Color

My last post caused me to think a lot about how and why we see colors. Let's talk.

Colored light is exactly the same kind of radiation as X-rays, gamma rays, UV rays, radio waves, or microwaves. The only difference is in its frequency (the number of times the wave can oscillate between two maxima in a second) and wavelength (the distance between two maxima). Other than that, it's all the same thing. We call light having a wavelength of about 400-700nm (100nm = 10^-7m) visible light only because it ends up that our eyes process it when it hits them. But all of it is light. So what's going on that makes us see certain wavelengths as color?

First off, why do objects give off some wavelengths of light but not others? There are two ways an object can have (or lack) color. First, an object can emit light all by itself. You don't do this in the visible range, but the stars do. The graph here shows the light output of several different kinds of stars. You'll notice that each star emits light in all of the visible colors, but in one more than all the others. That's why some stars look blue and others red. Ours looks like the middle curve and actually appears white in space (emitting all of the colors fairly evenly) although it appears yellow on earth (we'll get to that in a bit).

The next way an object can have color is by scattering light that is incident upon it. Depending on the chemical composition of the material, it will absorb some wavelengths and scatter others. Obviously, only the wavelengths that get to your eye are the ones that your brain processes, so you perceive distinct colors in objects illuminated with white light. Scattering is a rather prevalent phenomenon. One of the most common occurrences happens with white sunlight traveling through our atmosphere. It just so happens that the size of air molecules corresponds very well to scattering smaller wavelengths of light. Blue, having the smallest wavelength in visible, is preferentially scattered in every direction, which is the reason we see it when we look at any part of the daytime sky (this is called Rayleigh scattering). If we looked at the source of the light, the sun (note: do not look at the sun), we would expect to see the remaining light; white minus blue, which we call yellow. In other words, if our sky scattered red light, our sun would look green instead. Particles much larger than molecular gas particles (such as water vapor particles) scatter light, but do so evenly. Clouds (composed of water vapor) thus scatter all incident light that they receive evenly, causing us to see white (a phenomenon called Mie scattering).

So, when (scattered or emitted) light reaches our eyes, how does our brain distinguish between all the colors? As you are well aware, our eyes have four kinds of small photoreceptors in them called generally rods and cones. Each, by a process known as phototransduction, transmits electrical impulses to the brain when hit with light. However, not all of them respond to the same wavelengths. Some only respond to blue, and others only to green or red. The graph here displays the response functions by wavelength of the three different kind of cones in our eyes. You see that one transduces primarily in the blue range whereas there are two that transduce in almost the same range, but one slightly redder than the other.

Color, then, is just the end product of our eyes' response to a source. Imagine a source at 450nm. The blue receptor responds strongly and green and red each respond to a much lesser degree, but green a little more than red. Thus we see mostly blue with a much smaller dose of red and green. In other words, we see blue on its way to becoming purple. Looking at the response graph, one can deduce that the easiest color to see is at almost exactly 550nm. Here, red and green respond equally in strong measure, producing a sickly-yellow color. It as at this intersection point where the largest number of photoreceptors are giving some kind of response. Interestingly, a human's ability to see this color so well is the reason that they started painting emergency vehicles this color (as pictured here).

All of the colors that we see are simply combinations of red, green, and blue. Sometimes they are represented in the form <ratio of red, ratio of green, ratio of blue>. The "pure" colors are ones that can be represented by only one wavelength. In other words, if you can produce a color by drawing a single vertical line on the receptor graph above and mix the resulting ratios of red, green, and blue, you are seeing what a "pure" color. Some colors require that at least two wavelengths of light combine to create the response in our eye. Brown is the most common example. Consequently, that's why brown is not part of the rainbow; a rainbow diffracts light and allows you to see white light (a combination of all colors) split up into single wavelength portions. Since brown cannot be created in the human brain without at least two stimuli, it cannot be in the rainbow.

The science behind scattering, absorption, and reflection is much, much deeper. But I hope that this allows at least the first look into the beautiful complexity of optics and biology as an application of physics (of course). The resolution of our eyes is astounding. The difference between blue and red light (the extremes of our vision) is only about 10^-7m yet our eyes distinguish the myriad of colors and details that make our world vibrant and beautiful.

