This one's a fossil of an extraterrestrial...

Julia posted about an e-mail she recently received, in which her correspondent described finding a fossilized head of a sea horse and a fossil heart. And it reminded me that my other half wanted me to tell a story about a tag that I've used before. So, Jay, this post is for you. (Correct the story if I blow it.)

Back in the early 90's, there used to be a funky art festival in northeastern Vermont called the Bread and Puppet Circus. The group apparently still tours with their giant puppets and political theater, but in the 90's, they held a big weekend gathering at a farm in Vermont's Northeast Kingdom, with various skits and lots of bread (cooked in outdoor ovens). The festival grew to something that involved camping, vendors, and all the trappings of a Phish show except the music.

We went up there in one of its last years as a summer festival. I had just started doing fieldwork a bit south of there, so I combined a geology scouting trip with a cultural event, and Jay and I headed out to check out the scene.

The parking lots were a bit like those at a Grateful Dead show - veggie burritos, drum circles, jewelry, bumper stickers, twirly skirts and bare feet. But there was one guy with a lot of rocks sitting on the ground. I would have avoided him - I have had enough experiences with people wanting to talk about the coming Earth Changes as it was - but Jay likes talking to unusual characters. So we went over to talk to him.

Oh, yes, he had interesting rocks.

"This one is a dinosaur!" (I squinted. It looked like a moss-covered calcareous schist, and no, I don't mean it was a coprolite.)

"This one is a dinosaur egg!" (Well, maybe it was kind of oval-shaped...)

"And this one is the fossil of an extraterrestrial!" (Waits River Formation. Not even a single darned garnet.)

I smiled, nodded, and backed slowly away.

I don't think Jay has ever forgiven me for avoiding that long discussion of alien fossils.

(Jay is traveling for work, which is why I'm talking to him via my blog.)

Geoscience uses for calculus (and beyond)

I've heard many geology students rant about calculus. It's confusing. It's boring. It's useless, at least for geology. So why do they have to take it, then, other than as a form of ritual torture?

I admit that I don't make students use calculus in my classes. I don't want students to miss an intuitive understanding of a topic because they're bogged down in the math, and I don't want to set up pre-requisites that prevent students from graduating in a reasonable amount of time. So I take other approaches - analogies and demonstrations, mostly - to try to make sense of quantitative subject.

I don't do calculus directly in my research, either - at least, not in the sense of calculating derivatives and integrals. But the fieldwork that I do is based on theoretical work that, in many cases, would be impossible without calculus and other post-algebra math. I don't often have time to go into most of it in class (though I've been looking for excuses in Structure this fall, ever since my students made the mistake about ranting about calculus before lecture one day).

I'm putting this list together off the top of my head, and I know that it's horrendously incomplete. (Partly because I forget things, and partly because my research experience is limited to certain subdisciplines.) If you have examples to add, please do, and I will edit the post to include them. If you sign your post, I'll give you credit for your additions. (And if you've got any references to books or papers or online sources that explain more about the use of the technique, I would love to include them, as well.)

Geologic time

The radioactive age equation is probably the most obvious example of a geologic use of calculus. (It was even in my undergrad calc textbook.) The decay rate (dN/dt) is proportional to the amount of the parent isotope present. That makes a simple differential equation, and leads to an equation with natural logarithms. (It also makes radioactive dating challenging to explain to intro classes. I know I do a terrible job of it, and probably leave students figuring that if they're confused, it's probably wrong.)

Structural geology

Something as simple as the attitude of a layer is actually related to calculus. It's simple (well, with practice) to describe the orientation of a plane, but how many geologic layers are really, genuinely planar? And yet we measure the orientation of planes around the surface of a fold. But we aren't measuring the curved surface - we're measuring a plane that's tangent to the surface. It's actually kind of the derivative of the curved surface, except that it's in three dimensions, which makes it really complicated. (It also makes it a subject requiring 3rd semester calculus.) Lots more information about this (and other shapes) is in Dave Pollard and Ray Fletcher's structural geology textbook, in the chapter on differential geometry. (I found myself trying to explain the chapter by writing about an ant traveling along a wire. I suspect the book could be improved by somehow combining the math and some creative analogies.)

