Friday, March 27, 2009
Wednesday, March 25, 2009
Monday, March 23, 2009
A friend who must have seen my previous posts about fractals in food forwarded a link to the Evil Mad Scientist Laboratories website and this article about fractal cookies.
The cookies illustrate a fractal known as the Sierpinski carpet. Notice the self-similar structure consisting of a dark chocolate square within a surrounding field of white.
The process used to generate these fractal cookies involves stretching long blocks of dough, then stacking eight stretched pieces around a central original piece.
The process is repeated as many times as you like. The pictures shown here take the dough through three iterations. If continued indefinitely, this mixing scheme would disperse the chocolate evenly throughout the lighter dough -- a good result for us chocolate lovers.
My original post about fractal food involved broccoli. Now we have cookies. I wonder how many other fractal foods there are?
Friday, March 20, 2009
The program did not include a topic that was on all our minds: financial market dynamics.
This topic was on our minds, of course, because it was on everyone's minds that day. Earlier in the week investment firms had begun to fail, the stock market had been plunging and governments around the world were scrambling to determine what, if anything, they could do to stop what appeared to be a global financial catastrophe. We all wondered if our bank accounts would be empty by the time we got back to our home countries -- if we got back.
As we sat in the lecture hall, prepared to listen to discussions of epidemiology, traffic planning and climate change, speaker after speaker approached the podium, said a few words about their assigned topic, then switched to -- you guessed it -- financial market dynamics.
The speakers were in remarkable agreement: what we were observing in the global financial system had all the hallmarks of a phase transition, a sudden, discontinuous change that cannot be stopped once it is started. And the speakers all said the same thing: none of the interventions being discussed by governments and politicians was likely to have any affect whatsoever on the collapsing economy.
The phase transition that these speakers had diagnosed is like an avalanche. Before an avalanche begins, the snow field is stable. Then, one snowflake too many is placed on the side of the hill and the slightest perturbation -- a sharp noise, perhaps -- can cause the entire hillside to collapse and rumble to the valley floor.
Nothing we do after the avalanche has started will stop it.
Two days earlier, an OpEd by physicist and science writer Mark Buchanan had appeared in the New York Times saying what all those speakers also said that day at our conference: the financial markets appeared to be acting like a complex system, characterized by feedback loops that create instability.
Buchanan discussed some simulations of model, or virtual, economies using these complex systems ideas: "The instability doesn’t grow in the market gradually, but arrives suddenly. Beyond a certain threshold the virtual market abruptly loses its stability in a “phase transition” akin to the way ice abruptly melts into liquid water. Beyond this point, collective financial meltdown becomes effectively certain."
Shankar Vedantam wrote recently in the Washington Post about research using a complex systems approach which identifies a particular trigger for the financial avalanche which followed those early signs of collapse last October.
I do not know if the trigger identified by these researchers is actually the one that led to financial collapse, but this is one of the few mentions of this important topic I have seen in the press since Buchanan's early editorial. If you know of others, I would be interested to learn about them.
To read more about these ideas, you might wish to consult the Oxford Press book by Neil F. Johnson, Paul Jefferies and Pak Ming Hui entitled "Financial Market Complexity: What Physics Can Tell us About Market Behavior."
Wednesday, March 18, 2009
Monday, March 16, 2009
A lot has been written about the evolution of life, but just what is it that causes life to emerge from inert matter? What drives atoms and molecules together into the complex forms we know as DNA, proteins, cells, tissues, and organs? How do atoms and molecules arrange themselves into entire organisms that live and move and even think?
Scientists call these “big questions” or "grand challenges," but, so far, we do not have a satisfactory answer to any of them. We do, though, have a name for the process by which this miraculous thing happens: we call it Emergence.
What could be a bigger question than how life emerges from molecules? Well, how about this one: Where did the molecules come from?
Physicists have recently determined that the sum total of all the atoms and molecules in all the planets, stars and galaxies accounts for only 4% of all the “stuff” of which the universe is made. About 22% of the rest is something called Dark Matter while the remaining 74% is Dark Energy, neither of which is well understood.
