Wednesday, January 30, 2013
Researchers from the University of Cambridge took a big step forward this year in understanding how our brains work. It seems that the brain has a fractal organization. This likely gives us much of what we consider human. And at a deeper level these findings may help to connect us in a very fundamental way to the rest of the natural world. The research team of Kitzbichler, Smith, Christensen, and Bullmore published their results in an article called "Broadband Criticality of Human Brain Network Synchronization," which is available on-line for free. I've had the article for about six months and had been meaning to post something on it. So at the outset I'd like to thank "Neel" for getting me going to actually re-read the article and post something with an interesting question he posed about neurological complexity and intelligence to the Chaotic Life blog at Psychology Today last month. I'd also like to thank my friend and colleague from NY, Grant Brenner for alerting me to the article when it first came out. The design, results and context for this study are very sophisticated, and the implications are quite abstract. So I'm going to do my best to be clear. First the context: Many natural systems exhibit fractal organization and behavior. A fractal is a branchlike structure. Think of a tree: (1) Trees have many more small branches than large ones. This characteristic is also sometimes called a "power-law" or "inverse power law" or a "1/f" organization. Each of these terms means that there are exponentially more small branches compared to big ones. (2) Trees are "self-similar," meaning that small branching patterns resemble larger ones. This characteristic is also sometimes called "scale invariance" or "scale free" because no matter the size you are looking at, the general branching shape is the same. (3) The complexity of tree branching patterns can be quantified. Fractals are called "fractals" because they exist in fractional dimensions. A line fits perfectly in one-dimension. A plane (like a piece of paper) fits in two-dimensions. Fractals fit in between a line and a plane (or in the real world between two and three dimensions). More simply, because they are so complex, with huge numbers of tini tiny branches, trees never quite reach three dimensions. If you put them in a box, there will always be some space left over. You may quickly recognize that many other natural structures besides trees are fractals: Neurons, rivers, the respiratory system, the circulatory system, geological fault lines, snow-flakes, and so on. Natural systems also produce fractal behavior over time or in dynamics. Earthquakes are a common example. There are many more small earthquakes than large ones (which is nice by the way). Other examples include the size of extinction events in animal species, numbers of academic publications (a few researchers do huge amounts of work and the rest of us do just a little), numbers of hits to web-sites, wait times in stop-and-go traffic, and word usage in literature (i.e., zipf's law). Why do systems do this? There are many reasons. Essentially, fractal systems have many opportunities for growth, change and re-organization. Yet they also are very robust. They maintain their coherence; they hold together well, even under tough circumstances. They are balanced in this respect, between order and chaos. They are simple, yet also very complex. This balance is often referred to as "criticality," thus the title of the article: "Broadband Criticality." And the term "self-organized" is often added because systems tend to become fractal on their own, simply by putting a lot of system components together and allowing them to exchange information. Think of a party. All you need to do is come up with enough people at the same place and time and they will start to form complex patterns of connection with one another. Self-organizing critical systems are also very good at connecting, both internally and also to other surrounding systems. The branches of a tree are connected in a very lovely way. If you shake one branch, you'll see broad shaking across the tree. Fractal structures hang together nicely. Yet they branches may be trimmed without affecting the overall structure. Indeed, if you trim them far enough out (above the growth bud, "post-traumatic growth" or "whatever doesn't kill you makes you stronger") they will often grow even stronger, with more complex connections in the outer branches. Finally, branchlike patterns easily connect to other systems - a literal web of life. A tree with many fractal branches (and also roots) can better connect to the sun (and soil) to gather and exchange life sustaining nutrients. In the past 10 to 20 years, researchers in psychology have been finding increasing examples of fractal patterns across each of the domains of psychology: Including intentional behaviors, visual search, and speech patterns. In my own lab within the past few years we have found that interpersonal relationships are organized as fractals and most recently that the self-concept is a fractal, with complexity being associated with health in both the psychological and social domains. Furthermore, it appears that fractal complexity (or rigidity) is routinely exchanged among biological, psychological and social processes. Fractal personality structure helps us to grow and connect, as do fractal relationships, and each likely has direct influences on physical health by encouraging integration and flexibility among circulatory, respiratory, and immune systems. The study by Kitzbichler et al (2008) has added to much prior research suggesting that the brain exhibits fractal behavior. This makes a necessary link between the physical processes of the brain and each of the larger scale fractals we see in broader personality and social relationships. It is clear that biological, psychological and social dynamics are highly interlinked across scales, each impacting the other over time in myriad ways. With fractal organization at each of these scales, one may propose that they in some respects they are all part of the same fractal tree so to speak. Kitzbichler et al (2008) used two measures of synchronization across brain systems: (1) the "phase-lock interval" and the "lability of global synchronization." The phase-lock interval is the amount of time that different brain regions are doing the same thing together - the amount of time in which they are synchronized. Essentially, this is a time-based measure of brain system coordination. The other measure, "lability of global synchronization" is a space-based measure. This measure tells you how global are the shifts in brain system synchronization, how broad are they, how far reaching. Leaving out the many wonderful technical details of their analyses, they found that both measures showed clear-cut fractal patterning. This means that the amount of time that different brain regions spend in sync is branchlike - with many short linkage times and fewer long ones. And the spread of these linkages across brain regions was branchlike too, with many small spreads and few large ones. These results, along with the evidence that has come before them, provide a much truer picture of how the brain is organized and how it works. Such is the core of basic research. The applications of these results may be considered to be virtually unlimited, and will over time impact every branch of applied neuroscience - intelligence, consciousness, empathy, body-mind medicine, psychiatry and psychotherapy. What I would prefer to speculate upon instead would be the broader implications. Indeed what these robust results within the brain suggest is a possible mechanism for the "Broadband Connectivity" we share with the rest of the natural world. Inasmuch as fractal dynamics in broadband synchronization exist at every scale of measurable reality - from quantum to cosmic, perhaps human consciousness is both simply and profoundly a portal through which such fractal connectivity flows. Perhaps the linkages that so effect our growth and integration at the biopsychosocial scales extend much deeper into the roots of matter, and much farther into the cosmos than modernist science has ever imagined. Science appears to be nearing a period of neo-vitalism, with scientifically grounded ways of exploring the attractive worldview of our root-civilizations - that everything in life is connected and that all of the universe is alive within these connections. Sure - some connections are more proximal than others. Kitzbichler et al. found that functionally connected brain regions were more likely to find and stay in sync with one another for longer periods of time, yielding fractal complexity measures that were less flexible than the connections among more distant regions. Similarly, one's life-partner will be more likely to drive you crazy than the moon. Nevertheless, it will be interesting to see if certain systemic states encourage coherence, magnifying the connections among apparently separate systems. For example, the human stress response is a likely candidate for increasing the short-term coherence among biological, psychological and social processes. When you are stressed, your bodily systems band together, your psychological systems become clear and focused, and your social dynamics become coherent as well as you band together and form strict leadership hierarchies. Does human stress have broader impacts? Can their effect be measured even as far as the quantum realm? Conversely, can quantum systems become "stressed" leading them to reach into our macro world? Maybe so, maybe not. One thing is for sure, this blog is already way to long and abstract to fully consider these possibilities. Perhaps another day..? Source: http://www.psychologytoday.com/blog/the-chaotic-life/200909/fractal-brains-fractal-thoughts
Posted by Chris Mansel at 2:54 PM
Sunday, January 20, 2013
Posted by Chris Mansel at 2:31 AM
Monday, January 14, 2013
Posted by Chris Mansel at 7:56 PM
Saturday, June 19, 2010
Shing-Tung Yau is a force of nature. He is best known for conceiving the math behind string theory—which holds that, at the deepest level of reality, our universe is built out of 10-dimensional, subatomic vibrating strings. But Yau’s genius runs much deeper and wider: He has also spawned the modern synergy between geometry and physics, championed unprecedented teamwork in mathematics, and helped foster an intellectual rebirth in China.
Despite growing up in grinding poverty on a Hong Kong farm, Yau made his way to the University of California at Berkeley, where he studied with Chinese geometer Shiing-Shen Chern and the master of nonlinear equations, Charles Morrey. Then at age 29 Yau proved the Calabi conjecture, which posits that six-dimensional spaces lie hidden beneath the reality we perceive. These unseen dimensions lend rigor to string theory by supplementing the four dimensions—three of space and one of time—described in Einstein’s general relativity.
Since then Yau has held positions at the Institute for Advanced Study, Stanford University, and Harvard (where he currently chairs the math department), training two generations of grad students and embarking on far-flung collaborations that address topics ranging from the nature of dark matter to the formation of black holes. He has won the Fields Medal, a MacArthur Fellowship, and the Wolf Prize.