And then there's stress. And strain, actually. Both stress and strain are physical examples of tensors - functions that relate one vector to another vector. To work with tensors, you need to know matrix algebra (which I learned in linear algebra). Tensors are important for describing the properties of all kinds of things that vary depending on direction - the stress experienced by different fault planes, the changes in length of stretched fossils with different starting orientations, variations in compressibility with direction, and so forth. (They apply to subdisciplines other than structural geology, too - the weird ellipsoid called the "indicatrix" in optical mineralogy relates the speed of light to the orientation of a crystal, for instance. And if groundwater can flow through material with different permeabilities in different directions.)

Petrology and geochemistry

Metamorphic phase diagrams show which minerals are stable under various temperatures and pressures. The slopes of the boundaries between the areas where different minerals are stable depend on the properties of the minerals (like the entropy and the molar volume).

And... well, mineralogy, petrology, and geochemistry are full of ideas taken from chemical thermodynamics. And thermodynamics is full of multivariable calculus. (How does changing the pressure change the amount of calcium in garnet vs the amount of calcium in plagioclase? The question is a partial derivative.) From my own favorite, metamorphic petrology, there are all kinds of techniques for using metamorphic minerals to tell stories of heating and burial and cooling and exhumation. And none of the techniques would be possible without calculus. (Or, in many cases, differential equations.) I'm sure igneous rocks and ore deposits have similar uses of thermodynamics.

Geophysics

Probably every subdiscipline within geophysics uses calculus, linear algebra, differential equations, and so forth.

I've played more with heat flow than with most other topics within geophysics. And heat flow is defined using ideas from calculus. The equation for conduction of heat in one dimension, for instance, relates the transfer of heat to the change in temperature with distance (dT/dx). Add more dimensions, or move the rocks around, and it gets even more complicated. Heat flow equations make it possible to predict how hot a rock can get beside a magma body, or can test whether a continental collision could really result in growth of a certain high-temperature mineral. I love it. It takes arm-waving and gives it substance and testability.

I'm sure there's more. (Groundwater hydrology, for instance, uses differential equations to describe the movement of water and the chemical reactions between the water and minerals.) I need help remember what some are, though.

Sedimentary geology

Brian points out that fluid dynamics is based in calculus. (Tell me more about the modeling of sedimentary systems, though - I mean, most modeling that I know of uses calculus at least, if not differential equations, because changes in time or in space (or both) are part of the model, and if changes are involved, calculus is useful.)

The world's oldest rock is punny

I finally found time to read the paper describing the new World's Oldest Rock. I wanted to blog about why news reports seemed cautious about trusting its age (for instance, see Richard Kerr's write-up in Science). I need to spend more time thinking through the isotope geochemistry of the heavy rare-earth elements before that's possible, unfortunately. (Maybe a fan of extinct isotopes could help, since the argument is based on decay of 146Sm?)

But the problem, really, is that I got distracted by the mineralogy of the gneiss in question. The rock is described as a "faux-amphibolite," and is made of plagioclase, biotite, quartz, some garnet, and...

...wait...

...cummingtonite.

That's right. The world's oldest rock contains one of the favorite minerals of dirty-minded geology majors.

Other discussions in the geoblogosphere:

The Volcanism Blog
NOVA Geoblog
goodSchist (Chris mentions familiarity with the 146Sm-142Nd system; maybe he could help evaluate the paper)
olelog
About.com geology

(And they did a good job of linking to discussions in the media, so I won't try.)

Open question for readers: surviving calculus

I just got this question in a comment to another post, and I thought I would throw it out there for readers to help with:

Anyone out there have to take a year of calculus even though it wasn't their strongest subject? How did you survive?

I would love to know answers to this question as well. Not because I'm struggling through calculus myself, but because many of my students are, and I'd like a larger toolkit of suggestions for them. At the end of this summer, I went to a discussion with the math department about ways to help students succeed in the precalculus-calculus sequence, and if anyone has great ideas, our math department has a big education grant and might be able to implement some.