Astrophysicists say that, at some point in our universe’s history, ordinary matter emerged from dark matter and energy in a process somewhat like cooling a pool of water to 32 degrees. The "ice" that forms is the ordinary matter solidifying from this watery, mysterious dark “stuff.” The newly solid ordinary matter goes on to collect into stars and galaxies and planets—and eventually us.
To me, this is miraculous. Both the fact that it happened and the mechanism by which it happened are awe-inspiring. How could a thinking person not be awe-struck by the complex and intricate process that happened in just such a way that you can now sit here and read this essay with eyes and brains made of molecules that used to be dark matter?
The late Alan Watts, a mystic, one-time Episcopal priest and prolific author (among other things), described the planet Earth as “peopling” in the same way that an apple tree apples. He imagined visitors from outer space, out touring the neighborhood and looking for signs of intelligent life, but bypassing the early earth with not so much as a glance, saying, “It’s just a bunch of rocks.”
Several million years later when they come around again, they stop, pointing and say, “We thought this planet was just a bunch of rocks—but, look! It’s peopling. It must be intelligent after all.” [Alan Watts, “The Book On the Taboo Against Knowing Who You Are,” Random House, 1966]
So where is God in this? Is God the explanation for all the gaps in the scientific creation story? (Just what is that dark matter, anyway?) Intelligent Design advocates would have us believe that life is irreducibly complex, and that this proves the existence of God, but science is making progress toward understanding what complexity is all about and where it comes from.
A “God of the gaps” who enters our faith only when science has not progressed far enough to answer all the questions will ultimately disappoint us, since the gaps will eventually be filled.
I confess that I once was very bothered by the seeming gap between science and religion, but I have come to see the two approaches to “asking the big questions” as equally valid, and to understand my own self as one whole, integrated human being who can marvel at the miraculousness of life in all its minute detail and simultaneously praise the One who made all this possible.
In my view, God cannot be separated from life. Divinity infuses every part of life: God is in our bodies and minds, in our cells—even in our molecules! I believe the universe is alive and we have been blessed with brains that allow us to know this.
I leave you with a quote from Rumi [“Teachings of Rumi,” Andrew Harvey, Ed., Shambhala Press, 1999], a great poet who seemed, every day, to catch a glimpse of the majesty of God and think to write it down:
“How can I — or anyone else — ever cease being astounded
That He whom nothing can contain is contained in the heart?”
Saturday, March 14, 2009
So, I am going back to the original look, but will try to use larger fonts for my posts so that things will be a bit easier on your eyes.
Back to science tomorrow with a new blog topic I haven't yet touched on: emergence.
Friday, March 13, 2009
This week, with the lifting of the ban on federally-funded stem-cell research, we have seen much in the news about the proper relationship between science and faith. It is an ongoing debate that comes to the fore often and is generally portrayed in the media as a black-and-white issue: either you believe in God or you believe in Science.
Meanwhile, many of us believe in both.
I have been writing in this blog about how scientific investigations of complex systems have helped me in my personal life, indeed in my spiritual life, particularly at times of great turmoil and transition. I believe that Science can provide a window to the divine.
Science, after all, is a set of tools for learning about and understanding the universe, all of creation. Science extends our eyes and ears and other senses so that we can observe this glorious universe at length scales and time scales that were not available to ancient peoples.
And it is glorious. I, for one, feel a sense of reverence for creation when I see photos beamed back to us from the Hubble telescope. Far from making me feel small and insignificant, these photos remind me how wondrous this universe is that I am privileged to be a part of.
This is why my blog sidebar displays one of these Hubble photographs, a famous one showing the birth of stars in a nebula. I have added my own title, "The Creation," because that is precisely what this photo shows.
Just think about that: we are privileged, in our time in history, to be witness to the creation of stars. I can think of nothing more awe-inspiring than that.
Some eagle-eyed blog readers noticed earlier this week that my blogger profile changed slightly to include the fact that, in addition to being a writer and scientist, I am the Abbess of the Urban Abbey. While this change in profile was more due to me finally figuring out how to combine two different blogger accounts (!) than it was due to a desire to hide this fact from anybody, I admit I didn't go out of my way to advertise it.
And the reason is simple: many people assume that a scientist who is also a Christian is a Creationist, believes in Intelligent Design, and is out to subvert the practice of science.
