Excellent video from the EarthScope project, showing the seismic waves from the August 23rd earthquake zipping across the United States. Note that the height of the wave was only 20 micrometers (20 millionths of a meter or 0.02 mm) as it passed through the midwest.
One question that might occur is, why are there so many seismic stations in the middle of the continent? My guess is that it has to do with monitoring of the New Madrid fault zone, which produced
More details about the earthquake can be found on its IRIS page.
While it’s nice to have the math concepts arranged nicely based on their presentation in the textbook. Since my plan is to give just a few overview lessons and let students discover the details I’ll be presenting things a little differently based on my own conceptual organization. So I’ve created a second graphic map, which looks a bit disorganized, but gives links things by concept, at least in the way I see it.
Concept map for an introduction to pre-Algebra based on the first chapter of the textbook, Pre-Algebra an Accelerated Course, by Dolciani et al., (1996).
This morning I presented just the first branch, about equations, expressions and variables. The general discussion covered enough to give the students a good overview of the introduction to Algebra. Tomorrow the pre-Algebra and Algebra topics will start to diverge, but I think today went pretty well.
We’ll see how it goes as we fill in the rest of the map.
Link to live video feed from the ROV ROPOS surveying a cable on the ocean floor at the Juan de Fuca midocean ridge.
Live science. The remotly operated submersible ROV ROPOS is surveying an undersea cable recently laid across the the Juan de Fuca midocean ridge.
This scientific expedition will be going on until the end of August, and there’ll be live feeds every time the rover is deployed (which depends a bit on the weather at the surface).
If you have questions, they’re also answering your tweets.
Right now, the rover’s heading toward the caldera of the axial seamount volcano. It should get there some time tonight (if they don’t have to stop for anything). So far, we’ve seen dumbo octopuses, crabs, weird fish, brainless worms, sponges, deep sea corals, starfish and lots of pillow basalt. The basalts are unsurprising because these are the rocks produced when volcanos erupt under water.
I was trying to figure out how I could create a graphic organizer/mindmap to outline my math class that my students could access online. Even better would be if they could also edit the map online. That way I could set up the outline of my lesson notes and they could fill in definitions for vocabulary words. Mind42 (pronounced mind for two) allows just that. It’s free to use and allows you to link to or embed your mindmaps (e.g. pre-Algebra/Algebra) into other websites:
It’s almost perfect, all it needs is for you to be able to save the state of the map, with certain branches collapsed for example, or with a set zoom level. Right now the best way to explore the above map is to collapse all the nodes (use the second button on the lower left) and gradually expand them out as you go through.
I do think the style of the nodes and lines on the maps are elegant and make it easy to read. It’s also really easy to create the maps.
Apart from putting your maps to other websites, you can also print them out as pdf’s or images (png), or you can save the map itself in a format that other mindmapping software, like Freemind, can use.
I really like this website, and as soon as they add the ability to save zoom levels and collapsed nodes I’m going to try using it for my classes.
Puberty starts somewhere in the age range of 8 to 13 years for girls and 9 to 14 years for boys. However, in Norway, in 1850, girls hit puberty at around seventeen. Over the next 100 years that age decreased to thirteen and a half, where it has stabilized, but a similar trend has been seen in pretty much all the industrialized countries, including the U.S.. No one knows quite why, but there are a number of theories, including:
Better nutrition,
increased stress, and
artificial chemicals in the environment or in the diet.
The trend in the timing of puberty in girls (menarche) for four western countries, from 1850 to 1950. Figure via NIH via INSERM.
It seems clear that this trend has something to do with improving living conditions. Rapidly developing countries like China are experiencing the same trend in earlier puberty right now. Wealthier areas in developing countries have girls starting puberty at the same age as girls in “privileged” countries, while their compatriots in the poorer areas do not. Also, Overweight kids tend to start puberty earlier.
However, explaining the earlier puberty is difficult because no one knows for sure what exactly triggers puberty to begin with. The genetic switch that tells the hypothalamus to start the process probably involves multiple genes that are affected in complicated ways by how and where a person grows up (when the environment affects how genes are expressed it’s called epigenetics; NOVA has a nice little program that explains how epigenetics results in differences in identical twins.).
Increased stress might be another explanation. Girls in Bosnia and Croatia started having puberty later and later during the war in the 1990’s. However, it appears that other types of stress, such as from insecure relationships with parents and adoption, can do the opposite and trigger even earlier puberty (note: really early puberty in kids as young as 9 is called precocious puberty and is a growing problem).
Certain artificial chemicals that disrupt the endocrine system, which is responsible for hormone production, have also come under suspicion, but their effects have been hard to prove.
Whatever the reason, the earlier onset of puberty has lead to an increase in the length of adolescence (which tends to start with puberty and ends somewhere in the mid-twenties). It’s hard to say though, if all the extra time is beneficial, since it does give the developing brain extra time to adjust to a more complex society, or if it just makes for a longer period of trying times.
Here’s a wonderfully serious piece in the magazine Foreign Policy on what the wizarding world should do to recover and reconcile now that Voldemort has finally been vanquished.
… if history teaches us anything (consider the bitter legacy still lingering from the 17th-century Goblin Wars or the recent experience of American Muggles in Iraq and Afghanistan), it is that the defeat of Voldemort by Harry Potter may have been the easy part. Indeed, one might even say it was child’s play. The hard work of postwar stabilization still lies ahead.
It’s a bit long, but it’s worth reading at least through the first section on, “Transitional Justice and Reconciliation”.
