Queen of Fractal Beauty’s Neighborhood

This is a reboot of the previous post, which got tangled in hidden formating codes.

Yep - here we go again! A new version of Chapter 4, in which we discover Earth's minerals, rocks, and layers.
Please - be brutal! The more you help me improve this, the better it will be for the students who have to use it!

4.1 Earth’s Composition

Most of our information about earth’s interior and its composition comes from indirect observation; the deepest drill hole to date has penetrated less than 25 km into the earth, or about 0.004% of the distance from the surface to the center. Nevertheless, we have learned much about the chemical makeup of earth's interior from komatiites, which are believed to represent upwellings from the mantle, and meteorites, which are believed to represent earth's starting composition. Similarly, earth tides, gravity, magnetism, and inertial measurements tell us much about earth's mechanical properties. However most of what we know about earth's interior comes from seismic energy released by earthquakes, as we saw in chapter 3. The thickness of the layers and their velocities (fig.4.1, center) may be found using the arrival times at stations around the globe; in certain instances, the behavior of the energy at the layer boundaries is also informative (e.g., at the D’’ layer that is believed to be the core-mantle boundary).

The challenge before us is to interpret these curves in terms of the geology. Changes in the curve may represent places where the material suddenly changes from one chemical to another. Or they may be places where the composition is constant but the material suddenly becomes denser. Each boundary seen in the seismic data may represent either of these situations, and various lines of evidence need to be studied to determine their nature.

What we do know is that each layer has consistent properties (Fig. 4.1), from the high water content of the aesthenosphere to the absence of S-waves in the outer core. The properties of each layer come from its physical conditions (pressure and temperature) as well as from its chemical composition. But how the layers are defined depends on which property is most important. Geochemists study earth based on its chemical properties and so define a different set of layers than do geophysicists who divide earth’s interior based on mechanical properties. Mechanically, the layers are the lithosphere, the upper mantle, the lower mantle or D’’ layer, the outer core, and the inner core. These layers have been primarily defined by their seismic characteristics, including P-and S-wave velocities. We will examine this in more detail in later sections.

For now, let us consider earth’s chemical layers. Chemically, earth’s interior is subdivided into the crust, the aesthenosphere, the mantle, the core-mantle boundary, the outer core, and the inner core. Each chemical layer is made from a specific set of rocks or materials with a consistent chemical composition (Table 4.1-1). For example, the mantle consists primarily of peridotite and the oceanic crust is primarily basalt and gabbro.

The rocks in each layer are made up of naturally-occurring compounds which form molecules known as minerals. Though more than 100,000 different minerals have been identified, the bulk of earth’s interior is made from only thirteen compounds (Table 4.1-2) that combine in various ways to make fewer than fifty minerals. Similarly, each compound is made up of atoms with consistent properties known as elements. Earth’s main elements are oxygen (O), silicon (Si), iron (Fe), magnesium (Mg), aluminum (Al), calcium (Ca), sodium (Na), potassium (K), cobalt (Co), and nickel (Ni). The distribution of these elements is different for each planet and follows a distinct pattern (Chapter 10). For now, we will focus on the distribution of these elements in earth’s interior.

Each element is a specific type of atom with a defined number of positively-charged protons and electrically neutral neutrons in a central nucleus which is surrounded by concentric, non-spherical regions called orbitals that act as holding tanks for negatively-charged electrons. An electron must gain or lose specific amounts of energy in order to move from one orbital to another [1]. The number of neutrons in an element can vary. This changes the mass of the atom, creating isotopes which have the same chemical reactions but at different rates. More neutrons creates a heavier atom which reacts more slowly than one with fewer neutrons. As we will see, this effect creates a "thermometer" that can be used to determine the formation temperature for a mineral. The mass of an atom is shown as a superscript to the left of the chemical symbol. For example, carbon (C) is commonly found as with six protons and six neutrons, for an atomic mass of twelve (¹²C). However, it also has isotopes with seven neutrons (¹³C) and eight neutrons (¹⁴C).

It is the number of electrons that determines how each element reacts chemically, and the number of protons that determines how many electrons an atom can hold. Initially, these are equal. However, this can change in two ways. The number of protons and neutrons can change by nuclear decay (chapter 5) or fusion (chapter 10). If the number of protons has changed, the atom becomes a new element. The number of electrons can change when they gain so much energy that they leave the atom entirely and join another atom forming ions. The number of electrons lost or gained is shown by a superscript on the right of the chemical symbol. For example, when hydrogen (H) gains an electron it is written as H⁻ but when it loses one it is written H⁺ . Protons and neutrons are more than 1,000 times more massive than electrons. Thus, gaining or losing electrons only changes an atom’s mass by an insignificant amount.

