The Gateway to Educational Materials

A Cantor Set on an Egyptian column. Click to enlarge.An excellent resource for any teaching, but especially K-12, can be found at the Gateway, a site run by the U.S. Department of Education and Syracuse University.  The site is  the project of  a consortium whose member institutions join what is known as GEM, the Gateway to Educational Materials.

The Gateway is an essential site, both for educators, and for anyone interested in anyone learning any topic on-line.

You will use the Gateway primarily for its very sophisticated search engine, specifically designed to search for  educational materials.  When you search for a particular topic, e.g. "fractals", you will get a nice listing of hits that describe not only online educational fractal resources, but also a categorization scheme linked to the appropriate educational setting.  This is implemented on-screen by a category list that appears in a right-hand pane following a search.  Similar to clusty, the categories allow you to instantly narrow your search into one of the categories.  The categorization is an incredibly helpful way of finding the right resource for you class.  For example, back to the fractal search:  categories include areas such as curriculum support, lesson plans, and individual categories for grades 1 through 12.

The real benefit of the categorization scheme, however,  are the categories that you probably aren't aware exist - these are the ones that allow the cross-connections across all disciplines to become evident.  One of the categories that appear when searching for "fractals" is Cultural Perspectives on Mathematics.  A click here yields 5 hits, one of which is  African fractals: modern computing and indigenous design, an article on a fractal geometric view of the " self-organized location of huts in Tanzania, art design among the Mangbetu in central Africa, and Mali windscreens."

So plan to spend plenty of time on the Gateway - learning, teaching, and marveling at the sophistication and power of a search engines designed specifically for the educational community.

Information Science Blogging

I've read the articles of Joyce Kasman Valenza for years in the Philadelphia Inquirer, where she is a columnist in the tech.life@inquirer section, but I've just now come across her blog, and her library page for Springfield Township High School.

Joyce  is pursuing a Ph.D. in the Interdisciplinary Doctoral Program at UNT’s School of Library and Information Science.  Her blog,  Joyce Valenza's Neverending Search, is an incredible resource or all things info-and ecucational-technology-related.  She is also an EduBlog 2005 winner. 

A nice feature of her site is a blogroll that consists of many dozens of information-science blogs.

So look into Joyce's work, and sites - they are invaluable for any type of information literacy course.  You will also e able to find many posts on the efficacy of blogging and wikiing in the classroom.

Stem Cells as Lightning Rods

French lightning-rod experiment based on Franklin's ideas. Click to enlarge.The lightning rod is considered to be one of Benjamin Franklin's greatest inventions, combining basic scientific discovery, understanding, modeling, prediction and intuition in producing a truly life-saving device.  Certainly it is one of his most useful, and essential.  To produce such a device meant learning about the nature of lightning, which first had to be shown to be a manifestation of electricity - itself a poorly understood phenomenon in the 18th Century.  Franklin's work is part scientist, part engineer, and wholly practical - a homeowner trying to protect his house and family from the vicissitudes of electrical storms.

Some excellent sources on lightning rods and Franklin can be found in The Jan 2006 issue of Physics today (by E. Philip Krider) and at Answers.com. 

Interestingly, lightning rods were the subject of intense religious debate at that time.  In a manner not unlike the religious right's campaigning against -take your pick -genetic engineering, cloning, stem cells, etc. - research,  lightning rods were viewed as "presumptuous" because they interfered with the will of God.  Franklin had anticipated this reaction, but even his preface to the 1753 editi0n of Poor Richard's Almanac  describing the discovery of rods as a gift from God did not stem the cry.  Here's Franklin:

It has pleased God in his Goodness to Mankind, at length to discover to them the Means of securing their Habitations and other Buildings from Mischief by Thunder and Lightning.

Consider the argument against lightning rods, and what it implies about a Creator.  It is certainly a vengeful God who would not want us to protect ourselves if we could.  Given that churches  were often the sites of extreme lightning activity due to their soaring steeples and metallic bells, maybe it was natural for priests and clergy to occasionally wish that their place of worship,  rather than being a sanctuary of safety,  was instead a stage for manifestations of God's wrath. Note the paradox on the flip side of the picture, however -  God is powerful enough to cause lightning to punish earthly sinners, yet is so powerless that he couldn't come up with another method if lightning were not available?

