December 2014 Stitch Fix

This past week, I received my monthly Stitch Fix box!

For those of you who don't know, Stitch Fix is a service that sends you 5 items of clothing and/or accessories picked out by a stylist. I started this service because (1) I can't style myself; (2) I hate shopping; and (3) I'm clueless about dressing professionally.

Stitch Fix costs about $20 a month, although that's applied to the cost of the clothing item(s) you choose to keep. You get a 25% total discount if you keep the whole box. For more information, see Stitch Fix's general information.

Ever since I switched to law, I realized that I was hopeless when it came to dressing professionally. I came from a science background: my parents were scientists, my friends were scientists, and my role models were scientists. In science, dressing professionally meant you wore jeans with no holes in them.

Law was a whole new ball game.

Thus, my obsession with Stitch Fix was born.

So, without further ado, let's see what they sent me this month!

1. Jago Short Sleeve Studded Sweater Dress

 

This navy blue sweater dress is very comfortable. It has small studs throughout that add a little sparkle, which I think will be perfect for holiday parties. The top also has some nice subtle cutout detailing. Also, although this dress is a sweater dress, it's not especially warm or thick, which means I could probably wear it in any season. Overall, because of the comfort, I love this dress.

Verdict: KEPT.

2. Elaine 3/4 Pleat Waist Dress

This burgundy dress is really flattering for my body type. I love the cinched in waist, and the color is gorgeous for this time of year. And... it has pockets! This dress is also great for both work (throw on a blazer!) and after-work hours. The only bummer with this dress is that the zipper was broken. :( I'm actually holding the dress together in the picture, ha ha! Luckily, my mother knows how to fix zippers.

Verdict: KEPT.

3. McQue Solid Lace Sleeve Blouse

Casual, with jeans.

Business Casual

Close up of lace sleeves

I pinned this top, and boy do I love it! It's navy blue (a color I love), fits wonderfully, and has lace sleeves! Lace sleeves! I wore this last night on a date with Phil.

Verdict: KEPT.

4. Bethany Lace Bib Half-Button Blouse

Casual

Business Casual

Lace detailing on back

Not going to lie, when I first pulled this out of the box, I thought "grandma shirt." But the special thing about Stitch Fix is that you have to try everything on before passing judgment. I ended up really liking this shirt. I think it's better suited for work attire than casual, although I'll have to figure out how to disguise my bra straps better before I'm comfortable wearing it in a formal environment. I love the color (so versatile and crisp!) and how it's just slightly see through. I think luxury when I wear this shirt.

I'm pretty sure I'll be wearing the blouse with the navy pencil skirt (and matching blazer, of course!) for my oral argument on Monday.

Verdict: KEPT.

5. Ivy Feather Print Blouse

 

And last but not least, this shirt was also one that I didn't think favorably of when I pulled it out. The feather print made me think that this shirt was "so San Francisco," in that it reminded me of hippies in the 70's. However, when I put it on, I liked it as well. It's a comfortable and flowy shirt, although a bit oversized, and deep down I'm a sucker for anything with birds. (I used to have a big birdfeeder at my old apartment in Tucson, and I kind of miss it). 

Also, I'm attracted to this shirt because it reminds me of San Francisco. I'll be working at a firm in San Francisco this summer, so it'll be nice to have something fun to wear while I'm there!

Verdict: KEPT.

So, yup... I kept the WHOLE BOX! My stylist knocked it out of the park on this one. I got a bunch of pieces that I love and are great for both work and weekend wear. What more could a girl ask for? Thanks Stitch Fix!

What do you think? Are there pieces you disagree with me on? Also, if you're interested in Stitch Fix, here's my referral link to give it a try!

Referral

Money, Superstition, and Vaccines

It was a place of death.

It was a place where women went to die for their sins.

It started with a fever in the maternity wards. That fever was accompanied by severe headaches, nausea, and bilious vomiting. The back, hips, and pelvic area were wracked with pain. Defecation was immediate and uncontrolled. Urination painful. Women's bellies swelled to enormous sizes.

After the fever ran for a few days, the disease acquired a more putrid form. Death was quick and painful. At the time, it was the single most common form of maternal mortality.

It is now very rare to die from this infection. Prevention was rather simple. The single most important factor for preventing this disease? Doctors in the maternity ward needed to wash their hands before examining patients.

But in the 1800's, they refused to wash them. European doctors and clergy were convinced that childbed fever was God's punishment to women for the act of childbirth. They didn't want to think of themselves as "dirty", even when some medical professionals like Dr. Ignaz Semmelweis desperately pointed out that using antiseptic soap reduced the number of deaths by a whopping 90%.

