The Death of a Small Star

A few weeks ago we talked about the birth of a star, how tiny pieces of matter start clumping together in very cold and dark regions of space, becoming a protostar, and blowing its shell out with the massive amount of energy from fusion.

A star is born in the darkness. It lives anywhere between millions of hundreds of billions of years, then the star dies just as fantastically. We’re new to this party, we’ve only been around for a tiny piece of history, because we are the sons and daughters of a star that died a long time ago.

Like in birth, the way a star dies has everything to do with how massive it is. We start with stars with a low mass.

Structure of an Asymptotic Giant Branch (AGB) star

Low Mass Stars (less than about 4 solar masses)

As a star burns, all the hydrogen in the core is being converted into helium. As the hydrogen is depleted, in a complicated sequence of events, helium will start to fuse together in shells and will start giving the star enough energy to expand. The star eventually becomes a red giant  - stars with very large sizes with relatively cool surface temperatures. The star’s core could be the size of the Earth, and its envelope be as big as the Earth’s orbit!

The Dredge-Up

Energy in a star is conducted in two ways: convection and radiation. Convection is what happens in a stove when you heat up water, the water at the bottom gets warm, loses density, and will “float”, and will be replaced with cooler water which will eventually heat up and rise. Water on top of the pot will cool off, get heavy, and sink to heat up again. This causes a “convective loop”.

Radiation is what makes you warm when a fireplace is running, the infrared radiation will excite the molecules on your skin and warm you up. It’s how the sun makes you hot in a hot sunny 4th of July beach day. Good thing you’re sitting on the water, because it’s really freaking hot. Great, now I want to go paddleboarding, but my body will never forgive me.

When a star starts fusing helium in the core, three elements are created: carbon, nitrogen, and oxygen. These elements then rise to the surface of the star through convection. A star’s life may have up to three dredge-ups, the third is very rich in carbon, and when a star undergoes this it’s often called a carbon star.

Mass Loss and Stellar Wind

So the star is now huge, and luminious, and gravity at the surface is very weak – the core is very low in density and spread out over a very large area. Any kind of disturbance would send star-stuff out into empty space. Remember that the outer layer has carbon, nitrogen, and oxygen? These stars actually blow soot into space.

It is this carbon soot that is the building block for our carbon-based life forms, and it’s this nitrogen and oxygen that you’re breathing right now.

Taste that air, feel your skin. You are experiencing what once was the core of a dying star, blown into space during a star’s death.

Planetary Nebulae

We’re going to use the previous picture to guide us for this one.

The helium burning shell is burning, pushing the hydrogen shell away, and creating carbon and oxygen that fall into the middle of the star. As the helium in that shell burns out, the hydrogen burning shell can crush into itself, and creating more helium, which falls into the temporarily dormant helium shell. After a certain point in temperature, a helium-shell flash will occur, which blows star stuff out of the star, increasing the luminosity of the star, and then starting the cycle again. These flashes happen every 100,000 to 300,000 years, and they give rise to the planetary nebulae. We discussed these some time ago, they are very beautiful objects that only live for a few ten or hundred thousand years or so.

The Ring Nebula M57, located 2,300 light years from Earth, is an example of a planetary nebula.

The Eskimo Nebula (or the Clownface Nebula) - notice the small, hot nucleus of the star in the middle. Super hot and about the size of our Earth, it is densely packed with carbon and oxygen in the center, and helium, and hydrogen in its outer shell.

As these stars blow their shells in a stacatto, their hot, bright centers are discovered further and further. These, in turn, become what are known as white dwarfs – hot, bright stars that used to be the heart of a very large red star. They are not very large, sometimes they’re similar to the size of the Earth. The odd thing about them is that the heavier they are, the smaller they are. This is backwards from what we’re used to, it’s due to something called electron degeneracy. To put it simply, in a white dwarf the size is supported by degenerate electrons. The more massive the star, the bigger its density, which creates an increase in pressure, and it overcomes the repulsive force of these electrons, so it shrinks.

It takes a loooong time for a white dwarf to twinkle out, they are very hot, but they are very dim.

This is the end of a star that’s less than four solar masses. It changes fuel sources, starts blowing its shell, increases in luminosity, and the core will start pulsating to release what’s left of it: a carbon-oxygen rich core that will cease to burn fuel and will become dimmer and dimmer over billions of years until it becomes a black dwarfs,  stars that have stopped emitting significant heat or light, objects of theory since the universe is not old enough to have produced any.

Soon: a large star dies very differently – you may have heard of it – a supernova. The most cataclysmic explosion since the Big Bang.

Categories: Astrophysics | 2 Comments

The Standup Paddleboard Project

What did I get myself into? I was supposed to save money, but after a string of expenses I ended up paying the same as a cheaper paddleboard, and about $200 more of what I could have gotten at Costco. This board is mine now, and when I come up with a design from the front, it’ll be mine forever.

Here is a brief journey from day zero to day, what, 50??

Categories: Astrophysics | Leave a comment

The Doppler Effect

Today we’ll talk briefly about a popular phenomena that few people understand: the Doppler Effect.

Sound and light are waves. The pitch of the sound and the color of light are a result of the frequency of these waves, that is to say, how many times the wave “peaks” in one second. This is otherwise known as “Hertz” – the musical note “A” is 440Hz, therefore it peaks 440 times in one second.

Visible light corresponds to electromagnetic waves between 400 and 790 THz, that’s Terahertz, or trillions of times per second. But there’s another way to look at it, the higher the frequency, the shorter the distance between the wave peaks. That’s what is referred to as wavelength.

The wavelength for visible light is 390nm to 750nm (that’s nanometers, or a billionth of a meter). The small wavelength corresponds to the highest frequency, because the shorter the distance between peaks, the more times it “peaks per second”.

Visible light colors by wavelength, in billionths of a meter.

Distilling the above diagram to break down the waves into what they individually (sort of) look like,

Lower frequency waves (red) have longer wavelengths. High frequency waves (magenta/purple) have shorter wavelengths.

So there’s an inverse relationship between frequency and wavelength, and it is expressed by a very simple equation:

f = \frac{c}{\lambda}.

Where f = frequency, c = speed of light (300 million meters per second), and the funny squiggly line (lambda) is wavelength. For example, if lambda was 1 meter, frequency would be large (300000000/1, which equals 300000000 Hertz, the frequency VHF TV signals). If we increase the wavelength, to say, 100 million meters, then the frequency would be very small (300000000/100000000, which equals 3 Hertz, the frequency of ELF waves). So when one goes up, the other goes down. This is why algebra is important, people, a lot of the theory is accessible to you with only a basic understanding in mathematics.

We are assuming, however, that the source of these waves is static. But everything is moving. What happens if something is approaching you, or if something’s getting further away? What happens is the Doppler Effect.

If you're in front of the red particle, waves seem to be of a higher frequency and shorter wavelength. If you're behind it, it looks like the waves are of a lower frequency and higher wavelength.

This is readily apparent when a police siren zooms by you, as it approaches, the sound has a higher pitch, but when it passes you, the pitch seems to drop to a “lower note”. The wavefront has passed you and now the waves are “stretched out”.

