Networks versus Trees: Ways of Analyzing the World

Manuel Lima contrasts the traditional, hierarchical, view of the world (evolution’s tree of life for example) to a more network oriented perspective.

One interesting part is the interpretation of the history of science as having three phases, dealing with Problems of:

  • Simplicity: Early scientific efforts (17th-19th centuries) was focused on “simple” models of cause and effect — embodied perhaps in Newton’s Laws, where every force has an equal and opposite force.
  • Disorganized Complexity: Think early 20th century nuclear physics — Heisenberg’s uncertainty principle for example — where the connections between events are complicated and sort of random/probabilistic.
  • Organized Complexity: Systems science sees the interrelatedness of everything: ecologic food webs; the Internet; horizontal gene transfer across the limbs of the tree of life.

RSA Animate The Dish

Butterfly on the Bench

Great Spangled Fritillary (Speyeria cybele). View of the underside of its wings (ventral view).

This little guy seemed to like hanging out on the bench near the back door. I believe it’s a Great Spangled Fritillary (Speyeria cybele).

Dorsal (top down) view of a Great Spangled Fritillary (Speyeria cybele).
Great Spangled Fritillary (Speyeria cybele).
Great Spangled Fritillary (Speyeria cybele).

Momentum

A ball rolling down a ramp hits a car which moves off uphill. Can you come up with an experiment to predict how far the car will move if the ball is released from any height? What if different masses of balls are used?

Students try to figure out the relationship between the ball's release height and how far the car moves.

For my middle school class, who’ve been dealing with linear relationships all year, they could do this easily if the distance the car moves is directly proportional to height from which the ball was released?

The question ultimately comes down to momentum, but I really didn’t know if the experiment would work out to be a nice linear relationship. If you do the math, you’ll find that release height and the maximum distance the car moves are directly proportional if the momentum transferred to the car by the ball is also directly proportional to the velocity at impact. Given that wooden ball and hard plastic car would probably have a very elastic collision I figured there would be a good chance that this would be the case and the experiment would work.

It worked did well enough. Not perfectly, but well enough.

Spittlebugs

40x magnification of the head of the spittlebug nymph.

On the wildgrass-covered slope next to school, you can see a lot of these little foamy things, that look like spit, on the stalks of the tall grasses and herbs.

Spittlebug "spit" is mostly made of a froth of the plant's sap.

One of my students collected some to look at under the microscope. We thought it might be the collection of eggs of some creature. It turned out that, at the center of the foam, was what looked like an immature insect. A quick google search for “spit bugs” turned up froghoppers, whose nymphs create the spit to protect them from the environment (heat, cold) and hide themselves from predators.

They suck the sap of the plants they’re on, and can be agricultural pests.

Spittlebug nymphs on a slide.

Tavern Rock Cave

Tavern Rock Cave.

Note to self: The Tavern Rock Cave, where Meriwether Lewis almost fell to his death, is 45 minutes from the St. Albans Lake (walking at a fair pace mind you), not “just 20”, no matter what the students claim.

It’s a little tricky to get to, and we couldn’t spend more than a few minutes there because of the longer than expected walk, but it’s a nice place to visit because of the history and beautiful geology (jointed limestone and dolomite outcrops; scree slopes at the angle of repose; Ordovician fossil imprints).

Rapelling down an overgrown scree slope.

P.S. The National Park Service has an excellent site on the Lewis and Clark Expedition that includes maps, their itinerary, and a long list of sites they visited.