This fever, consequently, has been forever dubbed "The Doctor's Plague". Their adamant refusal of a truth they did not want to accept caused countless, needless deaths.

And now, in modern times, this scenario can happen again. Unfortunately, the sufferers will be our children.

The cause of Puerperal fever, aka childbed fever or "The Doctor's Plague".

There is a movement underfoot - a movement to reject modern science. You know them as the anti-vacciners. This movement is considered crazy and on the fringes of rational thought. It is not supported by science. And the people heading this movement? They rely on emotional appeal and deliberate misrepresentation of data. They do not possess medical degrees. They do not have studies of their own. Why go to all this trouble?

Because, I suspect, they want to sell you something.

They want to sell you unregulated drugs. They want to sell you books that sell because they're scandalous. They want to sell you the idea that waving a quartz crystal over your head will cure your cancer better than chemotherapy would. They want to take advantage of you when the doctors give you a realistic evaluation of your health, and you lie in bed at night trembling in fear. In doing so, they can make a very comfortable living. Furthermore, to protect their profits, they need to make the public distrust the very people who can expose them as the frauds they are.

There comes a point when we all need to champion scientific reason and advancement, no matter if we are scientists or not. There comes a point when we need to expose those who make fraudulent claims and make baseless assertions about subjects they know nothing about. We need to correct our friends and family. We need to have this conversation with as many people as possible.

We need to have this conversation now.

We are in a Golden Age, and life in the present has been the best it ever has been. Science can do truly wonderful things. It saves countless lives every day. Imagine how many lives it can save tomorrow. Imagine, if superstition wins, how many lives will be needlessly, painfully lost. Perhaps we'll return to the kind of thinking where death is rationalized because people deserve God's punishment.

In the moment we shut our eyes to science, we no longer deserve to reap its rewards.

And that, my friends, is not a place you want to be.

Experimenting With Almond Flour

Almond flour... photo shamelessly stolen from http://www.elanaspantry.com/why-almond-flour.

Hello people...

So... it's been a while since my last post. Yup, I got really behind. And busy. As much as I like blogging, school always comes first.

And boy, have there been changes. Since my last post, I passed my prelims, defended my Master's Thesis, and applied to law school.

Because of this, the focus of my blog has now changed from being about astronomy to something more casual. I can post whatever the heck I want now, and that's more than ok with me. I've decided to hijack this blog to post cat photos, food photos, and other things I'm generally too embarrassed to post on facebook.
I mean, as much as I like my cats, I'm not overly fond as being known as a crazy cat lady.

So... the first thing I want to talk about is almond flour. I bought some from Trader Joe's a while back on a whim. I baked some things with it, but now that I'm slated to move soon, I wanted to use it up. I shopped around on Pinterest and found some easy recipes that I already had the ingredients for.

Now, a bit of warning. I am a newbie at cooking.

And I'm not very good at it.

As a high school student, I wanted nothing to do with such a "feminine" activity (you know, something about breaking out of gender roles). Now that I realize that health comes from learning how to cook, I've since reassessed my previous attitude towards cooking. However, that means I have a lot of lost time to make up for, ha ha!

So the first thing I made was almond flour crackers. Here's what they looked like:

My very own crackers! Yay!

 They were so easy to make! The recipe I followed is here, but I decided to use herbs I had on hand (thyme, basil, and garlic). They go great with almost anything because they have a delicate taste (if not a little nutty, but I love that!). You can put any sort of cheese or meat on them. I've put raw tomato paste on them with a drizzle of pepper.

Don't ask why I like pure tomato paste. I just do.

Next, I made some almond bread. However... I had a much larger pan than the recipe called for, so my bread came out weird looking (and not at ALL like how the pic in the recipe looks, ha ha!). No matter, it still tastes delicious!

 My weirdo bread. I just eat it like a muffin... and just like a bran muffin, these things clean out your colon.

The bread is so think and filling, I think of it more like a bran muffin than anything else. It's nutty, slightly sweet, and buttery (although no butter was used in making it). I did make some blackberry butter to use as a spread, which was absolutely delicious! Although, how can you go wrong with butter, honey, and blackberries?

So yup! Those two recipes depleted my store of almond flour. Both taste delicious and were very easy and quick to make. I think I spent more time on clean up than on actual cooking, which is great for a lazy cook like me!

Finally, I just wanted to say that these recipes are great for people cutting out gluten. I personally don't care about going gluten-free (I've never had any medical problems from eating wheat), but these recipes tasted good on their own merits. So... people with gluten sensitivities... feel free to try these! Maybe yours will turn out better looking than mine, ha ha!

