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THE FOURTH DIMENSIONAND THE PRINCIPLE OF LEAST ACTION: Why the Clock Says “Tick-Tock”

It has been suggested that two major themes of this website are now converging in such a way that each throws light on the other – namely, the Fourth Dimension, and the Principle of Least Action. The following essay aims to explain this connection. This may in turn throw special light on the discussion of Karl Marx, the final stop on our Dialectical World Tour – coming next!

WHAT IS “MOTION”?

Least Action – whatever our understanding of this challenging term – is certainly a way of characterizing natural motion. Natural systems, the principle asserts, move in such a way that their action shall be least. Before we concern ourselves with the mystic term action, we might do well to focus on the no less mysterious term, motion. Not only will this help us to understand the intent of the principle, I think it will lead us to see a deep link between the Principle of Least Action, and the Fourth Dimension.

What, then, is motion? We moderns tend to think of it in instrumental terms – as the means of getting from intention to accomplishment: in between planning to be something, and actually being that intended thing. In this view, motion is a sort of intermediate, between intent and accomplishment: something to be gotten over, usually as quickly as possible. “Time is money,” we say – meaning, a cost. This colorless idea time accords with the mathematical view of time as a line: our lives pass along this continuum from goal to goal, the moments between, mere means, to be passed through as expeditiously as possible. Time is money, we say, meaning cost. This uniform, colorless continuum Newton mastered by finding a way to measure motion at a point, as if the now were its dwelling-place. Taking this to the limit, he gave us the mathematics of conventional physical science: the differential calculus. Absolute, mathematical time, Newton was sure, flowed calmly through absolute space, in God’s divine sensorium.

As so often happens, the ancients had a different, more interesting point of view, suited to a richer and wiser concept of Nature itself. Calling Aristotle as our witness, we’re told that being does not lie merely at the two ends of a span of intervening motion. Rather, being inheres in the notion itself. There, in that very motion, we find ourselves in the fullness of our being. As we might expect, Aristotle has a word for this. energeia: being-at-work. And since the work is at every stage shaped to its end – its TELOS – we can call this richer, organic concept of living, EN-TELECHY.

Rest assured, this old view is by no means a threat to modern science. Leibniz, already in Newton’s time, was developing a more complex form of the calculus suitable to this richer view of motion. Instead of zeroing-in on the passing moment, it looks to the whole span of the motion, from inception to closure. It’s called the integral calculus. In its variational form, it weights every moment with respect to the goal, and hence meets Aristotle’s test of entelechy. Whether it’s a radiating atom or a busy mouse, every stage of its motion is inherently – by Nature – shaped to its goal. The motion, then, is truly whole.

Aristotle goes on to say a funny thing about time. Time, he seems to say, is the number of motion(s). To clarify, he illustrates by saying we count the number of times the horse goes around the track. More generally, in the order of being, first there is the race, and then, secondarily, we count the laps, and time arises. The whole, which is the motion, is primary; motion doesn’t happen in time. Being comes first; time is merely the count of the generations of being.

Come to think of it, that’s the way we encounter time in daily life. Our encounter with time is mediated by some motion: we count the clock which tells the time. That’s why the classic clock says, tick-tock. The swings of its balance are counted by ah escapement, going first tick, and then tock, to mark the completion of one cycle: one motion The time it tells is the count of its motions. More modern clocks, it is rue, speak in other voices, but they’re all counting motions of some sophisticated sort.

 

HOW THE FOURTH DIMENSION UNDERLIES LEAST ACTION

If we’re satisfied that a motion is essentially whole, we’re ready to turn to Least Action. All the natural world runs on the Principle of Least Action, so this is important to know about. Here is the Principle: Every natural motion, atom or mouse, unfolds in such a way that over the whole motion, total “action” will be least. Think of “action”, then, as activity-summed-over-the whole motion. Action thus refers to something Newton missed. Contra Newton, you can’t have action at a moment! More positively put, nature accomplishes the overall goal with the least possible fuss. There’s a “good reason” for that; fuss (haste) makes waste. Every activity entails heat-loss (that’s why our bodies run so hot). The horse will ultimately run at top speed, but getting-up-to-speed will be accomplished by nature as gradually as possible. In turn, once up to speed, the myriad processes throughout he body will themselves run, collectively (organically), in such a way hat the speeding horse will be expending as little energy over each cycle of the gait, as possible.

