What Do we Mean by the Term "Elementary"?

What do we mean when we use the term ,”elementary”, in relation to a science? Does it refer to an easy introduction, as contrasted with an “advanced” treatment of the same subject? Or does it mean a solid account of the very foundations of the science? Or, for that matter, are these the same thing?

Maxwell had a tendency toward writing “elementary” texts: he wrote one on heat, and another on mechanics, both for use in classes for workingmen – a project to which he was deeply committed. Finally, at the time of his death he was at work on his “Elementary Treatise on Electricity and Magnetism, intended to serve as the Cambridge text to support a new degree in experimental natural philosophy at Cambridge University.

My sense is that Maxwell endowed each of these with earnest attention – that he regarded the “elements” not as evident, but as a topic to be approached with great care. Our decision as to what is elementary in a science has a great deal to do with our sense of the form the finished product will take – so that the most difficult issues may focus on the most elementary beginnings.

For example, Maxwell wrote his workingmen’s text in mechanics, Matter and Motion, only after he had hit on the fundamental idea, new to him, of Lagrnagian mechanics and generalized corrdinates. This would not be a mechanics in Newtonian form, in which the elements would be assumed to be hard bodies acting upon one another according to laws; rather, elements of this sort would be the least known components of the system, represented by generalized coordinates.

In this view, what we observe initially is a whole system of some sort; it is this whole which is fundamental, and truly elementary. The parts which compose it, we may never know. Our science can be complete and secure even if that question remains unresolved, or unresolvable.

This is the point of view I believe Maxwell had come to, underlying his approach to the new program at Cambridge as well. If so, must it not represent a truly revolutionary inversion of our very concept of scientific knowledge?

It fitted the primacy he – following the path of Farday – was giving to the concept of the electromagnetic field. In this view, he field would not be a secondary phenomenon, a composite or consequence of simpler “elements”, but itself both simple and whole.

If the elementary is what is primary, then in the case of the field it is the whole which is the element, from which we deduce what we can, concerning lesser components. Faraday had felt strongly that in the case of electricity, there was no “charge” lying on the surface of a charged body, but what we call a “charge” was a field, which filled the room.

Isn’t it the case that when we ask for the “explanation” of a physical system, we are asking for an account in terms of its elements? If so, then the field is itself explanatory, and we would not seek explanation in terms of the actions of some lesser parts. What will be the consequences if we extend this view to physical explanation – or explanation beyond the realm of physics -- more generally?

"The Dialectical Laboratory": A lecture on behalf of holism in the sciences

My lecture, the “Dialectical Laboratory ” (see the "lectures" section of this website) , was given as a sort of parting statement to the St. John’s College community in Santa Fe.  But though directed to the college, and expressed by way of references to certain of the “great books” of that tradition, its message is of far broader import.  The “dialectical” issue – meaning, a watershed of western thought – is between a science based on mechanical actions between disparate parts, and a holistic science in which wholeness is respected, and whole systems are regarded as fundamental, not as mere aggregations of parts.  

Each of these two very different scientific approaches has its rigorous theory, and either can be used to solve engineering problems.  But conceptually they are worlds apart, and I am convinced it’s crucial that we follow the way of holism, and learn, before it’s too late, to appreciate and work with systems – from the least living organism to the global environment – which are more than the sum of mechanical parts.  Science is moving in this direction, but there is now no time to lose! 

Comments on these remarks, as well as on the lecture itself, will be welcome in reponse to this posting. 

In Praise of Generalized Coordinates

I've been expressing my enthusiasm for a holistic approach to the understanding of nature -- in relation to my favorite topic, the electromagnetic field, this takes the form of the Lagrangian equations for the field as a single, connected system characterized by its energy, not by forces.  It was crucial to Maxwell's development of the equations of the field in his "Treatise on Electricity and Magnetism" that they be formulated as instances of such a connected system -- i.e., in Lagrangian terms, and NOT on the basis of Newton's laws of motion.  (The difference -- very fundamental to our understanding of nature -- is developed in "The Dialectical Laboratory", in my "Lectures" menu.) Now, the question arises: "If we start in this way, from the 'top down', how do we ever arrive at the elements?"   The answer is, "We DON'T!" We move logically "downward" by finding the dependence of the energy of the whole system upon ANY set of measurements we want to make -- provided only that it's a complete (i.e. sufficient to determine the state of the system), with each measure "independent" of the others. We find such a set of measurements by doing experiments -- and when we get them, they are called "generalized coordinates".  The important thing is that there may be many ways we can define them, each set as good as the others: and in the whole process we never get any"real,underlying elements" -- we don't need them!  Reality is founded at the top, not the bottom, of the chain of explanation.   This is Maxwell's new view of physical reality, founded upon the field.  It is the opposite of the notion of "mechanical explanation", and it is the direction which our approach to nature desperately needs to take as we approach the challenges which lie before us today.  In terms of the philosophy of science, Maxwell it seems was far ahead of his time.  I propose to call this the "Maxwellian Revolution". 

Indigenous Views of Nature and the Deep Roots of Western Science

When I wrote yesterday about the "deep roots" of Western science, I intended to point to a possible relation this opens up between the domain of "science" and Indigenous views of the natural world.  If we follow that line of development which leads from Aristotle through Leibniz to the holistic mathematical physics based on the Principle of Least Action, we find ourselves in a position much closer to that of Native American thinkers than we might have expected.Modern science in its mechanical mode cuts off "science" from any sense of wholeness or, especially, of purpose. It wants to reduce all quality to quantity, all motion to the operation of laws which bind matter apart from any sense of goal or meaning, and sees "nature" exclusively as an object from which we stand apart as mere observers. None of these limitations apply to the physics in the holistic mode.  Least Action applies to whole systems, and sees systems moving directionally toward the optimization of a quantity which applies to the system as a whole.  Although this goal may be no more than the optimization of a mathematical quantity, it opens the way to thinking of systems such as organisms or ecologies as moving as wholes toward ends -- a line of thought of which the modern world is in desperate need.One more link in this line of thought: the modern computer is bridging the gap ;between "quantitative" and "qualitative" thinking.  What goes in as number typically comes out on the computer screen as a graphical image readily grasped by the intuitive mind and conducive to interpretation in terms of purposes and goals. We can see how systems are moving, and where they "are going".   Nothing stands in the way of reading these in terms of purposes, and that is what we do on a daily basis -- think for example of evidences of the consequences of global warming emerging from complex computer modeling.  Thinking in this way in terms of whole systems,  understanding their motions in terms of a mathematics of optimization, and bridging the gap between quality and quantity -- all this is yielding an approach to science at once new and old -- in a continuous thread leading from Aristotle into the age of the modern computer.  If we follow that path and think of modern science in terms like these, then it seems to me the gap between a holistic science and Indigenous relations to the natural world is not as deep as it had seemed.  Set aside mechanistic thinking, embrace the sense of nature as a whole of which we ourselves are part, admit goal as a category amenable to science -- and then the old gap between Indigenous, or simply hunan views of the world, and those of "western science", begins to dissolve.   Thus the Cosmic Serpent project, designed to consider this relationship, begins to look much more promising than it otherwise might have.