Cephalapod Fractals

Complex SutureSteve LaMonte, a student in my Fall 2007 version of Chaos and Fractals, has noted the fractal-like shapes that are formed by suture lines in ancient cephalopods. He points out the correlation between fractal structure and the ability of the cephalopod to withstand extremes of water pressure. He writes:

One often pictures fractals as consisting of pretty pictures generated by computer programs, but they are quite prevalent in nature. A notable example can be found in the fossils of ancient cephalopods, specifically nautiloids and ammonoids. Nautoloids and ammonoids are the ancient ancestors of modern squids, octopi, and the nautilus. The ancient organisms looked like modern squids and octopi with shells, some elongated and some coiled like a snail. These shells had internal chambers that the organism filled with gas for buoyancy. Each chamber is separated by a wall, or septa. The contact line between the septa and the inner shell wall is called a suture line. The structure of the suture line determines how well the organism can resist water pressure and adjust its buoyancy. The evolution of suture lines follows an increasingly fractal-like pattern from straight sutures to highly undulated sutures. In complex sutures, the dips and folds in the undulations are called lobes and saddles, respectively.

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Where the Hell Are They? Now pass the pasta...

Klaatu barada niktoOne of the great lines in all of 20th century science was uttered over lunch by Enrico Fermi. In a discussion of the possible likelihood of many advanced civilizations in our galaxy, Fermi said something to the effect of "well, where the hell are they."

I may have taken some liberty in the way Fermi expressed himself, but there's no doubt that Fermi's questions is one of the more provocative off-the-cuff statements ever made because of the response that it generated, including immortalization as a named dilemma: The Fermi Paradox

In 1961, approximate 10 years after Fermi's lunch-time query, Frank Drake developed an equation that he used to predict the number of advanced civilizations in our galaxy. Upon reading about the Drake Equation many years ago, I was struck by its simplicity and its audacity. Here it is in its full glory.  (Read all about the parameters here ) 

N = R* f_p n_e f_l f_i f_c L

The equation consists of a chain of probabilities, all multiplied together in the fashion of the probability of a string of independent events. Depending on the values of the individual probabilities, estimates of the average number of advanced civilizations/galaxy range from several thousand to less than one.

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DNA in Series and Parallel

quattro-colored dna pastaModeling biological systems sure seems to be radically different from modelling something such as a chain of balls on springs. For balls on springs, Newton's 2nd law is written for each mass, yielding a pretty straightforward system of differential equations. The positions and velocities of the masses in time are the solutions to the system. Each variable x(t) in any of the differential equations refers directly to the actual position of a specific mass. For bio models, however, modeling is done more at a meta-level using a systems approach. For example, you wouldn't normally see Newton II applied in pharmokinetic modeling; instead a compartment model where the compartments are body systems such as blood stream, gut, etc. is typically used, often with great predictive power.

What about population modeling, and especially modelling of interacting species? Is this closer to balls on springs, or a compartment model? The differential equations that are typically used to predict the behavior of these populations employ mathematical expressions of the interactions chosen to produce a desired population behavior. Predator-Prey, mutual competition, and cooperation models are really the same with just minor changes to the terms in a differential equation system. I then think of this type of modeling more like compartments - the interaction terms are plugged into the differential equations in a manner analogous to building models with compartments.

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Intelligent String Theory Design - Patently Falsifiable

String Theory by Marlene Healey Prediction plays a crucial role in the continuing debate of whether string theory and intelligent design are linked by a common lack of falsifiability. Here's how this argument goes:

1) ID does not make predictions that are testable, and therefore not falsifiable, failing Popper's main criteria for categorization of a theory as scientific.

2) String Theory has not produced a prediction that is testable because it requires that there exist objects that are simply not observable - e.g extra dimensions. Therefore it is also not a scientific theory, making it analagous to ID (in a falsifiability sense).