If we image a running horse by means of a three-dimensional snapshot, we’ll evidently miss Nature’s point. We need to see that motion whole: each whole cycle of the gait as one single image. Our three dimensions are not enough: we must add a fourth axis to our image. In addition to our three spatial axes, we need a time axis as well. The resulting image will then encompass in a single geometrical figure the motion as that whole which, by its very nature, it is.

Though such four-dimensional imaging can indeed present this wholeness effectively to our physical eye, a larger aim must remain: through this visual experience, to extend this same insight to the eye of the mind. We might then perceive all natural motion in this four-dimensional way – and thus, in turn, achieve a larger grasp of the wholeness of that motion of ultimate interest, life itself.

Mathematical physics has widely accepted the Principle of Least Action as its basis. Taking the term physics in its old, true meaning, as the science of all nature – the fall of a leaf, or the beat of a heart – it’s nice to know that the more modern the science, the more it attests to wholeness, and to the richness of every moment: not as transient as it may seem.

Maxwell’s Mathematical Rhetoric: Rethinking the “Treatise on Electricity and Magnetism”.

The Green Lion Press has just announced the publication of my study Maxwell’s Mathematical Rhetoric: Rethinking the “Treatise on Electricity and Magnetism”. Although this is by no means a new work, its implications for the most part still remain to be explored, and I am delighted to greet its appearance in this form.

Maxwell's Mathematical Rhetoric

What is meant by this curious phrase, mathematical rhetoric? To explain, it may be best to go back to the problem which first led me to undertake this project. Maxwell’s Treatise had been a candidate for the list of “great books of the western world” from the outset of the seminar program at St. John’s College in Annapolis – but it soon became apparent that no one could “crack’ this massive work. It introduced, indeed, Maxwell’s equations of the electromagnetic field, and with them, the recognition that light is an electromagnetic phenomenon. But these equations, and that theory, could much more quickly be reached by way of any modern textbook. What secrets might Maxwell’s work harbor, beyond the stark narrative those textbooks could offer? I set out to explore this question by reading the Treatise as a work of literature. By great good luck, I discovered that Maxwell had written with just just that intent: to compose a work of literature artfully shaped to convey a weave of interconnected messages. To this end, his primary instrument would be the art of rhetoric.

The basis of the art of rhetoric is the distinction between what is said, in a simple declarative sentence, and the way that thought is expressed.  A nuanced statement may convey meanings very different from the literal content of a sentence. Surprisingly, perhaps, the same is true of a mathematical equation. Its literal content is the numbers which it serves to compute; but its rhetorical content is the thoughts it suggests to the mind of the reader. Rhetoric is often used to win arguments, but Maxwell’s intention is very different. His aim is to suggest new ideas, and he shapes his equations to open our minds to new ways of viewing the natural world.

Maxwell’s Treatise has, in effect, two plots. Its first, overt role, is to provide a text in electricity and magnetism to support the addition of those subjects to the highly mathematical, severely demanding tripos examinations weeding out candidates for a degree at Cambridge. Maxwell however weaves into his work a much richer, more subtle plot, very nearly antithetical to the first. Throughout the book, this second plot increasingly shapes equations to give expression to the new and far more interesting ideas of Michael Faraday — who himself knew no mathematics whatever. Late in Part IV of the Treatise, a sharp turn of the narrative and the adoption of an altogether new rhetoric – a new form of the basic equations of physics — gives final victory to Faraday.  Thus when Maxwell’s field equations emerge in the Treatise, they belong to a breathtakingly new view of the natural world, while the conventions of the tripos exams have been left far behind.

That new rhetorical form, shaped to fit Faraday’s way of thinking as well as the idea of the space-filling field itself, is collectively known as Lagrange’s equations of motion. They speak not of forces, but of energies, and through them, explanation flows from a whole system to its parts, not from part to whole.

Whether we use Newton’s equations or Lagrange’s, the calculated results may be the same; but the contrasting form of the equations bespeaks a correspondingly transformed view of the natural world. Our very idea of causality is reversed. As we increasingly come to recognize the deep connectedness of the systems which surround us – from ecosystems to single cells, our own bodies and minds or a global economy – we desperately need the insight which Maxwell’s Treatise has so carefully crafted.

