terms, cosmographers). Every so often they'll discuss some astronomical term, like eccentricity or the analemma. There's even a part where they mention how they correct for the distortion caused by the atmosphere- basically a simple description of adaptive optics, which we use in astronomy today:

I got ready to explain how the newmatter mirrors worked, using guidestar lasers to probe the atmosphere for density fluctuations, then changing their shape to cancel out the resulting distortions, gathering the light and bouncing it into a photomnemnonic tablet.

Setting / World Building
This is were Anathem really shines. This is set in a separate world, Arbre, which is both more advanced and less so than ours. Many terms are introduced and used throughout the book, such as fraa, suur, fid, avout, anathem, etc. In fact, those terms can be a hinderance at the beginning as you struggle to understand the world. Be advised that there is a very useful glossary at the end (in addition to the definitions throughout the text). I checked the glossary when I was about 50 pages into the book. You don't really need to go through it (and I didn't check all the entries), but it helps to confirm what you think the terminology is, as well as to remind yourself of any words.

In addition to the terminology, the world also has a rich history spanning five thousand years. At first, this isn't too important, but eventually you start hearing about the Sacks, and the Rebirth, and the Reconstruction, and other historical events. At that point, say 100 or so pages into the book, I would advise checking or rereading the Note by the Author. A very useful timeline is provided there that helps you keep track of when historical events happened.

But don't let these two things hold you back: the world is absolutely fascinating. There are a series of places throughout the world were academics gather to study and discuss their ideas. These sound a lot like universities (or more accurately: monasteries), and they serve a similar purpose. However, these places (or maths) are closed off from the rest of society (the Sæcular world) through a series of gates. The Unarians hace access to the Year gate, which opens once a year for 10 days. The Decenarians, like fraa Erasmas, have access to the Decade gate, which opens only every 10 years, and again only for 10 days. Hence, the Decenarians are far more isolated than Unarians in terms of their research and cultural development. But it doesn't end there- there are gates that open once every 100 years and ones that open only once in every 1000 years. In the history of the mathic world, these millenarian gates have only been opened 3 times (well, technically the Sacks mess things up). It is great to hear how this society works and sustains itself and, just like the characters, you start thinking and wondering what goes on in the Centenarian and Millenarian maths in their long periods of isolation. That itself is a main driver of the story.

Final Thoughts
I thoroughly enjoyed this book and can recommend it to fans of good world building, philosophy, and science. While some of the science and philosophy discussions can be a bit over one's head, they are still very interesting particularly as they pertain to the story line. The characters and plot are also quite good, though not the best I've seen. In general, I would read this story for the setting. While it can get heavy at times with all the Dialog and calcas, it is still a worthwhile read. The book touches on several things, such as the importance of science in the advancement of society; the separation, or not, of science and religion; and even briefly on racism and both technological and social progress.

I started writing this review about halfway through the book, when I was most excited. The ending, while good, wasn't supremely satisfying, though it fits the story quite well. I still agree with all I wrote earlier, when I was more passionate about the book.

Now is switching back to some fantasy with N.K. Jemisin's The Kingdom of Gods.