There are four main ways of joining atoms together to form molecules (Table 4.1-3). The electrons can be shared between atoms in a covalent bond. Glass is a material with strong covalent bonds. Alternatively, an atom can become a positively-charged cation by losing an electron or it can gain an electron and become a negatively-charged anion. The electrical attraction between cations and anions creates an ionic bond. Salt is a common material with an ionic bond. Electrons can also move between atoms, forming a metallic bond. Not surprisingly, iron and gold have metallic bonds. Weak bonds known van der Waals bonds can also form between molecules. The exact nature of these weak bonds is complex and beyond the scope of this text. Ice is an example of a material with van der Waals bonds (and covalent bonds).

Covalent bonds are the hardest to break. Covalent bonds reduce solubility (as this depends on ionic bonds) and create materials with higher melting points (stronger bonds require more energy to break). Materials made with covalent bonds do not break easily or smoothly. Ionic bonds create materials that are poor conductors of electricity and that dissolve easily in water. They are not as strong as materials made with covalent bonds and will break along well-defined lines. Materials with metallic bonds conduct electricity easily and can be hammered into a new shape without breaking. The weakest bonds are those formed between molecules with the van der Waals force. These materials have little strength and will break evenly along a plane.

The number of each element in a molecule is given by a subscript to the right of the chemical symbol. For example, the main component of air is two nitrogen atoms (N₂) held by a covalent bond. The size of the orbitals and the atomic bonds create molecules with distinct shapes and sizes. A crystal is formed when these bonds create a solid from molecules, ions, or atoms in a repeating pattern. For example, salt (NaCl) is a crystal with alternating sodium (Na⁺) and chlorine (Cl⁻) ions held together by ionic bonds. Similarly, ice is a crystal formed from covalently bonded H₂O molecules linked together by van der Waals forces. Because atoms are three-dimensional and can form multiple bonds, the resulting molecules can have different sizes in each direction.

One common tool for finding the bond size is X-ray diffraction. X-rays are simply a type of light not visible to the naked eye. In 1670, Isaac Newton discovered that visible light could be split into colors using a simple prism. In 1800, Frederich Herschel discovered a color of light that could not be seen. Because it lay beyond red, he called the color infrared. Since then, we have discovered that visible light is just a tiny fraction of the whole electromagnetic spectrum, which ranges from long radio waves to short gamma rays (fig 4.1-2).

Though the spectrum contains both "waves" and "rays", light is actually neither. Instead, it is a photon that sometimes acts like a wave and sometimes acts like a particle [2]. Photons can create interference patterns, like waves, but individual photons can carry only discrete amounts of energy. The amount of energy (E) that a photon carries is:

where c is the speed of light, lambda is the wavelength of the photon, and h is Planck’s constant (6.626x10⁻³⁴ Js). A gamma ray photon (wavelength 10⁻¹⁶ m) has 10²¹ times the energy of a radio wave photon (wavelength 10⁵ m). The photon’s wavelength also determines its color.

[1] Einstein won the Nobel Prize for Physics in 1921 for his description of this effect.

[2] This is similar to the "cameleopard" which has the hump of a camel and the spots of a leopard. Despite the name, it is neither a camel nor a leopard. The modern name for a cameleopard is "giraffe"

4.2 Earth’s Minerals
Earth is mainly made up of silicate minerals, which form around groups of four oxygen (O) atoms covalently bonded to one silicon (Si) atom. The chemical notation for this is SiO4 . The silicon atom’s radius is about 1/3 that of an oxygen atom, so the silicate forms a tetrahedron with the silicon in the center. Aluminum is about the same size as silicon and frequently substitutes for it. Silicate tetrahedrons can form covalent bonds, or may gain up to four electrons to form ionic bonds. Common silicate cations include Na⁺ , K⁺, Ca²⁺, Mg²⁺, Fe²⁺ (ferrous), Fe³⁺ (ferric). In general the cations are smaller than the anions. Thus, most of the crystal's volume is anions with cations put into the gaps.

What is the most important technology every businessperson should understand to make his/her business successful?
Sponsored by HP.

The smile, followed closely by the handshake. Businesses are social, if they want to succeed. But too many treat customers as interchangeable units, there to be milked and then sent away.What businesses (especially big businesses) don't understand is that today's economy is a commodity-driven one [1].

Very few businesses offer something that I can't get elsewhere. So the deciding factor is almost always going to be the quality of customer care they offer. Treat me well, and I will continue to spend money with you. Treat me badly, and I will leave you. Treat me very badly, and I will make certain that my friends know why I've left you!

