Resha Caner

Any comments on this? My impression is that it's largely a political attempt to accomodate genetics with taxonomy. Similar things happen in my field where people try to accomodate QM and classical physics when there isn't really any need. QM is the rock star, and classical physics wants to bask in the same spotlight. Shrug. As an engineer classical physics remains much more useful to me even if the prevailing opinion is that QM is more phenomenological. Anyway, I 'm not a biologist so I was looking for other opinions on Twin Nested Hierarchy.

Well, then I'll be patient and wait for you to solve my problem. If I had the resources, I'd fund someone to help me do it ... Maybe someday.

Sure, they're interested. But I haven't seen many with practical solutions. I can make up a host of nonlinear equations with exact solutions for special cases. But are they applicable to a known system? As an engineer, one of the first questions I get when a crazy new idea comes along is: is it practical? But, as I said, it may just be that I'm unaware of the available solutions. For example "soliton" and "jet bundle" are new terms for me. I'll look them up. Exactly - except it would be a nonlinear superposition principle. I'm aware of some math that would allow me to do that, but I struggle every time I try to apply it to a real problem. The pendulum would be an example. The solution of pendulum response to gravity is known. But (as far as I know), no exact solution has been found for anything beyond that. If you add some damping to the problem, or a periodic torque, every paper I've seen then resorts to numerical methods. The problem is that the known solution is given as a Jacobi elliptic function (the elliptic sine, sn(u,k)). The k parameter is a function of the initial potential energy of the pendulum. So, if you change the energy state of the pendulum with additional force, it would mean the k parameter becomes a function of the work done on the pendulum (or a function of time). From there I don't know of an exact, closed form solution. But, as I look at the math, it seems to me to imply that I need a change in my reference (i.e. a different formulation of time) or a different formulation of force. The convenient one would be one that compliments the nonlinear superposition I would use, but I haven't been able to make that work. As I said, though, there are enough smart people in the world that I figured someone must have looked at this by now. Maybe the answer lies in some of the possibilities already suggested.

Alright. I shall do that. In the meantime, maybe I'll continue to elaborate a bit more to see if it strikes a chord with anyone. Merged post follows: Consecutive posts merged Yes and no. Let me continue, because I consider nonlinear models a bandaid for systems that don't fit linear models (despite the elaborate math). Maybe that is just a philosophical issue of whether the system is "really" nonlinear, but hear me out. Because nonlinear models can be solved numerically, many people have stopped looking for the underlying physics (at least within my circle). It's too easy to plug equations into a computer and let it chug away. But the chosen form for the nonlinear model is not a settled matter. I know of one paper that makes a case against a priori selection of nonlinear models and another that demonstrates how the selection affects the results. Further, there was a "definitive" paper written on nonlinear models for elastically mounting machinery. The paper actually suggested 2 options. Both options allowed for bifurcations. A subsequent paper chose yet a third option that did not allow for bifurcations. These papers were rather old by the time I came across them, so I've had difficulty contacting the authors to ask if the elimination of bifurcations was intentional. The data to which it is compared seems to imply this, but it is never explicitly stated. The issue concerns me because I have had discussions with 2 of the world's leading experts in (macro) nonlinear dynamics. One asked me if I believed bifurcations were real because he had never personally witnessed one in the lab. Another, when I asked for help in using stochastic methods, told me not to bother - the effort wasn't worth the small payoff. All the frustrations I've encountered have gotten me to thinking about the limits of existing models. For example, I noticed that everyone uses displacement and the first 2 derivatives (velocity & acceleration) in their models. But no one uses the third derivative (jerk) - except to post-process data. I even found a comment in DenHartog's book that it's fruitless to integrate jerk into a dynamic model (which implies he tried it). I tried as well, and have to agree with him. Or think of a mass suspended on a spring. Had the idea of an imaginary coordinate not come along, people would likely have concluded it's motion was nonlinear. After all, the motion fits pretty well to a polynomial of the form x = t - t^3/3! + t^5/5! - ... (that's a joke you hopefully get). So, are we concluding certain systems are nonlinear when, if we knew how to properly represent them, we'd find they actually aren't? Or, at least, that the nonlinear behavior has a much simpler form than we tend to use. I could explain further with a pendulum example, but I'll pause here to give a chance for this to soak in.