Well, it just so happens, light behaves the exact same way!! Since red is a lower frequency than blue, when objects race away from us they turn just a tinier bit red (because the frequency is lower on the back end), and objects coming close to us turn a tiny bit more blue!

You may be asking yourself: “to know that something is a tiny bit more red,  you’d have to know its original color. This stuff is remarkably far away from us. who do you think you are, you loon??”

I actually have an answer for you. Every element gives off a signature color band. Just like gold is always yellow, Hydrogen and other common space elements have a signature “light spectrum”, and if this signature shifts all the way to the red a little bit, we know how fast this Hydrogen (or whatever it is) molecule is getting away from us. Here’s a great graphic I found on a certain open-source collaboration wiki that’s very popular in the internet and teachers absolutely hate:


Redshift of spectral lines (the little black bands) in the optical spectrum of a bunch of galaxies (right) as opposed to our own sun, which we know ain't going nowhere (left). Notice how the galaxies on the right have spectral bands that have moved up towards the red.

ALAS we come to the point of the blog post: everything in the observable universe IS SHIFTED TOWARDS RED. Only ONE THINGS could explain this: THE UNIVERSE IS EXPANDING EVERYWHERE.

I’m  going to blow your mind one  more time: the bigger the “redshift”, the faster the object is getting away from us. It just so happens that the further away something is, the bigger the redshift, which means that farther objects are going faster than closer ones. THE UNIVERSE SEEMS TO BE EXPANDING EVERYWHERE AND ACCELERATING TOWARDS THE EDGES. This is described by Hubble’s Law using Hubble’s Constant. We can look at an object, know how fast it’s going, and therefore know how far away it is.

We have just taken a look at the sun, then we look at a distant star, and just from their colors we can discern whether it’s getting away from us or coming towards us. When we look pretty much anywhere, the same thing is happening. We even realized that the universe is ballooning at an exponential rate, and we can use this to infer distances in the range of millions of freaking light years.

Humans may be tiny and meaningless specks of dust living on a slightly bigger speck of dust in the middle of a bright speck of dust amongst a cluster of beautifully colored specks of dust. Yet we have managed to unlock some of the biggest mysteries just by looking at old light from minutes after the Big Bang occurred. Avoiding an anthropocentric ego-trip, there’s something special about us, but it’s not necessarily in the way we handle our business and treat ourselves, but in how sometimes we achieve what seemed to be once impossible.


Categories: Astrophysics | Tags: , , , , , , , , , , , | 2 Comments

What is Anti-Matter?

Anti-Matter! Stuff from legend, science fiction, both good and terrible books in the strange section at Barnes and Noble, is it real? What’s it like? Why is it so hard to find? And why is it so uncommon?

These questions, and more, summarily answered by science’s hive mind. I’m only but one small remora sucking from the side of the massive whale of knowledge.

What’s it Made Of?

Anti-matter, strictly speaking, is made of anti-particles. There’s an anti-version of every existing particle out there, leading to atoms of anti-particles. Hydrogen has anti-Hydrogen, Lithium has anti-Lithium, and so on.

Anti-matter (and anti-particles, but from now on I’ll just refer to them as the former) behave in exactly the same way as their opposite particles. If a baseball was made of anti-leather, anti-hide, and anti-rubber (or whatever baseballs are made out of), it would fly just the same as a regular baseball, it would look the same, it would weigh the same. It would be near impossible to detect what kind of particle it’s made of. In fact, we could even say we’re made of anti-matter, and that regular matter is very hard to detect.

How Do We Even Know it Exists?

We’ve observed it, and very recently (at the CERN particle accelerator in Switzerland) we were able to create many anti-Hydrogen atoms and held them in place for about 17 minutes ( This is a lot longer than previously achieved in other experiments, and now we can do some really good science on these observations.

The anti-particles eventually escape their lock-down and annihilate with particles around them, giving us otherwise-unexplainable flashes of light. So here we are: we have Hydrogen locked in a chamber, and it looks like regular Hydrogen, and behaves the same way, weighs the same, but then it disappears in a flash of light. It ain’t magic.

So How Do We Know it’s Anti-Matter?

Matter and anti-matter annihilate when they come in contact. Annihilation is the conversion of these particles into gamma (high energy light) and other particle-antiparticle pairs. To know that a anti-matter makes up a baseball, we’d have to throw it into something made of matter and see if it blows up in a fantastic flash of light. Chances are your hand is made of matter too, so even holding it would bring some unfortunate (but awesome) consequences.

How Do We Know the Earth is Made out of Regular Matter?

If there was anti-matter in the Earth, it’d be annihilating with the surrounding regular stuff, and we’d be able to detect it. But so far nothing has really been observed, with one exception: it was just recently discovered that anti-matter thunderstorms create anti-matter above them (

So If it’s So Similar, Then Equal Amounts Were Created in the Big Bang!

Not quite so, it seems. Anti-matter is a lot less prevalent in the observable Universe as matter is. Why? No one knows for sure (actually, do we *really* ever know *anything* for sure?)

Baryogenesis is the process by which there’s a population difference between the two kinds of particles. Baryons are the names of the elementary particles that created everything we know after the Big Bang, so the question is, why were there more Baryons than anti-Baryons? Hint: the most popular Baryons are protons and neutrons.

You HAVE to Have Some Practicality to This.

And there is – anti-matter is used in the medical field for PET imaging, and recently it’s been found effective in the treatment of some cancers (

No, it’s not currently feasible to make anti-matter weapons, Dick Cheney. Nice try.

The Universe continues to marvel us, the deeper we look, the more we realize that we have no idea about where we come from and where we could end up, and the things that we could achieve. When you hold something in your hand, you’re not holding just a coffee mug full of hot liquid, but a microcosm of particles that were created and survived many billions of years ago. It’s a bit much to think about, at times overwhelming, but it’s important to have the presence of mind to realize that we’re just a thread in a massive weave of existence.

Categories: Astrophysics, particle physics | Tags: , , , , , , , , , , , | Leave a comment

Resonance and Harmonics

Acoustic resonance is the increased tendency for an object to vibrate at a particular frequency that it’s configured for. For example, a guitar string tuned to E will vibrate on its own when it “hears” another E – you don’t have to strike the first string in order for it to move.

Harmonics are multiples of a base, or fundamental, frequency. The “A” note is known to be 440Hz. Another note that plays with A that is a multiple of 440Hz is a harmonic – 220Hz, 110Hz, 880Hz.

In music, resonance and harmonics are used to create complicated orchestras and symphonies that defeat our understanding of nature. We can always describe a musical note as a wave, but no book in science truly understands the effect that music has on us.

My point is – we don’t have to be in similar frequencies to understand each other, nor do we have to wait for someone else to take action – we play our string so others’ start moving on its own.