Through it all, Yau has remained bluntly outspoken. In China he has called for the resignation of academia’s old guard so new talent can rise. In the United States he has critiqued what he sees as rampant errors in mathematical proofs by young academics. Yau has also strived to speak directly to the public; his book The Shape of Inner Space, coauthored with Steve Nadis, is scheduled for publication this fall. He reflected on his life and work with DISCOVER senior editor Pamela Weintraub at his Harvard office over four days in February.
You’ve described your father as an enormous intellectual influence on you. Can you tell me about him?
He went to Japan to study economics, but he came back to help the Chinese defend themselves before the Japanese invaded in 1937. By the end of the war he was distributing food and clothes to the poor for the U.N. After the revolution in 1949, he worried about getting in trouble with the Communists, so he brought the whole family to Hong Kong. We were very poor—at first we were almost starving—but my father had a large group of students constantly at home to talk about philosophy and literature. I was 10, 11, 12 years old, and I grew accustomed to abstract reasoning. My father made us memorize long essays and poems. At the time I didn’t understand what they meant, but I remembered them and later made use of it.
Did part of you ever rebel?
I read most of the Kung Fu novels in secret. I quit school for more than half a year. I’d wake up and say I was going, but I’d spend the whole day exploring the mountains and then come back—but I did the homework that my father assigned to me at home.
I heard you led a gang at one point.
I had a group of friends under me. I’d go around, and sometimes we ended up in fistfights with some other groups. So?
How did you go from that rough-and-tumble young man to the focused person you are now?
In the early 1960s my father was chairman of the department of literature and philosophy at Hong Kong College. The college president wanted to make a deal with the Taiwanese government to send in spies. My father refused to go along and resigned. That created a big money problem because he had eight children by then. My father had to run around among different, distant colleges to support the family. Back in China he’d lent a friend some money, and after the Communists took over, the friend moved to Macau, a city near Hong Kong, and ran his own schools. So he told my father, “I cannot return your money, but your daughter can come to my school, and I’ll give her free room and board and free tuition.” So my older sister went to Macau to study and got some flu, some funny disease, we never knew exactly what. She came back and she was treated, but she died in 1962. Then my elder brother got a brain disease; at the time we didn’t know what it was. My father had all kinds of burdens on his shoulders and then he got a disease, which I believe was cancer, but we didn’t know much in those days. My mother was running around trying to get funding to help my father. Finally we raised some money, but it was too late. He died after two months in the hospital in 1963, in the middle of my studies in the ninth grade. We could no longer afford our apartment, so we were kicked out. That’s when I realized I would have to make decisions for myself.
What did you do then?
After a while the government leased us some land, and we built a small house thanks to money from friends, but it was in a village far from school. The other kids looked down on us for being poor, and I had to ask the school president to allow me to pay tuition at the end of the year, when my government fellowship came through. It was humiliating. But I studied hard and did very well, especially in math. Then a former student of my father started a primary school in a town closer to school. He said I could help teach math and stay there at night. I had to take care of myself, I had to wash things and all of that, but I learned how to survive.
What happened once you made your way to college?
I had fallen in love with math early on, but at the Chinese University of Hong Kong I realized that mathematics was built on standard actions and logic. Soon I had arranged to take tests for the required math courses without actually attending while sitting in on more advanced classes, and no one seemed to mind. In my second year, Stephen Salaff, a young mathematician from U.C. Berkeley, came to teach in Hong Kong. He liked to talk to the students in the American way: He gave lectures and then he asked students questions. In many cases it turned out I could help him more than he helped me, because there were problems he couldn’t solve during class. Salaff suggested I apply to graduate school early. I was admitted to Berkeley and even got a fellowship. I borrowed some money from friends and flew to San Francisco in September 1969.
What did you think of California when you arrived?
The first thing that impressed me was the air. In Hong Kong it’s humid, hot, but in California it was cool and clear. I thought it was like heaven. A friend of Salaff’s came to the airport to pick me up and took me to the YMCA, where I shared a big room with four or five people. I noticed that everybody was watching baseball on TV. We didn’t have a TV at home. My neighbor who was sleeping there was a huge black man. He was talking in a language I had never heard before. He said, “Man, where the hell you come from?” It was fun, but I had to look for an apartment. I was walking around the street when I met another Chinese student from Hong Kong and we decided to share, but we couldn’t afford a place. We looked around and found another Chinese student, from Taiwan, so there’s three of us and it’s still not enough. Then we found an Alaskan also studying math, also on the street. So four of us went in together and the rent for each was $60 a month. My fellowship gave me $300 a month, and I sent half of it home.