ajb, thanks for the reply. I hope you won't regret it. I did some digging around, and found that many people are working on the edge between classical and quantum mechanics. One example would be Dr. Friedman from Amherst, but there are others. My search here involves a bit of thrashing about for several reasons. First because my training is mainly in classical physics, so I only have the vaguest grasp on quantum physics. I know that if I'm to be serious about this, I need to take the plunge into quantum physics sometime. Second, I do have some ideas that I'd like to formulate, but I suspect others have thought of it before me. So, I'm digging to see if that is the case. I suppose I should have become a physics professor (rather than an engineer) so it would be my job to do this sort of thing. Anyway, my point is that symplectic manifolds might be the answer I'm looking for, but since I don't know what they are, that's hard to say. And it's a daunting task to start with some elementary text and work my way up to understanding it only to find it's not what I'm looking for (I've done that several times now). I know I'm leaning on the kindness of strangers to tell me: oh yeah, that's been done by so-and-so in this-and-such field of research. Instead, you have every right to say: why is this my problem? I'll try to further clarify my thoughts, and we'll see if someone can recognize that it's been done, that it's a stupid idea, or that it's just not important. In Newtonian physics, "force" is the central concept. Without force, a body maintains its state of rest or uniform motion. Newtonian physics, then, becomes the study of how force changes motion. Lagrange, Hamilton, etc. reformulated physics using "energy" as the central concept (or the variational principle of least action). As it turns out, it's pretty easy to show that these two formulations are equivalent. Then along comes quantum physics (and I won't attempt to state it's central concepts for obvious reasons, though I know it's based on the idea that energy only occurs in discrete quanta). I also understand that quantum physics arose because of the attempt to explain the behavior seen in the micro (i.e. subatomic) world rather than the macro world. That is why it interests me. I mentioned Newton's second law earlier, and how people have extended it to include deformation and dissipation. But the concept of "stiffness" (force proportional to displacement) and "damping" (force proportional to velocity) are really only mathematical conveniences. Once one begins to ask what causes stiffness, one descends into the world of materials science and then chemistry and so forth, and finds there is no good link between those sciences and the concept of "stiffness". It gets even worse if the stiffness is not linear. That is when I start to ask myself: even though Newton's idea of force is convenient for a select number of linear problems, is there a better way to formulate the problem for those cases where it does not fit well?

Would anyone know if there is "new" work going on with respect to classical physics? To further clarify that question, let me explain that I'm sure there is work being done to (as Kuhn would say it) further articulate the paradigm. You know of what I speak. Someone writes a paper on the general stress in flat plates. Then someone writes a paper on circular plates with fixed edges. Then someone writes a paper on circular plates with fixed edges supporting a tabby cat. Then someone writes a paper on circular plates with fixed edges supporting tabby cats with a cold ... that's not what I'm interested in. I'd be more interested in work related to classical-quantum correspondence. I know there are several different directions one can go from there. The most obvious would be people seeking to unify the two. Next would be those who are attempting to show that one or the other is completely unfounded (i.e. that quantum physics is all wrong and classical physics can be used to explain everything). But I'm looking to split the hair even further. Amongst those looking into such matters, have any suggested that a classical-quantum correspondence most likely needs to be achieved by modifying classical physics? Let me give an example. Newton's second law (F=ma) applies to rigid bodies. If one considers deformable bodies, a stiffness term is added (F=ma+kx). If one considers how mechanical motion is dissipated as heat, damping term is added (F=ma+cv+kx). One could theoretically go on forever adding terms to capture different phenomena. So, is anyone trying to extend or reformulate the laws of classical physics? If so, I'd be interested in a name so I could educate myself (or at least attempt it). I'm sorry that this got so long, but I was hoping to make my question as clear as possible.

Moving from that instance, can a general statement be made? Could we say that in cases like Newton's 1st Law, where we would not formulate an opposing law, it is axiomatic rather than a law or theory?

I like how you broke this down. Among those you listed, #5 is the closest, but maybe I should pick #6. Let's see if Newton's First Law will serve as a better example. Though stated somewhat colloquially, this law says that a body at rest will remain at rest or a body in motion will maintain uniform motion unless acted upon by an external force. Is there an opposing theory for this? Not that I am aware of. I do not know of a theory that says a body at rest will suddenly spring into motion even though no external force has been applied. So, is this a law for which no opposition can be formulated? It has been suggested (by Poincarre, I believe) that Newton's first law is not a law. Rather, it is a tautology (self-evident merely due to the way it is defined). Should we see a body at rest begin to move, we would never presume that the 1st law has been violated. We would presume a force has been applied to the body - even if we cannot explain that force at the moment. If we can't explain it, we will devise an experiment to quantify it. So, is there anything that would ever falsify our belief in the 1st law? Or, do we merely append data to explain events within the context of the 1st law?

