Calculus for History Majors

As we discover the huge role complex natural systems have in change of all kinds, we’re finding that evolving systems are our environment, the whole context and much of the shape of history.   It’s high time history majors learned about the best method available for reading their changes.   A most curious and revealing thing about complex systems is that the first evidence of emergent change is often a display of the physical property that corresponds to the central mathematical idea of calculus, continuity.   In a mathematical function you can define a slope, and the same is true of almost any real change in complex systems.    Complex systems evolve through progressions, and applying a logic like that of calculus to measures of change over time shows you where the progressions emerge from the noise and when they shift.   It reveals a great deal about the nature of a system because it provides direct evidence of it’s creative behavior as a whole.  

 

That has never been the reason for teaching calculus, but it should be.   The usual reason for teaching calculus is to give students their first (after 9^th grade geometry) emersion experience in rigorous mathematical thinking.    For history majors a little taste of that would give insight into the history of ideas, but it would give them little of use for understanding the world around them.   Natural systems are not snapped together out of perfectly fitting parts like a mathematical proof is.   They go through periods of eventful and uneventful change, well, like the history of civilizations, climates, ecologies, languages and life in general do.   The basic partly mathematical question is when can you look at a series of dots, and call it a curve?    When can you say change has shape?    If it has shape, it likely involves a complex system, and you can read the dynamics of the shape to identify change in the system’s internal structures.   There is no single test, of course, since no series of dots gives a definitive description of anything, especially not a complex system.   It’s a kind of forensic exercise, finding shapes in the data, and clues in the shape that can validate them, often taking special note of periods of growth or decay, isolating the central continuity by reading through the noise and fluctuations, to find the consistent progressions that hold up to scrutiny..    

 

In a sense what historians will be doing with a tool like this is original systems-physics research on the subjects in which they are immersed, since natural systems are essentially locally original worlds of internal physical relationships, unique separate universes.   Some complex natural systems might be amenable to mathematical description, but surely not most.    What they’re more amenable to is story telling, which can be very usefully grounded in fact by directly reading the shapes of their evolutionary events, using the underlying ideas of calculus.   It’s just calculus reshaped a little for exploring things beyond mathematics in the new world.

Phil's state of the planet 06

Last week I had a rare privilege to be exposed to some of the best of the visionary hard science and planning for saving the Earth from its more glaring human catastrophes. There’s a very bright picture, with an unusually dark side. Were in genuinely deep trouble. The conference was put on by Columbia Univ. Earth Institute, Jeffrey Sachs director and leader.

The bright side is that there does seem to be a path for changing energy consumption technologies in the developed world to keep ocean levels from rising more than 3 to 10 feet in the next century, holding it to a quarter of what it might well be, if we follow a fairly tightly scripted science-led and politically driven global program. There are also slightly less clear but equally hopeful ways to keep the rapid growth of impoverished and incompetent human populations from increasing to a point of combined environmental and population collapse. There are a variety of neat technologies and excellent strategies embodied in the UNs Millennium Development Goals (MDG), for developing competence in impoverished communities, but these also need to be science led and politically driven.

No, political movement I know of has ever done anything like these things before, except for the US A-bomb or the moon shot projects, but not to worry. The insurance companies are onto the severe consequences of failure and some of the big conglomerates are getting the idea quickly too. Its in no businessman’s interest to operate on a failed and humiliated Earth with population collapse, the loss of most historic coastal development, and the rest of the long list of shocking and embarrassing probable losses. Still, there’s a fighters good chance of turning things around, if everyone joins in and nothing else comes up.

Its hard to pick favorites among polished gems and I just wish everyone had a chance to hear the two days of rapid fire displays of great work in this save the planet field. Two of my favorites among the 30 or so were Steven E. Koonin, the scientist hired by BP to lead their green energy effort, and Stewart Hart who made a very convincing presentation on how visionary investment in the bottom ¾ of the human pyramid (BOP) could power Earths economic development for the next century. I highly recommend that you look around the conference website (below). The original. Power Point presentations are all supposed to be available soon, though I don’t see where they're posted yet.

The dark side it that this save the planet stuff may all be fantasy. The threats seem real enough, and the desire and organizational talent for doing something are quite real too, and its quite impressive how aggressively this community of scientists and planners are expanding their experience with the nature of the global problems we discovering. The problem is no one seems to be looking beyond their experience to why were discovering this stream of huge new nearly insoluble problems. There was no mention of the exploding footprints of endlessly accelerating economic development, no questioning of the economys rigid rule of ever more rapidly accelerating expansion. Its quite ridiculous, but they acted as if it was just dandy to trundle buckets around for the sorcerers apprentice. I think its a total disaster. Were stupidly accepting as our quest and duty to solve ever more insoluble problems and dont give even 5 minutes of time to what is making our amazing ever increasingly complex problems ever more insoluble. There’s science for that too, but somebody’s got to ask!

Another of my favorite presenters at the conference, who pointed out how our ways of solving problems sometimes consistently make them worse, was Parker Mitchell of Engineers w/o Borders who went through a variety of stories of how the best intentioned technology interventions in 3rd world communities failed the test of organic fit. A 'failure of organic fit' a precise statement of what’s wrong with our intervention in Iraq, for example. We have great intentions but are making a God awful mess because we have no idea what were doing, trying to reengineer someone else's natural human communities that have completely different ways of thinking from us. Our failure with the under developed world is the same thing. It is my belief that the whole rapid growth of the incompetent majority portion of the human population (see John Coomber & Joel Cohen ) is the direct fault of incompetent charity over the past century, and that’s where we really need soul searching and better technique. Well, that, and understanding the growth imperative and how to get rid of the stupid thing.

State of the Planet 06
http://www.earth.columbia.edu/
http://www.earthinstitute.columbia.edu/sop2006/about.html

4 of many great presenters
Steven E. Koonin,
http://www.earthinstitute.columbia.edu/sop2006/bios/koonin_s.html
Stewart Hart
http://www.earthinstitute.columbia.edu/sop2006/bios/hart_s.html
John Coomber
http://www.earthinstitute.columbia.edu/sop2006/bios/coomber_j.html
Joel Cohen
http://www.earthinstitute.columbia.edu/sop2006/bios/cohen_j.html
Parker Mitchell
http://www.earthinstitute.columbia.edu/sop2006/bios/mitchell_p.html