Fractals, fractals, Everywhere!

Thanks to Elliot for this one:

http://www.fractal-recursions.com/

Fractals can be used to describe the world. With Benoit Mandelbrot's breakthrough geometric study, secrets of the world have been revealed. I found this website especially cool because of all the examples of magnificent fractals in the world. Fractal geometry has been vital to new forms of art and computer graphics and areas of science and technology, and will continue to change the world.

Some Advice - To Embrace Complex Networks to Find Simple Solutions

Scientist Eric Berlow shows a few examples of how one can think about complex systems and networks in order to find simpler structures and solutions. In networks where there are hubs (i.e. agents of the network which have many connections compared to most agents), one can look and focus on the first few orders of connectivity to begin looking at the key components and eliminate 'noise.' Rather than be freaked by a complex problem, step back and look at the overall picture to pick out the key pieces of the problem. Sound familiar? This is the approach we take for something like those systems with tension. We only look at the forces that may affect the motion and don't worry about the others. So we continuously try to simplify the complexity into simpler pieces. Or in circuit analysis, we isolate smaller networks of resistors, and simplify those to single resistors, until a complex circuit is redrawn as a series circuit. This is the idea Berlow is promoting. Check it out, and let me know what you think!

Do keep in mind, though, that this is not foolproof. Some times this approach makes a problem more manageable and it can lead to some sort of solution, or at least some sort of approximation, but other problems have so many intricacies that this approach leads to nowhere. It is a strategy you may try to see where it takes you.

Emergence and the universe

This is an old post from my main blog some of you may find interesting and relevant to class. It deals with emergence, or the natural formation of something new from a variety of individual parts. The collective system is very different and follows different rules than what the individual components of the system follow. An example is how society emerges from individuals, whether it is humans or ants. Check this out for the 'emergence' of our universe:

Our Universe: Continual Emergence

In my last post I tried to offer some mix of examples of systems that involve emergence. Again, emergence refers to many-body systems of all types (physical, biological, social, economic, etc) where the rules/principles that govern the behavior of individual components of the system are different from the organizational rules/principles that govern the behavior of the collective system.

As others pointed out in comments, the field of complex systems and emergent behavior includes phase transitions and environmental concerns and influences as well. This discussion has got me thinking about the role complexity theory and the notion of emergent behavior will play in the next few decades. Being a relatively new area of study (at least new in the sense that large numbers of people are working on it...perhaps on order of 15-20 years), it is difficult to predict exactly where it will end up, but just from a physical science point of view consider the following progression of events and phenomena where new levels of organization, i.e. emergence, are reached:

• Big Bang, where energy and spacetime itself emerges from a singularity.

• Matter (quarks, leptons, some bosons) emerges from the energy (a type of phase transition).

• Fundamental particles, the quarks, organize into baryons (such as protons and neutrons) and mesons, via strong nuclear force.

• Nuclei (isotopes of hydrogen, some helium) emerge from a sea of baryons and gluons.

• Simplest atoms emerge from sea of hydrogen and helium nuclei and electrons, via electromagnetic force.

• Gas molecules of hydrogen and helium emerge from sea of atoms.

• Gas clouds emerge from sea of gas atoms, via gravity.

• Protostars and stars emerge from gas clouds.

• Heavier elements (up to iron) emerge from thermonuclear processes inside star cores (nucleosynthesis).

• Clouds of heavier elements (up to uranium) emerge from first generation supernovae.

• Second generation stars, first generation planets/solar systems emerge from gas and heavy element clouds.

• Primitive atmospheres and terrestrial environments emerge on various planets.

• For earth, more complex molecules, including carbon-based molecules, emerge in the chemical mixtures of the atmosphere and oceans (this includes amino acids, which can be formed naturally when lightning occurs in the primitive atmosphere, as shown in experiments).

• Still more complicated molecules, including proteins and RNA, emerge, and from this mixture first set of single-celled life emerge.

• Multicellular systems emerge from sea of single-celled critters.

• Ultimately great variety of life emerges, including humans, from evolutionary processes.

• From this point, social organization occurs, language emerges, technology emerges, social networks emerge, economies emerge, and so on.

In each of these separate eras of the development of the universe and life as we know it, we are talking about a transition from simpler, smaller components that organize into larger entities whose behavior and properties are vastly different from the individual components that make it up. We are at the point where we know an awful lot of the physics that describes how particles, atoms, molecules, stars, galaxies, planets, geological processes, and solar systems behave individually. Chemists and biologists know an awful lot about individual reactions, molecules, organelles, cells, tissues, organs, and organisms. This is what science has worked on for the last few centuries. In other words, we know a lot about the basic rules and principles that govern individual components for each individual step of the evolution of the universe and life on earth.

However, what we don’t understand very well is how steps make the transition to the next step. We don’t understand the organizational principles or the rules that govern the phase transitions between steps, which means we don’t understand the emergence of complexity in our universe. This is where we are now and, in my opinion, such studies will dominate whole fields of physical science, biological science, mathematics, economics, social science, behavioral science, technology, and even philosophy, for decades to come. To those who have suggested the end of science is near, think again.