Nomarski Imaging

As per request, I'm going to cover an application of physics today that is really on the proverbial cutting edge. Differential Interference Contrast (DIC) microscopy or Nomarski imaging is an exciting optical method that allows us to "see" microscopic, translucent biological material. As is becoming a theme, I'll need to explain a few concepts in optics before continuing to the meat of DIC imaging.

Prerequisite Light Discussion:

It's no secret that light is a rather complicated beast. First of all, a photon (basic unit) of light is simply a packet of electromagnetic radiation. Sometimes it acts like a wave (it refracts, diffracts, and reflects) and sometimes it acts like a particle (we can shoot photons one at a time, which is no more wave-like than a single water molecule by itself on the beach). To be clear, light is neither a wave nor a particle, but it acts like one or the other depending on the conditions under which we observe it. The wave part of the wave-like side of light is the behavior of the electromagnetic field of which it is composed. The electric field grows stronger and weaker with regular oscillations as does the magnetic field (oriented perpendicularly to the electric field). It is from these oscillations that we determine frequency, wavelength and other wave-like characteristics.

Polarization is the term we use to describe how all of the photons' electric and magnetic fields from a specific source are aligned. If the field oscillations in each photon have random orientations, the light is unpolarized. If all of the electric fields of each individual photon are oriented up and down, we call this vertical polarization. We can also achieve circular polarization by causing the electric fields of each photon to rotate either clockwise or counterclockwise such that at any instant, each of the photons are oriented in the same direction. This is more applicable than you might think. We use polarized filters in sunglasses to cut out reflective glare, in films to produce three dimensional effects (if you wear those silly glasses) and in astronomy (of course).


Phase is another important concept in light that we'll need to consider here. As shown in the image, two waves can be identical in amplitude, wavelength, and frequency, but can still be out of phase. This means that their moments of maximum field strength happen at different times. Phase is the reason that photographs don't look the same as real life. A picture can record the differences in intensity of light hitting the screen, but (except for in holography) film cannot record the phase difference in light adequately enough to reproduce it for the observer. The image comes out flat-looking.

DIC Imaging:

Differential interference contrast imaging uses a combination of applications in polarization and phase to image translucent images. 45-degree polarized light is split into two beams, one of 90-degree polarized light and the other of 0-degree polarized light. Though polarization is divided in this split, phase is kept constant. That means that two photons -- one 90- and the other 0-degree polarized -- that passed through the beam splitter at the same time will keep the same relative phases that they had when the beam was together. Each beam is indepentantly but simultaneously passed through the the material using a converging lens. The material is not necessarily homogenous throughout. It will have regions of high density and perhaps regions of differing composition. Since light travels a little bit slower in dense media (with a higher index of refraction), the photons passing through denser parts of the material will take a longer time to get through it. Thus, the phase of each beam becomes variable over the beam, not constant as it was at the beginning.

The beams (each now identically phase-shifted and perpendicularly polarized) are brought back together and projected onto a film. Here, you'll notice that both phase and polarization are recorded in each beam. As the beams combine, not only will they interfere (due to phase differences), causing the texture of the material to become visible through a series of brighter and darker contours, but the three-dimensionality of the material (its thickness, for example) will come out because of the polarization. To see in three dimensions, we must have two slightly different views of the same thing (such as through your left and right eyes). Polarization provides just that sort of perspective, rendering the image in three dimensions. This splitting and recombination of beams to measure objects is known as interferometry and is prevalent in optical and astronomical research, having many applications.

Thus, even though we cannot actually see the material that we are analyzing, its variable density lends itself to visible analysis by exploitation of the propensity of light to slow down in denser media. The images we get yield the kind of extreme detail required to learn about microscopic, organic materials.

Enrico Fermi

b. 29 September 1901
d. 28 November 1954

Noteworthies:

• Nobel Laureate, Physics
• Namesake of Fermium on the Periodic Table
• Namesake of Fermi Labs
• Significant contributor to the Manhattan Project
  

Fermi, an Italian-born physicist, is probably the most complete physicist since Newton. He was equally and exceptionally gifted in both experimental and theoretical physics and is a contributor to (even arguably the father of) modern nuclear and particle physics. His life and gifts are extraordinary and are worth talking about.

He grew up in Italy, schooled by his mom in their unheated house. It was apparently so cold that he devised a way to turn the pages of his books with his tongue to keep from having to use his hands which he sat on to keep them warm. He was always a great experimenter, using his brother as an assistant. His interest -- or, rather, obsession -- with physics theory came at the tragic and early death of his brother. His first tutor recognized his unique ability to understand and remember physics and math.

