Weird thought: I’m wondering if entrainment reduces the effective dimensions of a complex system? If so, then it should be eas(ier) to detect using Poincare sections.
I'm in Hawaii this week (yay!). Here are a few things of note for the week:
Worked on Max patches for recursive video and made some progress. I'm inclined to go back to some basics next week when I return to Phoenix and want to set up a video camera in the video room in Matthews. More to follow.
I will be doing a brown bag talk on Thursday at 12:00 noon in Matthews regarding Dynamical Systems.
Made a bizarre observation regarding Nene geese. The Nene is a goose endemic to the Hawaiian Islands and is thought to have evolved from the Canadian goose that came here about 500,000 years ago (according to Wikipedia). When I was a child in Hawaii, the Nene was nearly extinct and I only saw one in the Honolulu Zoo. Now there are thousands of Nenes and they congregate on the lawn of the condo on the North Shore of Kauai.
I observed that Nenes often line up next to one another and "stare out at the ocean." I was wondering about this and looked for long periods at the ocean trying to figure out what they were looking at. The Nene is still endangered and it is illegal to approach them. Sometimes I call to them and they are very tame, walking over to me and turning their heads to look at me. I woke up a few days ago with an insight. When the Nenes line up in a row, they are not looking at the ocean. They are looking at each other! Their eyes are on the sides of their heads, so they have to turn their heads to look at me. It occurs to me that this is a characteristic of flocking birds. They fly in formations by looking at each other, not looking at what is ahead of them but to the side. This makes sense in terms of flocking. The birds must adjust their flight in minute response to the geese on either side. The Nene has not migrated in 500,000 years and rarely flies, but still lines up in a rigid formation with the wind at their beaks.
From my experience, birds of prey such as hawks, owls and eagles, usually have their eyes forward in their heads, presumably to enhance stereoscopic vision for hunting.
This may be obvious to biologists and others who study birds, but I had not thought of it.
In tango and other couples dancing, we are instructed to not look at our partners. This is a strict rule. Looking at one another would inhibit the ability to sense the shift in body weight and the touch of the other.
This is making me think there are rich ideas to be explored around vision and flocking (non-verbal communication).
Activities for Week of August 29, 2016
1. Met with Prof. Mohamed Moustaoui (https://webapp4.asu.edu/directory/person/730672), my math professor for Applied Dynamical Systems, and discussed the recursive video project. His thoughts were around how to collect data from the experiments that could be used to calculate key parameters in more classical dynamical systems methods. He is very interested in learning more about what we do in Synthesis and would like to have more exposure.
He started in theoretical physics, went into weather systems and is now a mathematician.
2. Met with Todd Ingalls regarding the video feedback Max algorithms for looking at dynamical systems and he provided a quick-and-dirty Max patch to evaluate.
3. Xin Wei also pointed me in the direction of a Max tutorial around recursive video.
4. Received a zipped folder of MatLab projects from Anirudh for Lyapunov exponent calculations, based on Vinay's paper. Spent some time updating my MatLab installation with the required Chaotic Systems Toolkit. I'm still not quite sure how to use this, but I'm confident of my progress.
Work for Week of September 5, 2016
1. I'll be in Hawaii in the midst of a major hurricane. I'll take photos.
2. Work on recursive video of faucet flow in Max. I have video.
3. Outline a proposed brown bag presentation re dynamical systems.
Summary of Current Projects
1. Recursive Video as an experimental environment for the study of high dimensional dynamical systems. (Rhythm Analysis)
2. Lyapunov exponents: how to generate them in MatLab from time-series data (ideally) that can be used to inform Max implementations.
3. Brown Bag: what I learned over the summer that changed my life regarding how the world works wrt dynamical systems.