Categories: music | Tags: , , | 5 Comments

The Large Hadron Collider

The new LHC particle accelerator in Geneva is operating at 480 bunches per beam. A bunch is about a hundred billion protons, each one carrying the energy of about a mosquito in flight. When put together, 480 of these bunches have the energy of a 20,000 ton aircraft carrier going at 3 knots. When the LHC is at full capacity, because it’s actually designed to run at 2808 bunches per beam, the beam will have the energy of the same carrier going at 13 knots. Imagine a carrier going at 13 knots and hitting just about any object. I can’t imagine any man-made object that could resist such an impact.

To imagine how many protons are in a bunch, if these protons were each the size of a marble, a bunch would be as long as the distance between Earth and Uranus, and about as wide as the distance between the Earth and the Moon. They are so far apart that the distance between the marbles would be from Miami, FL to Charleston, SC. These bunches are made to collide against each other to cause proton-proton interactions, but they’re so far apart that we only get a few events per beam.

Particle physics is a statistical game, so we have to get a bunch of events and samples in order to get results. The LHC has already exceeded its expectations, and it’s not even at a fifth of its capacity.

For more pictures of the LHC during construction, see the following:

Categories: particle physics | Tags: , , , , , | 2 Comments

The Moon’s Locked On

Ever notice that we always see the same side of the moon? If all planets rotate, and all moons rotate, and even the sun rotates, why is it that our moon doesn’t seem to?

In fact, it does, but it’s our fault we only see one side. The moon is in Tidal Lock with the Earth.

Ride the Tide

We all know the tide to be something very specific: the water in the ocean goes up and down throughout the day. It is caused by the gravitational tug of the Sun and the Moon, when the Sun is directly overhead, there is a tendency for water to rise a few feet in some locations. If both Sun and Moon are overhead, then we get the Spring Tide when levels are particularly high.

What’s that Got to do With the Moon?

Interestingly enough, the Moon suffers the same ailment, and to the Moon, we’re its Sun.

Many many (MANY) years ago, when the moon was originally created, it was rotating just like any other satellite. Over time, however, the surface of the moon was deformed ever so slightly, made oblong, with the pointy end facing the Earth:

As the moon rotates, it keeps this bulgy shape, but now the pointy end isn’t pointing towards Earth anymore. Earth’s gravity will try to reshape the moon so the pointy end points towards the Earth, but since the Moon is made out of rock, that’s not so easy.

The result is that the Earth produces a force that tugs on that bulge, into something called Bulge Dragging. (editor’s note: searching for “bulge dragging” images on Google can be a disturbing experience, I ended up settling for a Wikipedia image.)

The Moon spins, but it has a bulge the Earth can tug on

In the top green Moon, the Earth’s gravitation re-shapes its surface. In the bottom one, the Moon has rotated to its red configuration, but Earth still tugs on the bulge (creating torque), and tries to keep the bulge facing towards itself. Since the tug is stronger than the Earth’s ability to re-shape the Moon, the Moon slows down more and more until one day it stops giving us a different face. If the moon were made out of water, it would be so easy to re-shape the bulge that the Earth would never have a sideways bulge to tug on!

So in a nutshell, our intense gravitational field made the Moon into a bulgy shape, giving us a bulge to tug on. Since the Moon is hard, it’s not easy for that bulge to flow across its surface, we exerted torque on the Moon until we eventually left it permanently oblong in the same direction, and we shall never see the other side of the Moon from Earth.


The moon is not perfectly still to our eyes, however, because all of this we just described is true to the center of the Earth, and we’re really just on its surface. Also, the Moon has an eccentric orbit, and our spin direction and the Moon’s are different. This effect has us see slightly more of the Moon’s surface over the course of time, but over a long period of time, we can see almost 60% of the Moon (so that’s an extra 10%). Here’s a simulated image showing Lunar Libration:

So, What’s the Other Side Look Like?

The other side is interesting: it’s seen too many space collisions. This makes sense, since the part that faces us is a lot less likely to be hit by asteroids or comets.

It’s nothing like what we’re used to. It was only recently photographed. We call it the Far Side of the Moon. (Note to Pink Floyd fans: there’s no “dark side” of the moon, all sides are equally lit as the Moon travels around its orbit.)

Categories: Astrophysics | Tags: , , , , | 1 Comment

A Map of the Night Sky

Have you ever wanted to be able to look at the sky and know right away what it is you’re looking at? If you’ve spent 5 minutes with me outdoors at nighttime you may have seen me point out over two dozen bright stars in the sky. You’d be surprised to know how easy this is to accomplish. I don’t memorize a map of the stars, instead, I’ve learned what the relative positions of stars are. During the winter, I use Orion, and in the summer, I use something else. That is what we’re here for today.

If you wait ’til nighttime, you can look into the sky and see one of the most recognizable constellations in the sky: Ursa Major, otherwise known as the Big Dipper.

The Big Dipper is special, everyone knows what it is, and it is a roadmap for the rest of the sky. If you know a few points on the map, you can point out several other constellations as you become more familiar with the spring-summer night sky.

A simplified roadmap to the late spring/early summer sky

The Big Dipper has a long handle, a top and a bottom to the pot, and two sides: one towards the handle and one away. Let’s learn some of these rules and then use the two images below to help you find these stars, that way you don’t have to go outside and get used to night vision or stand in the bitter cold. Use the drawing on top to get a quick familiarization, then find Ursa Major in the next three drawings for an accurate depiction of the night sky. Now let’s try some quick and simple exercises. (hint: the first star in the Big Dipper is named Alkhaid. This will assist you in finding it. If the black screenshots are too small, there’s one with a green border at the bottom that should assist you).

  • If you follow the arc handle starting from the pot and going away, you end up in Arcturus. It is commonly known as “Follow the arc to Arcturus”. It is the major star in the Bootes constellation.
  • If you keep going along that Arc, you’ll come against another bright star: Spica, the brightest star in the Virgo constellation.
  • Follow the star connecting the handle to the pot, and go down from there to the bottom star in the handle-side of the pot, and you eventually make it to Regulus, the brightest star in the Leo constellation.
  • With the handle-to-pot star, and going to the opposite star in the pot, you go straight to Pollux: one of the two (and the brighter of) the Gemini Twins. The other is Castor.
  • A very important one: follow the two pot stars, opposite the handle, going “up” the pot: this goes straight to Polaris, the famous North Star. It’s not super bright, but it’s bright enough, and it’s also the first star in the Little Dipper. I like to remember this as “The Pot Always Spills North” (I made that up, which is why it’s kind of a lame mnemonic)
  • If the first star in the Big Dipper handle is a certain distance away from the Gemini Twins, at the exact “opposite” side of the Twins is Betelgeuse: Orion’s Shoulder. This is a red supergiant that is ready to supernova in the “near” future – you and I may have been dead for hundreds of thousands of years before this happens, but when it does, it’ll outshine the moon for a few days.

See what other patterns you can discern, and make your own rules. Go out one night and see if you can spot just one of these. If you do this occasionally, before long, you’ll know all of the brightest stars in the sky.

A screenshot of the Stellarium software, free for download from! My apologies if it's all too small, it was a challenge to fit all of this in here :)

Same Stellarium screenshot, this time with constellation lines

Again the same screenshot, but this time it's got art.