So if you want to make me a happy consumer, liable to buy more of your stuff, make it easy and pleasant to buy things. Make the inevitable problems [2] something that gets smoothed over quickly and with a minimum of fuss, not something that I spend ten hours tearing my hair out over. Make using your product something I enjoy, not something I dread. If you want to use my data, ask me politely and let me control how it is used [3]; if you insist that your need to know how I found your website is more important than my order, then you will get neither order nor information [4]. And don't sell my information to anyone else. If you are a business, I'll start shopping elsewhere. If you are a charity, I'll stop giving [5].

Remember that I can do without you. You can't survive without me. And that will be the best technology that you can have.

John

[1] I.e., one in which the goods from Sears look just like the ones from WalMart - except for the price tag.

[2] No product, ever, has been put out without flaws and defects. Heck, look at man...

[3] Don't force me to join a "club" to buy from you. I'll just go elsewhere. You aren't the only source for music (Amazon), books (Cafe Press), flights (Expedia), or food (Kroger's).

[4] A sad-but-true story - the Calyx and Corolla web site will not allow you to place an order unless you tell them how you heard about them.

[5] Another sad-but-true story - I have stopped giving to several charities (including Feed the Children and the ACLU) because they sold my information to other groups who then solicited funds from me.

Have you ever broken a bone? If not, what's the worst injury you've sustained?

Amusingly, I never broke a bone until I was in grad school - and then I broke four in two years! My right radius in a freak slip on ice in Chicago. My collar bone and a cracked skull in an absurd bike accident [1] in Monterey, CA. My left ulna in an absurd bike accident [2] in Alexandria, VA.

You know what's really unfair about all of this? Four broken bones, and I've never gotten a cast! My little sister had had three casts by the time she was six [3], and would hit us with them and then go crying to our mother that we had hurt her!

John

[1] I hadn't wanted to take the bike, but the people that I was house-sitting for insisted. On the way back from work, I ended up at the bottom of a 30-ft deep bike path/ditch with traffic whizzing by on the street overhead and no way that anyone could see me. So I climbed out of the dicth and across to a motel where I asked the manager to call an ambulance for me. The folks on the ambulance were worried because I was too rational following the accident (I gave them my pulse rate, pupil dilation, and medical diagnosis on the phone) and refused to give me any painkillers until five hours later when they were sure I didn't have a concussion.

[2] Biking back from Mt. Vernon, the front tire folded when I put on the brake to slow down. Naturally, this happened at the bottom of a hill more than a mile from anything. The lesson: Never allow me to ride a bike in a city; especially if that city has hidden places where I can break something and not be found...

[3] Fell out of a tree, run over by a car she put into drive, fell out of another tree. I got dropped from the car into highway traffic and only got a small scar on my lip. She trips over a piece of paper and gets a cast. It is't fair!

Looking at the exchange rate for euros today and swirling that together with the national debt figures gave rise to the following:

On May 25, 2001, the Euro was worth US$0.8591; that is, you could buy $116.28 in Euros for US$100. At that time, the US national debt was a mere US$5,660,883,342,386.72 [1].

On May 25, 2008, the Euro was worth US$1.5669; that is, you could buy $63.69 in Euros for US$100. On that date, the US national debt had increased to US$9,492,245,770,788.70 [2].

Converting the debt into Euros is interesting - in 2001, the debt was the Euro equivalent of $6,582,422,491,147.35 whereas today it is a mere $6,046,016,414,521.46 in euros. In other words, the value of the United States (as measured by the worth of our debt) has decreased by nearly 9% since 2001.

This isn't the only indicator of the drop in the value of the US. The Euro is now the world's most popular currency. Foreign investment into US debt has slowed. And exchange rates continue to climb.

So ask yourself one simple question the next time you talk to your politician: Have the past eight years improved the US or made it worse? And then vote appropriately.

John

[1] That works out to $19,855.64 for every US citizen alive in 2001.

[2] Or $31,169.40 for every US citizen alive today.

For the 7th day of the 7th month, show us 7 of something - OR - something lucky.

It would be lucky to remember that 7 is not lucky in all cultures. In parts of China, it sounds like a vulgar word and so is very unlucky.

John

As you know, I just got a new toy, er, car. As part of the deal, they gave me six months of free Sirius radio. You know - the radio that claims to be "100% commercial free". However, while listening to the thing, I've noticed that not only can they not count [1], they also put out commercials on a regular basis. Admittedly, these aren't for pimple cream or hemorrhoid cream [2], but they are still trying to sell you stuff (more Sirius radios, to be specific). So I wrote their customer service department. here is my email and their reply:

Why do you say that you have "100% commercial free programming" when you don't? Ignoring the annoying station identification blurbs, many of your channels frequently feature DJs flogging Sirius products. Those are commercials. So why lie?

Dear John, 

Thank you for contacting SIRIUS regarding announcements made by the on-air DJs.  We're here to help you!