(In the meantime, lacking any better ways to help my students succeed in calculus, I let my structure lab go early - during the stereonet lab, no less - because half the class had a group calculus exam scheduled to start right when the lab was supposed to end, and I didn't want them to go into their exam feeling overwhelmed and confused by stereonet rotations. Oh, and to former students, I was planning to give them a short lab next week anyway, so I'm just going to do rotations and drill-hole problems then.)

My approach has been to point out the connection to calculus concepts whenever I see them. (Strain rate? Derivative! Oh, and how is a graph of stress vs strain rate related to a graph of stress vs strain?) That, and to make the students use algebra as much as possible in a geology context, because it seems like succeeding in precalculus and calculus is often a matter of doing algebra well. It would be nice to have more suggestions beyond the math cheerleading, though.

Congrats to Dave Montgomery - MacArthur Fellowship

Geomorphologist David Montgomery of the University of Washington has just received a MacArthur Fellowship. (These are the "genius fellowships" that give the awardees $500,000 with no strings attached.)

His book Dirt: the erosion of civilizations has been on my to-read list for a while. (I bet it will be available at the GSA meeting. Maybe there will be signed copies?)

Congratulations!

Open Lab 2008 is taking submissions

For the past two years, a volunteer group of bloggers has been publishing an anthology of great science blog posts, and publishing it in a dead-tree edition. (Yes, I realize there's something odd about that.) They're looking for posts now:



The call for posts is here.

Bora at A Blog Around the Clock has a list of current submissions. I don't see anything from the geoblogosphere yet. Last year, Chris Rowan and I had posts included in the anthology. The geoblogosphere has grown immensely in the meantime - I hope that many of you will submit your posts (or posts you loved reading) for this year's collection.

Climate change and intro geology textbooks

A few days ago, I got the semi-annual phone call from my textbook rep. What am I teaching next semester, do I need any new books, how do I like my current textbook (Exploring Earth), etc, etc, etc. And then she told me that the book was being revised, and did I have any comments for the authors.

"Yes," I said. "I like the book overall, but I've got one criticism..."

It's in the section discussing global warming. The discussion is good, except... well, except for the waffling.

Here's the intro to the climate change spread of pages. (Bold type is added by me for emphasis. Italics are original in the book - they are the way that new terms are introduced.)

Most data indicate that some global warming is occurring. Many scientists propose that human activities, including the burning of fossil fuels and the clearing of forests, contribute greenhouse gases to the atmosphere. Astronomical factors, such as Earth's orbit around the Sun and an increase in sunspot activity, can also contribute to warming. Other factors may lead to global cooling, such as ash from large volcanic eruptions and an increase in certain aerosols in the atmosphere.

Here's an excerpt from discussion of ice cores:

Many scientists infer that these increases in greenhouse gases are partly responsible for the recent increase in temperature, but there remains debate about this controversial topic.

And here's the discussion of climate modeling:

The simultaneous rises of anthropogenic (human-caused) CO2 and temperature may be related. Climatologists use computer models to account for the effects of the various factors that might cause warming. Some model results are consistent with observations of past climates, so may be reliable. Some models suggest that anthropogenic greenhouse gas emissions are a contributor to warming in the last century. The relative roles of different factors over the last 100 years, as predicted by these models, are shown by this bar graph.

The facts (and the supporting graphs and discussions of the factors that control atmospheric temperature) agree with my understanding of the science. But the statements are all qualified in ways that leave room for people to argue that we don't really understand the problem. "Many." "Some." And then there are the references to sunspots and the Earth's orbit, which are certainly discussed in the literature, but which may not deserve a spot in the large font at the beginning of the section. And there are the references to debate, and the subtle implications that there could be problems with modeling. (Models "may be reliable." And then again...)

So I told my textbook rep about my complaints about the wording. She was surprised at my particular complaints...

...because she's been getting the opposite complaint. That the statements about climate change are too strong.

She asked if I would be willing to review chapters for the revised edition. I said yes - but that climate change is not my area of expertise. (The youngest rocks I've worked on are around 100 million years old. The shallowest rocks I've worked on were metamorphosed at depths of around 10 km. Young surface processes? Very important, but not my expertise.)

So if you are a climate scientist, and are willing to review climate science for an introductory physical geology textbook, McGraw-Hill needs you. Please, somebody, make sure that introductory geology books reflect the best evidence that's out there.

