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.After the national build-up over the Dover trial, I was somewhat surprised that most of the articles appearing about the fossil find did not discuss how ID’ers or creationists reacted to the news. After reading an excellent Wall Street Journal piece by Sharon Begley on the finding and the reactions, I’m even more disturbed that more journalists did not “cover the controversy”, as the ID’ers chant. Begley quotes John Morris of the Institute for Creation Research - Tiktaalik “is just a variety of fish. There is still a huge gap [between fish and land-dwellers] that has to be filled.”

Tiktaalik RoseaeOf course, I am mixing the creationists and ID’ers - something that the ID community tries awfully hard to disengage from, and maybe in this case there is a difference. With creationists openly believing that there are no transitional forms (because every species is created), Tiktaalik can only be understood as a divine intervention, and Morris’ quote is disingenuous at best - no creationist believes, or desires, that the new “gaps” be filled. I am guessing that ID’ers want the opposite. If the “gaps” are filled in, then there isn’t such a large complexity-distance between fish and land-dweller, and divine intervention does not need to be called upon to explain the extra complexification now present in the fossil record.And now back to the popular media, who pushed the Missing Link angle, but mostly ignored the reactions of the anti-evolution camps and the ramifications for future Dover situations. As in the articles that proliferated around the time of the Dover ruling, the popular Media again lost the chance to deliver an important lesson -namely what is science, and what isn’t. Tiktaalik can be understood in terms of evolution, and predictions can be made about future fossil finds from the same period and in the same geographical region. This understanding and prediction (there I go again with the magic double-edged sword of modeling in chaos, fractals, and everything else) are the hallmarks of a real theory. All that creationists and ID’ers can do is claim that there is still something left to be explained, and therefore nothing is explained.The presence of a creature as odd as a Tiktaalik not only cries for an explanation, it is itself an explanation of how we all emerged from the sea, taking our first baby steps on scrawny, ugly flippers. Creationists and ID’ers can’t deny Tiktaalik’s existence, and they sure can’t explain it either. Evolution can, and does.The popular media again missed the big link - between creationism, intelligent design, and their lack of scientific substance. In trying to explain the sui generis Tiktaalik, well, they are theories that just “aint got legs.”(Illustration of Tiktaalik by Shawn Gould, ©National Geographic Society)

Originally Posted by Matt Venanzi

CHAOS theory could help monitor the effectiveness of treatment for Parkinson’s disease and aid in earlier diagnosis, according to physicists who have developed a method to monitor how much sufferers tremor.There is still no definitive test to identify Parkinson’s disease in its onset. Now Renat Yulmetyev at Kazan State University in Russia and colleagues have adapted a statistical technique based on chaos theory, and used to study earthquake vibrations, to monitor the distinctive progression of symptoms such as tremors.Sixteen people in Canada who had Parkinson’s disease held their index fingers in the path of a laser beam for measurements of tremor frequency in their fingers and the team analysed the results. In patients in the early stages of the disease, the tremor pattern is more chaotic, says Yulmetyev. As the disease takes hold, the tremors not only become more pronounced, but they become much more periodic and regular. Medication with the drug L-dopa causes the tremor patterns to become more chaotic again (Physica A, DOI: 10.1016/j.physa.2006.01.077).

 Who painted this "Study of Clouds"?With the recent flurry of art and fractal controversies, it's time that chaos enter the mix: and what better way to do this than through weather - the dynamical system that colors pretty much everything that happens on earth, and is the real butterfly that began the modern science of chaos theory.

Since early march, there has been a very timely show at the Abington Art Center. Titled out of the blue, the exhibition …

...explores weather and climate change through the works of 22 artists in a variety of media. The exhibition focuses on the dynamics of human creativity as a metaphor for geological and atmospheric phenomena. Treating issues of weather both literally and symbolically, out of the blue approaches the creative process as a kind of weather system. Ideas, like hurricanes, seem to come "out of the blue" though they arrive through complex, interacting forces. This exhibition presents creativity as a process that generates its own weather conditions, a storm of artistic, social, political, atmospheric and geological influences.

