Why Do Our Mathematical Models Of Complex System Fall To Chaos Theory?

Why is Murphy’s Law so revered by academics, scientists, engineers and laymen so widely? It’s like these select group of people can’t agree on anything else, most all of the time. Could it be because there are too many daily examples of Murphy’s Law to deny it? Yes, that’s probably it isn’t it? Okay so, this is a cool topic something we can discuss for a moment, something everyone can relate with. Specifically, I’d like to address why it is that our mathematical models of complex systems are so hard to predict and why it is that at the end of the day Chaos Theory rules it.

By the way if you haven’t read it, I’d like to stop right here and recommend a very good book you might read; “Chaos – Making A New Science” by James Gleick, Penguin Book Publishers, New York, NY, 1987, 254 pages, ISBN: 0-14-00-9250-1.

Now then, not more than a few years back I was speaking with a mathematics grad student about the topics of complexity and mathematical modeling, and how more accuracy was better with more points on a 3-D system in fluid dynamics to predict outcomes to the point of absurdity – the proverbial butterfly flapping its wings and disrupting the airflow in the Amazon Jungle for instance.

My acquaintance stated a truism about such modeling and why climate science models were most likely going to be wrong ALL of the time and how chaos played the biggest part in all of it. He stated; “Trying to be super accurate might end up in a model being too complex as there would be too many variables to include.”

Yes, and what super computer could handle the actual data and not derivatives of the lesser points collected, after all we cannot have infinite points, right. What about something other than fluid dynamic modeling does the same theory on the complex nature of the mathematics rule the day also? What about in economics? No computer could handle all that, or could it, and if it could should we use it for that purpose?

Well, if you take every world transaction and plot the trends from there, with that many inputs added to your model, you’d be more accurate, but VERY complex. Super computers and AI work better with more information, and multiple variations do help give better guidance to probability within marginal error sets from the mathematics.

This helps with fuzzy trend lines, and prevents stupid humans from making mistakes leading to unintended consequences then hiding their mistakes with bad data “garbage in, garbage” out with politically influenced scientific economists doing what humans do, producing the equational results asked for forcing a created political reality, that not only can’t exist in reality, but never even came close to the actual derivative trend lines.

Bad for decision makers, good for honest economic practitioners who also use that to their advantage, but in doing so, they become wealthy market makers + manipulators who then take their money and play it again through crony capitalism. How do you hope to quantify the “human element” in your trends, those who blow up bubbles in sectors, right before a down-trend sector rotation put off for months in the interim? Please consider all this and think on it.