A slightly more technical shot of the night sky around these times



Categories: Astronomy | Tags: , , | 2 Comments

Nebulae – Clouds Alight in a Deep Ocean of Darkness

We took a brief look at nebulae, but some of you fed back to me that we didn’t take far enough of a look. A nebula, as explained a few days ago, is a big mass of gas and dust that either reflects or fluoresces light. They are a showcase for the stars that inhabit and surround them, much like a beautiful personality makes a stunning woman even more brilliant.

In this post, we shall look at some of the most beautiful nebulae ever witnessed, both from the ground and from our in-orbit superstar, the Hubble Space Telescope.

There’s many other amazing things to witness through the telescope eyepiece, like the Magellanic cloud and the star cluster, but those shall have to wait.

The Eagle Nebula

The Eagle Nebula is part of a diffuse emission nebula, if you recall from a few days ago, emission nebula shine because a nearby star ionizes the gas and excites its electrons, and when they de-excite they give off light via fluorescence. The most famous portion of this nebula is called “The Pillars of Creation” because gas-forming dust is part of the tips of these pillars, and if you also recall, these are small chunks of dark nebula where the protostars form.

The Pillars of Creation

The Triangulum Emission Garren Nebula

Another emission nebula where the gas is ionized by a cluster of stars in its midst. This nebula is a region inside the Traingulum Galaxy, and it exists 2.7 million light years away. That is, by any measure, extremely far away. It is so bright that if it were equally far away from us as the Orion Nebula it would outshine Venus, the brightest object in the sky after the sun and moon. What a sight to behold:

The Triangulum Emission Garren Nebula NGC 604

The Crab Nebula

The Crab Nebula is a supernova remnant that has a strong pulsar in the center – a rapidly spinning neutron star that acts very much like an x-ray lighthouse (specifically, this one spins about 30 times per second, about as much as an old phono record, and measures about 30km across, about as much as a a small city). After a star is destroyed in a cataclysmic explosion, the new elements that are manufactured from the explosion are blown away further in pulsar winds and are ionized by this high energy flux.

The Crab Nebula

The spinning star in the center requires some special attention, because it is so freaking cool. How can something so large and so dense spin so fast? Imagine a mass of several suns, in the area of a small city, spinning 30 times per second. Its magnetic pole is putting out the x-ray and gamma radiation, which is the source of its lighthouse beam. Remember Emily Noether and her conservation of angular momentum? Surely you’ve sat in a chair, with arms and legs stretched out, and started spinning slowly. As soon as you contract your extremities your spin becomes much faster. This is conservation of angular momentum – this star went from being very large to very small, and has essentially sped itself up by shrinking millions upon millions of times in size. Here is a picture of this monstrous beauty:

The Crab Neutron Pulsar

You can see the direction it sweeps in, the gas ionized in a disc by the super intense x-ray and radio radiation being emitted from the pulsar. It’s a good thing we can look at it from this far away: the radiation created from this pulsar would wipe all life from our planet in the  blink of an eye.

This is the sort of thing that’s left over after all the atoms in our body were created.

The Flame Nebula

Another emission nebula, this time in everyone’s favorite constellation Orion. It is lit by the easternmost star in the belt, that is to say, if you’re looking at the belt and Betelgeuse (the red supergiant) is on top, and Rigel (the superhot blue) is on the bottom, it’s the leftmost of the belt.

The dark strands in the middle are dark nebula, that tenuous place where the building blocks of life are put together for the first time.

The Flame Nebula NGC 2024

Planetary Nebula

The Cat’s Eye Nebula, pictured first, is actually a planetary nebula: a star lost its envelope via a process called mass loss. The star runs out of hydrogen to burn, so it stars fusing other materials, then it switches back, and these thermal pulses shoot out in intervals. The star essentially ejects its outer shells and atmosphere into some of the most complex celestial constructs ever witnessed by our species.

In the second picture, the concentric circles from this thermal shock are processed to make them more obvious. It’s important to remember that not all of these pictures are what you would see if you peered at the nebula, sometimes exposures are hours long to gather as much light as possible, and sometimes invisible colors are recolored to show structure.

Discovered in the 18th century, these cosmic butterflies were named for their resemblance to gas-giant planets. Planetary nebulae are actually the remains of stars that once looked a lot like our sun. When sun-like stars die, they puff out their outer gaseous layers. These layers are heated by the hot core of the dead star, called a white dwarf, and shine with infrared and visible-light colors. Our own sun will blossom into a planetary nebula when it dies in about five billion years.

The Cat's Eye Nebula NGC 6543

The Cat's Eye Nebula, processed to show its concentric rings from thermal shock, or so we think, sort of.

The Ring Nebula M57, located 2,300 light years from Earth, is another example of a planetary nebula.


This infrared image from NASA's Spitzer Space Telescope shows the Helix planetary nebula, located about 700 light-years away in the constellation Aquarius. Spitzer's infrared view of the Helix nebula, the eye looks more like that of a green monster's. Infrared light from the outer gaseous layers is represented in blues and greens. The white dwarf is visible as a tiny white dot in the center of the picture. The red color in the middle of the eye denotes the final layers of gas blown out when the star died. The brighter red circle in the very center is the glow of a dusty disk circling the white dwarf (the disk itself is too small to be resolved).

Protoplanetary Nebula

Protoplanetary nebula are the period during the asymptotic giant branch event when the initial mass loss starts the planetary nebula formation. What I’m saying is, a protoplanetary nebula is the precursos to the planetary nebula we just saw.

The Boomerang Nebula and the Egg Nebula are excellent and beautiful examples of this: stars are currently ejecting themselves as they form into things of the sort of the Cat’s Eye Nebula. These objects are dazzling and many times defy logic.

Boomerang Protoplanetary Nebula

The Egg Protoplanetary Nebula

See? Even stars suffer from flatulence.

False Color Imagery

Earlier I mentioned that most astrophotography has to be enhanced in order to bring out the detail, structure, and mystery from many of these celestial bodies to light (pun intended). Here’s an example of an emission nebula, the Pelican Nebula (also known as the North America Nebula due to its shape). This is a very active nebula in both formation and star generation, so in a few million years it’ll look like something completely different.

Depending on what portion of the light spectrum you look at, you see different features of the Pelican Nebula. Only the "visible" shows "true" color.Of particular notice is how visible light can't see many features infrared can - especially protostars.

And That’s Just a Tiny Fraction Of It

There are so many trillions upon trillions of galaxies, and each of them holding million of nebula, all unique, a true sight to behold. The telescope in my balcony can only see a few of these, for example, the Crab Nebula looks like a little swath of white light. I’d have to tether my camera to the eyepiece for an entire hour, while my telescope tracks the sky with specially built drive motors, in order to get an exposure that would bring out the detail in its structure.

Now that we have some of these supertelescopes in orbit we are able to witness the universe in a new light, free from atmospheric turbulence and interference from light pollution and our own sun and moon. The next generation of orbital telescopes are on their way to space right now, and we shall peer even deeper into the incredibly rich 15 billion year history that precedes us.

