My Topic?

OK - this is my first attempt to verbally articulate my thoughts on my dissertation.  First some background.

We traditionally say that Physics is the Hardest Science, Chemistry and Biology are Hard Sciences and Psychology, Sociology, Education, etc are called Soft Sciences.  Of course some people think that refers to the difficulty of the material, but actually it refers to the expected rigor applied with regards to the "scientific method."  (OMG!  I'm writing like a researcher.  Yuck!  But I think I've figured out why - more on that later).

OK - so my thought is that these are in backwards order.  Most people think Physics is the most difficult because it uses Calculus (oooo!  scary!).  But actually Physics uses fairly simple formulas to model fairly simple systems subject to relatively easily-controlled, relatively easily-measured forces.  Traditional chemistry (as taught in my High School in the 70's) didn't use much more than arithmetic and geometry; while Biology just used basic observation and classification (which is math - at the early elementary level).  (Of course my Biology class just had to listen to my soon-to-retire teacher discuss his financial plans - but that's another story.)  So some people think the relative hardness is related to the necessary mathematics.  The "soft" sciences just use that "soft" math of Statistics.  But Statistics is actually something that comes after Calculus.  However it is taught at a Freshman/Sophomore college level as an introductory course because so many people need to use it.  People need to know how to interpret statistical reports and evaluate statistical arguments in everything from political science and law to medicine and education, even if they don't understand the theoretical math.  Everything is supposed to be supported by research and research means Statistics.

Chemistry stuff is harder to measure than rolling a canon ball and a marble down an incline, and biology is still harder.  These are hard to measure and model mathematically because they are made of so many "moving parts", so to speak.  I can prove both spheres hit the ground at the same time regardless of temperature, barometric pressure, humidity, or anything so confusing as people.  As science gets "softer," it is studying more complex systems.  Then suddenly (10 or 20 years ago?), someone did the impossible - mapped the human genome.  (I'll admit that most of what I know about DNA analysis came from various forms of fiction - TV, movies and murder/suspense mysteries.  I love Robin Cook & Tess Gerristern.)  Anyway, that DNA stuff took an awful lot of math and computer stuff (programming).  So now I'm thinking along the lines of what comes after - arithmetic, algebra, geometry, analysis, calculus, probability (& statistics), . . .  What comes next?  Well, I've always consumed info, especially when it comes in popular media, so I know the answer.  There's topology & differential geometry (they were around popular back in the day).  Then came Game Theory, Fractals, Fuzzy Logic, and Chaos Theory.  There may be more, but those are the ones I've read about.  I know a very little about fractals and fuzzy logic; I need to learn the basics of game theory & chaos theory.  But what I do know about these fields is that they are useful in modelling complex systems - like a classroom!

So now I'm there.  I'm scanning papers for good background on how these various models have been used on complex systems, including social systems (dang, mustn't forget the social networks & that math).  There's one or two on education so the background does exist.  This could be serious, breakthrough stuff.  Scary! Seriously scary!!!