Of course, this exhibit must address explicitly or implicitly the issues of global warming, and so curator Amy Lipton writes that the exhibit was created in the context of the tension between weather as inspiration for artists, and the "negative influence of humankind on the planet’s weather systems."<

You will find links to all of the artists and pictures of their exhibit pieces at outoftheblueproject.org.

While at the site, also check out StrangeWeather.Info , a blog started to coincide with the out of the blue project, and which is billed as "a resource hub about climate change for artists, writers and activists."

The show will close on May 6, 2006, and will then travel to another location (that is not yet listed on the web site.)

With out of the blue, and Swarm at the Fabric Museum, Philadelphia is the nexus of art/fractals/chaos and now weather. If only Chaos and Fractals had been held this semester!

(The picture at the top of this post is not from the exhibit. Knowledgeable readers will clearly recognize the Study of Clouds by John Constable - c.1822)

Originally Posted by Jeremiah Noll

Click on image to enlarge At the beginning of this course I was much more certain of things! I have learned quite a bit, but with this learning came new mysteries. Studying chaos has expanded my mind and taught me things I never would have dreamed. When you sit and think about the concept and the principles which founded chaos it just makes sense. Butterflies can start El Niño’s and the stock market is predictable to a small degree. But sensitive dependence on initial conditions is not the only principle of chaos, there is also the fact that extremely simple rules can produce infinitely complex results. Who would have thought a couple lines of computer code could produce the Serpinsky Triangle or model the population growth of a small nation. But the coolest things I have ever seen are fractals. Through this course I have developed a great understanding of the image, mapping, and product of fractal code. Simple functions and an imaginary plane can model infinity in the most accurate and beautiful way. I enjoyed fractals so much I decided to make them my semester project. The value of this course is a tremendous amount of insight into how the world works and how things thought to be random can really be very simple. I feel as if I have been shown a piece of how God put this universe together and how he made it so complex in only six days. Like deciphering the human genome code chaos makes us more able to predict, heal, and understand the way things work and why events happen.I still use fractal software today and it is still interesting and novel even though I have been exposed to it for some time. I still have my own fractals on my website so that I can, hopefully, get others interested in math and science too. My friends never thought Math could be so intriguing. Since the Fall semester I have progressed in the ability to create lifelike landscapes from fractal software.

Stanislaw Lem, the great Polish "science fiction" writer died on March 27, 2006, at the age of 85. Two of Lem’s works have played a role in the Chaos and Fractals course, and I describe the connection below. First, though, must be a tribute to this extraordinary writer. Even though I know many who read, or have read a great deal of science fiction, I know very few who have read any of Lem’s works. This is very odd, given that Lems’ works have been translated into over 40 languages, with an estimated 27 million sold. (Some do read and prosper: Will Wright, the creator of the wildly popular SimCity simultaion game credits Lem’s The Cyberiad as inspiration. ) With sci-fi readers (in the U.S., at least) not paying attention, what hope is there for more readership of this essential 20th-century author who is usually listed as I wrote above - a science -fiction writer, only without the quotes. It has always been unfortunate that Lem’s works are described as science fiction. This is itself a fiction. Lem - a brilliant scientist, writer, and thinker - told wonderful tales with an unnerving mixture of darkness, humor, philosophy, and theology that just happened to be placed deep in space, or inside a computer. While the location and time period of his stories are essential to their plots, Lem’s stories are often more relevant to our current time and place because of his ability to paint rich characters in situations that are paradoxically both imaginable and impossibly strange.

Lem’s life as a scientist and writer growing up in Poland, through Nazi occupation and Soviet rule, is much of the reason for his chosen genre, as described in the Times of London obituary -

He began to write fiction, his first works being in the tradition of socialist realism acceptable to the authorities. But he graduated to literary "fantasies", which he succeeded in hoodwinking the humourless and dogma-bound authorities into believing were innocuous, though they were in fact highly subversive and satirical.