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Classifying Stars – Luminosity, Brightness, Temperature, and Color

Stars come in many different colors and sizes!

A few days ago, we talked briefly about how stars are made. But no two stars are identical: they can vary in size, internal pressure, temperature, composition, age, mass, mass loss, density, spectra, brightness, and luminosity. Today we’ll talk about some of their visual characteristics. Tomorrow, we’ll talk about their types, and how these two are related.

Luminosity and Brightness

Luminosity is the amount of energy a star gives off each second. It is measured in watts (just like the light bulb). Brightness is the apparent energy that reaches us, and it depends on distance. The farther away a star, the less bright it looks. It is measured in watts per meter squared.

brightness = luminosity / 4*pi*distance2

If we measure the brightness of a star via equipment on Earth, and we can figure out the distance using methods such as parallax (which we also talked about a few days ago), we can figure out the luminosity of a star! This is the first step towards identifying what kind of star we’re looking at.

luminosity = brightness*4*pi*distance2


The color of a star is determined by its surface temperature. Kinda like the flame you see on occasion, we know that the red flame is the lamest, followed by the yellow flame, so on until the blue flame which is the hottest. Same with stars, except many times hotter. Different than a flame, however, is that colder stars can emit in the infrared (and therefore invisible to the human eye), and really hot stars emit mostly in the ultraviolet (which is equally invisible). 70% of the stars in our galaxy are in the infrared, which is why we have infrared telescopes, and they must doctor their images to false color so you and I can marvel at their artificially natural beauty.

A star actually emits at many wavelengths, for example, our sun emits across the visible spectrum but we all know that it also emits UV (which is why we wear lotion in the beach) and the infrared. The hotter the star, the more it emits in general, with a peak at a certain wavelength. Observe the following charts,the colored bars represent visible spectra.

Stars emit their peak energy at different wavelengths depending on their surface temperature (shown in the Kelvin scale). The hotter the star is, the bigger the area under the curve (therefore putting out more energy in its photons) and the peak energy shifts to the left towards the ultraviolet. Lower energy stars emit less energy, and peak towards the right.

Our sun is a bit like the chart in the middle, it puts out light at all frequencies in the visible range at about the same rate, with a slight peak in yellow, which is why it’s kind of yellow.

Some stars are SO HOT at the surface that they put out nothing more than x-ray radiation. They are so dense that all they’re made out of are neutrons, with the mass of several suns compressed into the area of a small city. If you held a chunk of this in your hand (assuming you could) and you let it drop, it would crash through the ground, shattering rock and iron until it cut its way into the center of the Earth, overshoot it, come back, overshoot again, until being assimilated into our iron core. How will I ever explain this to the insurance agency?

Wien’s law states that the peak wavelength is inversely proportional to temperature, and it gives us a number in nanometers.

wavelengthpeak = 2900000nm/Temperature

There You Have It

So this is why stars look different colors: they are different temperatures. Using some back-of-the-envelope math, we can figure out the surface temperature and emission spectra of stars. It’s very reliable too – so when things don’t match up, we can ask followup questions to the nature of these fusion behemoths. Tomorrow we’ll put more of this together and dive deeper into the mystery of our stellar ancestors.


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On Induction

I recently read a book that introduced me to the concept of induction.

The theory and philosophy of knowledge, known to smarty pants as epistemology, is a rich and complex field of study where bearded men in ivory towers lined with mahogany think for years upon years without really going outside, therefore kind of losing touch with reality and being aware, really, only about themselves. This is why philosophers often ask about whether a table really exists, because they spend all day with their elbows and foreheads on them. After learning about this I decided to grow a beard, manscaping was a bit difficult but I purchased a new grooming kit that helped me.

This, of course, brings us to another question, which is “are we really aware of anything other than the data our senses feed us, and since we seem to be feeling something, about ourselves?”. Perhaps these crazy old men are onto something, to best understand the world we must force ourselves into seclusion. I’m not that type of person, rather wanting to be outside, or drinking $15 margaritas, so I may not be cut out to be a professional philosopher.

Since this blog has a very strong scientific undercurrent, because I don’t really know anything else, I wanted to bring this induction deal to your attention. The question is not very difficult to ask, it happens to be immeasurably difficult to answer.

Theory? Proof? Law?

Science is a simple hand that can grab the most complicated of objects. Like any other hand, it has nerve endings, and it feeds us with information so we can better figure out the shape of this object. It is a tool for us to deal with the world, and a tool to help us manipulate it.

We make some observations, and we form a hypothesis. We create an experiment to prove this hypothesis, we gather data, analyze it, and decide whether we were right or wrong. From that point we re-formulate our hypothesis and move forward until we whittle down that ugly tree stump into a finely carved statue. Science is about truth, about elegance, and most importantly, about making more science.

The problem is, can we ever know that the law we currently believe in is the ultimate law? Every time you slam your hand against a table, there’s a rapping sound that’s unmistakeable. If the table is made out of wood, the sound will always be similar, it won’t sound like you hit a pane of metal or a stack of newspapers. We therefore gain almost absolute certainty that hitting a wooden table with our knuckles will make a rapping noise.

Could this, however, not be the case one day? Is nature uniform enough to where no matter where in the universe we are, if we rapped our hand against wood, would the same sound be made? If we hit it on the moon probably not, since there is no air to carry sound waves. In this case, our “wood punch law” would no longer hold true. The tree that falls in the forest makes no sound if the forest is in such a place.

“The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.” -Bertrand Russell, The Problems of Philosophy

We’re not as dumb as the chicken, so from now on, we will always disbelieve everything we’ve ever known because we’re continuously reminded about how wrong we’ve been in the past.

The Principle of Induction

The principle of induction can be summarized in this way:

(a) when a thing of type A happens, and type B happens in association, and they have always been observed as to happen together, the more times the types A and B happen together the more likely that they will be associated in a future occurrence.

(b) enough times of (a) happening will make their association near certainty. Operative word is near.

The inductive principle can only speak of things that have already happened – to make a prediction is to make an inference completely dependent on this inductive principle. It cannot be proved. One day, our data gathering will become better, and we will see a better association between A and B, and the old law will be thrown away and the new one will be in place.

A classic example of laws that are supplanted are those of motion and gravitation: Aristotle’s laws of dynamic motion were replaced by those of Galileo, then Newton, and then those of Einstein. We already know that relativity doesn’t work at every scale, so one day Einstein will be proven inaccurate. It’s just a matter of time.

Can We Really Know Anything With Absolute Certainty?

I don’t know the answer to this question, but my attitude is: do I really want to?

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Fictitious scenario: My science project is due tomorrow! I’m supposed to talk about stars, and planets, and such! Better run to Wikipedia and grab some quick facts. (Note: I do not advocate the use of Wikipedia for academic research, but it’s sometimes a good place to start to familiarize yourself with a topic)

According to this crowd-sourced website, Proxima Centauri is the nearest star to us. It’s about 4.2 light years away. But how do they know how far away it is?

Turns out, it’s not that hard. If you have the right kind of eyes, of course.

