Hon. (Wow!) Mathecologist Silvert and Forum: If "we" can prune pride from the bush somehow, we need have no fear of brainstorming, provided we are prepared to resist the temptation to mount the bandwagon du jour and take a hard look at the actual as opposed to only the "virtual" outcome. Even though I am suspicious of biocalculus (not knowing s--t about it, I'm hardly in a position to be critical), I'm even more suspicious of bandwagons. Actually, I'm a closet fan of outliers, of insignificance. When the context shifts, they're ready to go! But then, I think I got at least two or three "D's" in statistics--from pitying and charitable professors. I trust that all cockamamie ideas, whilst they may enjoy a fan-tastic reign of terror for a time, will eventually reach the end of their battleship curves, and self-terminate. This may be the price to pay for the eventual triumph for the toilers in the fields or, perhaps more accurately, those who leap from rock to hard place with little regard for their citation indices.
I am most interested in learning as much as my limited "command" of arithmetic will allow (2+2 is quite a challenge) about the Laws of Ecosystems, and if I have to put on a hair shirt and try to understand fixed-point trajectories and bifurcation theory, particularly if they will lead to Great Insights into ecosystem function, I may venture from the precipice after all. As long as computer simulations predict actual phenomena rather than simply confirm the assumptions that went into them, I'll be converted to a Great Fan of those too. And Catastrophe sounds like a theory I could warm up to. It would be a bit too risky for me alone to suggest that, while bifurcations go all the way down and up, that theories do not drive phenomena like speciation, but could be reasonable representations of what happens when speciation occurs, rather than being the "mechanism" itself. Perhaps I draw too ridiculous a dichotomy. I might venture into deeper water on the matter of fishy theories of population dynamics--lordy be, I'm in hot enough water as it is, and I've already hogged enough posting space. But I'm willing to be recruited--as long as I don't have to go too far beyond the jiggling and fuzzy "bounds" of my environmental gradient diagram. And my own tangents (no geometry implied) are beginning to stick to my boots. I've just had a pint, so that's my excuse. Y'all's Ob't. Sv't. from outlier-land, WT At 03:21 AM 7/21/2007, William Silvert wrote: >Wow, quite a post! A few comments tangentially related to Wayne's reply. > >I am actually quite skeptical about biocalculus, at least as applied to >ecology. Although I consider myself a reasonably skilled mathematician (my >PhD is in theoretical physics), I make very little use of math in my >ecological work. So far as calculus goes, one first-order ordinary >differential equation (uptake-clearance) is practically all that seems >necessary -- no second order, no PDEs, etc. Furthermore, since most >realistic models include environmental driving forces, one usually has to >use computer simulation rather than analytical mathematical techniques to >handle them. > >There are some interesting mathematical concepts that apply to ecosystems, >mainly in a qualitative rather than quantitative way, and these have largely >been ignored by most ecologists. Catastrophe theory for example, which >provides a good understanding of phenomena like pest outbreaks. Fixed point >trajectories can account for periodic locust occurences. Bifurcation theory >as a mechanism for speciation. > >Despite their complexity, I believe that ecosystems obey some fundamental >laws, such as conservation of energy. Not all ecologists agree with me on >this point. > >Of course there are some very pig-headed mathematicians out there who >develop elaborate theories having nothing to do with reality. I recall one >such at a Gordon Conference who presented a fascinating theory of fish >population dynamics. When I pointed out that one of his assumptions about >recruitment was wrong, he just shrugged and replied "Then fish aren't very >interesting, are they?". Such people can safely be ignored. > >Bill Silvert > > >----- Original Message ----- >From: "Wayne Tyson" <[EMAIL PROTECTED]> >To: <ECOLOG-L@LISTSERV.UMD.EDU> >Sent: Friday, July 20, 2007 10:33 PM >Subject: Re: ECOLOGY Mathematics and the metamathematics of evasive ecology? >Re: Request: Data sets for biocalculus project > > > > Honourable William Silvert and Forum: > > > > Uh, oh--I've screwed up again. I keep forgetting that levity is > > contrary to Newtonian physics (R.I.P.). In an attempt to levitate a > > heavy subject with iron-y, it appears that I gave the impression that > > my skepticism meant that I was "against" a biocalculus course. On > > the contrary, I find intellectual variation an interesting analogy to > > biological evolution and quite welcome, and its proponents quite > > courageous.