And Women Inherit the Internet

Women are the routers and amplifiers of the social web. And they are the rocket fuel of ecommerce.

–Aileen Lee (2011): Why Women Rule The Internet on TechCrunch.com.

Last month I observed that the girls in my class were blogging a lot more than the boys. It’s still true, and now there’s an informative, if somewhat hyperbolic, article by Aileen Lee that asserts that the blooming of social media websites is driven, primarily, by women.

I’m always a bit leery about articles like this one. There are lots of statistics, a few anecdotes, and a brief reference back to some scientific research (Dunbar numbers), but the overly excited language coming from a venture capitalist is enough to remind me of the irrational exuberance of the dot-com bubble.

The writing is so over-the-top, that I’m truly surprised that there isn’t a single exclamation point in the entire article! Although, based on Ms. Lee’s first words in the comments section, this might be due to the herculean efforts of a good editor.

My antipathy might also be due to my irrational, visceral distaste of the language of business and commerce, which is so geared toward breaking people into faceless demographic groups to be marketed to that it verges on being dehumanizing. I suspect my feelings are truly irrational because I’ve seen scientists do similar parsing of demographic statistics and have had no trouble; although, perhaps, I may have been a little more empathic because the scientists were looking at issues of vulnerability to disease, infant mortality, and the like.

However, since the article’s anecdotes correlate with my own anecdotes, I find it hard to disagree with the underlying premise: women are more inclined than men to make and nurture social connections so they are a key demographic in understanding the future of the internet.

It’s also a reminder that the social atomization typified by the dominance of the nuclear family at the expense of extended family, is now being ameliorated by social networking, which suggests some interesting social and cultural changes in a, possibly, more matrifocal future.

(hat tip The Daily Dish).

Trail of Tears State Park in Missouri

trail-of-tears-outlook-panorama_b — View over the Mississippi River from the scenic outlook in the Trail of Tears State Park. The outlook juts out over rocky bluffs, which allows you to see the flood plain across the river.

Driving through Missouri last week, I stopped at the Trail of Tears State Park, which may be an excellent place to study the post-colonial history of Native Americans (perhaps as part of our civil rights discussions), and observed the Mississippi River and its flood plain before it becomes engorged at its confluence with the Ohio River.

In 1830, President Andrew Jackson passed the Indian Removal Act, which called for the removal of American Indians living east of the Mississippi River to relocate west of the Mississippi River. …

While some of the Cherokees left on their own, more than 16,000 were forced out against their will. In winter 1838-39, an endless procession of wagons, horsemen and people on foot traveled 800 miles west to Indian Territory. Others traveled by boat along river routes. Most of the Cherokee detachments made their way through Cape Girardeau County, home of Trail of Tears State Park. While there, the Indians endured brutal conditions; they dealt with rain, snow, freezing cold, hunger and disease. Floating ice stopped the attempted Mississippi River crossing, so the detachments had to set up camps on both sides of the river. It is estimated that over 4,000 Cherokees lost their lives on the march, nearly a fifth of the population.

–Missouri Department of Natural Resources: Remembering an American Tragedy

The small museum at the main park building does a very good job of trying to dispassionately tell the tragic story.

View Trail of Tears State Park, MO in a larger map

trail-of-tears-nature-walk — Taking a break on the Nature Walk behind the park's museum.

There’s a short, 1 km nature walk behind the building that was nice on a beautiful, sunny day in early spring. Warm, with the trees just barely beginning to bud you can get a feel for the ridge-and-valley topography of the park, which is in stark contrast to the flat floodplain of the Mississippi on the other side of the river. The park’s roads weave up and down the ridges, and I wished I’d had my bike with me.

riverside-campground-barge — Barge going downstream on the Mississippi River, past the river-side campground.

This early in the year (mid-March) most of the campgrounds in the interior of the park seem to be closed, but there is one down on a beach of the Mississippi River that was empty but open. This one has electrical hookups which is not a bad thing if you have the place all to yourself.

The scenic outlook is a wooden platform that juts out through the trees so you can see across the Mississippi to the flat floodplain and farmland beyond. Sitting on a cliff of sedimentary rock (it looked like limestone from a distance), the outlook is high enough that you can just make out the shapes of old meander bends and ox-bow lakes.

It’s a small park, probably worth a visit for the museum, and the outlook is nice, but probably not somewhere you’ll want to spend the night unless some of the upland campgrounds are open.

The museum’s focus on the relocation of the Cherokee would be a nice followup to the pre-Columbian focus of the Chucalissa Museum in Memphis.

cape_giradeau-river-wall — Cape Girardeau River Wall.

If you’re looking at river processes, you’ll probably also want to stop in Cape Giradeau, which boasts a fromidable wall to protect the downtown from the Mississippi River’s spring floods.