See Franklin's Unholy Lightning Rod for more details on religious efforts to thwart the lightning rod, and the ultimate victory of Franklin's method and device.

It is natural for opponents of new, cutting-edge science to resort to scare tactics, and gloomy prognostications of the calamitous effect of unleashing unseen forces.  But conjuring up a God who will do even worse - by asserting that God will bring on Armageddon because of scientific attempts to understand nature and use it for our own well-being brings us all back to the 18th Century and before.

Without a rod, and without a reason to do all that we can to improve our health and safety.

There must be strongly enforced safeguards in all research that involves the human condition - not outright bans in the name of a vengeful creator.  As we have seen,  this stance only leads to paradoxical results about the powers, or lack thereof, of such a creator.

Heisenberg and The Conscious Object

From "Seven Attempts at Liquifying the Self" by N. Schultz in his Experiment in Private Self-Consciousness Heisenberg's Uncertainty Principle is rightly seen as the first 20th Century result that puts an absolute limit on what can be measured, and, by implication, known about the world.  The principle states that complementary variables such as the position and momentum  of a particle  cannot be simultaneously discerned to any arbitrary degree of precision.  The principle is often illustrated with a standard thought experiment:  in trying to observe smaller and smaller objects, the wavelength of the light used to "illuminate" the object must use a smaller and smaller wavelength, i.e. photons with larger and larger energy.  This large energy then gives the particle to be sighted some momentum change that makes it impossible to determine the particle's momentum.  This explanation, referred to as the Gamma-Ray Microscope thought-experiment,  is widely used at many educational levels. See the Discovery Education site for Grades 9-12, for example.   A more interesting use of the  illumination example can be found at the Fly in the Honey blog ,  posted by Mary (that's all the info I can determine about the author other than I believe that she is a teacher), where she claims to be very poor in math and science, yet is incredibly moved by the standard conclusion of the Uncertainty Principle: "the very act of observation changes the object being observed." 

The Gamma-Ray Microscope thought-experiment, a mythological story that began with Heisenberg himself, has been de-valued as a good example of the principle. It turns out that the world is much weirder than that pictured in the thought-experiment. (I will explain this in a future post.) Regardless, it does not diminish from the fundamental idea that observation affects the observed in fundamental ways that cannot be eliminated with more precise and careful instrumentation and methodology.

On one hand this is a very deep concept;  on the other it appears to be tautological, especially when both the experimenter and experimental subject are conscious agents.

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Science by Blogging

Particle Physics Tracks in a Bubble Chamber. Click to enlarge.Blogs are normally thought of as more personal diary/opinion vehicles, but  I have believed in the potential for blogs as an exciting teaching tool ever since my small success with blogging in the Fall 2005 Chaos and Fractals course. 

This potential is taken to the nth degree in a very informative article by  Sean Carroll in APS News (May 2006).   There Carroll describes his own view of blogging as "a great opportunity for physicists to exchange ideas more readily with each other, and to let the rest of the world share the thrill of the process by which science truly progresses." 

Carroll, is a a member of the Cosmic Variance group blog whose physicist/astrophysicist contributors write about "science, art, politics, culture, technology, academia"  (the similarity to FractaLog is not intentional - but I am heartened to see all of these scientists out there willing to place their science in the context of life itself.)

Read Carroll's article for ideas of how blogging helps him, and how it might help you - in teaching, research, and, everything else.

Carroll describes a number of interesting blogs.  I list them here as a resource.

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The Spam Artist

Spam Plants - Click to enlargeOne of the most innovative and creative artists working today is Alex Dragulescu, a Romanian "visual" artist who heads  the Experimental Game Lab at the Center for Research in Computing and the Arts at University of California, San Diego. 

His images are absolutely fascinating.  Some of them are beautiful and organic-looking, while others appear to be views of some alien architecture.

But it's not the images that are interesting so much as the process.  Dragulescu uses spam to generate some of his images.  He does this by using words in spam mailings to trigger different structures to be digitally rendered.  The image at the top of this post comes from his Spam Plants series.

Dragulescu definitely pushes the art/mathematics interface to an extreme, with the random detritus of life thrown in for good measure.   He describes his projects as "experiments and explorations of algorithms, computational models, simulations and information visualizations that involve data derived from databases, spam emails, blogs and video game assets."