"When he read a book, even once, he knew it perfectly and didn't forget it," (1) commented Adolfo Amidei when asked to recollect his student's progress. Later in his life he would even recite whole chapters of physics texts out loud while driving on long trips. His grasp of theory was so concrete that his friends nicknamed him "The Pope" for his infallibility. At college he would often pass his time lying on the grass writing textbooks from memory without any kind of notes or scratch paper. His writings were never interrupted with erased or crossed our words. Often, the director of the research lab where he worked would seek him out (he the student) and say simply, "teach me something." (1)

One of the skills for which Fermi is particularly well known is that of estimation. He possessed the ability to look at a system or a problem and produce remarkably accurate results without any research or calculation except for what was already in his head. When working at Los Alamos labs on the bomb, he accurately estimated the yield (explosive size) of a bomb by dropping scraps of paper as the shock wave passed him. He is also attributed to, without any sort of research or other-than-mental calculation, accurately estimating how many molecules were stripped off of a car tire each rotation, how many piano tuners were in the city of Chicago, and the number of molecules of water in a teaspoon versus the number of teaspoons of water on the planet. These kinds of problems are now actually referred to as Fermi Problems.

His Nobel prize was awarded for his work in nuclear physics, which described the actual process of beta particle emission. For years before, physicists knew that electrons were emitted from atomic nuclei, but were unclear as to where they came from. Fermi determined that a neutron in the nucleus of the atom actually turned itself into a proton by splitting into a proton and an electron-neutrino pair. Inherent in this is the discovery of subatomic particles—quarks—which has led to our knowledge of the history of the universe as well as our current descriptions of the cause of fundamental forces like gravity and magnetism.

He further categorized a class of particles known as fermions which follow certain quantum statistical rules, the understanding of which has led to our comprehension of the behavior of stars, the flow of electricity (and thus, cooper pairs and superconducting materials), which are used every day in current scientific research.

Most notably, Fermi invented or engineered many of the components of elementary nuclear reactors, which now power whole countries (not our own, unfortunately), and the United States Navy's submarines and aircraft carriers. He introduced the cadmium control rods that protect against meltdown during critical-phase nuclear reactions.

Fermi totally immersed himself in every project he undertook, often working around the clock (not because he was under a deadline, but because of his natural interest). He died of stomach cancer at the age of fifty three. "Fermi told [a friend] in 1945, at the end of the war, that he had then completed about one-third of his life's work. By that reckoning, when he died nine years later, Enrico Fermi had given us no more than half of what he had to offer." (1)

1. Cropper, William H., Great Physicists. New York : Oxford University Press, 2001.

Universe Synthesis: Part I

Lifetimes of research have been dedicated to discovering how the universe was formed, and what it looked like and how it behaved during its stages of development. The topic is a little lengthy, so it will be divided into several independent posts. But first (as usual) we need to address a critical concept: time.

Astronomers estimate that the age of the universe is something like 14 billion years. Imagine what it will look like in twice that time, another 14 billion years from today. Do you expect it to look the same? Clearly not. Most of the stars currently in the universe will have extinguished and exploded and new ones (made up of the less pure remnants of the recently departed stars) will have taken their place. With these new stars (known as population III stars), it is entirely possible that everything we currently know about the behavior and interactions between stars will have changed. Their compositions, lifetimes, and nuclear reactions will be different. With that established, it doesn't seem like a stretch to say that doubling the age of the universe changes it significantly.

Keep that in mind as we explore the first few epochs of the existence of the universe. They take place fractions of seconds after each other in what would today be termed rapid succession. Remember, however, that when the universe was 10^-30 seconds old (a trillionth of a trillionth of a millionth of a second or so), it was millions of times older than it was when it was 10^-40 seconds old. Back then, time wasn't very old. The age of the universe doubled in units of time too small to think about. So, at that time, fractions of a second were as significant as billions and billions of years would be today. Let's take a look at the earliest stages of the life of our home.

The universe started as an immensely massive, yet infinitely tiny point. At some point in time, something caused it to expand at an astounding rate.