It follow then that if you dismiss ID, you have to dismiss string theory. (See, e.g. W. Dembski's Uncommon Dissent blog)

But do you? An interesting argument against this conclusion is provided by Amanda Gefter's editorial in the Philly Inquirer titled A Scientific Leap Without the Faith. Gefter points out the distinct difference between string theory and ID as one of explanatory power combined with the internal elegance of the mathematics. In fact, it is the presence of mathematics that provides the oomph that catapults string theory over ID:

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Constructal Theory of Everything?

A very interesting text that describes what appears to be a bold new approach to modeling many possible systems - even human ones - is about to be released. Titled Constructal Theory of Social Dynamics and  edited by Adrian Bejan and Gilbert W. Merkx, the text "brings together for the first time social scientists and engineers to develop a predictive theory of social organization, as a conglomerate of mating flows that morph in time to flow more easily (people, goods, money, energy, information). These flows have objectives (e.g., minimization of effort, travel time, cost), and the objectives clash with global constraints (space, time, resources). The result is organization (flow architecture) derived from one principle of configuration evolution in time (the constructal law): "for a flow system to persist in time, its configuration must morph such that it provides easier access to its streams."

Begin and Merkx are from Duke. The Duke press release  is very enticing - this is certainly a text that will serve as a reference for the chaos and fractals course, or perhaps a primary source.

Some tantalizing tidbits:

Why does a railway network look like a river? Why do the streets of old Rome look like a leaf? Because whether their shape is determined by the interactions of molecules or the choices made by individual humans, all of these systems of flow are governed by a relatively simple new principle of thermodynamics.

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Cosmic Legos

Escher Legos. Click to enlarge.In his book God's Universe, Harvard astronomer Owen Gingerich attempts to reconcile intelligent-design and evolution. This seems to be an almost impossible task, so I was curious as to how Gingerich would approach this division.

Unfortunately, the reviews and descriptions I have read leave me bewildered because Gingerich's argument seem to be of an anticipated form, namely that God created the laws and then let everything develop on their own.

Gingerich does riff on the idea that the physical constants and various energy levels of appropriate atoms are so fine-tuned as to allow life - (shades of the anthropic principle!) that there is some "higher purpose." So what then is different in his argument from intelligent-design? God created the building blocks and the physical laws and just stood back and watched. This is not so different from the views of many scientists, so I'm not sure where Gingerich is headed that adds anything to the debate. Unfortunately, in the quotes I have read, he does seem to rely on an unsubstantiated claim of an underlying imperative for the existence of our universe, and, by extension, all of us:

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Cross-Species DNA and Accelerated Evolution

Protein molecular evolution. From M. Deem.A recent article in the May 2007 APS News describes the use of a physics model to understand accelerations in evolution that occurred between the appearance of 1-celled organisms 3.5 billion years ago, multi-celled organisms 1 billion years ago, and everything other organism that has since appeared on earth in only the last billion years.

The modeling is by Michael Deem of Rice U. His model allows for  "cross-species genetic exchange" - in effect DNA from one species is adopted by another which then realizes an evolutionary advantage. Successful DNA adoption is called HGT - Horizontal Gene Transfer. Deem's approach is based on field-theoretic techniques. The net result: species can evolve much quicker because they contain fully-functioning "genetic modules" from another species. The implications for our own genome are startling, and it may be that a "significant portion of our DNA was donated by viruses and bacteria that infected our ancestors" over millennia.

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The Evolution of the 40 - 40 Club

This just in from the Nov. 28, 2006 Onion -  Kansas Outlaws Practice Of Evolution:

TOPEKA, KS - Any living being that undergoes genetic modification favoring survival could face jail time under the new law.

A really clever piece on our favorite state, I enjoyed reading it today probably a whole lot more than if I had seen it yesterday - a day of unfortunate and fortunate events.

I was at Penn State attending a meeting of the Scientific Benchmark subcommittee of the PA Governor's Commission on College and Career Success.  The subcommittee's charge includes proposing revisions to the current PA state teaching standards.  This was my first meeting, and I was amazed to meet such an energetic and dedicated group of secondary and higher-ed faculty working on this important project.  Everyone in the room has one overarching goal - to ensure that ALL students learn essential mathematics and science concepts  and skills - necessary for success in today's, and especially tomorrow's world.

