Monday, August 24, 2009

Moai Model and Base Shape

This is a see-through version of the moai that I've been working on. It is derived from a photosynth of a face-up fallen moai that is located along the south coast moai road (east of Charlie Love's excavation for those in the know). The redlines show the location of the center of mass.


I'm now wondering whether the shape of the base has something to do the location of the center of mass and the general process of moving. Thinking about how tipping the statue to one side would make having a round front edge advantageous since the statue could effectively and smoothly "roll" along the front back and forth, minimizing friction, "rubbing" on the bottom, and making it easier to transfer the pendulum motion from one side to the other. Take a soda can, for example, and tilt it forward to a point before it tips over. If you rock the top of the can back and forth, the can will "roll" along its front edge and the shape of the travel will be along the shape of the curve of the bottom. Note that the front is the important part if the statues moves in that direction. Also note that the shape of the curve dictates how much of the statue makes contact with the ground at any point in time. The sharper the curve, the less surface area makes contact. The "flatter" the curve the greater the surface area.

Consider this photo of the base of a moai from just outside of Rano Raraku. Matt and Deb are in the photo for scale positioned 5 meters from each other (as measured by the tape). It is a big statue. Here the shape of the base is circular towards the front one-half and more rectangular towards the back. The front curve is consistent with the "rolling" idea in the walking - small surface area during the rotation. The less curved sides also make sense since the greater length in contact with the ground means less pressure/surface area. This would avoid deadly pressure flakes that show up on "road moai" due to the gravity and the reflected force of the tilted statue on the welded tuff.


Humanities and Education: Dehumanized

Dehumanized: When math and science ruled the school

Mark Slouka's recent article (September 2009) in Harper's Magazine makes some interesting observations about the nature of teaching in the humanities that that are thought provoking, useful and interesting. Slouka points out the clear value of humanities -- but also makes the point that not ALL humanities teaching is necessarily of value. Assessment clearly has a strong role here (i.e., are students more capable of thinking critical after they take a class or get a degree or not - or are they just "older"). He makes an excellent point that the importance of humanities is that they ARE value-laden and thus politically volatile. The point is that we need to be able to conceive of these values and understand their relation in terms of the world we want to live in. Instead, we get toothless introspection. His quote here is a good one about the restless futile inward debate that comprises much of the "social sciences": "Politically neuter, we now sing the politics of ocularcentric rhetroic. Safe in our tenured nests, we risk neither harm nor good." Ultimately, I think Slouka downplays the integrative role of mathandscience (as he puts it) and humanities (where it's not the former telling the latter what's what, but humanties using tolls from mathandscience to asses the degree to which we can get to our value-laden goals). But it's the fodder for some interesting thinking.

Saturday, August 22, 2009

Moai models II - Fallen statues walk again...

I've been working to build a model of a "transport" moai. These moai are found fallen on the roads that lead from Rano Raraku to areas across the island. Maps of these roads can be found at our via the downloadable KML files (and Google Earth). These statues are ones that have "failed" in transport -- for whatever reason, they toppled over and were not re-raised (largely impossible on big ones and any that could not be "excavated" back onto the landscape). Modeling a fallen moai is a key task since the ones that reached the ahu were often modified at that point to trim the bases and make them more upright (rather than tilted forward).

The hard part about doing this is that the statues are, by definition, fallen and thus are not easily photographed in 3 dimensions (unlike the upright ones). If a statue has fallen on its back, you get reasonable information about its front (and vice versa). I did my best with a statue that fallen on its back. You can view the photosynth of this moai here:

To generate the new model, I created a point cloud out of the photosynthed photos. I then used VRMesh - a trial version of a commercial software package -- to build a mesh object. It took a lot of tweaking to turn this into a watertight object given the noisy pointcloud and the lack of a backside for the moai. Then using AutoDesk 3ds Max (a 30-day evaluation copy), I turned the mesh into an object in a physical object. This is the result (below). The palm tree is in there just for goofs - it is not a jubea palm so not even remotely appropriate for Rapa Nui, but you only get a couple of choices...).


Now I've got to figure out how to make the moai "move" in a physical realistic way. That is going to take learning a lot more about Autodesk 3ds Max - which is insanely complicated and probably vast overkill for what I'm trying to do (but, for 30days at least, it's free to try).

Using Autodesk 3ds Max, however, I can calculate the center of mass, though. This tells me, as I expected, that center of mass is forward, towards the leading edge of the bottom. The center of gravity is not, as I was thinking, low. In fact, the center is precisely in the middle of the moai. Why is this?

I think the answer is because that is where you would want it to be if you were going to "walk" the moai across the landscape in the inverted pendulum model. If you put the center of mass low, you would have a stable object, but rocking the object would take a great deal more energy since you'd have to move the top quite a bit before the low center of mass moved at all (imagine what would happen if it was a cone and the COM was basically even to the ground). Putting it higher allows the minimum amount of investment in tilting the object to get it to move. But if you put it too high, it would be really unstable and more likely to fall over. So the best solution, is to put it right in the middle.

Of course, this placement makes no sense at all if you moved the statue while it was horizontal and on a bunch of logs (as many might claim). In fact you'd probably want to have the center of mass closer to base to making standing it up easier. That way, you would have to invest the minimum amount of effort getting it tilted up before it "rights itself." Another clue to moai transport.

Thursday, August 20, 2009

Moai Models

One of my goals this summer was produce volumetric models for moai in order to determine center of mass and other physical parameters. Although $100K provides one the funds to purchase a 3D laser scanner, my approach was to do this using nothing more than a camera and photosynth. Using 100s of photos,, a point cloud extractor and some mesh editing software, this turned out to be laborious but possible. As a first step, I started with this photosynth of a statue that stands on a small ahu just a little ways from Tongariki.  

You will need to install a VRML plugin on your machine (see: or (much preferred - MeshLab for which there is a mac, linux and windows version). But when you do, check out: or (and install MeshLab from

I went from this (note that all the photos in the synth were taken in portrait mode and photosynth was unable to reconcile that fact with the landscape).


to this:


Tuesday, August 18, 2009

Zombies, Math and Modeling

Given the imminent threat of a zombie outbreak, it is good to know that some mathematicians/epidemiologists are taking zombies seriously. In Munz et al (2009) "WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION" recently published in an edited volume (Infectious Disease Modelling Research Progress) [and yes, the last author's last name really has a question mark at the end. see: ). According to their model, only quick aggressive attacks have a chance of staving off the end of the world. The abstract describes it all:

Zombies are a popular figure in pop culture/entertainment and they are usually

portrayed as being brought about through an outbreak or epidemic. Consequently,

we model a zombie attack, using biological assumptions based on popular zombie

movies. We introduce a basic model for zombie infection, determine equilibria and

their stability, and illustrate the outcome with numerical solutions. We then refine the

model to introduce a latent period of zombification, whereby humans are infected, but

not infectious, before becoming undead. We then modify the model to include the

effects of possible quarantine or a cure. Finally, we examine the impact of regular,

impulsive reductions in the number of zombies and derive conditions under which

eradication can occur. We show that only quick, aggressive attacks can stave off the

doomsday scenario: the collapse of society as zombies overtake us all.

This graph says it all: