Pithlet wrote:
I like learning the concepts and theories, but I don't like doing all the work. That's why we get computers to do that kind of stuff for us.
One discovers things by doing the work and not just learning "the concepts and theories." Sometimes, these are just new ways to visualize that are more broadly useful in other areas -- for example, doing the grunt work of solving systems of equations might lead one to initially develop and then greatly expand on the idea of matrices and linear algebra and vectors, leading into vector fields on manifolds and their application in helping visualize shapes in higher dimensions, etc. Or it might help one gain new insights, such as the arrival of the idea of angular momentum as something derived from the fundamental geometry of euclidean spaces and not just some "concept or theory" that was discovered and then absorbed.
I really love learning theories and concepts, too. And that is a good part of how undergrad physics is usually taught, too. But without doing the actual work itself as well, much intuition and inspiration is lost in the process. It's hard to know the balance here. I'm not trying to say one has to go calculate all the numbers, for example. Or do grungy manipulation of symbols forever. But there is a very, very important role to be played in having to do that work, too. And it's not just a matter of being able to do these things when your computer is down for repair. It's about seeing patterns in the work and gaining new insights from there.
Some time ago, there was a science news report on some software that together with some force-feedback gloves and special goggles was used to simulate the forces of electic potentials between molecular fragments. A chemist would put on the glasses and wear the gloves and would see himself/herself in a virtual reality where they could grab up a peptide chain, for example, and try to bring it near to some protein receptor or the like. The computer would calculate all the forces involved and press back via the gloves, so that the chemist would get some direct feedback. Over time, these chemists would begin to develop an instinct that they couldn't get any other way, about what could be done chemically. Granted, here the computer is doing the tiny calculations to operate the gloves and virtual reality simulation, but the chemist wasn't just learning about the concepts and theories here. They'd already been through all that, before. This was about sitting there trying personally to actually get two molecule pieces to orient themselves and bond, if possible, and to get some sense about what all those complex forces actually "feel" like, from "doing it manually," so to speak.
In any case, I've learned a lot of insights that no book was able to teach me just from having to actually sit down and "do the calcs," manually. Things that teachers don't teach, books don't publish, and insights about new ways to think about how things work that no one else around me had ever even considered before. I know, because I've explained some of these insights to other physicists and have received the accolades one gets when others "see" what you see and find it very helpful. And you don't get that from books. You get it from doing things, personally.
Galileo wrote something about this process, though I'd need to write a lot more to get the fuller context across. Just a sec.... Ah, yes. Here it is. Keep in mind that in his time, the term 'philosophy' was roughly equivalent to today's use of 'physics', but not quite the same, but note that in included math in the meaning of it as physics often does. It was Galileo himself who developed the idea of philosophy into the much better idea of experimental philosophy (closer to modern scientific methods.)
Galileo, in some notes on Lagallia's book wrote:
The difference between philosophizing and studying philosophy is that which exists between drawing from nature and copying pictures. In order to become accustomed to handling the pen or crayon in good style, it is right to begin by redrawing good pictures created by excellent artists. Likewise in order to stimulate the mind and guide it toward good philosophy, it is useful to observe the things that have already been investigated by others in their philosophizing; especially those which are true and certain, these being chiefly mathematical.
But men who go on forever copying pictures and never get around to drawing from nature can never become perfect artists, or even good judges of painting. For they remain unpracticed in separating the good from the bad, or the accurately from the poorly drawn, by means of recognizing in nature itself as a result of countless experiences the true effects of foreshortening, of backgrounds, of lights and shadows, of reflections, and of the infinite variations in differing viewpoints.
In the same way a man will never become a philosopher by worrying forever about the writings of other men, without ever raising his own eyes to nature's works in the attempt to recognize there the truths already known and to investigate some of the infinite number that remain to be discovered. This, I say, will never make a man a philosopher, but only a student of other philosophers and an expert in their works. I do not believe that you would esteem as a good painter a man who had made so great a study of the drawings and canvases of all painters that he could promptly identify the style of each one, even if he could also imitate them.
The point here, to my mind, is that learning good concepts and learning good theory is certainly part of a process. But only part. That the hard work of going forth and actually doing the drudgery and discovering for yourself what others have also discovered, but doing so on your own right and with your own hard work, has its value. To learn to separate the good from the bad takes direct, hands-on experience.
One can _learn_ about the theory of pendulums from a book. But when you set out to build them, one after another, and test what the theory says, you may find something new on your own or gain some new insight that others may have missed. Doing the work teaches you an eye for recognition of something important that cannot be had from learning good concepts from others, alone. For example, in the practice of making pendulums in class, one finds that students will often make slightly different sized holes that the pin rocks inside of as the pendulum swings. The relative diameters of pin and hole actually can affect the period by say 2-3% or so. Much more than the error of timing devices commonly found in the lab and much more than the locally known error of 'g' and much more than the approximation equation (the commonly found equation is NOT an exact one, as the 2nd order differential equation has a transcendental in it that complicates the solution) error of the common equation used. Most students will just do the experiments and chalk up the error as some random flaw they don't even bother to investigate or worry about. Learning to discern when it is important to dig deeper is a skill you learn by doing and no book will teach you that skill. It comes from gaining a practiced eye.
Anyway, it all goes together -- theory and practice.
Jon
_________________
Say what you will about the sweet mystery of unquestioning faith. I consider a capacity for it terrifying. [Kurt Vonnegut, Jr.]
03 Feb 2008, 11:22 pm