A Quick Experiment

Hold your finger, pointing up, in front of your eye, and keep it there. Now focus on something that’s on the other side of your finger, the farther away the better. Now move your head from left to right (kinda like Michael Jackson while pretending to be an Egyptian). Notice how your finger seems to be moving relative to the distant object, while the distant object is moving very little or not at all. This is called parallax. The less something moves as we move our heads, the farther away it is. Our finger moves a lot because it’s right there. If it were an inch from your nose it would seem to move about as much as your head has.

If you want, do the same experiment with two distant objects in-line with you, notice how the one in the middle moves so much less in relationship with the far one.

Moving Our Heads Isn’t Good Enough

It’s a bit hard to measure a star’s distance from us by simply moving our heads, so our clever little brains figured out that the solar system kind of takes care of this for us. We take two measurements 6 months apart. In January, we’re on one side of the sun, and in July we’re on the other one. That’s as good as we can get.

Simple Enough, How’s It Done?

Notice how for a nearby far-away star (on the left), the parallax angle (the circle on top) is way smaller than that on the right.

The equation is so ridiculously simple my child could do it! Granted, my child started reading at age 3, but hey, I’m a proud parent.

Where d = the distance to the star measured in pc (parsecs), and p = the parallax angle measured in arcseconds.

A parsec is 3.26 light years, and a light year is the distance light travels in a year. Note: light goes really freaking fast. 300 million meters per second fast. That’s 671 million miles per hour. An arcsecond is 1/3600th of a degree (a degree has 60 arcminutes, and an arcminute has 60 arcseconds)

In Practical Terms

So if we looked at the sky and saw a star next to another, much distant star, then we looked again six months later and it had just moved 0.1 arcseconds away, the parallax angle is 0.1. Since d = 1/p, therefore d = 1/0.1, and the star is 1 parsec away, or 3.26 light years away.

Here’s the tricky part: it’s hard to measure deflections that are smaller than 0.001 arcseconds, even using powerful instruments, so we can only use this for nearby stuff. We can probably reliably determine distances of about 1000 parsecs (or 3260 light years). After that, we have to use some really creative methods which are beyond the scope of this post. How wide is an arcsecond? Hold a human hair at arm’s length. This is, of course, a lot easier when looking through a telescope. When looking under an eyepiece at regular magnifications, the entire field of view is usually just one degree, and it’s much easier to separate it into sixtyeths.

There’s actually a really neat trick for figuring out angular distances in the sky: your hand!

The sun and the moon are about half a degree wide.

It’s hard to overestimate our insignificance. It’s also hard to underestimate how much we’ve figured out from out little corner in the middle of nowhere. We will continue to discover things and feel great, then brought down a notch when we realize we haven’t put a dent into the amount of things that remain to be discovered.

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A Star is Born

We see them twinkle at night, we make odd shapes out of them, and one of them is a major component of our daily lives as members of a race and components of a complex ecosystem. But what is it, and how did it come to be?

The Interstellar Medium

When we look into space at night, we see little dots of light, and nothing else. It looks empty, but in fact it is not empty: space is full of gas and dust. This is what’s called the Interstellar Medium (ISM for short from here on out, so remember!)

The majority of this ISM is Hydrogen, which happens to be the most common element in nature. The rest is dust, but not the dust you’re used to, more like carbon, silicon, and its compounds such as CO, HCN, etcetera.

The ISM is not spread throughout space evenly, it has clumped in some regions and is extremely sparse in others. In the same fashion, some portions of the ISM are hot, and some are cooler. Let’s then consider that the ISM has two important qualities: density and temperature. (Note: since the ISM is mostly hydrogen, then the density of the ISM can be considered to be the amount of hydrogen atoms in a cubic meter).

This medium has an extremely wide range of densities and temperatures: there can be as little as 100 particles of ISM in a cubic meter, to about 1017. Same with temperature, it can be as low as 10K (that’s almost absolute zero, way below freezing) and as high as a few million K (the temperature inside a burning star, hundreds of thousands times hotter than our sun’s surface which is about 5000K).


Nebulae are clouds of ISM that are dense enough and lit enough to be observed via infrared, x-ray, and visible light. There’s several kinds:

  • Emission Nebulae have stars in their midst that energize the cloud gas itself, exciting it, and causing the nebulae to give off its own light. In this sense, the gas itself becomes the source of light, and via the process of fluorescence the gas will glow. An example is the Eagle Nebula:

Eagle Nebula

  • Dark Nebulae differ from other nebulae by the fact that they do not shine. Instead, they are detected because they block light. They are vast clouds of gas molecules and dust grains. These dust grains are very small, but they are covered in mantles of water or ammonia ice, making them about ten times larger. They are not super dense, they are just incredibly good at extinguishing light. A prominent example in the night sky is the Coalsack Nebula, which blocks out a chunk of light from our own Milky Way.

Coalsack Nebula

  • Reflection Nebulae shine by the lights reflected from the stars within them or from nearby stars. The grains are so small that they selectively scatter light from certain wavelengths, giving a very specific color to the nebulae and in many cases giving them an internal composition and structure. One of the most famous reflection nebulae is the Orion Nebula, located in Orion’s Sword within his constellation. The four stars that light it up are known as the Trapezium. You can even see it with binoculars!

Orion Nebula

  • There’s other types of nebulae such as planetary nebulae and supernova remnants but these don’t have as much to do with star formation so I’ll just have to talk about them later.  Supernova are amazing events, the most likely candidate to supernova next is the red supergiant Betelgeuse, it is Orion’s shoulder. The day it blows up it will outshine a full moon, and it’s about 600 light years away.Supernova remnants are so freaking cool, however, that I’ll include the picture of a popular one here:

The Crab Nebula

Molecular Clouds

So space is filled with gas and dust, and higher concentrations of these in the vicinity of stars will shine (or block) light to give rise to nebulae. The areas that give rise to star formation are called Molecular Clouds. They are HUGE and contain ridiculous amounts of Hydrogen, their mass can sometimes be that of millions of solar masses, and diameters of 40 to 400 light years. That’s a lot of gas in a lot of space, so if that particular gas density was bottled in front of you you would still not be able to see it: it’s only about 200 to 300 hydrogen molecules per cubic centimeter – it is a trillion trillion times less dense than the air we breathe.

A protostar is not visible in the visible spectrum, so devices like the Spitzer Infrared Telescope can unlock some of their mysteries. This picture is drawn in false color since these wavelengths are invisible to the human eye.


In an ISM (remember? dust and gas?), where the temperature is low, and the density is high, gravity starts pulling all that hydrogen and dust together. The only place that this can happen is in the dark nebula. The other kinds of nebula are too hot: the temperature will overcome gravity and they will just dissipate and be pretty to look at. In the dark nebula, gravity can dominate, and the star can begin to form.

As the dust and gas comes together, its density and temperature will increase into something called Barnard Objects, and this blob will continue to heat up and compress. As the cloud becomes more opaque (less transparent), radiation will have a hard time escaping, and will be contained in the blog causing a spike in temperature and pressure.