The Planck Epoch
0 to 10^-43 seconds

Light and heat are the only two things able to exist. Due to an extremely high temperature (~10³² °C), nothing solid can form and remain formed. Much in the same way that ice can't remain ice at high temperatures, any energy trying to form itself into matter disassociated (broke apart) immediately due to high energy light and became energy again. During this time, it seems that all of the forces that we are familiar with (gravitational, electromagnetic, and nuclear forces) were combined into one unified force that governed all things.

The Grand Unification Epoch
10^-43 to 10^-36 seconds

As the universe expands, it cools (the same amount of energy is distributed over a larger space), causing gravity to establish itself as a unique, fundamental force. The smallest and most fundamental particles (Higgs Bosons) also form.

The Electroweak Epoch
10^-36 to 10^-12 seconds

At a whopping 10²⁸ °C, the universe separates the nuclear strong force into a unique and fundamental force (the word fundamental here is not a contradiction even though the force came from something else. I only mean that in these conditions, the force becomes fundamental). During this epoch, we suspect that a rapid expansion period took place known as the cosmic inflationary period. The volume of the universe expanded enormously for several thousand trillionths of trillionths of seconds (during which the total age of the universe doubled about 5000 times). The temperature dropped significantly and quarks (the building blocks of protons and neutrons) formed out of the now cooler energy.

--

We're still a trillionth of a second away from the first whole second of the universe's life, but we have already traversed three major epochs in the formation of the universe in which we live. Stay tuned for the next major age of synthesis.

The Second Law of Thermodynamics

The Second Law of Thermodynamics is perhaps the most important governing principle of which we are aware in the physical universe. Strangely, of all of the physical laws that we use to describe physical systems, it is the only one that is not -- strictly speaking -- a law.

Let's take Newton's Third Law of Mechanics (for every force, there is an equal force in the opposite direction) as an example of a classically true one. No matter what you do -- if you push on a wall or throw a baseball or kick a dog (note: don't kick dogs) -- the object will exert the same force on you that you exert on it. Don't believe me? Go punch a wall as hard as you can and see what happens (note: don't do this either). It always happens. Always.

Conversely, the Second Law of Thermodynamics is actually just a declaration of statistics. Simply, it states that entropy tends to increase over time. Let's define entropy with a little example.

Imagine that you have a coin and you flip it. What is the probability that it will land heads-up? Right. 50-50. Now flip ten coins. What is the probability that five of them will land heads-up and five of them heads-down? You might be surprised to find out that it's about 25%.

I've included a little table to prove this to you. A microstate is the total number of possible arrangements of the corresponding number of coins showing heads. In other words, there is only one way to show no heads (all tails) and there are ten ways to show 1 heads-up coin (coin 1 heads up and the rest tails, coin 2 up and the rest tails, etc.) and so on. Beneath the "Microstates" column is a sum of all of the possible states. Divide the number of microstates for a certain coin combination by the total number possible and you get the probability of that many heads showing.

So what does that have to do with entropy? Well, what if you flipped all ten coins a billion times? You would expect that the most likely combination (5H and 5T) would show up most often. And that's what happens. Well, that's entropy. If you take the natural logarithm of the numbers in the "Microstate" column, you'll get the entropy of that particular combination of heads and tails. And since the natural logarithm of x gets larger as the value of x increases, the most likely combination has the highest entropy. So when we say that entropy tends to increase, all we mean is that over time, the most likely organization will tend to display itself. In other words, the Second Law of Thermodynamics can be quite simply stated as "Things that are likely to happen are likely to happen."

But you'll notice that this is a statistical certainty, not an absolute one. If you flipped ten coins ten times, you may notice that 6H and 4T showed up more. We can only be absolutely certain of the outcome with really really large numbers. Fortunately, the things we try to describe (heat transfer between two objects, for example) with this law have big numbers in them (objects that transfer heat regularly have billions of trillions of molecules). To illustrate, let's flip 100 coins. The odds of landing 50 heads is relatively small, about 8%. But that's something like eight times more likely than flipping 60 heads, 100 million times more likely than flipping 80 heads and one million billion times more likely than flipping 90 heads. As the number of coins increases, the likelihood of there ever being anything but a 50-50 decreases to zero.