Solaris fractalThere is one scene in Solaris that I always think of when teaching Differential Equations or Chaos and Fractals. Occasionally, streams of liquid shoot from the surface of the the liquid planet, freezing/crystallizing briefly into shapes that are impossibly complex, fragile, and mesmerizing. After many years of analysis, scientists come to believe that these shapes are the visualization of the solutions to certain non-linear equations. Even though Solaris was written in 1961, well before the Mandelbrot set and the work of Ruelle and Takens on systems of non-linear differential equations , I can’t help but imagine that the liquid structures are fractal-like, in their infinite complexity, and suggestive of the strange attractor at the heart of chaos theory. The deeper link between Lem and Chaos and Fractals is Non Serviam, one chapter from Lem’s 1971 A Perfect Vacuum. This is an extraordinary book - it is a set of fictitious book reviews of fictitious books, with each review written as an in-depth New Yorker-length essay. With wonderful recursion, the book also contains a review of itself. (Click here for a real review of this book of fictitous reviews of fictitious books.) Non Serviam is a review of a recently "published" book on personetics - the study of personoids - artificially-intelligent beings that are created via software that reside in computer memory, and who grow, mutate, and replicate in a universe that exists solely on a mathematical substrate.

Of tales of artificially produced personalities that include Frankenstein and I Robot, Non Serviam is at the far end of the continuum, the ultimate story in this genre. Lem’s brilliance allows him to imagine that, with true personoids, consciousness will be guaranteed, along with a concomitant burgeoining of philosphy and theology among them. From the researcher whose work is described in Non-serviam:

A "world" for personoid "inhabitants" can be prepared in a couple of hours… A specific personoid activity serves as a triggering mechanism, setting in motion a production process that will gradually augment and define itself; in other words, the world surrounding these beings takes on an unequivocalness only in accordance with their own behavior… From four to seven personoids are optimal, at least for the development of speech and typical exploratory activity, and also for ‘culturization’… It is possible to ‘accommodate’ up to one thousand personoids… Many different philosophies (ontologies and epistemologies) have arisen among them…

I can enlarge their world or reduce it, speed up its time or slow it down, alter the mode and means of their perception; I can liquidate them, divide them, multiply them, transform the very ontological foundation of their existence…

After writing the previous post on the Jackson Pollock Fractal Forgery Fuss, I remembered that I had come across a poem about Pollock and fractals written by Theresa Hawkes a few years ago. The poem, titled The Artist Under Glass Talks Back, is a paean to artists , who are defined by their prescient ability to know the world …They feel the timbre and tenor of their timeslong before they have facts to back up their impressions –
   light and dark shadows of an entire world’s thoughts and dreams   are automatically recorded deep inside them   not quite as distinctly   as the first photographic plate   of silver halides laughing back images   of the sun slanting over a Parisian rooftop   recorded what it saw.Jackson Pollack coughing up fractalsonto the cold floor of a barnin the middle of a centurystuck in the shallow veneer of appearance,uncovering depth-soundings of the intricacy and interwoven trajectoriesof everything above, between, beyond.To my reading, the poem is also a rejoinder to those who might believe in the power of science, and, by implication, mathematics, to produce art. So I’m intrigued by the juxtaposition of Pollock’s passion and the mathematics implied by the term “fractals.” Here Hawkes’ painful-sounding image of “coughing up fractals” neatly removes the paradox, making Pollock’s work organic, and the antithesis of a mathematical process. The poem then adds an interesting counterpoint to the fractal analysis of Pollock’s work that is so much in vogue.I think that I may be misreading the poem, or Hawke’s sentiment. After I had put a link to Hawkes’ poem on the Chaos and Fractal course site back in Fall 2003, she came across my reference and wrote me a letter describing her efforts on marrying science and the arts …“Good afternoon Dr. DiDio. I publish The Oracular Tree, an alternative ezine using serial fiction, poetry, and essays to imagine and describe our world as it might become as we transition from our agricultural and industrial past to a future based in science and the technological advances of modern western civilization. I came across your Chaos and Fractals Seminar site purely by accident…I noticed this seminar uses Ray Bradbury and a poem by me (Teresa Hawkes) to help illustrate concepts of chaos and fractals. This is tremendously heartening to me to see that artists can help illustrate scientific concepts. Many artists are deeply inspired by the work of scientists and attempt to incorporate it into their work in an accurate manner, as I’m sure you know.”

Well, I didn’t know much about artists incorporating the work of scientists (other than fractals), so now I regularly visit the Oracular Tree, where I often find some new poem, or essay with an interesting science component, often accompanied by a beautiful fractal image. A recent example is the 3/26/2006 “meditation” The Aperture Problem and the Group Mind, also by Hawkes.See the Oracular Tree for more info on Hawkes and all of the art and artists that make up the site.