I knew I shouldn't have used that example. Remember, it's an example. The point was to ask if all theories necessarily imply an opposing theory. - - - For those interested in the example, let me defer you to these two sites: http://plato.stanford.edu/entries/physicalism http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof And, let me clarify one point. This is an issue of logic, not of empiricism. Whether John's sister exists (and what evidence we have for or against) is a whole other question. The question is whether assigning something a property entails that something else does not have the property. I was not trying to claim this entailment. I was asking a question. In the Stanford entry on physicalism you will see that Hume proposed a solution to the problem, and I am inclined to accept his solution (even though I'm no fan of Hume). If one accepts his solution, does this mean it would be possible to formulate a scientific theory that has no opposing theory? That seems illogical to me ... so maybe I should reject Hume altogether.

Even if you can falsify one theory, it does not mean you can fomulate another to take its place. I think we are agreeing, but I don't want to be presumptive. The Bayesians have the idea of the "catch-all". It represents those theories that oppose the one in question, but does not attempt to formulate that opposition. It seems to me that stating any theory entails that an opposing theory can be formulated. That was only an example. I didn't mean it to be the main thrust of the discussion. Regardless, I don't think I would agree with you. I wouldn't say that "non-physical" contains no items. Rather, discerning if any items exist is outside the realm of science. You would need to "know" the non-physical by other means. But that is a very philosophical discussion. I don't really want to go there.

Could you clarify? Which part do you think is incompatible?

So, do we need a "philosophy" forum? I keep looking for a good place to put these questions, but I haven't found it. First, I will apologize if someone thinks this post begins inappropriately, but I think it necessary to demonstrate the intent of my question. Philosophers have wrestled with a problem of logic involving "properties". To say that something has a property entails that something else does not have that property. For example, to say that a geometric figure is "square" because it has four sides implies that a triangle is "not square" because it has three sides. This seems trivial at first, but this logical principle has been used in some very interesting and controversial ways. For example, Godel based a proof of God on this principle. If we say that something has the property of being "physical", then we must accept that something exists which has the property of being "non-physical". And, if we insist that something "non-physical" can be "dead", then we must accept that something "non-physical" can be "alive". And if we accept that a "living non-physical" thing can be finite, then we must accept that a "living non-physical" thing can also be infinite ... and so forth. I have probably bungled Godel's proof, but hopefully you get the point. I think most would agree this "proof" is no proof at all, yet when one sets out to unseat the logic behind it, one encounters many daunting difficulties. So, I finally get to my question: does any theory exist for which there is no way to formulate an opposing theory? (and I mean a reasonable opposing theory)

There ain't no free lunch. The question is whether the advantages outweigh the problems. I'm not throwing out calculus. I'm replacing one calculus with another. It depends. Some machines advance, some don't. Some of the old stuff is very rugged, which relates to one of my earlier comments about watching machines working belly deep in mud. Some paradigms are hard to break. Using more advanced technology (for us) often means more sensitive equipment. Then we have to protect that equipment, and that means $$$. If you want to pay more for all the products my machines dig, cut, push, and lift, then I can do that. There are many changes I wish I could make, but "it's cool" doesn't justify much in the business world.

Very interesting. I understood this last post - at least enough to grasp a few ideas if not the details. And, as you predicted, it raised some questions for me. But maybe I'll save those for another day. I've been working on some stuff of my own, though it is a little more "down and dirty" than yours - and that seems to be my problem. My job is related to rotating machinery, and I have an interest in the nonlinear dynamic behavior of those machines. Within the heavy equipment industry where I operate, the typical procedure is to linearize everything. After beating my head against a wall for many years, trying to convince engineers to use nonlinear techniques, I decided to try a different approach. I realized that engineering is not only tied to Newtonian mechanics, but it is also tied to Newtonian calculus. By switching to a different calculus, I can produce some very interesting results that look much like the linear techniques that engineers love to use. If you think hard enough, you realize that the switch I propose changes common definitions such as "stiffness", "damping", and possibly even "time". People don't seem to like that. I've been trying to convince them that it's really just some fancy curve fitting, but have not gotten far. In trying to present this to professional journals, so far I have lacked the mathematical background to rigorously develop the idea, so I'm stuck. I appealed for help to some acquaintences with world-class skills and reputations, but they have declined to participate. The recommendation is that I do this as a dissertation for a doctoral program. I can't afford to do that right now, so I make what progress I can and bide my time.

Thanks for doing this. It may be that my understanding of the math you referenced is insufficient. If so, I have some responsibility to slog through it and learn more. I don't expect you to give me an online course. Of course any help is greatly appreciated. You are kind to help me out. My purpose with this thread was to gage experience with the philosophy of science. I'm glad that it seems several here are knowledgable and/or interested. I don't think that's the case in the general scientific (or engineering) community. Maybe I'll pose other questions in the future.