(Why do I care? Well, I don't like misleading students. And anthropogenic climate change is an important topic beyond the political and economic issues that it raises. The ideas of climate scientists drive research in other areas of geology - see Dave Petley's post today about the possible effects of global warming on landslides as just one example. Waffling about climate change seems like... well, it reminds me of waffling about plate tectonics in 1987. There were plenty of skeptics about plate tectonics in the 80's, but students were poorly served by the textbooks that portrayed plate tectonics as some wacko idea. And, yes, there were books in the 80's that did just that - my undergrad sedimentology book, for instance. I still feel cheated by that book.

I don't want to cheat my own students by teaching them outdated or misleading science.)

Advice wanted: rugged digital cameras

I went on a lovely hike above 11,000 feet today, checking out the access for a structure field trip in a few weeks. There was a dusting of snow on the north side of some peaks, remnants of a storm a few days ago, and I took a picture of a great angular unconformity (Precambrian gneisses beneath young volcanics).

And I can't show you any pictures, because I dropped my digital camera on the ground and broke it.

(Actually, the story is more complicated, and involves a five-year-old taking photos of an artistic arrangement of hand-held radios on the tailgate of the truck, and a mother with clumsy hands reaching for the camera at the same time as he reached for it. But it doesn't matter. The camera has a dent, and the lenses won't retract.)

So I'm in the market for a new camera. And I'm curious what features the rest of you have found useful. I know I want something with macro capabilities, and with decent resolution. The old camera was very lightweight, but I would be willing to carry something heavier if it were a bit more rugged. I would also like to find something with batteries that I could replace in the field - if I'm backpacking, I can't use my charger.

I am not a great photographer, and even in the days of my entirely mechanical 35 mm, I never got really good at adjusting f-stops and shutter speeds until I got the best image. (I never got the hang of the manual settings on my broken camera, either. I don't know if that means they were poorly designed, or whether I just didn't have the patience to play with them enough.)

Any suggestions for things I should be looking for, this time around?

(And any suggestions for an inexpensive but rugged digital camera that a five-year-old can experiment with? I want to let him explore his interest in still-life images of outdoor gear, but, ummm, not with my camera.)

Student-generated glossaries and intellectual honesty

I'm experimenting with an online course management system this semester. (My college adopted the open-source system Moodle last year, and I'm still learning what it can do.) It's got lots of neat little ways I can make online assignments. For instance, tonight my students are doing an open-book quiz relating the minerals from this week's lab to the mineral groups we talked about in lecture. (I think they'll remember more when they've looked up the information themselves, and repeated the quiz until they got everything right, then they would from a rapid-fire list of mineral names during lecture.)

Because I'm using a textbook that doesn't have a glossary at the end of the book, I decided to have students make their own group glossary on Moodle. Every week, each student has to find one new word, enter it onto Moodle, and define it. I've got it set up so that students can read each other's definitions, but so I am the only person who can comment on all of them. (The students can edit their definitions as they go, as well.) After a week and a half of classes, I've been impressed by the terms and definitions that they've found.

In an exercise like this, I expect the students to use all kinds of different sources to understand their terms. The textbook, the lectures, the labs... and the internet. They're doing this online, they've got access to Google, and, well... if I ran across an unfamiliar term outside my field of expertise, I would probably start by Googling it or looking it up on Wikipedia.

As I read the definitions, though, I began to wonder whether any students had simply copied the definitions from other sites. And then I wondered whether it mattered in this situation. (The assignment is being graded based on participation, not on the quality of the definitions. I'm using it to encourage students to study in a particular way, not because I'm interested in their finished product. And, well, glossary entries can only be so original.) But I hear that many people don't think about intellectual property rights on the internet, and I want to encourage students to be honest and to respect and acknowledge the work that other people have done. (Even if those people are anonymous.)

So here's what I'm thinking of doing. I'm planning to go to class tomorrow and tell the students that I'm impressed with their definitions, and that I have an idea that might make them even more useful. I'm going to ask them to include links to any useful web sites that they find, for three reasons: 1) it will make it easier to find the site again; 2) it will point other students to useful web sites, and 3) on the internet, it's polite to link to sources and other related sites.