* My skepticism is a given, but I try not to fulminate > > into cynicism. Variation = Resilience. (I can't prove this, and I > > have seen no proof, but if some other inflated ego hasn't claimed > > V=R, I am herewith rushing it to publication, puff, puff.) > > > > Kindly please note where I was referring to a fraction (who knows how > > significant) of mathematicians, not all of them (a classic cop-out, > > perhaps, but true). However, I confess that I failed to repeat that > > qualifier when I wrote ". . . the mathematicians' claims of > > omnipotence." But William's point is well made and well-taken. He > > helps build clarity. Still, I hold, for the moment, to my point that > > ecology as a phenomenon (for want of a more descriptive term that > > distinguishes it from the discipline) is too complex to be reduced to > > numbers, and that some fraction of biologists, ecologists, > > statisticians (and now, I'm relieved to be informed, no > > mathematicians at all), and bean-counters continue to mislead the > > unanointed with mathematical (or, if you prefer, pseudo-mathematical) > > smoke and mirrors. This is, of course, a mere generality that I > > merely assert. It is either true or untrue, mostly true or mostly > > untrue, "fair and balanced" at some absurd balance-point between > > equally ridiculous extremes, or not. It is either worthy of > > exploration or it is an absurdity to be dismissed and ignored before > > it infects a perfect discipline. Perhaps my mistaken impression > > about mathematician-omnipotence is due to my interpretation of their > > sniffs as condescension. I am reassured that no such mathematician > > exists. Again I happily concede a significant (but of unknown size) > > population of mathematicians who are not "that arrogant." > > > > As to "significant digits" I can only say hurrah! Perhaps what > > biology and ecology need is a strong injection of Silvertian > > mathematics. I would consider a simple rounding to be progress, but > > I'm sure mathematics (as a tool) has much more to teach, such as, for > > example, the concept of congruence. What I really mean is relevance, > > a squishier concept, more "metamathematical." I am tempted to go > > further with this, but as a believer in shorter posts than I usually > > write (the spectre of hypocrisy haunts), I truncate it thus. > > > > If for no other reason (there are many), I hope that William will > > continue** to press for fuzzy logic to analyze a fuzzy > > phenomenon. Are numbers but static artifice, and as such cannot be > > applied to a moveable, moving, evolving, jiggling, oscillating > > phenomenon like life--or, for that matter, the universe? Is > > everything fuzzy? Will nothing hold still for > > analysis? Bean-counter is perhaps a too-general term for the > > amorphous police who strangle variations like biocalculus and other > > straying from linear reductionism in ecology (fuzzy folks need not > > apply), but it (bean-counting) either is there or it is not there, > > and regardless of its fraction (irony rears its ugly head once more), > > and regardless of the numerical significance of that fraction, who > > knows how influential it is on the course of ecology as an > > intellectual pursuit? > > > > As to the apple analogy, how apt! In the context of gravity (or the > > pursuit of any observation) the essential ingredient is relevance, > > no? Green or red, greeness or redness, must pass the relevance > > test. But heck, why not throw them into the equation anyway, just to > > confuse the heathen? > > > > Finally, I endorse William's call for ". . . try to get at the > > essential characteristics of a[n] [eco]system and try to describe > > even complex systems in simple terms." > > > > WT > > > > *Talk about deadly--just try to publish negative results. Does this > > admit of error? Hell, it has it's own journal: http://www.jnr-eeb.org/ > > **"Never, never, never--never give up." --WC > > > > > > At 03:02 AM 7/20/2007, William Silvert wrote: > >>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: <ECOLOG-L@LISTSERV.UMD.EDU> > >>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 > >> > > > > >