John, our emphasis is on the music and entertainment you want.  Master music programmers and on-air personalities, who are true experts, host our music.  They back up the music with compelling information about the song being played.  We do not consider announcements and on-air host discussions "commercials;? we simply want to ensure that our listeners remember who they are listening to so they can come back to their favorite channels to make requests.  We apologize for and frustration caused by the announcements and on-air host discussions.

I hope this helps to resolve your issue, John.  Have a great day!

We are committed to providing you with the best in customer care.  If you have any more questions, please feel free to contact SIRIUS Customer Care.  For your convenience, we are available 24 hours a day, 7 days a week at:

1-888-539-SIRIUS (7474)

As well as by email at:

www.sirius.com/customercare

Sincerely,

Robert
SIRIUS Customer Care

Did you know that SIRIUS has great money-saving billing options?  You can get 1-14 months free depending on the option you choose.  Call us at 888-539-SIRIUS (7474) and we?ll help you choose the plan that?s right for you!

SIRIUS Satellite Radio, The Best Radio on Radio

There are two ways to read their response. The first, and most charitable, is simply that my question wasn't clear enough for them to understand. I'll resubmit it with clarification [3] to see if that helps. The second, and most likely, is that they simply have a script that they use to reply. Notice how they don't reply to my question, but to something that they can read into my question [4].

In any case, this is just something to do to keep myself amused. Based on the quality of their service, stupidness of their terms [5], and low variety of their music, I definitely won't be paying for this anytime soon.

John

[1] For some reason, they keep playing songs from as early as 1954 on their "60's Vibration" and from as late as 1967 on their "50's" channel. Do they really get that confused that easily?

[2] One way or another, they're gonna getcha...

[3] "You did not answer my question. Let me rephrase it for clarification. I have heard your DJs asking the listeners to buy additional Sirius equipment. NO music was discussed. This was, pure and simple, a commercial for Sirius products. How then can you claim to be commercial free?"

[4] Obviously they've been learning from politicians...

[5] You have to buy a new subscription for each and every radio you have. One radio, one subscription. Two radios, two separate subscriptions. Three radios, three individual subscriptions. It adds up - quickly. Cable did this until the local communities forced them to stop. Who will force Sirius to go to a more rational billing model?

One of the strengths of the American system is that it allows itself to make mistakes and then correct them [1]. Today, we were witness to one of them, in Breyer's dissent where  he said:

"In my view, there simply is no untouchable constitutional right guaranteed by the Second Amendment to keep loaded handguns in the house in crime-ridden urban areas."

Let me get this straight - folks in a neighborhood where the police fear to tread in a city known for its high murder rate have no right to keep loaded handguns [2, 3]? IMHO, that is the best reason to uphold a broad interpretation of the second amendment. Had he said "There is no untouchable constitutional right to keep loaded handguns in gated suburban communities with low crime rates", it would have seemed almost reasonable. But to say that folks who live in a crime-ridden area have no Constitutional right to use guns to defend themselves is just silly.

John

[1] Dredd Scott, anyone?
[2] The DC law was a wondreful mass of contradictions. You had to apply for permission to have a handgun, which had to be stored unloaded, trigger-locked [a], and disassembled - but they wouldn't punish you if you used an unlicensed gun to defend yourself. What kind of sense does that make?
[3] Of course, you could strain at gnats and say that the modifier he used ("untouchable") means that there could be some rationale under which you would want those folks not to have guns. But I'll be damned if I know what it is.
[a] The trigger lock makes sense, IMHO - too damn many parents are sloppy about where they store their gun. Hey, Dad - if i can find your stash of Playboys, I can certainly find your 45!

Okay, my friends know me to be a lazy person. Actually, I'm so far at the leaning edge of the spectrum that I should invent a new word for lazy.

But enough about me....I am finally ending my self-imposed blog vacation to let everyone know that I am walking tomorrow night in the American Cancer Society's Relay for Life.

For those who don't know, Relay for Life is an overnight fundraising event. Teams join up and walk from roughly sunset to sunrise, the walk is held at night for practical (1) and symbolic (2) reasons.

Anyway, I wanted to publicly thank those of you who have donated to the event and urge everyone to check out both Relay for Life and the American Cancer Society. After I'm done, I'll post pics and commentary....then I'll go back to seclusion for another 5 months.

WenDragon

(1) Are you frackin'/frelling kidding me??? It's Oklahoma....in the summer, oops. Sorry, John, MIDsummer.
(2) The walk also symbolizes a cancer patient's journey, from sunset, which represents the first diagnosis & starts the long night of the soul, to the exhausting and weakening treatments--usually around 1 or 2 a.m. Finally, around 4-5 a.m., the walkers can start to see the beginnings of morning, symbolizing the end of treatment for the cancer patient.