What do you all think? Linking seems like the polite thing to do these days, and I think it encourages students to acknowledge the ideas of other people. (And I do think that links would be useful for the students, as well. Some students are already adding them, and they're great additions to the definitions.)

Five most important minerals to know

Following up on yesterday's Fifty Great Minerals meme, Callan at NOVA Geoblog asks a related question:

So let me issue a new challenge for my fellow geobloggers... Which five minerals do you think are the most important ones to know, and why? In other words, if you had to introduce a non-geologist to just five of the earth's multitudinous building blocks, which ones would you choose to share, and offer a justification for each.

It's a great question (particularly during the week when I'm covering minerals in my intro course). I'm going to answer it without reading the rest of Callan's post, so I'm not influenced by his answers.

Quartz: It's made of the two most common elements in the crust (silicon and oxygen). It's in every type of rock - igneous, sedimentary, metamorphic. It survives weathering, which makes it a major component of well-traveled sand. It's hard, it's chemically tough, it makes pretty crystals, and it's ubiquitous.

Calcite: Calcium carbonate. Either calcite or its polymorph aragonite makes up the shells of lots of marine organisms, which can then become limestone. It reacts with acids, which means that it's useful to treat an upset stomach or acid rock drainage. It dissolves to make caves, which are beautiful, capable of transporting groundwater (and groundwater pollution) rapidly, and capable of collapsing. It's used to make concrete, and polished slabs in fancy bathroom walls, and (especially as marble) great art. And when it's buried by a continent-continent collision, it carries carbon dioxide away from the atmosphere and into the mantle.

Pyrite: "Fool's gold" is not an ore mineral itself (at least, not most of the time), but it's common in many ore deposits, in slates, and in coal. And when it comes into contact with the water and oxygen, its weathering creates sulfuric acid. It's pretty, it sparkles, and its chemistry creates an important side effect to many kinds of mining.

Clay minerals: This is cheating, because they're a group of minerals, and kaolinite (which has the simplest chemical formula) is one of the less interesting members of the group. They're diverse and chemically complex, but they're one of the major groups of minerals on Earth's surface, because they form from weathering most silicate minerals. They are especially important in soils, because they retain water. Some of them swell when they get wet or dry. Chemical reactions that occur on their surfaces can change the ions dissolved in groundwater. They're important indicator minerals for exploration for ore deposits. And if you heat them to 500 degrees Celsius and 4 kilobars, they turn into really pretty stuff (none of which make my list of Five Most Important Minerals, alas). (You can also make pottery from them at surface conditions, which is also nice.)

And one last one... hmmm.

I'm going to go with olivine, to represent the mantle. I've focused on minerals that are important on Earth's surface, because that's where people live. But most of the Earth is not crust - it's mantle, iron- and magnesium-rich silicate minerals. Olivine is the prettiest and easiest to recognize, and I think the mantle should be proud to have olivine as its spokesmineral.

And if you are one of my students reading this: yes, these are likely to be on a test at some point.

Fifty great minerals meme

Ok. My AGU abstract is submitted. My quizzes are graded. My powerpoints (both Monday's and tomorrow's) are uploaded onto the course management site, so students can print them if they prefer to do that. (I'll still encourage them to draw.) Lab is done, the kid is at a soccer clinic, and the plants are watered. It must be time for a meme.

From Chuck:

Use bold to indicate minerals you’ve seen in the wild. Italics is for those seen in laboratories, museums, stores, or other non field locations. Ex pet nerds may use underlining to indicate those that they’ve grown with their own two hands. And I won’t bother with stuff you intend on seeing- if you didn’t want to see all these minerals yourself, you’d be spending your precious lunch hour on a physics or biomedical blog.

I'm going to underline minerals that I've probed, dated, or had some other intimate acquaintance with. Because this is a tell-all geology blog.

And I'll put an * beside any minerals in my intro class's mineral lab.

