Tuesday, October 7, 2008

Dynamical Systems as Models for Long Term Behavior

Dynamical systems, also known as systems of ordinary differential equations, form the backbone of the mathematical sciences -- physical, biological, or social. They have been formed into spectacular tools for short-term predictions of natural systems. But they generally cannot predict long-term behavior  reliably. This fact -- well-known to dynamical systems theorists in the pure math community -- seems unknown to many practitioners in the modeling community. The math behind this fact is known as bifurcation theory, and more information may be found in my MS#127, The Misuse of Mathematics, at the bottom of my article list (click the title of this blog).

2 comments:

Robert said...

That is all well and good, but what form does your argument take with reference to Lovelock's paper, http://www.jameslovelock.org/page24.html, including this statement,

"The long term history of the Earth suggests the existence of hot and cold stable states. What the geologists refer to as the greenhouses and the ice houses. The best known hot house happened 55 million years ago at the beginning of the Eocene period. In that event between one and two teratons (Tt) of carbon dioxide were released into the air by a geological accident. We are fairly sure about this from measurements made by Professor Elderfield of Cambridge University and his colleagues and from the researches of Henrik Svensen and colleagues of Oslo University."

"Putting this much CO2 in the air caused the temperature of the temperate and Arctic regions to rise 8C and of the tropics 5C and it took about 200,000 years for conditions to return to their previous state. In the 20th century we injected about half that amount of CO2 and we and the Earth itself are soon likely to release more than a Tt of CO2."

But for that, there is this statement also, I wish you would respond to,

"The positive feedback on heating from the melting of floating Arctic and Antarctic ice alone is causing an acceleration of system driven heating whose total will soon or already be greater than that from all of the pollution CO2 that we have so far added. This suggests that implementing Kyoto or some super Kyoto is most unlikely to succeed."

Finally, considering the fact that time may be being wasted (from the butterfly's point of view, or better yet, the bread-and-butterfly's), are you aware of the significance of the text available for free on this site, www.blacklightpower.com? I think, for the culmination now of the lack of management in history of planetary dynamics on an economic as well as ecological front, or for the duration of western civilization experiencing some sort of transformative principle, perhaps, the combination of working out Mill's angle on controlling CO2 output through applying the energy of hydrinos, plus Lovelock's utilization of oceanic tubes suggests a viable, and perhaps, paramount means for beginning such management. What do you think of this? Is there consistency with designing this approach and gaining insight in the process?

SGKO said...

Hello Professor Abraham,

I want to thank you (mahalo) for setting up this BLOG...in particular with providing an easy link to various articles you've written over time (my personal - professional interest being on Dynamical Systems and model applications for long term behavior prediction.)

I aim to come up with a functional - working mathematical model that will allow for specific - identifiable tracking of human behavior over time, in relation to patients suffering from various mental illnesses, while pressing for changes in congressional health care policies in the U.S., thus securing needed funding for developing the appropriate and needed treatment - recovery interventions to assure patient improvement with the individual diagnosis as well as marked improvement with quality of life.

All within my life time of course.

Anyway, keep up the optimism and thinking outside the box.

Aloha No Professor Abraham,

SGKO