This is simply not true - for me, or for the many PhD-level scientists I am privileged to know through my church. I am a member of the Episcopal Church, which our Abbey is associated with. Our leader, Presiding Bishop Katharine Jefferts Schori, is a scientist. She is also, of course, a priest and bishop.
Shortly after her selection and installation as Presiding Bishop, Rev. Jefferts Schori sat for an interview with Time magazine that, while short, is a forceful statement about the proper relationship between science and religion.
A blogger friend, Anne Minard, in a thoughtful post in early February, posted a link to a teaching document of the Episcopal Church on the proper understanding of creation and evolution. As this document makes clear, we do not believe the Bible is a "divinely-inspired scientific textbook." These are the words of physicist and Anglican priest John Polkinghorne who has written widely about the relationship between science and faith.
I commend this document to you for its thoughtful handling of the subject of evolution. I need to be clear: it is totally possible to believe in God and accept our current scientific understanding of the creation and evolution of the universe and life on earth as long as we don't insist on a literal interpretation of scripture. Those who insist on a literal reading of scripture end up with tortured and convoluted explanations that conflict with known scientific facts.
This drives people from the Church. While it might not drive people away from God, it communicates the message that religious leaders are non-thinking, anti-science crusaders who are more interested in being right than in caring for the earth and its people.
I am personally more interesed in exploring questions that affect our personal lives, than continuing a tedious argument about evolution. A lot has been written on this topic and while I am grateful to my colleagues for their thorough treatment of the controversy, I don't believe that people seeking to know how God might be working in their lives are served by a continuous rehashing of the topic.
So, that is why you will not see much more from me on the evolution-creationism controversy. I am much more interested in people and how people sense the divine in their lives. And, on that topic, Science has much to offer you.
Wednesday, March 11, 2009
Monday, March 9, 2009
This change came about as the result of a workshop I took this past weekend on "Blogging Tips and Tricks," offered through the Writer's Center in Bethesda, Maryland. The Writer's Center is a wonderful organization that not only offers excellent workshops on topics of concern to writers but also provides a place in the Washington, DC area where writers can meet. If you are a writer living in the DC area, I highly recommend that you check the Center out.
One thing I've learned from my not-quite 3 months of blogging experience is that you have to pace yourself when it comes to making changes to your blog. So, while I am still absorbing and slowly trying out the long list of "tips and tricks" I learned in this workshop, one tip was very easy to implement:
- Never - never! - use white text on a black background
So, here you are: a new clean lay-out with black text on a white background, including:
- Text set off with bullet points
- Lots of white space (notice how many paragraph breaks I'm using?)
Later this week: more on complex systems science and how we can apply insights from this fascinating field to our lives.
Friday, March 6, 2009
In these not-quite three months I have gotten to know many interesting people, first through Twitter, then through visitors to this blog and, recently, via FaceBook. Many of you I don't even know by name, but only through your online handles - and, yet, I feel a strong connection to you. One of the first things I noticed when I began interacting with this online community, was a warmness I did not expect or predict. And, perhaps in response, a gradual letting down of the walls between the two halves of myself has occurred. I have felt my bifurcated life merging, the two sides of my persona melding back together.
And today I woke up to the realization that I am becoming whole again.
I'm not exactly sure when the wall started to come down, but I know why it did. It was because of you, the readers of this blog. You have been an enthusiastic, encouraging bunch, providing feedback and showing interest in my ideas. Because of your interest I have been emboldened to share my, at times, half-baked thoughts on topics that I am, nevertheless, passionately interested in: topics from science like attractors and fractals and self-organization - but also topics about faith, the origin of life and the nature of God. And to share these in the same forum, not hiding one part of my life away from the other.
Your acceptance of me and my ideas has allowed me to accept all the parts of my own self. This is a very interesting outcome, and one I never would have predicted that day back in December when I signed up for Twitter.
So, thank you for this incredible gift! And thank you, also, for reading my blog and providing feedback. I look forward to more interesting discussions with all of you.