In that sense, perhaps, both Maxwell’s work and this study of its rhetorical trajectory are more timely today than ever before. We have already spoken on this website of Lagrange’s equations and their contrast to Newton’s, which I have called a truly dialectical alternative, and further studies of Maxwell’s rhetorical strategies, in direct reference to Maxwell’s Mathematical Rhetoric, are planned. “Stay tuned” — and as ever, comments are warmly encouraged.

A Project For Viewing Objects In The Fourth Dimension

A new menu item has just gone up on this website, at which images will be displayed of objects in the fourth dimension.  Since it is widely agreed that we are by nature incapable of seeing four-dimensional objects, something evidently needs to be said at the outset to justify this new approach.

The Case Against

The case against seeing 4D objects is easy to make, and does sound convincing. We human beings by our very nature belong to a three-dimensional world; we have neither retinas nor brains capable of seeing objects in higher dimensions. We can see projections of such objects as the  4D hypercube, for example, into our 3D world–but we have no power to see the thing  itself. We are like Abbott’s Flatlanders (Edwin Abbott, Flatland (1884), confined in their case to a 2D world, and unable to conceive a world beyond it.  We laugh at them, but Abbott’s initial point is that we are the Flatlands–confined in our case to a world of three dimensions, and unable to envision a world beyond.

But Abbott makes a further point, and his real story is one of courage and release.  The turning-point of Flatland is the breathtaking escape of his hero, A-Square, who is swept out of Flatland and indeed does view, to his amazement, a world beyond his own, as well as his own from a new vantage point–outside. Surely Abbott’s real point is to challenge us, stuck in three dimensions, to break out of our own confinement. That is the experiment we will be undertaking on this website.

The difficulty is not mathematical. In our drawings, we place the viewer’s eye at a definite, fixed position in a four-dimensional coordinate frame, and define simple objects within it. The objects lie before the eye, in relations which can be calculated and depicted. The huge question remains, however: what will such an eye actually see? Not much, we might think–for our limited, 2D retinas would seem to have no power to capture 4D images.

Response to These Objections

But here’s a problem: by the same argument, the same 2D retinas must be inadequate to see the very 3D world in which we live!  Mathematically, it is true, we’ve never actually seen our own, familiar world: we would have to be outside it, to actually view it. But that does not stop us from knowing it intimately, and seeing it in another sense.

Evidently, real vision is not simply a mathematical question: the eye is not a camera. Rather, it is a powerful extension of the brain, actively searching and interpreting, constructing a meaningful and coherent understanding of the world we live in, and love. We “see” objects growing smaller as they recede into the distance; but from infancy, our interpretive visual system has learned the tricks of 3D visual intuition: we know automatically that the objects remain unaltered.  And if this is the case, there would seem to be no obstacle to carrying out our project, exploring the possibilities of a visual experience of four-dimensional space. Maybe our visual intuition is capable of learning new interpretive tricks!

The New Proposal

We propose therefore to look directly at the mathematically defined objects within it, with the aim of building a new structure of visual intuitions appropriate to the fourth dimension. It’s hardly necessary to stress the importance such a capability might have, given the striking ability of the visual cortex to “see”–graphically or otherwise–the relationships among groups of interrelated factors. The ability to visualize complex functions in a four-dimensional coordinate frame might be enough to convince mathematicians and scientists of the practical value of such an augmented power of visual intuition.

For an initial example of the method at work go to my webpage on the fourth dimension. Where you can post any comments which occur to you.

The Two Minds of Charles Darwin

I’ve wanted for some time to write this note, but have hesitated because there are so many others who know Darwin far better than I. Nonetheless, I have a certain conviction I’d like to share.

Two minds seem to be at work as Darwin surveys the natural world and its evolution. One sees natural selection in terms of confrontations between individuals or species in the search for limited resources. We all know that scenario, which in most of our discussions has become the very paradigm of Darwinian selection.

