The Straitening of Science

Stephen L. Talbott

From In Context #3 (Spring, 2000)

The geometer’s straight line, the line of infinitesimal width and unerring rectitude, does not exist in this world. Not as a material thing. Perhaps the closest we come to it is in the play of sun and cloud, when luminous shafts shape the razor-straight pillars of a temple celebrating the light's penetration of darkness. But this spectral architecture refuses our urge toward minute inspection and verification, forcing us to fall back upon our own conceptual finesse. Yes, we know that there are straight lines; but the reason we know is not that they are given to us ready-made in the world. We must cooperate in sending them forth.

We are not, however, always justified in doing so.

We Are Children of Abstraction

On the first day of the creation of modern science, Newton said: Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed on it.

There is an odd historical shift here. No objects of our acquaintance ever move in straight lines. Even to produce approximately straight motion, we must subdue the natural tendencies of things, employing all our cunning and artifice to isolate the possibilities of movement along just one dimension of space, abstracted from all the rest. To bind and constrain nature in this way, forcing it to reveal narrow possibilities it would not otherwise entertain, was once considered the genius of science. Francis Bacon, widely regarded as the preeminent father of the scientific method, believed that:

The secrets of nature betray themselves more readily when tormented by art than when left to their own course. (Quoted in Butterfield 1965, p. 112)

And yet, just a half century later this compulsion, this tormenting, was already second nature and forgotten, at least in the one mind plotting the future most surely. When Newton looked out upon the world, what he saw was inert bodies moving naturally and serenely along the geometer's improbably straight lines. Only so far as they were compelled by external forces did these objects consent to the deviate pathways of everyday life.

The historical shift, then, was this: Bacon could have accepted Newton's crucially simplifying abstraction only as a confession wrested from the confusion of everyday appearances through a kind of torture. Newton, no longer heedful of the torture, just “saw” the abstraction directly as if it were the fundamental manifestation of nature; the messy, everyday appearances, which he attributed to external and inessential compulsions, faded from his view.

Today, of course, like inert objects ourselves, we have followed upon Newton's trajectory, turning neither to the right nor to the left. With Newton we understand well that the moon is always trying to move in a straight line—this despite the evidence of our senses, which tell us that virtually everything in the universe, from the smallest trickle of water to the most remote galaxy, is always trying to find a center it can spiral around.

We are children of abstraction. We even construe the circle as an infinite collection of infinitesimal straight line segments — not because we really believe that roundness is straightness, but because we're not particularly interested in either quality, preferring instead to gain effective methods of calculation and prediction. But the thoughts facilitating calculation are not always the thoughts leading most directly to understanding.

There is No Canonical View

Moreover, once cut loose from reality, abstractions sabotage an observation-based science by denying us our starting point: accurate observation. Where the two walls and ceiling of my room meet in a corner, upward and to the right of the desk I am now sitting at, I can scarcely tell whether the three angles present themselves as obtuse or acute. I know they are exactly 90 degrees, so my eyes insist on seeing textbook right angles. My senses, protective of my cherished abstractions, “lie” to me.

“A harmless thing,” you may reply. “And in any case, regardless of your peculiar position right now, the corner consists objectively — not just abstractly — of three right angles. If you ever try to build a house, you'd better not forget this fact.”

But this reply can only mislead. I’m not denying definite form to the three walls, but if you wish to claim a privileged place for one particular appearance—even for the one you call “objective”— you'll have to justify your choice.

My “peculiar position” right now is, in fact, as good as any other. After all, the walls present themselves to me as they do without the wood being wrenched out of shape. The appearance from this vantage point is what it ought to be — it is one aspect of what a right-angled corner is — and a carpenter could build the walls correctly if given drawings from my vantage point. It might be more difficult, but this has nothing to do with the truth or the importance of the representation.

Moreover, the vantage point we naively take to be the single, “objective” one showing three right angles is, strangely enough, the one vantage point it is impossible to achieve. That's why we normally give the carpenter a series of separate, two-dimensional drawings. Any drawing in three-dimensional perspective, however accurate, must represent some such view as the one I now see.

What we have done is to take certain abstractions — especially measurements — and vaguely assume that these give us a canonical view of what we have measured. But measurements do not give us a view at all, much less a canonical one. To understand a thing is to see how it presents itself under the most varied circumstances. Only then do we approach a full realization of what we are studying.

Tom Stoppard once wrote a dialog that neatly punctured the idea of a single, canonical view of things. It ran, I distantly recall, something like this:

1st speaker: We are fortunate that, beginning with Copernicus, people were willing to do violence to their senses, accepting a heliocentric view of the solar system despite the fact that it looks as if the sun revolved around the earth.

2nd speaker: And what would it look like if it looked as if the earth revolved around the sun?

The answer, of course, is that it would look exactly as it now does look from our vantage point — just as the corner in my room looks exactly as such a corner should look from where I am sitting. Every object presents manifold possibilities of appearance, each of which is an aspect of the truth. Our task is not only to distinguish among these possibilities, but also to hold them together, without prejudice. The more deeply we grasp a phenomenon, the more readily do all its appearances become a dynamic unity for us.