It's impossible to describe Dragulescu's work without seeing the images, so check his website for much more. 

Be sure to investigate some of the other work being created at the Experimental Game Lab , where "somewhere between media art, scientific visualization and computer gaming a new territory of expression is emerging." Sheldon Brown's Scaleable City project is one such project.

It is hard to imagine how amazing it must be to teach or go to school at a university like UCSD, where anything short of the absolute limits of creativity is viewed as abject failure.

Prediction, Fiction, and Science Policy: The Jurassic Park Syndrome

Michael Crichton needs to visit an ER for an arrogancectomy...

It's amazing to me how global warming is now accepted as fact, when not too long ago it was still being described as possibly a climate condition that appears, and has appeared, from time to time in the course of the lifespan of the earth.  There now seems to be an article every week in the major press about the latest discoveries confirming a warming trend that does not appear to be part of some grand cycle through earth's history.  This has led several countries and continents  to proclaim global warming to be the BIGGEST threat to humanity in the not-so-long term, enacting legislation and controls that will stem the tide of further warming.  

The U.S. is not one of them, of course.  Hopefully, this sad state of affairs will begin to change with the  new makeup of Congress.   If so, it will be those who aren't fans of Michael Crichton that may make the difference.

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The Most Expensive Fractal in the World

No. 5, 1948 (click to enlarge)The basic free market model of supply and demand is pushed to the limit in the case of the price of art pieces. Just how much will someone pay when the supply is only one, i.e. when the piece is one of a kind?  Especially when the artist was truly one of a kind?

Last week the Jackson Pollock painting No. 5, 1948  was sold at auction for $140 Million, the most money ever paid for an American painting. (Click here for story) 

This stunning number is now going to color the debate on the validity of the Pollock paintings discovered earlier this year and claimed to be possible frauds because they were not fractal enough.  (See my previous post on this controversy.)  Given that computer software can regularly produce fractals with the same fractal dimension as any of Pollock's paintings, determining if a painting is an original Pollock or a computer-generated image should be a concern for anyone with $140 Million to burn.

This  situation suggests that a lucrative, niche career-op exists for anyone who can discern the difference - a fractaconsulter.

The Economic Modeling of Religion

I usually view economic modeling as a more asymmetric activity than, modeling in physics. In physics, models are used to both understand why something happened or happens, and predict what will happen in future circumstances - the twin pieces of understanding and prediction. This is probably a biased view on my part, or a woeful lack of knowledge of the predictive power of economic modeling, but it seems to me that most economic models I read about are more useful in explaining the past. Any extrapolation of the model into the future basically depends on assuming similar conditions. Physics models are often tested by finding out what they predict for future situations under different conditions. (I am not including econometric modeling here, which I consider to be a qualitatively different activity - it is modeling that is more empirical in the sense that data crunching is used to establish the coefficients of the model equations.)

Again, my opinion may be totally nearsighted. If it is, let me know.

I write this because of a recent book titled The Marketplace of Christianity by R.  Ekelund, Jr., R. Hebert, and R. Tollision, which was described in a recent issue of the Chronicle of Higher Ed. (Nov. 3, 2006, page A13) In the book the authors use economic analysis to describe such things as the number of different Christian churches through the centuries and the different acceptance rates of the Protestant Reformation.

Some of the models, at least as reported by the Chronicle, seem very far-fetched - a huge, Procrustean stretch, if you will.

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Art and Science Transvergence: Glowing Bunnies

Updated on Monday, February 12, 2007 by R.A. DiDio

Albo, the GFP Bunny

On first glance, the intersection of art and technology should have a much more complicated boundary than the intersection of art and mathematics, or even art and science. Mathematics and the sciences are relative newcomers in terms of their effect on the arts; available technologies have been used to produce art forever. Here I am using a broad definition of technology as formulated by Edward Tenner, author of Our Own Devices - The Past and Future of Body Technology. For Teller, technology is the "human modification of the natural world" - a definition that encourages us to view fundamental objects such as the shoe, chair, and eyeglasses as transformative technologies.

By extension, then, the technologies of the paintbrush, paints, and perspective -invented to create visual art- are inextricably mixed with art. There really is no boundary.

Until very recently, I didn't believe that the same statement could be made about science and art. What got me thinking was coming across some very provocative art/technology essays in a fascinating journal of art and technology called SWITCH...

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