The seed of the star is born – the protostar.

The Birth of a Star

Not all big, cold, dense clouds collapse under gravity to become stars. Remember there’s two effects acting against each other: gravity, the force that brings two massive objects together, is fighting thermal energy, which wants to drive molecules apart. A star is born only when gravity wins, and the core has reached about 10 million K. When the core of the protostar is this hot, assisted with the unholy amounts of pressure, hydrogen molecules can start meshing together in a process called fusion. As soon as this happens the gravitational collapse of the star will stop. Our star has become a hydrogen-burning main-sequence star. And this is why we call stars “fusion reactors”, because in essence, they fuse hydrogen molecules, and therefore release vast amounts of energy through the proton-proton chain.

Remember that all of this was happening inside a dark nebula, so a star that’s being born is not visible to the naked eye. It can only be detected in the infrared and x-ray wavelengths, therefore special telescopes have to be used (such as the Chandra Space Telescope). After the star is born, it’ll blow away its shroud and will become visible. This cloud, after it’s blown away, will go on to become a reflection or emission nebula. These are often referred to as star nurseries, and the Orion and Horsehead Nebula are two good examples.

My Favorite Part – The Big Picture

As if the picture weren’t big enough.

Hydrogen is the most common element in all of the universe. In some places it’s more dense than others, even though of extremely low density. Combined with little pieces of molecular dust, it clumps up into large clouds of material that starts coagulating, and via the gravitational force and assisted with low temperatures, a seed is born. This seed will continue to gather mass and further compress, becoming hotter, until one day it’s hot enough to start a fusion reaction. The immense loss of mass and emission of energy from the new star will blow away its motherly shell and will become one more of the trillions upon trillions of stars existing in the universe.

This is where we were born. In the core of one of these fusion reactors. We all started as itty-bitty pieces of hydrogen and carbon and nitrogen dust, compressed into existence, ejected catastrophically from a runaway explosion, thrown away in space, and captured in the gravity well of our star the Sun.

So here we are.

Categories: Astrophysics | Tags: , , , , , , , , , , , , , , , , , | 2 Comments

Entropy: the Mathematical Description of Inevitable Disorder

Today, I shall talk about one of the most interesting aspects of thermodynamic law: the concept of entropy.

Entropy is simply a measure of the energy in a system that is not available to perform useful work. It is the reason why machines are not considered completely efficient. For example, entropy in your body is all the heat that you generate and is not used for bodily processes. In a cold day, the entropy is lower, because some of that heat generated is good for keeping you warm.

Another important (if not loose) use of entropy is to describe it as the amount of disorder in a system. Systems that start out organized will become more disorganized over time, but disorganized systems do not become organized unless energy is applied to them.

As defined by the second law of thermodynamics, entropy in an isolated system remains constant or increases, but it never decreases. To show this point, I shall point out some real-world examples of entropy at play.

The Disorder that Surrounds Us

Consider a billiards table. The balls are all racked into a triangle shape, and let’s say that all the numbers are facing up and readable from one end of the table. We could say that this billiards table has the minimum amount of entropy. Since no one has played the cue ball, entropy remains the same, the balls won’t move on their own. We can then apply energy to the system, because no system is truly isolated, and the cue ball hits the racked balls and they all start flying into different parts of the table. The level of disorder is increasing, therefore so is the entropy. The further along the game goes, the more disordered the table is, until it can’t be in any more disarray. The only way to bring order back to the table is to re-rack the balls (by applying external energy), or by putting the balls into one of the 6 pockets (also by applying external energy). There is NO way that hitting the cue ball will end up putting all the balls into a triangle with the letters facing up and north.

Another good example is holding a ceramic coffee mug – its ordered state makes it look like a nice coffee mug. I almost won a Socrates coffee mug in a philosophy contest, but some better philosopher took it from me. If we were to drop the mug onto the ground, it would shatter into many pieces, if we dropped those pieces again, it would shatter further, until it couldn’t shatter any more. You will never drop those shattered pieces and end up with a perfectly crafted coffee mug with Socrates’ mug drawn upon it.

For you gearheads, consider what happens at the brake disc in your car. When you brake your car, you dissipate the car’s forward momentum and the angular momentum in the wheels into heat at the brake pads and discs. This energy cannot be used to create any more work, it will be dissipated into the atmosphere, and will have heated up the planet’s air by the tiniest of amounts. Guess how some Hybrid cars work to regenerate some battery charge – by trying to recover highly entropic systems! Some (if not all) hybrid vehicles have regenerative devices in their brakes, using magnets and the such to generate some electricity, and in turn the electricity generated creates a magnetic field that counteracts the spinning magnet (See Lenz’s Law).

The Arrow of Time

There is a direction that entropy takes, and it is called the entropy arrow of time. Systems always go from ordered to disordered or will remain constant, without exception. More formally stated, entropy in an isolated system never decreases with time.

Entropy is the only physical quantity that requires a particular direction in time. You, for example, could go to the mall or to church at any given time, but regardless of where you go you’ll be about an hour or two closer to death. Just like thermal energy is always transferred from hot to cold, isolated systems as a whole never decrease in entropy.

The Largest System of All

We talked about the billiards, we can consider the pool table the closed system, and it’ll continue in disorder until we apply external energy to reorder it. If you think about it, you just made yourself part of an even larger closed system, and the entropy of the human&billiards sytem is going up – you burn calories to exert energy in reordering the balls. You can make up the energy by eating a delicious orange, and now you’ve disordered your kitchen, etcetera. We can keep increasing the scope of this system, until we reach an inevitable limit: everything that has ever existed.

The known universe is believed to be a closed system. This means that the total entropy of this system is constantly rising, and it has been a matter of speculation that we will be subject to a “heat death” in which all the energy in the universe will be distributed, and no work can be extracted from any source because it’s all just a big soup.

Since gravity ties every piece of mass in the universe together, and black holes are considered to be the maximum entropy objects for their size (I would imagine that the mass of 1,000 suns fitting into something much smaller than the head of a needle would be), then all matter will eventually end up at the core of a star that collapses into such a singularity.

Of course this is all speculation, so our demise may be at the Gates of Heaven. Let’s hope it’s the latter.

In Conclusion

Entropy is a relatively simple concept, tied to one of the laws of thermodynamics, that tells us not what the world will look like 5 minutes from now, but definitely knows what it *won’t* look like. We are all subject to it, and now you know what it is.

Let us take a second and consider what the ramifications of constantly increasing energy dissipation and disorder mean to us: the universe must have started at a maximum level of order, at a single point in space and time where everything blew apart and created every particle that’s ever been in existence. Fast forward some billions of years, and a star supernovas and creates a bunch of space junk that includes everything we’ve ever been made of. We are made of the bowels of a super-hot fusion reactor in a star that couldn’t maintain its monstrous size. We are, as Carl Sagan once said, made out of star stuff. We are the product of catastrophe and disorder. The molecules in your skin, made out of organic matter, were manufactured in a million degree furnace many billions of years ago. The calcium in the strand of hair on a Chinese man’s scalp may have been right up against the oxygen atom that’s in your lungs right now, cozied up right by a piece of iron that’s deep in the heart of Jupiter’s volcanic moon Io.