This was the fortunate event.

The unfortunate events were my reading two disturbing articles earlier in the day.  In one, I read a report of the August survey done by Jon Miller of Michigan State University. The results of the poll suggest that only 40% of the U.S. believe in evolution (BTW, the only country with a smaller percentage is Turkey, while countries such as Sweden and Denmark have an 80% belief rate)  Miller's study attributes this disturbing dichotomy as a perfect-storm effect of religion, politics, and LACK of GENERAL SCIENTIFIC KNOWLEDGE of core biological ideas.  (Check out the National Geographic report on the poll.) 

The other article was even more depressing:  The Chronicle of Higher Ed reported that in a survey by the American Council on Education, 46% of those polled said that colleges and universities should not require students to take more courses in math and science, while 46 percent said students should be required to do so. This deep division is evidence that all of the messages and news about American students falling farther and farther behind in terms of essential skills for the 21st Century are not being heard.  (Click here to read the original study - "Math and Science Education and United States Competitiveness: Does the Public Care?")

Where is the Math/Science PR?  With the constant stream of news stories about American students falling further and further behind the rest of the world's students, it seems to be everywhere, but no one (or at least 40% aren't listening.

Luckily for me, but really luckily for our students and our country, the fortunate event outweighed the unfortunate events.  The effort to make science standards the best they can be as a preparation for our students' future success will also produce a perfect PR machine, as students who are successful realize that it was the mathematics and science that formed the foundation of their success.   And the students who follow them will generate the demand that will lead to more math and science at all education levels.

Then we won't be in the 40-40 club anymore, which will be quite an evolution!

Fish with Feet: Media's Missing Links

Shawn Gould, ©National Geographic SocietyIt was just a month ago that the world's media outlets fell over themselves proclaiming the fossil findings of a half-fish - half vertebrate as the Missing Link -the Smoking Gun of fossil evidence that finally starts to fill in those notorious "gaps" in the fossil evidence so gleefully pounced on by creationists and intelligent designists.

For the most part, the scientific community is far more reticent about the Missing Link claim for the Tiktaalik - the name given to the species whose fossils were discovered on Ellesmere Island - preferring the more sobering "transitional" (See Newfound Fossil Is Transitional between Fish and Landlubbers at Scientific American News.)

How could the media resist - Tiktaalik is already a star, with a wikipedia page, and its own web site at the University of Chicago?

While the Tiktaalik find does provide a tantalizing clue on how and when the fish/tetrapod transition occurred, it is always true that plugging a gap introduces two more gaps between the existing fossils and the "Missing Link." Is it a shock then that creationists and ID'ers aren't impressed? Doubling the gaps will always work to their advantage.

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Chaos & Complexity in the Evolution vs. Intelligent Design Debate

The 12/20/2005 ruling by Judge John E. Jones 3d in the Kitzmiller vs. Dover Area School District case may be a landmark one. In his far-reaching decision, Jones rules that:

The overwhelming evidence at the trial established that ID is a religious view, a mere re-labeling of creationism, and not a scientific theory.

More to the point about whether ID is really science:

... we find that, while ID arguments may be true, a proposition on which the court takes no position, ID is not science. We find that ID fails on three different levels, any one of which is sufficient to preclude a determination that ID is science. They are: (1) ID violates the centuries-old ground rules of science by invoking and permitting supernatural causation; (2) the argument of irreducible complexity, central to ID, employs the same flawed and illogical contrived dualism that doomed creation science in the 1980's; and (3) ID's negative attacks on evolution have been refuted by the scientific community

(Click here for the complete judicial ruling)

While Jones' ruling is a wonderful relief (which may only be temporary) from the problem of religion driving what can be taught, regardless of facts, I have been disappointed by the lack of explanations in the mainstream media about the contributions of chaos and complexity theory to our current understanding of evolution.

As Judge Jones clearly understood, the ID fight against evolution was based on a "contrived dualism" - i.e. one either believes in evolution, or believes that a Supreme Being

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