Panyee F.C.: Soccer on the Lake

This cute, little, true story of how a bunch of kids (they look like adolescents) living on rafts in a lake built their own soccer field (on rafts), and eventually created the Panyee Football Club, is actually an advertisement for the Thai Military Bank (TMB), but it’s quite inspirational nonetheless. The setting and videography are also superb.

Editing and Reviewing

Even if seven editors and seven reviewers, marked it up for half a year, I doubt they’d be able to completely clean up the mess I post to this blog every day (and they’d be full of bitter tears). However, in case they were willing to try, I thought it would be useful to be clear about what I mean by editing and reviewing.

Editing is catching all the grammatical errors, loose spelling, punctuation and so on that the author is liable to miss. Usually it is because he or she is reading what they thought they wrote, not what they actually typed. It might also involve checking citations to make sure they are right. In this case, it does not involve extensive fact checking, though at a real newspaper it would. Partly that’s because facts can be so malleable, but mostly it’s because I believe that making sure the facts are right are the responsibility of the author.

Reviewing is a lot harder, largely because, since it primarily deals with style, it is extremely subjective. I will admit that an awful lot of people are likely to consider my writing boring and atrocious, but I will often disagree. Good review is a process of negotiation. The reviewer tells the author what they like, and why, and what they don’t like, and why. Then, instead of yelling, the author carefully considers the comments and adjusts their piece accordingly. The reviewer then looks it over again and gives the same type of feedback as before. Ultimately, what’s published remains the responsibility of the author; they make the final choice about which comments to accommodate and which to ignore, but good reviewers are invaluable if used well.

So, if you see a tag at the bottom of a post saying “Reviewed by So and So”, or “Edited by So and So”, or even, “Reviewed and edited by So and So”, please spare them a moment’s thought because they’re not an easy or trivial jobs. This is especially true for a blog where the author sets themself the task of posting something every day, and finds it hard to stop writing once they’ve started. Even when they know they should. Like now.

Peat Pellets

We just planted seeds using peat pellets. The students are always impressed by just how much they expand when you add water, so one student decided to record it on video. Since they recently acquired a new iPhone app that reverses the video, they posted the video played backwards.

Tsunami Geometry: Calculating the Height of a Tsunami using Basic Geometry

Since we’re working on geometry this cycle, I thought it would be an interesting exercise to think about how we could use geometry to think about how the strength of tsunamis decreases with distance from the source.

Of course, we’ll have to do this using some intense simplification so we can actually apply the tools we have available. The first is to approximate the tsunami as a circular wall of water centered on the epicenter of the earthquake.

tsunami-geometry — Simplified tsunami geometry.

This lets us figure out the volume of the wave pretty easily because we know that the volume of a cylinder is:

(1) $! V_c = \pi r^2 h$

The size of the circular water wall we approximate from the reports from Japan. The maximum height of the wave at landfall was somewhere in the range of 14 m along the northern Japanese coast, which was about 80 km from the epicenter. Just as a wild guess, I’m assuming that the “effective” width of the wave is 1 km.

Typically, in deep water, a tsunami can have a wavelength greater than 500 km (Nelson, 2010; note that our width is half the wavelength), but a wave height of only 1 m (USSRTF). When they reach the shallow water the wave height increases. The Japanese tsunami’s maximum height was reportedly about 14 m.

At any rate, we can figure out the volume of our wall of water by calculating the volume of a cylinder with the middle cut out of it. The radius of our inner cylinder is 80 km, and the radius of the outer cylinder is 80 km plus the width of the wave, which we say here is 1 km.

Calculating the volume of the wave

However, for the sake of algebra, we’ll call the radius of the inner cylinder, r_i and the width of the wave as w. Therefore the inner cylinder has a volume of:

(2) $! V_i = \pi r_i^2 h$

So the radius of the outer cylinder is the radius of the inner cylinder plus the width of the wave:

(3) $! r_o = r_i + w$

which means that the volume of the outer cylinder is:

(4) $! V_o = \pi (r_i + w)^2 h$

So now we can figure out the volume of the wave, which is the volume of the outer cylinder minus the volume of the inner cylinder:

(5) $! V_w = V_o - V_i$

(6) $! V_w = \pi (r_i + w)^2 h - \pi r_i^2 h$

Now to simplify, let’s expand the first term on the right side of the equation:

(7) $! V_w = \pi (r_i ^2 + 2 r_i w + w^2) h - \pi r_i^2 h$

Now let’s collect terms:

(8) $! V_w = \pi h \left( (r_i ^2 + 2 r_i w + w^2) - r_i^2 \right)$

Take away the inner parentheses:

(9) $! V_w = \pi h (r_i ^2 + 2 r_i w + w^2 - r_i^2)$

and subtract similar terms to get the equation:

(10) $! V_w = \pi h ( 2 r_i w + w^2 )$

Volume of the wave

Now we can just plug in our estimates of width and height to get the volume of water in the wave. We’re going to assume, later on, that the volume of water does not change as the wave propagates across the ocean.