To illustrate, flipping 10²³ coins (there are about that many atoms in a just few grams of carbon), you could flip them all once a second every second for the entire age of the universe (10¹⁸ seconds) and still never find a result further away from 50-50 than 1%. When you get to the size of things we actually care about, there is absolutely no chance that any other arrangement than the most likely will ever happen ever. So, while the Second Law doesn't absolutely determine the outcome of statistical events, it is still certainly going to happen.

Applications:

So who cares about that? Didn't we already know that likely things happen? Isn't that why they are likely? Why does knowing this mathematically help anyone? To name a few things, this law provides the foundation for our heat transfer models that we use to heat homes, businesses, and cars. It helps determine the size of the fan on your computer or your car needed to keep it from overheating. It helps us know how big of a heat pump your fridge or freezer will need, how solutions tend to mix at a given temperature and when they will freeze or melt (which is how they invented antifreeze, solder and plastic), or at what temperature magnets will cease to be magnetized (more important than you think). It plays a part in determining the conductivity of materials at a given temperature (like the wires in your house or computer), the formation of minerals and rocks in the earth's crust, and the chemical distribution in our atmosphere. In short, the Second Law of Thermodynamics helped us either to develop or manufacture almost every household object that we consider to be common. That is no exaggeration.

To recap, the Second Law is more than just a "description of chaos" as many people choose to describe it. Rather, it is the statistical certainty of likely things to occur over time (which tends towards basic forms of energy—like heat—that could be described as chaotic). As I consider its implications, I am amazed at how such a fundamental law can be so simple while describing so much.

Louis-Victor de Broglie

b. 15 August 1892

d. 19 March 1987

Noteworthies:

• Nobel Prize laureate
• Fellow, Académie française
• Perpetual Secretary, Académie des sciences
• 7th Duke of Broglie
• Fellow, Royal Society of London for the Improvement of Natural Knowledge

Born into a rich, aristocratic family, de Broglie (pronounced /də'brɔɪ/) had really no need to become a physicist, or anything else for that matter. His interest in physics came as a combination of natural intuition and skill in the subject and (most probably) from the influence of his older brother, Maurice, who was an accomplished physicist himself. However, his entrance into the field was as well-timed as it was risky.

The last thirty years of science had been revolutionary. Einstein had recently declared light to possess characteristics of both waves and particles, introducing what is now known as wave-particle duality. Planck and Bohr followed up with the discovery of quantization, which is the simply but profound idea that waves (bound energy) can exist only in certain, specific denominations, between which energy propagation is non-existent. Since before, physics had been divided into two separate domains -- particle physics, and wave physics -- duality was something of a hot topic that caused frequent debates. Bohr even refused to believe the results of his own experiments, trying force his findings to fit a (consequently incorrect) model that he couldn't give up.

I know it may seem like a trivial thing to us, but this was groundbreaking work that seemed to be trying to convince the world that apples and oranges were the same thing. De Broglie found himself in the middle of a great schism with Einstein on one side and Bohr on the other. A wrong step could end any credibility he had gained and potentially end his career. Slamming together some of the most basic equations (E=mc² and E=hν), he boldly declared the impossible, initially based on intuition and faith that not only was light duality correct, but that all things exhibited such a behavior. Sometimes light acts like a particle and sometimes like a wave. It is, however, neither of the two by the classical definition. Even more surprising, sometimes matter behaves like a particle, and sometimes like a wave.

In other words, you have a wavelength. So does a grapefruit. And your car. At the right speed and in the right conditions, a stream of grapefruits would diffract around a corner exactly like a water wave does. At a large scale, this doesn't mean a darned thing. But on the scale of atoms and electrons, duality lies at the heart of basically every modern invention in the world today. Computers function because we understand how to control electrons because we finally figured out the they weren't little tiny balls bumping into each other and flowing along, but could instead be treated as a wave. There are hundreds and hundreds of applications stemming from duality that I could mention, but even if semi-conductors (things that help make computers go) were the only thing ever invented because of de Broglie, can you see the implications of his work? What doesn't use a computer to help it function?

The science here is too deep for me to go into (or even understand myself). But that's kind of a blessing because I'd rather focus on the lessons learned from de Broglie as he discovered these principles. He was under immense pressure not to believe in duality. He very easily could have embarrassed himself and his family (particularly devastating to a French aristocrat) and ended his career. On a simpler note, he could have dismissed his intuition as passing insanity and focused on what everyone else forced themselves to see just because that was what they had always believed. Instead, de Broglie challenged and followed his own ideas, discarding the false ones along the way, and became one of the founding fathers of modern physics and the technological age in which we live. His work demonstrates genuine curiosity and courage and is a perfect example of the true scientific method.