But Darwin has unmistakably another line of thought, which grasps the utter complexity of the selection process: not as a competition between individuals, but as a system whose complexity defies analysis. If we were to make an improvement in a breed in order to increase its chances of survival, we would not, he remarks, know what to do. In another passage, he remarks on the flourishing of a certain flower in one particular English village. What advantage does this plant have here, which it lacks elsewhere? The answer, he has decided, is the absence of dogs. (Dogs, he reasons, eat cats; cats eat mice; mice eat seeds.) I’ve forgotten why there are no dogs, it might be some village regulation. Whatever it is, there lies the strength of the flower: not in its own design alone, but in the structure of that ecosystem, which has at least for a time stabilized in a pattern collective survival –a pattern, we might say simply, of collective health.

This I believe is an overriding principle, which we have tended since Darwin’s time to miss. That principle, almost systematically ruled out of all facets of our thinking – even our very ideas of medicine or science itself, is the overriding concept of organism, the recognition that we live, flourish and evolve as a whole – not as a sum of individual parts. Only in recent years have we begun to study ecosystems, of all sorts and levels, as wholes. As a society, we’re far behind the demands pressing upon us in catching Darwin’s other, and I believe higher, insight.

The stereotype in describing the components of living systems, to ever-higher levels of resolution, is mechanism. Wrong! We will never understand living organisms as summations of mechanisms. A living system is a different concept altogether from a machine, and study of it calls for different strategies, and different conceptual tools.

Much new work is being done now in the spirit of this new understanding. I’ve found exciting studies of ecosystems to which I want to call attention in an upcoming blog posting. Indeed, it’s not a new thought on this blogsite, which has traced the idea of organism back to its rich source in the writings of Aristotle, and fast-forward through western history to Leibniz, Euler, Lagrange, Maxwell, Hamilton, Feynman and modern physics. But in the din of our celebration of Newton, isolation and competition, we haven’t heard, or perhaps have deliberately rejected, these other voices. We’ve caught only the lesser of the two voices of Charles Darwin.

Cancer and Ecosystems

Peter Gann was a member of our Aristotle discussion group at Pemaqud Point in Maine this summer.  In response to a question I had raised in the wake of our discussions, Peter has written a letter which I find so interesting that, with his permission, I’m reproducing it here a a sort of “guest blog”.  Dr. Gann is Professor and Director of Reearch in the Department of Pathology of the University of Illinois in Chicago.

Dear Tom,

Your question about cancer and ecosystems naturally leads to Virchow! It was he who recognized cancer (and other diseases)as disorders within the community of cells that make up an organ or an organ system. I find this to be a very useful analogy.

The healthy function of the organ requires that each differentiated cell carry out its designated role while remaining in its designated space. How this unfolds during organ development is fascinating and deeply mysterious, but it seems to involve special “tunes” – primitive ones – played out within the genome as well as lots of direct chemical communication between nearby cells.

At some point, once the organ has developed, these signals must change so that such rapid growth and morphogenesis can stop and a more “mature” ecosystem of stable, collaborating cells can emerge.

Cancer cells overcome the signals that maintain this stable ecosystem, and, even appear to hijack some of the genetic programs that are used to control normal development.

This is not too far from how the Ailanthus tree in our backyard (which Wendy identified this summer) threatens our local ecosystem by hyperproliferation, exploitation of local energy sources, and evasion of organisms that would otherwise control its spread. Left undeterred, the Ailanthus could be viewed as a pathological force that would eventually destroy the native Midwestern woodland that we consider to be healthy.

I suppose one could look at all invasive exotic species through the same analogical lens. [But then, thinking of that awful tree in the backyard, maybe this is just demonizing the enemy before going to war!]

The response of an ecosystem to this type of imbalance raises very interesting questions and it would not surprise me to learn that there are numerous examples of stressed ecosystems righting themselves, through adaptation, since the invasive force can be seen as a stimulus to natural selection, just as a change in climate would be. It would take a serious ecologist to deal with that question.

I believe I do recall that some of the early thinkers in the field of ecology (as well as some of the post-Darwin evolutionary biologists) were very interested in the analogy between cell communities and ecosystems. It would be interesting to know what Virchow thought of Darwin.

All the best,

Peter

The Aristotelian Pathway to the Modern World and Beyond

I’m just back from a week of seminars in Maine: an overview of Aristotle’s world-view, based on a sequence of selected readings.  Although I’ve long been curious about Aristotle’s thinking, and written about this to some extent on this website, I’ve never before caught the full coherence and impact of his world-view. I’ll leave details to future posts to this blog, but here’s an overview of a few highlights.