I daresay that many of us today, watching the sun overhead, do see, in a very direct sense, the earth rotating on its axis and circling the sun. It's now a natural thing; those are the concepts that inform the phenomenon for us. But if we can no longer also see the sun circling around us, then our understanding of the material world has been impoverished. The latter view, after all, yields a mathematically simpler description of certain twining, spiraling, and circling movements of plants.

The Motions of Real Things

If the Copernican Revolution freed us from a geocentrically fixated outlook, was it only so we could adopt a heliocentrically fixated outlook? Granted, it serves certain calculational purposes to imagine ourselves positioned in space northwards of the sun, looking down on a giant sheet of graph paper with the sun sitting on the origin. But surely there is no more magic about this position than the geocentric one. And what about the view from the center of the galaxy, where the audience enjoys a beautiful, twisting pas de deux between earth and sun? Yet we inform every new generation of students that the ancients had it wrong, and that we — who have simply repeated the old provincialism from a new province — finally broke through to the truth.

That graph paper with its origin and axes has enabled miracles of computation relevant to travel within the solar system. Without it we'd never have landed a man on the moon. But if our children's textbooks are any guide, the abstractions useful for computation seriously threaten our observational openness. We become rigid and inflexible, losing the diverse qualities of things. We reject other points of view — such as the medieval one — merely because they are other points of view, and we thereby fail to enrich our own point of view.

Abstractions — number and logic, for example — are like that. They push us toward binary oppositions, either-or choices. (Is that corner made up of 90-degree angles or not? If so, shouldn't there be a view that captures the fact, to the exclusion of all other views?) But if we live by abstraction alone, we no longer have the manifold richness of reality; we no longer have real things to choose between with our binary logic. We abandon the world.

At least the heliocentric view is one of the genuinely possible views. The motion of Newton's undisturbed inertial object can never appear, even in principle, since it is unclear what it would mean to remove the rest of the universe, leaving a single object to fulfill its now emptied and one-dimensional destiny. You can, of course, remove the universe notionally, through abstraction. We have done exactly that, and have failed to ask ourselves how we might rectify the consequent falsification of the world. If it is misleading to say that the nature of a circle is that of a straight line, it is even more misleading to say (as Newton's severe abstraction has encouraged us to say) that the nature of material objects “left to themselves” is to move in straight lines.

The problem here is that the material object has fallen from view, so that we can't rightly speak of it at all. We are left to contemplate the disincarnate motion we have abstracted from it. Only then are we tempted to agree with philosopher Daniel Dennett:

Central to Newton's great perspective shift was the idea that ... rectilinear motion did not require explanation; only deviations from it did. (Dennett 1995, p. 364)

But if we're trying to understand the actual world, then surely any object in strict, rectilinear motion would require explanation. After all, such motion is all but impossible. At the very least we should refuse to forget our own necessary role as “tormentors” in producing approximations to rectilinear motion. Or, insofar as we insist on treating the motion in abstract, calculational purity, we should keep in mind the fact that we have eliminated the object itself from consideration, and therefore we have no right to claim we are elucidating its nature when we talk about motion in straight lines.

What Dennett should have said is only that rectilinear motion does not require special calculation. When a motion is restored in our understanding to the objects from which we abstracted it, then a great deal may need explaining, including these objects' apparent preference for “deviating” from straight-line motion.

On the Nature of Things

I realize full well how shocking to our scientific sensibilities would be any suggestion that material objects, by nature, move curvilinearly. But it is a healthy exercise to realize at least this much: the fact that Newton's formulation conduces to effective calculation for certain purposes says no more about the straight-line-moving nature of the objects he is describing than our convenient graph paper with the sun at its origin tells us about some origin-occupying nature of the sun.

Newton simply was not talking about the “nature” of things. You cannot talk about things and their nature without talking about their qualities, and he took up his place within a scientific movement that had long preferred to ignore qualities, concerning itself instead with whatever quantities could be abstracted from them.

We have no right, then — standing by Newton's side — to scorn the view that material objects naturally seek a curving path. We may dismiss the very idea of an “intrinsic nature”— but then we had better not add under our breath that “really, objects by nature move in a straight line unless acted upon by an external force.” Either we give up the pretense that we're describing the nature of things — as opposed to developing some useful abstractions for approximately calculating the simplest material motions — or else we must open ourselves to the full and unexplored range of possibilities offered by a qualitative science.

Perhaps, after all, it is no accident that in the real world from which Newton abstracted his equations, external and compelling forces always just “happen” to be there. Perhaps it is no accident that the very meaning of “external” has been obscured by modern physics, so that the atom cannot, even in principle, be “left to itself” — cannot be defined apart from its interactions with every other particle in existence. And perhaps it is no accident that even those archetypically “straight” light rays breaking through the clouds — if only we can imaginatively achieve their vantage point, their scale of action, their natural habitat — are found to be pursuing great and sinuous circles touching the rim of the known universe.

References

Butterfield, Herbert (1965). The Origins of Modern Science. New York: The Free Press.

Dennett, Daniel C. (1995). Darwin's Dangerous Idea: Evolution and the Meanings of Life. New York: Simon & Schuster.