While I share Wayne's skepticism about the desirability of a biocalculus course, I find most of his comments misplaced. Consider for example his sentence, 'To be "science," they say, it must be reduced to numbers, to (endless, irrelevant) decimal points.' Hey Wayne, the people who add the meaningless decimal points are the biologists, and those of us with a mathematical background are the ones talking about significant digits. As for claiming omnipotence, I have met some pretty arrogant mathematicians in my time, but none that extreme.
I was pleased to see favourable mention of fuzzy logic in Wayne's post, as this is one of the areas that most interests me, but in general I find biologists are very reluctant to accept any innovative mathematical approaches. Some very interesting and potentially valuable work has been done to apply approaches like catastrophe theory and fixed point theory to insect outbreaks, but this work seems to have been generally ignored by biologistss. Even basic concepts like stability and instability are hard to talk about. I hardly think that the bean-counters have taken over ecology. As for Wayne's final comment that mathematical approaches are "limited by the fact that variables are infinite--or, well, too numberous to count any way.", the same criticism could be made of physics, where mathematical approaches have still proved very successful. Consider Newton's mathematical model of a falling apple, expressed by the equation F=ma. Physicists have used this formula for centuries, but I cannot imagine any biologist falling for such a simple model - just think of all the variables that Newton left out! What kind of apple? Ripe or green? Size? Shape? Flavour? Of course physicists try to get at the essential characteristics of a system and try to describe even complex systems in simple terms. Not biologists. Bill Silvert ----- Original Message ----- From: "Wayne Tyson" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Tuesday, July 17, 2007 4:15 AM Subject: ECOLOGY Mathematics and the metamathematics of evasive ecology? Re: Request: Data sets for biocalculus project > Dear Cheryl Heinz and Forum: > > The subject subhead is intended to be only a bit humorous. > > I respect mathematics, but I don't overrate it. What I am waiting > for is an equation or a computer program that can stand up to proof > and predict--describe the phenomenon in terms of principles--Laws, if > you will. I have to have that in order to respect the > mathematicians' claims of omnipotence. > > But bean-counters are, of course, in the driver's seat. They (a > fraction of self-proclaimed mathematicians) have taken over > ecology. This fraction likes to bully so-called non-mathematicians > with disdainful sneers about the "non-mathematical" approaches to > what they have gotten away with calling, without proof, > "non-science," including ecology. These number-bullies don't like > inference, chaos, and the like. To be "science," they say, it must > be reduced to numbers, to (endless, irrelevant) decimal > points. "Bionumerologists," one old-fashioned botanist once called > them. One smells a bit of put-down as a means of feeling bigger. > > Biology and ecology do require disciplined thinking, and certainly > math is a necessary and useful tool in making sense out of > observations, but the reductive nature of mathematics is impotent > when it comes to getting a handle on such a squishy subject as > ecology. The fact that it is so frustrating to study ecology, so > endless and without firm conclusions, does not mean that the human > need to conquer all will necessarily be satisfied. As my wife says, > "Nature bats last." Unraveling ecology, if that is ever "done," will > require a kind of "metamathematics," an infinitely complex array of > integrated principles that simply IS--not a construction of any > single person, even any team or IT (ironic, eh?). > > Good luck with your calculus--I hope it will prove me wrong, add more > light than heat. But don't be intimidated. Everything really is > connected to everything else, and while we should pursue a better and > better understanding of ecological phenomena, including by using > mathematics, my forbidden intuition suggests that we will have to go > beyond math as we now claim to understand it (and certainly far > beyond reductive statistics) if we want to get beyond cutting ecology > up into little decimal-pieces and making mere dissertations out of > them. But Homo doubly-wise has always preferred self-validated > fantasy to reality, no? Except, maybe, those who find sufficient > satisfaction in the Quest, who demand no ego-salving "certainty," > those for whom a significant dose of uncertainty is no vice, and for > whom outliers can be seen as just possibly where the cutting edge may > lie. Of course, since burning at the stake is no longer cool, > certain banishment shall be (has been) their fate. > > WT > > PS: "Fuzzy logic," gets closer to recognizing the trends and degrees > that make up ecological phenomena than anything else I've seen in the > region of math, but even that is limited by the fact that variables > are infinite--or, well, too numberous to count any way. Ask your > colleagues to "solve" for that. Again, I jest--a little. > > > At 11:38 AM 7/16/2007, you wrote: >>I'm involved as an ecologist in a project to develop a two-semester >>biocalculus course and textbook. As a biologist, my role is in helping to >>write snippets of the biology and help track down some data sets. (I keep >>trying to explain to my math colleague just how long it's been since I >>took >>a math course...) >> >>So, I'm asking the community if you have any datasets that you would be >>willing to lend that could be modeled using calculus -- potential topics >>(on >>the ecology side) include exponential and/or logistic population growth, >>succession, predation -- and much more. On the math side, the topics are >>ordinary differential equations, difference equations, matrix models, >>differential calculus, and more. >> >>Data are only to be used as examples for the course/ text -- we're >>thinking >>it would be nice to provide some real-world data (along with all the >>faults!) instead of simply generating data sets. (My colleagues in the >>math >>department -- and the PI for the project -- will likely be the ones to >>track >>down permissions as needed.) >> >>Tim Comar (in our math dept) is the PI and lead author of the text. >> >>I'd be happy to answer questions to the best of my abilities, and I thank >>anyone who has data to share in advance! >> >>Thanks! >>Cheryl >>-- >>Dr. Cheryl A. Heinz >>[EMAIL PROTECTED] >>Assistant Professor, Biology >>Benedictine University >>(630) 829-6581 phone >>(630) 829-6547 FAX >>http://www.ben.edu/faculty/cheinz/index.htm >