If that’s not a disorder that brings us together, I don’t know what is.

Categories: Thermodynamics | Tags: , , , , , , , | 1 Comment

Hi Danny! How do I subscribe to your lame blog, so you can stop spamming me on Facebook?

I just placed a link on the right that says “subscribe” – just click on it and use your favorite RSS or Atom aggregator, and if you don’t know what those things are then use the “email” tab and subscribe via email using feedblitz! Then tell your friends, your dog, your imaginary parrot, and your potted plant. Especially the plant.

Also note that the comment system I have installed has an email subscription. If you’re into heated comment there’s no better way to stop doing what you’re supposed to be doing to come attend to this important discussion. Besides, you’re probably wasting your time in the office playing basketball with orange peels.

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Women in Science

Before we can set our eyes on the stars and truly appreciate their wonder, perhaps we should get better at recognizing some of the amazing accomplishments that have happened right at our doorstep by none other than the female scientist.

For many centuries scientific or academic circles did not allow women to become members . Males were historically (and wrongfully) considered intellectually superior. This, unfortunately, is still reflected in the way we do business today. We pretend we’re tolerant, and that we value equal opportunities, but we simply do not. Did you know that the first person to ever discover a comet was a woman? Her name was Caroline Herschel, born in Germany in the 18th century. In August 1, 1786, she discovered her first comet, eventually receiving an honorary membership in the English Royal Astronomical Society. They couldn’t even offer her a full membership. Assholes!

Madam Curie is often regarded as one of the great female scientists in history, and for good reason. Unfortunately for her, she didn’t feel so great after dying from radiation poisoning. Who would’ve known that the pretty blue-green glow when the lights were out was actually symptomatic of highly charged helium ions and high energy electromagnetic radiation? The Curie, or a measure of an object’s radioactivity, is named after her.

The problem with identifying a problem and hastily addressing it is that we place ourselves in a position that gives us a false sense of security and accomplishment. We all recognize mothers are important to the healthy growth of the next generation of workers, creators, and world leaders, so we come up with Mother’s Day and call it good to go. What are you talking about, we celebrate mothers! There’s a day named after them!

It is with that message that I bring to you a name you’ve likely never heard before: Emily Noether. Emmy was not allowed to enroll in college prep school, and she had to fight her way through bureaucracy in order to finally audit a course, let alone be enrolled. Working at the University of Erlangen without any salary,  she had to scrape the bottom of the bowl for opportunities to engage with students as an unpaid substitute teacher when her father was ill.

Emmy went on to become a brilliant German mathematician and physicist. She is also the author of one of the least known but profoundly beautiful and powerful concepts in the theory that pervades us today. It is rightfully called Noether’s Theorem, which states that each symmetry of a system leads to a physically conserved quantity. Symmetry under translation (movement) corresponds to conservation of momentum, symmetry under rotation to conservation of angular momentum, symmetry in time to conservation of energy.

Some of you may read that paragraph and say “uh, yeah, when something spins, of course it retains angular momentum.” Emily was the first person EVER to be able to prove this in a way that would apply to ALL systematic symmetries.

Why are we still having this problem? Are you part of the problem, or part of the solution? It takes one thought to change the direction your life takes, and that of those around you. Take the time to recognize and appreciate the women around you that made you who you are, and that aren’t getting what they deserve. Most importantly, treat them with the respect you expect others to give you.

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All it Takes is One Mind

I posted this on Facebook a few days ago, but I really wanted it to be my first blog post.

Einstein formulated the general theory of relativity in 1916. It made predictions that he didn’t live to witness proven:

  • Gravitational deflection of light by a massive body (gravitational lensing)
  • Perihelion shift of Mercury’s orbit
  • The Shapiro effect
  • Emission of gravitational radiation by binary pulsars

Just a few days ago, he did it again. He proved that the Earth (or any other massive body) affects space-time not only by its presence, but by frame dragging, which is to say by spin. This is key to understanding the most violent catastrophes in astrophysics and the origin of inertia itself. A simple way to visualize this is imagine the Earth is in a vat of honey, as the Earth spins, layers of honey closest to the rotating mass will be dragged, and the further layers are dragged less. This is not unlike the magnetic forces that cause adhesion and cohesion in honey itself – just imagine the implication – gravity behaves in some ways like magnetism.

Theories follow experiment. This is central to the theory of induction. When we see A followed by B happen enough times, we say that the more it happens the more likely they are related, until we reach near certainty. The sun rises every day, therefore we expect the sun to rise again tomorrow. This led, of course, to the discovery of many phenomena such as the Earth’s orbit around the sun. One of the big questions in philosophy is whether our brains synthesize knowledge, or whether all knowledge is given and all we ever do is put old pieces of knowledge into a newer, shinier piece of knowledge.

So imagine experiment to be a man trekking up a hill, and he breaks loose a stone, and the man behind him picks up the stone and examines it. This man is called Theory and “Law”. We then come up with Laws, but then they’re supplanted when we can find a more elegant or complete one.

What Einstein has done is something incredible: a century after he made a prediction based entirely on the synthesis of his mind, he has continued to be absolutely right about what he expected to happen. The man following the trekker knows what the next stone to break loose looks like. This individual made predictions in an age of little technological achievement in terms of spaceflight, and it took us nearly a century to build instruments to realize that he was right. He made some observations on Earth and accurately made extrapolations that apply in the largest scales imaginable. His genius has rocked physics, and will continue to do so.

One of the challenges that’s a quagmire in theory is reconciling quantum physics and general relativity. In the large-scale, quantum physics can’t explain gravity (the team at LHC is currently working very hard in trying to figure out what gives particles mass, let alone the property of gravitational force). In the small-scale, relativity can’t make any predictions, and it breaks down in trying to explain things such as quantum tunneling and the energy levels of an electron as it absorbs or emits electromagnetic waves. String theory is a promising theory that could reconcile both, but there’s just a few problems with it. First, there’s like 7 different theories, none of it has ever been observed in a laboratory, and it’s the most complex thing you’ve ever laid eyes upon. Einstein, however, did it all in his scruffy looking head.

As an adult it’s easy to lose that sense of wonder and mystery that surrounded us when we were children. We don’t give a shit whether we can see the nucleus of the Milky Way in a dark summer’s night. We don’t care that we’re raping the only place we will ever call home. We act foolishly towards our brothers, sisters, and friends. When we hold our phones, we don’t think of the billions of instructions per second happening within a millionth of a meter, communicating with satellites in orbit and with antennas miles away, downloading the entire contents of a book in seconds. But every once in a while something shows up to remind us of how little we know, and how just an instant of curiosity can unlock the next secret that the universe holds.


Gravitational lensing is the General Theory of Relativity’s proof that mass bends space-time, therefore bending the travel of light. Notice how the same galaxy is lensed into several versions of itself due to a mass in the center of the frame. You can see the galaxy tinged with a blue ring, at 4, 8, and 10 o’clock positions. See: [].

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