Tradition has misleadingly titled many of Aristotle’s works. His “Physics” is not limited to what we today call “physics”, but actually addresses the foundations of the entire natural world, of all things that move, from stones to living creatures, including ultimately ourselves. Aristotle’s “Physics”, then, lays the foundation for his other works, and in the “Metaphysics”, of the cosmos itself. We ourselves he will say, are rational by nature.

What is “nature”?  An inner principle of motion, Aristotle says; things move not because they are pushed or pulled, but through inner tendencies. This is by no means nonsense. Within what we call “physics”, think for example of the second law of thermodynamics, which asserts, in more formal terms, that heat “tends” to flow downhill. Within our own lives, think of fear or love, and our innate desire to know. Thus in Aristotle’s inclusive world-view, there’s no occasion for the infamous split which today appears to divide our sciences from the humanities.

Such unification need not threaten the integrity of the sciences. Remarkably, within this encompassing perspective Aristotle lays a secure foundation for a fully valid alternative approach to modern science. Key is his concept of “energy” (the word, energeia, is his!); motion consists in the unfolding of energy from potential to kinetic form. Importantly, energy belongs primarily to whole systems, so wholeness and living, organic unity are foundational in Aristotelian science.

In the 17th century Leibniz, who knew his Aristotle, put this into mathematical form. He introduced, in open opposition to Newton, a version of the calculus which served to open alternative path into not just modern physics, but modern thought more generally.

As a result, we can discern two very different, parallel pathways through the history of western thought – one leading to Newton, Descartes, and a world of force, competition and mechanism; the other, prefigured by Aristotle, leading to wholeness, cooperation, friendship and life.

The path through Newton, Locke and Hobbes is very familiar to us; it has led t the world we know today, a world of strife, competition, and ever-escalating warfare. That other thread, which runs from Leibniz, Euler, Lagrange, Hamilton, Faraday, Maxwell and Einstein, bespeaks unity and intelligent cooperation. Within physics, this appears especially in the concept of the field; but more generally, it looks to a society of intelligent cooperation in the solution of our common human problems. It is easy to see, I believe, which is better suited to address the problems of warfare and environmental catastrophe which beset human society today.

Nobody, of course, is offering us this choice of roads into the future.  But we have independent minds, and it would be good to know that there is a difference in principle even if we see no way at present to pursue it in practice. I propose to write more about this in upcoming postings – and it will be good to know what others think of this Aristotelian way I’m convinced I’m seeing.

An Ecosystem As A Configuration Space

In my most recent posting, I’ve been exploring a quite classic mathematical model of an ecosystem: the Salt Marsh ecosystem model developed at Sapelo Island and described in the fascinating 1981 volume, “The Ecology of a Salt Marsh”. For those of us who are devoted to grasping the “wholeness” of an ecosystem, the question arises whether matching such a system to a mathematical model helps in grasping this wholeness – or whether it may even detract. The concern would be that true unity is broken when a whole is described in terms of relationships among discrete parts: as if the “whole” were no more than a summation of parts – in Parmenides’ distinction, an ‘ALL” (TO PAN), exactly the wrong approach to a true “WHOLE” (TO HOLON).

An excellent guide in these matters is James Clerk Maxwell, who faced this question as he searched for equations that would characterize the electromagnetic field in its wholeness. As soon as he learned of them, he embraced Lagrange’s equations of motion, and as he formulated them, his equations derive from Lagrange’s equations, not from Newton’s. For Lagrange, the energy of the whole system is the primary quantity, while the motions of parts derive from it by way of a set of partial differential equations. Fundamentally, it is the whole which moves, the moving entity, while the motions of the parts are quite literally, derivate.

The components of such a system may be any set of measurable variables, independent of one another and sufficient in number to characterize the state of the system as a whole. Various sets of such variables may serve to characterize the same system, and each set is thought of as representing the whole and its motions by way of a configuration space. If we have such a space with the equations of its motion, we’ve caught the original system in its wholeness: not as a summation of the components we happen to measure, but in that overall function in which their relationships inhere.