"Convergence" Click to EnlargeIn a bit of fractal irony, the latest Jackson Pollock controversy concerns whether or not recent paintings that have turned up are really his, or whether they are forgeries.On one side are art experts who claim that the paintings are real. On the other side is physicist Richard Taylor, who was the first to publish definitive studies of Pollock’s works that found a fractal nature that increased during his career. (For an excellent intro. to Taylor’s findings, see J. Ouelette’s 2001 piece in Discover Magazine)Taylor suggests that the newly-discovered Pollocks may be fake because they display a different fractal character than what he has measured in works that are definitely Pollock’s. (Click here for the story.)So for all of you on the side that fractals can’t be art, here we have paintings denied authenticity because they aren’t fractal enough.But this raises a very interesting question, and contradiction. If the paintings are forgeries, were they done by a computer? If so, why didn’t they match the fractal properties of Pollock’s works as measured by Taylor (fractal dimensions in the 1.5-1.7 range)? It would seem to be a simple matter to turn the dial on the fractal-generating software, choosing the appropriate fractal dimension of the counterfeiters desired Pollock period. However, if the paintings are forgeries not done by computer, then whoever painted them was a first-rate counterfeiter.There is an even deeper issue here, one that may be the most crucial because it touches on society’s ability to bestow the label of genius. As written by Don Foster in his NYT piece of Feb 19, 2006:

At the heart of the controversy lie critical questions about artistic meaning and value that have vexed literary scholars no less than art historians. Would the exposure of a hitherto successful forgery diminish Jackson Pollock’s reputation as a unique creative genius, by demonstrating that his work is replicable?

Meanwhile, Jackson Pollock may be chuckling in his grave: if the object of Abstract Expressionist work is to embody the rebellious, the anarchic, the highly idiosyncratic- if we embrace Pollock’s work for its anti-figurative aesthetic- may faux-Pollock not be quintessential Pollock? May not a Pollock forgery that passes for authentic be the best Pollock of all?

The Fractal-Pollock fracas has inspired a large number of inspired blog posts. One interesting counter can be found on the New-Art blog of "VVoi."A more detailed, and ultimately more damning rebuttal appears on John Haber’s The Fractal Geometry of Vision: Pollock’s Patterns and Rembrandt’s Eyes . Haber expands on the debate by comparing the complex, contextual aspects of attribution in both art and literature, ultimately asserting that Foster asks the wrong questions.I can only thank all the students of Chaos and Fractals, Fall 2005 edition, for asking the right questions about the validity of fractal art.

Click for the Heisenberg CafeThe underlying structure of the Chaos and Fractals course is the understanding-prediction continuum. Starting with the Chaos Game and proceeding through all of the readings and Classroom Chaos exercises, the elusiveness of true understanding of non-linear dynamical systems and the need to "settle" for mere prediction is common and unsettling. One can only wonder, then, about the possibility of true understanding of anything more complex than linear processes. Maybe this inability to understand is a symptom of a world that is fundamentally unknowable. Now I should know better than to leave the understanding-prediction axis and question the fundamental nature of reality. Jumping into the philosopher’s sandbox is often a prescription that leads one to lose sight of the day-to-day business of actually doing science or mathematics. So let me turn to those who really could live in that sandbox, mix it up with the philosophers, and jump out again to do their science and mathematics.

The defining work of 20th Century science and mathematics may just be the development of theories that posit fundamental limits to what we can do, what we can measure, and what we can know. Einstein’s relativity rests on the postulate that the speed of light is constant in all reference frames; a result that leads to limits on the velocity of particles with mass, and destroys the notion of absolute time and simultaneity. Heisenberg’s Uncertainty Principle puts an inviolable restriction on what we can measure and therefore know about a physical system. Gödel’s Incompleteness Theorem denies us the possibility of knowing or proving all mathematical truths. Do these limits tell us something about the world, or just about our ability to understand the world? Einstein, Heisenberg, and Gödel were very clear on this question: they believed that they were discovering the true nature of the world. This point is espoused by philosopher Palle Yourgrau in his book "A World Without Time: The Forgotten Legacy of Gödel and Einstein":

Einstein, Gödel, Heisenberg: three men whose fundamental scientific results opened up new horizons, paradoxically, by setting limits to thought or reality. Together they embodied the zeitgeist, the spirit of the age. Mysteriously, each had reached an ontological conclusion about reality through the employment of an epistemic principle concerning knowledge. The dance or dialectic of knowledge and reality – of limit and limitlessness – would become a dominant theme of the 20th century.