What about your math studies?
There were many holes in my knowledge so I’d wake up early and start class at 8 a.m. I took three classes for credit, and the rest I audited. I brought my own lunch so even at lunchtime I was in class. I was especially excited about topology because I thought it could help reveal the structure of space. Einstein used geometry in his equation to give us the local picture: how space curved around our solar system or a galaxy. But the Einstein equation didn’t give the overall picture, the global structure of the whole universe. That’s where topology came in.
What is topology? Is it like geometry?
Geometry is specific and topology is general. Topologists study larger patterns and categories of shapes. For example, in geometry, a cube and a sphere are distinct. But in topology they are the same because you can deform one into the other without cutting through the surface. The torus, a sphere with a hole in the middle, is a different form. It is clearly distinct from the sphere because you cannot deform a torus into a sphere no matter how you twist it.
Does that mean geometry and topology are really two perspectives on the same thing?
Yes. It is like Chinese literature. A poem might describe a farewell between lovers. But in the language of the poem, instead of a man and woman, there is a willow tree, where the leaves are soft and hanging down. The way the branch is hanging down is like the feeling of the man and the woman wanting to be together. Geometry gives us a structure of that willow tree that is solid and extensive. Topology describes the overall shape of the tree without the details—but without the tree to start with, we would have nothing.
It has always amazed me to observe how different groups of people look at the same subject. My friends in physics look at space-time purely from the perspective of real physics, yet the general theory of relativity describes space-time in terms of geometry, because that’s how Einstein looked at the problem.
Posted by Chris Mansel at 11:58 PM
Sunday, May 23, 2010
The Eco House Agent (www.ecohouseagent.com) is an online resource providing information about the implementation of “eco-friendly” devices in homes. The main goal of Eco House Agent is to help people make their house eco-friendly, reduce the use of carbon fuels, and become carbon neutral. While the vast majority of people perceive becoming carbon neutral as a lifestyle-altering commitment requiring a great deal of dedication, it is a process that when done effectively, will not drastically reduce the convenience of their daily lives.
Eco House Agent provides simple tips for homeowners such as walking instead of driving to local shopping centers, turning off lights, washing clothes at low temperatures, taking showers instead of baths, and turning appliances off instead of on standby. Eco House Agent also suggests resources that can be installed and implemented in your house, including solar power, photovoltaics, wind power, rainwater harvesting, insulation, and going “off the grid”.
According to Eco House Agent, based on the growing number of governmental incentives for reducing your carbon footprint, the time to implement these new strategies is now. “Soon we will be forced to reduce our Carbon footprint The government is looking to introduce environmental policies to encourage people to be more “Carbon Neutral”. The Carbon Credit Scheme will attempt to reduce the amount of carbon households produce. A Carbon Credit will be given for units of energy The government will reward those who use less Carbon, penalising less energy efficient households.”
The Eco House Agent teaches readers how to install new eco-friendly sources of energy, such as solar power, Photovoltaics, wind and rain power; harvest rainwater; and how glazing, installing insulation, and damp treatment can be beneficial for your money and the environment.
The website also offers a forum where users can “post all your green thoughts on Solar Power, Photovoltaics, Insulation, Wind Power & Rainwater Harvesting and energy saving, carbon neutral house ideas, helping us all to reduce our carbon footprint and have eco friendly houses.
The following topics are touched upon in detail on the Eco house Agent website:
Solar power energy: Explaining the importance and usefulness of harnessing light from the sun, Eco House Agent also talks about solar hot water heaters and how they are an ideal alternative to ordinary oil and gas hot water heaters. Also, solar power can be used to charge batteries in laptops, cell phones, iPods, and rechargable batteries.
Recycling: The recycling section supplies the importance of recycling and what methods and situations recycling can come in handy and be beneficial for you and the environment. The Salvo recycling centre is mentioned as an excellent source of materials that can be reused, such as doors, tiles, radiators, windows, timber, and furniture.
Finally, another notable section of Echo House Agent explains the benefits of having an “organic baby”. According to the website, “The decision to have children is arguably the most life-changing decision you may ever make, not only to yourself but also to the planet. You only have to look at some of the statistics associated with having children and the overpopulation of the planet to also make it one of the most guilt inducing decisions you’ve made.”
Posted by Chris Mansel at 1:37 PM