Reason for Disapearance...

Hello all,

I was terribly bad at updating my blog posts... not a post since Christmas. But I assure you, I was busy. I was busy doing this... And also studying for that test thing.... called the prelim or something like that. :)

Hardly working... I mean, hard at work. Yeah.

Merging Black Holes Pt. 3: Simulating Relativity

This is the third installment of the merging black holes posts (if you're just coming in, I suggest you read the intro post). This part will focus on some of the numerical techniques used to simulate black hole mergers. So, if you've ever been interested in how people actually simulate relativity, and what are the current limitations/problems we face, then read on! If not, well, this may be particularly boring for you, ha ha! Just skip the text and look at the pretty pictures (psst... it's what I do most of the time). Just know that when it comes to black holes, especially coalescing binary black holes, numerical relativity is complicated... much like a 12 year old girl's love life.

Bad joke. Anyway, moving on...

Black hole dynamics can be described reasonably well for most of its orbit. For example, analytic post-Newtonian expansions can simulate the early inspiral phase, and black hole perturbation methods can treat the late ringdown phase. However, sophisticated computational techniques are required for the late inspiral and merger phases, where, unfortunately (or fortunately?) gravitational waves are at their highest amplitudes.

There are three major hurtles in simulating these highly relativistic systems, which are:

1. Scale: The gravitational field is incredibly large around the black holes, but gravitational waves themselves are only small perturbations in the gravitational field. Simulations that cover the entire dynamic range from itty bitty waves to huge spacetime warping are extremely hard to write. In addition, simulations cannot deal with singularities themselves, which, unfortunately, is what black holes are. So it makes it challenging to find a numerical technique that can ignore those regions while still simulating their effects.

2. Non-linearity: Einstein’s equations are non-linear. This means that an element of chaos is introduced into the system. In a chaotic system, vastly different outcomes will occur from similar initial conditions - this is simply what results from non-linear equations of motion. Therefore, if the initial conditions are not exactly right, the black hole merger may display vastly different characteristics than it would in reality.

3. Wonky spacetime: current computational models need to decompose Einstein’s equations of General Relativity into equations computers can handle. Einstein’s equations very elegantly combine space and time into one quantity: spacetime. Unfortunately, computers decide to poop out on us. Why? To simulate a system that starts at a specific initial time, computational solutions demand that space and time have to be separated - to be decoupled. There is a way, however, to work around this. Einstein’s equations can be re-written using the 3+1 decomposition technique. In this technique, the equations are split up into two sets. One set describes the gravitational field at all points within a specific time, and the other set then evolves the gravitational field in time. In this way, once the initial conditions have been set, the code can evolve the merger.

Briefly, there are a couple of different numerical techniques that I know of that work around all these problems: finite difference mesh, spectral or pseudo-spectral, and adaptive mesh refinement. Finite difference involves equally spaced grids along the system. The partial differential equations are solved in the middle of each grid, and then extrapolated across the boundary. The picture below is an example of this kind of technique.

The grid spacing in this rendition is constant, which is the hallmark of a finite difference simulation.

The spectral and pseudo-spectral techniques expand the differential equations in a Fourier series, and the terms that pop out are used as the basis states of the simulation. This simplifies spatial and time derivatives, but also requires the extra step of actually Fourier transforming the field variables.

The last technique (adaptive mesh refinement), uses grids that change size in order to make the simulation more computationally efficient. The simulation essentially determines the number of grid points needed at a specific point in the domain such that the simulation can guarantee accuracy and efficiency. It can also change grid shape or orientation as needed. This can be particularly useful for General Relativity, which is the description of how space becomes warped in the presence of matter (in a gravitational field). This technique is the most commonly used one, although to simulate the full range of the merger, still higher level techniques must be developed.

Yes, the Simpsons got it right! Notice how the grid spacing changes size near the singularity. This is why it's called adaptive mesh refinement.

It should be noted that adding all spacial dimensions or throwing away symmetry arguments developed instabilities after only short integration times!

Next time, I'll talk about what happens when these simulations are implemented. There was a surprise when black holes merged, recoil, which is strictly a consequence of Relativity (and thus reinforces my conviction that Relativity is just plain weird). Stay tuned for more weird black hole fun... I promise to write about it in a timely fashion this time.

Merry Christmas!

Many years ago on this day, an amazing child was born. This child forever changed the way we understood the world, and his ideas opened up an unprecedented era of enlightenment and discovery.