Now, it seems to me that a mathematical model of an ecosystem, to the extent that it is successful, is exactly such a configuration space, capturing the wholeness of the ecosystem whose states and motions it mirrors. Specifically, the authors of the Sapelo Island Marsh Model were if effect working toward just this goal, though it may not have appeared to them in just these terms. All their research on this challenging project was directed toward discovering and measuring those connections, and the integrity of the resulting mathematical system was exactly their goal.

They had chosen to construct their model in terms of carbon sinks and flows; the measures of these quantities were sufficient to characterize the state of the system and its motions, and therefore constituted a carbon-configuration space of the marsh. A different set of measures might have been chosen, and would have constituted a second configuration space for the same system: for example, they might have constructed an energy-model, which have been equivalent and represented in other terms the same wholeness of the marsh. Carbon serves in essence as a representative of the underlying energy flows through the system.

I recognize that this discussion may raise more questions than it answers, and I would be delighted to receive responses which challenged this idea. But I think it sets us on a promising track in the search for the wholeness of an ecosystem – an effort, indeed, truly compatible with the wisdom of Parmenides!

Can An Ecosystem Model Help Us Think About Wholeness?

Readers of this website will be aware of my preoccupation with the question of “wholeness”. The more I observe the world’s current struggle to find its way through complex economic structures or global systems, the more convinced I become of the degree to which our deep-rooted commitment to individualism is betraying us. Individualism is both an ethic, which we are determined to impart to the world, and a habit of thought. This is not the moment to follow that line of thought further; it has been the subject of other postings, and it will be of more in the future.

My concern at the moment is to offer a new approach to this issue. On a visit to the Key School in Annapolis recently, on the shores of the Chesapeake, I was struck by the widespread awareness there that the Bay is sick: 27% of true health was the figure I was hearing. That led me to wonder about the concept of “health” of an ecosystem, and how it might be grasped. With the aid of the computer, I knew, the human mind is today able to reason about problems hitherto too complex to analyze. Could I find a computer model of an ecosystem?

By good luck, I’ve found not only such an ecosystem model, but a revealing account of a team project by which it was achieved. Teams of experienced scientists agreed to set aside their normal researches into separate compartments of the ecosystem, and direct their efforts  instead to a different kind of learning: to the common goal of constructing a coherent computer model which would capture the intricate interrelationships of these many components of one single system.

The system to which fortune had led me was a salt marsh at Sapelo Island on the coast of Georgia. The Book, edited by L. R.Pomeroy and R.G.  Wiegert, is “The Ecology of a Salt Marsh” (New York, 1981). Its innocent title fails to suggest the very special interest of the project it narrates. Quite elegantly, the book pulls together a fascinating account of the scientists’ experience in disciplining their work to this goal.

An aesthetic of wholeness is invoked at the outset, with lines from  Sydney Lanier’s poem, “The Marshes of Glynn”. We learn much about this new sort of scientific endeavor when the book closes with a section on the aesthetic of the marsh, and a final quotation from that same poem.

Though a layman in matters of biology, I’ve since been making an effort to follow the turns of this inquiry. I won’t say more how, beyond the remark that the effort proved successful only after the scientists had learned of a fundamental error they had been making, and accepted correction from the computer.

People whose judgment I very much respect have expressed their doubts as to the whether such a computer model is an appropriate means for approaching wholeness, or whether at this point I’m confusing true wholeness with a mere assemblage of parts by complicated aggregation. (My thoughts go back to Plato’s “Parmenides”, and the paradigm there of Hesiod’s wagon: I agree that the “wagon” is something quite other than an assemblage of its parts!)
In these terms, is a working computer model helping us to grasp the wholeness of a system, or betraying us into confusing true wholeness with a merely clever example of aggregation? In the case of a living ecosystem, in which the wholeness is manifestly organic, is the computer misleading us, tempting us to confuse organism with a complex structure of inherently inorganic parts?

My case for the computer as a welcome aid in advancing toward a  grasp of true wholeness must be made in future remarks which I plan to post soon.

The Modern Muse and the Science Museum

It’s great to be able to announce the arrival of a new entry to the Articles department of this website.  One of a series of studies I wrote over the years for the Encyclopaedia Britannica’s Great Ideas Today, it’s titled The Abode of the Modern Muse: The Science Museum. It can be reached by going to Articles on the menu bar; there, choose Great Ideas Today,; and finally, within Great Ideas Today, select the article itself.