This section points out that, sure, Voldemort’s henchmen need to be prosecuted before the law (and not just detained without charge), but it will be a lot more difficult to deal with the thousands who supported Voldemort in greater or lesser ways. After all, some of these only did what they did under threat. The article recommends a Truth and Reconciliation Commission like in South Africa.
Among their other recommendations are:
the breaking the monopoly of the Daily Prophet on the news media,
a Comprehensive Curse Ban Treaty,
more transparency at the Ministry of Magic,
a Charter on the Rights of Witches and Wizards,
“that the Wizengamot, the high council of Magical Great Britain, be split into separate legislative and judicial bodies,”
and closing Azkaban immediately.
You’ll notice that a number of these recommendations focus on expanding the rights of the individual and build in more checks and balances into government and the media. These, and the overall emphasis on building mechanisms to prevent future conflict, align well with the ideas of peace education. It might also be an interesting focus for a class discussion/Socratic dialogue.
I’d be curious to hear from any Harry Potter fans who might come across this post and have the time to read the article (even though school’s restarted and the homework’s being piled on).
Energy cannot be either created or destroyed, just changed from one form to another. That is one of the fundamental insights into the way the universe works. In physics it’s referred to as the Law of Conservation of Energy, and is the basic starting point for solving a lot of physical problems. One great example is calculating the average temperature of the Earth, based on the balance between the amount of energy it receives from the Sun, versus the amount of energy it radiates into space.
The Temperature of Radiation
Anything with a temperature that’s not at absolute zero is giving off energy. You right now are radiating heat. Since temperature is a way of measuring the amount of energy in an object (it’s part of its internal energy), when you give off heat energy it lowers your body temperature. The equation that links the amount of radiation to the temperature is called the Stefan-Boltzman Law:
where:
ER = energy radiated (W/m-2)
T = temperature (in Kelvin)
s = constant (5.67 x 10-8 W m-2 K-4)
Now if we know the surface area of the Earth (and assume the entire area is radiating energy), we can calculate how much energy is given off if we know the average global temperature (the radius of the Earth = 6371 km ). But the temperature is what we’re trying to find, so instead we’re going to have to figure out the amount of energy the Earth radiates. And for this, fortunately, we have the conservation of energy law.
Energy Balance for the Earth
Simply put, the amount of energy the Earth radiates has to be equal to the amount of energy gets from the Sun. If the Earth got more energy than it radiated the temperature would go up, if it got less the temperature would go down. Seen from space, the average temperature of the Earth from year to year stays about the same; global warming is actually a different issue.
So the energy radiated (ER) must be equal to the energy absorbed (EA) by the Earth.
Now we just have to figure out the amount of solar energy that’s absorbed.
Incoming Solar Radiation
The Sun delivers 1367 Watts of energy for every square meter it hits directly on the Earth (1367 W/m-2). Not all of it is absorbed though, but since the energy in solar radiation can’t just disappear, we can account for it simply:
Some if the light energy just bounces off back into space. On average, the Earth reflects about 30% of the light. The term for the fraction reflected is albedo.
What’s not reflected is absorbed.
So now, if we know how many square meters of sunlight hit the Earth, we can calculate the total energy absorbed by the Earth.
The solar energy absorbed (incoming minus reflected) equals the outgoing radiation.
With this information, some algebra, a little geometry (area of a circle and surface area of a sphere) and the ability to convert units (km to m and celcius to kelvin), a student in high-school physics should be able to calculate the Earth’s average temperature. Students who grow up in non-metric societies might want to convert their final answer into Fahrenheit so they and their peers can get a better feel for the numbers.
What they should find is that their result is much lower than that actual average surface temperature of the globe of 15 deg. Celcius. That’s because of how the atmosphere traps heat near the surface because of the greenhouse effect. However, if you look at the average global temperature at the top of the atmosphere, it should be very close to your result.
They also should be able to point out a lot of the flaws in the model above, but these all (hopefully) come from the assumptions we make to simplify the problem to make it tractable. Simplifications are what scientists do. This energy balance model is very basic, but it’s the place to start. In fact, these basic principles are at the core of energy balance models of the Earth’s climate system (Budyko, 1969 is an early example). The evolution of today’s more complex models come from the systematic refinement of each of our simplifications.
Advanced Work
If students do all the algebra for this project first, and then plug in the numbers they should end up with an equation relating temperature to a number of things. This is essentially a model of the temperature of the Earth and what scientists would do with a model like this is change the parameters a bit to see what would happen in different scenarios.
Feedback
Global climate change might result in less snow in the polar latitudes, which would decrease the albedo of the earth by a few percent. How would that change the average global temperature?
Alternatively, there could be more snow due to increased evaporation from the oceans, which would mean an increase in albedo …
This would be a good chance to talk about systems and feedback since these two scenarios would result in different types of feedback, one positive and one negative (I’m not saying which is which).
Technology / Programming
Setting up an Excel spreadsheet with all the numbers in it would give practice with Excel, make it easier for the student to see the result of small changes, and even to graph changes. They could try varying albedo or the solar constant by 1% through 5% to see if changes are linear or not (though they should be able to tell this from the equation).
A small program could be written to simulate time. This is a steady-state model, but you could assume a certain percent change per year and see how that unfolds. This would probably be easier as an Excel spreadsheet, but the programming would be useful practice.
Of course this could also be the jumping off point for a lot of research into climate change, but that would be a much bigger project.
References
Yochanan Kushnir has a page/lecture that treats this type of zero-dimesional, energy balance model in a little more detail.
I thought I’d fixed the commenting system, but apparently not. It should be working now. Special thanks to Deb for letting me know, and testing it out.