Happy birthday, Isaac Newton! 

* Thank you, Sam Collopy, for pointing this out. *

 

 

Merging Black Holes Pt. 2: Ripples in Spacetime

The above Youtube video shows a merging event generating gravitational waves. Now, this video shows two merging white dwarfs, but two merging black holes will do the same thing - only on a much larger scale. It seems crazy to think that this sort of event happens in the universe, but is currently invisible to us. However, in the coming years, that should change.

Gravitational waves are a hot topic in modern astrophysics. They are analogous to most waves, such as water waves or electromagnetic waves (light), except that they are ripples on the background curvature of spacetime itself.

So, what's the big deal with gravitational waves, aside from the fact that they're a cool physics buzzword?

Well, the most exciting prospect of gravitational waves is their potential in the study of different astrophysical phenomena. For most of astronomy, electromagnetic radiation has been the sole source of probing the universe (or, photons for short... it's amazing what we can learn from light rays). Electromagnetic radiation comes from the superposition of (mostly) randomly oriented photons being emitted or absorbed from electrons, atoms, or molecules. Gravitational waves, on the other hand, are generated most strongly from large bulk motions of mass. And, even more incredibly, gravitational waves are not dampened by intervening matter. As a result, the detection of gravitational waves should open an entirely new area of astrophysics previously unseen.  Perhaps, like the advent of infrared and radio astronomy, gravitational wave astronomy will usher in a new era of unprecedented scientific discovery and advancement.

Interferometers like the Laser Interferometer Space Antenna (LISA) and the Laser Interferometer Gravitational-Wave Observatory (LIGO) are currently the most promising ways to detect gravitational waves. Simply put, like most interferometers, a laser is shot at a beamsplitter, which splits the laser beam into two directions (usually perpendicular to each other). These beams hit mirrors, and are then reflected back to a detector, where they are recombined. *Note: I have simplified the process quite dramatically - I have never been very good with instrumentation, so I'm not going to try to go into any specifics.*

(Is it bad that I can't ever say laser without thinking of Dr. Evil's "laser")?

Very simple interferometer design, except for gravitational wave detectors, the movable mirror would not be moved by anything other than gravitational waves. The screen has a great example of what fringe patterns look like.

Since gravitational waves are ripples in the fabric of spacetime itself, a gravitational wave passing through a point in space causes the gravitational field to increase or decrease in magnitude. As a result, if a gravitational wave hits one of the mirrors, the oscillation in gravitational strength should shift the mirror back and forth. This causes the path length for one of the mirrors to deviate from the original value, so that when the beams are later recombined at the detector, the observed fringe patterns should change in accordance with the mirror oscillations. These fringe patterns can then be used to deduce the strength of the passing gravitational wave.

Gravitational wave schematic. The top portion shows the three phases of coalescence: the quasi-circular inspiral phase, the plunge and merger, and the ringdown. The bottom portion shows the amplitude of the emitted gravitational waves that correspond to the above merger process. (Image credit: Baumgarte and Shapiro 2011).

Black hole mergers, incidentally, are especially interesting in the study of gravitational waves. This is because gravitational waves are theorized to carry away most of the angular momentum and energy from these systems, which causes the merging black holes to coalesce. The above figure (that I scanned, sorry for the poor quality, ha ha!) shows a schematic of the phases of a black hole merger, and how those phases relate to gravitational wave strength. The top portion shows a cartoon of the merger, including the early quasi-circular inspiral phase, the plunge and merger phase, and the final ringdown stage. The bottom part shows the wave amplitude (or, strength) versus time. For two black holes approaching each other in the early inspiral phase, the emission of gravitational radiation causes the orbits to circularize and decay. Gravitational waves at this point will be at relatively low levels. But during the late inspiral phase, when the binary is in tight, circular orbits, and during the actual merger, gravitational waves should be at their strongest. This is where LIGO and LISA will be able to detect gravitational waves.

Unfortunately, even though the very early and late stages of coalescence has been simulated fairly easily, the actual late inspiral and merging phases are not as simple. For that part of the merger, post-Newtonian and perturbation methods break down. Therefore, providing templates for the signatures of merging black holes requires advancements in numerical relativity, which will push computational techniques to their limits. 

For more info, please see:
Abramovici, A. et. al 1992, Science, Vol. 256, pp. 325-333
Baumgarte, T. W. & Shapiro, S. L. 2011, Physics Today, Vol. 64 No. 10, pp. 32-3
Berti, E., Cardoso, V. & Will, C. M. 2006, Phys. Rev., 73, 6