I took the opportunity of this assignment to reflect on a long tradition beginning with the MUSEION, the grove sacred to the Muses of ancient Greece, and leading, I claim, in a way important to us today, to the role and concurrent  responsibility  of the modern science museum. Along the way the essay makes major stops, first at Alexandria, where it treats the celebrated “Library” as more truly an academy, and thus just such a meeting-ground of human minds; and finally, at our own Smithsonian Institution, regarded from its inception as a centerpiece of the scientific spirit of our nation.

One crucial role at the outset of this story is that of Aristotle, who affirmed, very much in his manner as thoughtful observer, that the human community is in essence one, and that a fundamental goal, alike of ethics and of politics, must be to realize this truth in practice. The tradition seems secure that Philip of Macedon, to free his son from the distractions of the court at Pela, hired Arisotle as tutor of Alexander, and sent the two of them off to the hills of Macedonia to focus on education.  The curriculum may have been cut short by Alexander’s early ascent to the throne, but it seems clear that Aristotle’s advice concerning the unity of the human community was foremost in Alexander’s mind when he made the founding of Alexandria in Egypt one of his first, and most successful projects.

There were to be many more Alexandrias as Alexander carried his campaign of munification across the Middle East. Readers may have encountered a recent exhibit of Ai Khanoun, an Alexandria discovered to everyone’s complete surprise under the sands of northern Afghanistan; my guide at the East Wing of the National Gallery in Washington reported there are believed to be perhaps a dozen more to be unearthed, if our own present wars might cease. But the Egyptian center was surely the best. It began, indeed, as a “library”, whose mission was to collect books from the entire Mediterranean basin; copies were made at a publishing house (apparently the building close to the harbor destroyed by the legendary fire).  The copies were sent back to the sources, while the originals were stored securely at Alexandria.

The books, however, were gathered to be studied, not simply to be stored, and in this sense Alexandria is better thought of as paradigm of the universitas, than as library, fundamental as the books themselves must be. As university, Alexandria was conceived to be a new center of human learning for the entire Mediterranean world. It succeeded in that role to a remarkable extent, and we today are its beneficiaries in ways of which we aren’t always aware. This was indeed a science museum, as the works of Ptolemy and Euclid, to cite just two examples, attest. Euclid’s Elements is a synoptic work, a gathering of contributions from probably widespread sources. What is most exciting in that work is Euclid’s own: his brilliant grasp of a profound unity arising out of these contributions. It is a true Alexandrian moment when Euclid perceives in this mathematics the pattern of the tragic trilogy: for those tragic texts were being gathered and assembled in their own unities by that single community of thinkers. It had not occurred to anyone-least of all to Aristotle!-that the human mind need be or could be, compartmentalized into separate academic domains as we have done today.  Academic labors could indeed be divided, but the human mind, as gathered at Alexandria, remained focused on the whole.

This understanding, the article claims, remained intact in the early days of our republic: it is not by chance that our corporate seal, reproduced on the dollar bill (as well as on the seal of my own college, St. John’s) depicts an Egyptian pyramid and an insightful eye. Nor that the leader of the procession dedicating the new Smithsonian Institution was reportedly wearing George Washington’s Masonic apron. When Smithson’s benefaction was accepted as a gift to this nation, the concept of the liberal arts and the unity of learning was still very much alive, and the institution founded in his name was meant as a center of new learning very much in the Alexandrian tradition. We tend to forget this, but other science museums, here and abroad, today wear that same mantle, whether we are always aware of it or not. Most unfortunately, we forget that is not just science, conceived as domain of human endeavor separate from others, but rather science as an integral component of that spectrum of all human thought, collectively the best we can do in understanding and guiding our precarious life on this planet today.

The essay closes with a severe criticism of the abandonment by the Smithsonian, under heavy industry pressure, of a project in conjunction with an exhibit of the Enola Gay. The exhibit had been thoughtfully designed to help the public review in a social and ethical context, the decision to launch our two atomic bombs. Some readers of the essay in the past have disagreed with this judgment on my part, and in this matter, as in all others, I would welcome readers’ comments.

Now more than ever we as a world community need to gather our collective wits by any means possible. Science stands at the center of many of our pressing concerns, and the science museum may still be one of the best institutions we can turn to, as the grove of our modern muse.