Reference no: EM133206516 , Length: Word count: 2 Pages

Assignment Task 1: Scale and pattern

You may have noticed from last week's videos that many fractal patterns are 'self-similar' at different scales. That is, patterns might persist or repeat themselves, perhaps in modified form, at vastly different scales. Natural branching patterns in particular are often like this. The sorts of patters that running water makes in the sand at your feet are very similar to the patterns that they might form at the landscape scale. It has been possible to examine hydrological patterns and design large scale structures in the landscape by using small scale models of water storage and flow. And as we'll discuss next week, human lungs have a huge internal surface area precisely because of their branching fractal geometry. I've often thought about relationships between different scales of space and time.

The ability to work with patterns forms the basis of much of AI, neural networks, etc. The following is an example of some work that I was doing with agent-based models and the patterns they form.

Examine: Demonstrating the effects of functional diversity in geospatial domains (1) [Gary Pereira]

Watch: The Science of Patterns [Systems Innovation]

The following locally shot videos of mine involve lichens and terracettes that form spatial patterns over long periods of time, and bird songs, which form patterns over very short periods of time.

Watch at least one of the following two videos:

Pattern formation in Nature 2: lichens and terracettes [Gary Pereira]

Pattern formation in Nature 3: bird song [Gary Pereira]

Assignment Task 2: Emergence

Watch: Emergence [Systems Innovation]

Watch: Synergies [Systems Innovation]

Emergence is one of a set of several key ideas that encompass contemporary theories of complexity, as applied to the physical world. Evolutionary theory in biology has also discovered many illuminating processes and principles that have proven to be useful at ecological and social scales. Indeed, the evolutionary history of the universe itself is the central topic of cosmology. For example, the appearance of the elements in the periodic table is the result of a kind of cosmic evolution. Most of the elements with which we are familiar first appeared hundreds of millions or even billions of years after the Big Bang, having been generated from within earlier generations of stars.

The significance of nonlinear phenomena (that is to say, most things) cannot be determined by simple additive or multiplicative reasoning. Imagine bumping into a wall at 1 mile per hour. No big deal. Now imagine doing that same bump 10 times in a row. It would be kind of OCD but still, no big deal. Now imagine running straight into the wall just once, at 10 miles per hour. Obviously, a very different result from bumping into it 10 times at 1 mph. Much greater than what you would get at 1 mph and just multiplying that insignificant effect by 10. At 20 or 30 mph, it could easily result in death. In order to translate velocity into significance, you would need to at least raise it to some power, rather than just multiply it by some value. That is the basis of nonlinearity. The events that might carry the most significance, possibly the only real significance, are often extremely powerful, carrying everything they interact with into qualitatively uncharted terrain. These are the sorts of events that actually change lives, nations, and civilizations.

Watch: Long Tail Distributions [Systems Innovation]

Agents of change exist at every scale. They can be far smaller or far larger than anything we as human beings can directly perceive. They can occur far more quickly than we could ever have time to respond to, and they can happen far more slowly than we might even notice. The pandemic that we are going through now illustrates this point. Each SARS-CoV-2 virus particle is approximately 50-200 nanometers in diameter. Let's say 100 nanometers, typically. That's four orders of magnitude smaller than a millimeter, which is the finest mark that you might find on a common ruler. Ten thousand individual virus particles can be lined up between each of those millimeter marks. Roughly a hundred million particles could cover a square millimeter of surface. Now compare that to the surface area of a pair of human lungs, which is the primary target of most variants of this particular virus. The alveolar surface area of a pair of human lungs is enormous, somewhere between 50 and 75 square meters! It is possible for Nature to fit such an enormous surface area into such a compact volume because lungs are exemplify a fractal branching pattern, terminating in hundreds of millions of alveoli for gas exchange. If a hundred million virus particles can cover a square millimeter, and there are fifty square meters of surface available, you can imagine the sorts of battles that are being fought within the vast terrain (from the virus's point of view) available within a single human being. Now think about the spread of that virus to billions of people. The potential power of anything cannot be determined merely by its size or by our current awareness of its potentialities. This is one of the things that nonlinearity implies.

Usually the discussion of solution to our collective vulnerability to powerful events strung out along the tails of event distributions (events like pandemics, floods, earthquakes, etc.) revolves around terms like 'resilience' and 'robustness'. However, an argument can be made (through simple observation of nature) that some other principle better characterizes the opposite of fragility: something that people have known about for a long time, but which Nassim Taleb recently termed 'antifragility'.

Watch: Nassim Nicholas Taleb explains Antifragile [Penguin Books UK]

Task:

1. How are patterns defined by the Systems Innovation video? How might patterns be defined in time as well as space? Give me some examples.

2. Describe the concepts of emergence and synergies, and try to illustrate them in the context of the natural sciences with a few examples.

3. What are long-tailed statistical distributions? How might events following a power-law or long-tailed distribution make assumptions of long-term normality nonsensical? In other words, are common statistical terms always meaningful? For example, can the mean of a power-law distribution ever be determined? This is an important point, given the fact that many natural distributions do indeed have very long tails.

4. What is antifragility? Try to explain how it can be seen as different from resilience or robustness. Why might you think this concept is important in an era of climate change and pandemics?