Wednesday, March 4, 2009
Monday, March 2, 2009
The word bifurcation is taken from the field of science now known variously as nonlinear science, complexity theory or, most recently, the science of emergence. “Chaos theory” is a part of this science and is probably the most widely popularized aspect of the field; phrases such as “sensitivity to initial conditions” and “the butterfly effect” have entered our vocabulary thanks to books such as James Gleick’s "Chaos: The Making of a New Science," and the “chaostician” character in the movie Jurassic Park. The popularizations of chaos theory seem to me, however, to have missed the most intriguing lessons that can be drawn from the science of chaos, focusing excessively on the unpredictability of chaos and our lack of control over the behavior of a chaotic system. Although all of this is true, of chaos and our lives, it is not necessarily a bad thing that we cannot predict the future and have no control over it. The “doomsday” interpretation of the butterfly effect seems to have distracted us from the positive lessons that can be drawn from this new science–and, hence, completely missed some of the more interesting of these lessons: that chaos is stabilized by an attractor and that significant growth in nature almost always occurs through the sudden, dramatic changes that accompany a bifurcation of that attractor.
A bifurcation is, literally, a “fork in the road” and was initially coined to describe the pitchfork-like shape of a particular graph that signaled its existence in laboratory experiments. The literal meaning of the word is, though, actually appropriate: when a bifurcation occurs, we have reached a point in our journey through life (either our individual life or our life as a group, such as a family, business or even nation) at which a decision must be made: Do we go right or do we turn left?
More often than not, I suspect, we don’t even see the need for a decision. We are often so caught up in the events of the bifurcation, often traumatic ones, that, as we approach the fork in the road, we close our eyes to the fact that the path we are traveling is ending. We are forced to make a choice about which new path to take, but we march right on through, out into the tall grass and weeds, oblivious to the fact that our life must now follow a new course.
Before we know it, our insistence on keeping things the way they were, sticking to the original path (which no longer exists), has left us far from any path at all, unable to find our way back to either the old life, the original path, or to locate our new life—one of the forks in the road we refused to take.
In fact, if we ever were able to find our way back to where the original path used to be, we would see that the old path we were once traveling no longer exists. This can be very confusing, especially if something as unsettling and disturbing as an illness or death has occurred. Now what do we do? What path do we follow?
We can sit at the bifurcation point, forever in confusion, not knowing how to move forward or get unstuck, as long as we refuse to bifurcate and choose one of the new paths opening out in front of us—if we even have a choice in the matter! It is much more likely that life will move us forward through the fork in the road and decisions will be made for us, by others or by life itself. It is our choice whether we allow this to happen -- or whether we fight it, wasting valuable energy which will be needed for the journey yet to come.
Transformational change can be both painful and exhilarating and it can happen to organizations and individuals alike. The characteristics of transformational change are the same whether it is an individual or a family, church, business – even a nation – that is undergoing it. Sometimes precipitated by an unexpected, and typically traumatic, event (but equally as often the result of natural growth), the individual or group undergoing this type of transformation suddenly know that the life they once led, individually or collectively, is now over. Their whole world has changed and the things they say to themselves and others reflect this certain knowledge: something fundamental about their former life, individual or collective, has undergone a transformation and things will never, ever be the same again.
Growth by bifurcation, or transformational change, sometimes occurs in response to a crisis or an unforeseen shattering event such as a serious illness or the death of a close friend or family member. More often, though, I suspect it occurs just because we reach a certain age: 13 or 18—or even 40. Like metamorphosis, bifurcation is wrenching and far-reaching, and not at all pleasant while it is going on. However, the end result of all this disorienting growth is quite literally a new life. The old life, the one that had existed before the bifurcation, is gone, replaced by a new form. What had driven us before is no longer relevant; the former driving force has been replaced by a new purpose. In the language of the science of emergence, the attractor that governed existence prior to the bifurcation has ceased to exist; the old attractor has died and been replaced by a new one.
In my own case, that initial twinge of shoulder pain was the sign of a much deeper, spiritual pain, a hunger for something I could not identify. The attractor that had organized and ordered my life before this happened -- the pursuit of a scientific career, a striving for knowledge, the accumulation of accomplishments -- fell away and was gradually replaced by a new attractor I did not recognize at first. Eventually, I came to understand that what I was hungry for was, quite simply, God.
When have you experienced bifurcation in your life? How did the driving force or organizing principle for your life change when this occurred? How is your life different, now that a new attractor has taken hold?