John Barrow, mathematician/physicist from Cambridge University, has been named the winner of the 2006 Templeton Prize. The Templeton Prize is awarded "for progress toward research or discoveries about spiritual realities." The judges who award the prize favor those whose work leads to communication between scientific and religious spheres. Barrow, a prolific writer (17 books and 400+ articles) often writes about the mysteries of the universe, the nature of physical laws, and mathematical truth. From the Templeton Prize announcement:

The hallmark of his work is a deep engagement with those aspects of the structure of the universe and its laws that make life possible and which shape the views that we take of that universe when we examine it. The vast elaboration of that simple idea has lead to a huge expansion of the breadth and depth of the dialogue between science and religion. In particular, Barrow’s engagement with frontier science and mathematics, developing multidisciplinary perspectives on subjects such as the mysteries of nothingness and infinity, and the potentially intelligible realms of the laws of Nature and the limits of scientific explanation, has jarred religious and scientific perspectives in such a way as to open pathways of understanding which may allow both to comprehend each other more fully.

Barrow has been richly rewarded for his work - The Templeton Prize award is $1.4 million - more than the Nobel prize. Sir John Templeton is a mutual funds pioneer, and is described as "arguably the greatest global stock picker of the century" by Money Magazine. There is also a local angle to this story: the Templeton Prize is administered by the Templeton Foundation, based in West Conshohocken, Pa. The Foundation does much more than just the Templeton Prize, funding other awards, special projects, and lecture series around the world. (See the web site for details, including grant opportunities and application procedures.) The Foundation takes a carefully-worded stance on intelligent design, attempting to find a middle-ground that is not politically or ideologically compromised. (Click here for the statement.) I’m not sure that the statement succeeds - I believe that it is much more inviting for intelligent-design supporters because of the following claim:

Thus while it is our judgment that the general process of biological evolution is well attested by many lines of research, it is not clear to what extent the process of evolution or the study of the history of life on earth may reveal hints of broader cosmic, perhaps even divine, purpose and intention.

I recently began re-reading Sometimes a Great Notion, Ken Kesey’s monumental second novel published in 1964, and one of my favorite books. Even though I read it over 20 years ago, I still remember many of the most famous scenes. More remarkable, perhaps, is the fact that I vividly recall the haunting descriptions of the Pacific northwest so magically captured by Kesey.When I read about the chaotic aspects of turbulence, especially as described by James Gleick in Chaos: Making a New Science, I am always reminded of Great Notion’s opening passage:

Along the western slopes of the Oregon Coastal Range … come look: the hysterical crashing of tributaries as they merge into the Wakonda Auga River. … The first little washes flashing like thick rushing winds through sheep sorrel and clover, ghost fern and nettle, sheering, cutting … forming branches. Then, through bearberry and salmonberry, blueberry and blackberry, the branches crashing into creek, into streams. Finally, in the foothills, through tamarack and sugar pine, shittim bark and silver spruce – and the green and blue mosaic of Douglas fir – the actual river falls 500 feet … and look: opens out upon the fields.”

According to Kesey (who died in 2001), “I think ‘Sometimes a Great Notion’ is the best thing I’ll ever write…Writing it was much different from ‘Cuckoo’s Nest,’ which often seemed like filling in the blanks. ‘Notion,’ to my mind, is a great piece of work. People sometimes ask me why I don’t write something like that again and I reply that I simply can’t. I can’t keep all that in my head at once anymore. Why, on ‘Notion,’ I used to work 30 hours at a stretch – you’ve got to have youth to do that.“I don’t know how the book fares on re-reading, 20 years after my initial reading. Maybe one must also “have youth” to really embrace the novel’s sprawling, non-linear, 627 page narrative. I do know, however, that I will always be mesmerized by the “the hysterical crashing of tributaries as they merge into the Wakonda Auga River…”