Source: Cropper, William H., Great Physicists. New York : Oxford University Press, 2001.

Gravitational Lensing

Gravitational lensing is one of my favorite physical phenomena. To introduce it to you, I'll first need to present two concepts that make gravity and energy a little easier to think about.

1) We often think of gravity as being caused by mass distorting something we call spacetime. Imagine a sheet stretched tightly and perfectly level. If you were to roll an extremely small marble across the sheet, it would travel in a perfectly straight line without interruption. However, if you put a bowling ball in the middle of the sheet and rolled the marble past (not even necessarily towards) the bowling ball, it's quite easy to imagine that the

marble would roll towards the bowling ball. This is a three dimensional simulation of gravity. In our world, space is a three-dimensional "sheet" on which large masses (stars, planets, etc.) are resting. They distort otherwise "straight" space, causing other masses to "roll" towards them.

2) A handful of scientists including Einstein (See? Now you believe me.) discovered that light and matter were, in fact, the same thing. It's kind of the same way that thunder and lightning are two different manifestations of the same thing. You see one and hear another at distinctly different times, but it was all caused by only one event. Thus, the path of light can be bent by gravity just like the path of a baseball is.

Around 1900, Einstein predicted that his model of gravity (discussed above) could be seen if we could observe a star the was directly behind the Sun during a total solar eclipse. They picked a star that would be directly behind the sun during the eclipse and attempted to observe it during the time of maximum darkness. Sure enough, they were able to see the star, the path of its light having been bent around the Sun towards Earth.

However, now we use it to sound the deepest, oldest reaches of the universe. By pointing a telescope at extremely massive clusters of galaxies, we can resolve several smudges or blurry images in the field, such as the blue objects scattered around the field pictured here. Each blue image is actually the same galaxy which lies behind the cluster in the center, but is being bent around it in several different directions. This phenomenon, called strong lensing, is useful in determining the shape and extent of our universe, which is currently calculated at approximately 14.5 billion light years across (about 90 billion trillion miles).

Closer to home, an effect called microlensing helps us solve yet another mystery of the universe. Currently, we can account for only about 4% of the mass that is "supposed" to be in it. Numerous factors (which require their own post) make it plainly obvious that all of the matter that we can see isn't even close to the amount that there needs to be to make it behave the way it does. We speak of dark matter, which is simply a (very mysterious and cool) name for "stuff that we can't see". And it isn't even all that far away. Dark matter governs the behavior of even our own galaxy, the Milky Way. But just because we can't see it doesn't mean that we can't see what it does. Occasionally, a hunk of dark matter crosses in front of a star, causing it to quickly change its apparent light output. These hunks are called MACHOS (Massive, compact halo objects, of course. . . what were you thinking of?) and are frequently observed. They give us enormous insight into what dark matter could actually be composed of, and its participation in our conception of the universe.

Incredibly, a simple concept like "gravity bends light" can be used to produce observable data that helps us to understand mysteries as complex as the age, size, dimension and composition of the universe.

Why?

Issac Newton was and is frequently congratulated for his brilliant successes in the field of physics.  His discoveries have probably influenced every single technological (to say nothing of philosophical) advancement in physics since he lived.  In his fame, however, he never forgot how he happened upon his ideas nor did he forget to acknowledge who was really responsible.  Humbly, he tipped his hat to his predecessors, and to God, with words now immortal:

If I have seen further, it is only by standing on the shoulders of giants.

I'm neither blind nor stupid enough to assume that he was only talking about physics, but even therein his point is valid.  How can we expect to become something greater than he if we do not take the time to learn what he taught us?

Continue reading this blog, and you'll find posts treating physical phenomena, small bios and anecdotes about the world's greatest physicists, and explanations of physical laws.  Sounds boring, doesn't it?  Well that's kind of my point.  I'm convinced that physics is beautiful, and the world even more so when we understand it.  This won't be a textbook, pointed at people who already know what I'm talking about.  Rather, it will (hopefully) be a simple, unassuming, and revealing look into a field that happens to infuse me with an unmatched appreciation for what God has given us.  

Still not convinced?  Just give me a chance.

Daniel