50 minerals everyone should see:
Andalusite
Apatite (I'm sure some of my rocks have had apatite, but the &^%# blueschists didn't. Good thing Trevor found some in the other rocks.)
Barite
Beryl
*Biotite
Chromite
Chrysotile
Cordierite
Corundum
Diamond
*Dolomite
Florencite
*Galena
*Garnet
*Graphite
*Gypsum
*Halite
*Hematite (I may have probed this while trying to figure out what was in a rock, too.)
*Hornblende (Ugh. I will never date a hornblende again.)
Illite
Illmenite
*Kaolinite
Kyanite
Lepidolite
*Limonite
*Magnetite
Molybdenite
Monazite (Only probed, not dated. And they were too small to see.)
Nepheline
*Olivine
Omphacite
Opal
Perovskite
*Plagioclase
*Pyrite
*Quartz (I've also probed it when I meant to probe plag. A lot.)
Rutile
Sanidine
Sillimanite
Silver (native)
*Sphalerite
Staurolite
*Sulphur (native)
*Talc
Tourmaline
Tremolite
Turquoise
Vermiculite
Willemite
Zeolite (Which one? Huh?)
Zircon (The ones in my rocks have been too small to see without a microscope.)

Minerals that should be on the list

*Calcite
Glaucophane
Rhodochrosite
*Muscovite
*Copper (native)
Gold (native)

I vote to ditch florencite, willemite, and illite in favor of three of these.

Edit: You know this is a really funny meme to be doing during the week when my intro class is talking about minerals. Especially when I've just finished writing an online assignment (well, open-book quiz, kind of) in which my students are supposed to find out which minerals from their lab are in which mineral groups.

Sometimes it's good to be the department Luddite...

I have a confession to make. I teach on a chalkboard. With chalk. You know, that white stuff that gets all over your hands and clothes (and fizzes with HCl, though I don't do that in most lectures). I'm gradually building a set of powerpoints, especially for images that I can't draw by hand (photos, maps, cross-sections...). But for the most part, I like chalk.

I like to write student responses on the board during discussion. I like building sketches little by little, explaining things as I go. I like the way chalk forces me to talk more slowly. (One of my students asked me if I grew up Out East. It wasn't my accent - I just talked too fast to be from around here.) Even when I use powerpoint, I find myself drawing on the chalkboard. (Last week I had a beautiful picture that illustrated the places where water is found, and I ended up drawing a lame-looking duplicate on the chalkboard, so I could add labels, and so that I could model Really Bad Drawing for students and show them that they, too, could draw pathetic cartoons in their notes to help them understand and remember the discussion.)

So I was mostly amused when something broke in the campus network today. No faculty could get onto the network. No e-mail, no file servers, no course management pages. Hard drives if the computer was already running. The web, if the computer was already running. But the computers in the classrooms? Nope.

I actually had a powerpoint ready for class, though I intended to spend more time having my intro students compare and contrast some samples. But when I couldn't get onto the network, I just reverted to my old Luddite ways. Chalk, ball-and-stick models of mineral structures, boxes of rocks, and group brainstorming.

I hope the systems comes back, though. I'm having my intro class create their own glossary (because the textbook doesn't have one), and I'm curious whether it has helped them read the book more carefully. (And I'm curious what they say about my new Google Earth exercise, too.)

But if it doesn't come back... well, I've got chalk.

(And someday I'm going to learn how to use a sliderule, because some of my older colleagues claim it is a great way to think about orders of magnitude.)

In search of pictures of mud

It's the end of the first week of class, and I'm looking for some good pictures of... ummm... mud. I'm introducing students to geology this week - yesterday, for instance, we talked about things that affect where people live, and about how water moves around the planet. On Friday, I want to talk about rocks. But I don't want to start by classifying them. I want to start by getting students to look at rocks as records of things that have happened in the past. I've got plenty of rocks, and I've got some good pictures of matching environments (pebbles for a conglomerate, lava for pieces of basalt). But I've got lots of pieces of shale around, too, and I would like to use them, as well.

But, well, I don't take pictures of mud.

I've looked on a couple blogs (Clastic Detritus and Hindered Settling both have great pictures and interests in sediments), but I haven't found the perfect image yet. My comparison rock, for people who know the stratigraphy of the western US, is the Mancos Shale. So I would like to find a picture of ocean mud, if possible. The gooier, the better.

Anyone got some marine mud they're willing to share?