(11) $! V_w = \pi (14) ( 2 r_i (1000) + (1000)^2 )$

rearrange so the coefficients are in front of the variables:

(12) $! V_w = 14 \pi ( 2000 r_i + 1000000 )$

So, at 80 km, the volume of water in our wave is:

(13) $! V_w = 14 \pi ( 2000 (80000) + 1000000 )$

(14) $! V_w = 7081149841 m^3$

Height of the Tsunami

Okay, now we want to know what the height of the tsunami will be at any distance from the epicenter of the earthquake. We’re assuming that the volume of water in the wave remains the same, and that the width of the wave also remains the same. The radius and circumference will certainly change, however.

We take equation (10) and rearrange it to solve for h by first dividing by rearranging all the terms on the right hand side so h is at the end of the equation (this is mostly for clarity):

(15) $! V_w = \pi ( 2 r_i w + w^2 ) h$

Now we can divide by all the other terms on the right hand side to isolate h:

(16) $! \frac{V_w}{\pi ( 2 r_i w + w^2 )} = \frac{\pi ( 2 r_i w + w^2 ) h}{\pi ( 2 r_i w + w^2 )}$

so:

(17) $! \frac{V_w}{\pi ( 2 r_i w + w^2 )} = h$

which when reversed looks like:

(18) $! h = \frac{V_w}{\pi ( 2 r_i w + w^2 )}$

This is our most general equation. We can use it for any width, or radius of wave that we want, which is great. Anyone else who wants to calculate wave heights for other situations would probably start with this equation (and equation (15)).

Double checking our algebra

So we can now figure out the height of the wave at any radius from the epicenter of the earthquake. To double check our algebra, however, let’s plug in the volume we calculated, and the numbers we started off with, and see if we get the same height (14 m).

First, we’ll use all our initial approximations so we get an equation with only two variables: height (h) and radial distance (r_i). Remember our initial conditions:

w = 1000 m
r_i = 80,000 m
h_i = 14 m

we used these numbers in equation (10) to calculate the volume of water in the wave:

V_w = 7081149841 m³

Now using these same numbers in equation (18) we get:

(19) $! h = \frac{7081149841}{\pi ( 2 (r_i) (1000) + (1000)^2 )}$

which simplifies to:

(20) $! h = \frac{7081149841}{ 2000 r_i \pi + 1000000 \pi }$

So, to double-check we try the radius of 80 km (80,000 m) and we get:

h = 14 m

Aha! it works.

Across the Pacific

Now, what about Hawaii? Well it’s about 6000 km away from the earthquake, so taking that as our radius (in meters of course), in equation (20) we get:

(21) $! h = \frac{7,081,149,841}{ 2,000 (6,000,000) \pi + 1,000,000 \pi }$

which is:

h = 0.19 m

This is just 19 cm!

All the way across the Pacific, Lima, Peru, is approximately 9,000 km away, which, using equation (20) gives:

h = 0.13 m

So now I’m curious about just how fast the 14 meters drops off to less than 20 cm. So I bring up Excel and put together a spreadsheet of tsunami height at different distances. Plot on a graph we get:

So the height of the tsunami drops off relatively fast. Within 1000 km of the earthquake the height has dropped by 90%.

How good is this model

This is all very nice, a cute little exercise in algebra, but is it useful? Does it come anywhere close to reality? We can check by comparing it to actual measurements; the same ones used by NOAA to compare to their model (see here).

tsunami-model-data-honolulu — The red line is the tsunami's water height predicted by the NOAA computer models for Honolulu, Hawaii, while the black line is the actual water height, measured at a tidal gauge. Other comparisons can be found here.

680_20110311-TsunamiWaveHeight — Tsunami wave heights in the Pacific, as modeled by NOAA. Notice how the force of the tsunami is focused across the center of the Pacific.

The graph shows a maximum height of about 60 cm, which is about three times larger than our model. NOAA’s estimate is within 20% of the actual maximum heights, but they’ve spent a bit more time on this problem, so they should be a little better than us. You can find all the gruesome details on NOAA’s Center for Tsunami Research site’s Tsunami Forecasting page.

Notes

1. The maximum height of a tsunami depends on how much up-and-down motion was caused by the earthquake. ScienceDaily reports on a 2007 article that tried to figure out if you could predict the size of a tsunami based on the type of earthquake that caused it.

2. Using buoys in the area, NOAA was able to detect and warn about the Japanese earthquake in about 9 minutes. How do they know where to place the buoys? Plate tectonics.

buoys-warning — The locations of the buoys in NOAA's tsunami warning system.

Update

The equations starting with (7) did not have the 2 on the r_iw term. That has been corrected. Note that the numerical calculations were correct so they have not changed. – Thanks to Spencer and Claude for helping me catch that.