| Blog entry: Newton's embracing bodies |
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| Written by Sean Miller | |||||
| Saturday, 07 October 2006 | |||||
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The following is an essay that considers classical Newtonian gravity as a conceptual metaphor.
This is Newton’s famous formula for gravity. It states that the force of gravity between two rigid bodies is equal to the product of their rest masses divided by the square of the distance between them multiplied by a gravitational constant. F is force, measured in newtons, which is the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.[1] G is the gravitational constant, estimated—using currently available technologies—to be 6.6742 x 10-11 m3/(s2km).[2] m represents the point mass of the respective bodies. r is the distance between the bodies.
Of course, patterns of change do play a significant albeit subordinate role—as the motions of these rigid bodies implicit in gravitational attraction and its correlate, acceleration. Change, in Newtonian ontology, is the motion of rigid bodies through space. Space has three dimensions, which correspond directly to the three axese in which our own bodies move: up/down; left/right; and forward/back. Significantly, in the Newtonian universe, time is also a spatial dimension. This becomes all the more apparent when one considers another compelling aspect of Newtonian ontology, a belief originating with Pythagoras: that the essence of the universe is number—a kind of form. By exploiting Cartesian calculus, Newtonian mechanics inserts time into the formalism as a variable that functions along an axis, just as the spatial dimensions do. Motion in space, then, as a pattern of change, operates in a background of infinite space and an absolute time infinite in extent and infinitely divisible.[6] What this implies is that space and time, taken as a totality, have one absolute synoptic observer: that observer is fixed, immobile, and presumably eternal; He (one imagines Newton reserving this role for an anthropomorphic God) observes the point-like rigid body of time moving along its space-like dimension. Another revolutionary inference in Newtonian ontology—that comes as a direct consequence of the formalism—is the unification of heaven and earth. Since the motion of rigid bodies due to the attractive force of gravity is a function of the square of the distance between them, what those before Newton considered distinct source-path-goal schemas merge into one formula. Rigid bodies on earth follow a parabolic trajectory in their descent, for example, a cannon ball shot from a cannon. Out in the heavens, rigid bodies follow elliptical trajectories, e.g. the orbit of the moon around the earth. Newton’s theory revealed the correspondence between these two seemingly disparate events: elliptical and parabolic trajectories are both functions of the square of distance at play in the force of gravity. This brings us to the last of the inferences that arise from a cosmology of rigid bodies and flat background space: force as causation. In the Newtonian system, a ‘location causation’ prevails: causation is the forced movement of an entity to a new location.[7] But what or who exactly does the forcing? To again employ conceptual metaphors from cognitive linguistics, in Newton’s universe nature is conceived of as a human agent.[8] Causes are a force exerted by this agent and events are the effects of that force. Thus, at the heart of the Newtonian worldview, the force of gravity is the action of a human-like agent at a distance, infinite in reach and instantaneous in its effect. In this reading, the rigid bodies of Newton’s universe are human bodies with invisible hands that reach out, grab hold of, and pull in other bodies. Ultimately, the source domain for the conceptual metaphor of the force of gravity is the pulling in, the embrace, of human hands. Much has been made of how the Newtonian cosmology is mechanistic—cold and lifeless. Ironically, if we take the trouble to coax out the metaphor lurking within the machinery of Newtonian formalism, we find that an almost maternal will to embrace animates the theory. In this sense, it is comforting to realize that the force of gravity holds the meta-body that is the universe together through its warm embrace. Newton’s precursors, notably Galileo and Kepler, saw out into space. Newton’s great contribution was, with his theory of gravity, to reach out into space. The Galilean epistemology is a knowing as seeing, whereas the Newtonian is a knowing as seeing through touching. As such, one can argue that the radical paradigmatic shift in Newtonian theory finds its impetus in the choice of and formal commitment to a novel conceptual metaphor. Along with being a revolutionary physicist, Newton was also master of a poetics of the physical. Yet to suggest that a human embrace informs Newtonian gravity is not to deprecate its potential efficacy. While over three centuries old, Newtonian physics has proven its aptness time and again: at slow speeds relative to the speed of light and on sufficiently large scales, its formalism has demonstrated an incredible accuracy. As the Apollo programme can duly testify, Newton’s theory played a pivotal role in successfully ushering astronauts to the moon. Nonetheless, devout Newtonians would see the theory’s canonical status become irrevocably problematised with the advent of Einstein’s theory of special relativity. [1] Clearly, Newton himself did not describe the gravitational constant in terms of newtons. This is a contemporary refinement on Newtonian mechanics. [2] Note: m, metres; s, seconds; km, kilometres. [3] The Principia states this notion explicitly: The relevant section is entitled De motu corporum, on the motion of bodies. See Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World, trans. by Andrew Motte and Florian Cajori. (Berkeley, CA: U. of California Press, 1962). [4] Lakoff and Johnson, Philosophy in the Flesh, p. 229. [5] The formula above does not incorporate other important aspects of Newtonian mechanics, such as time and the three dimensions of the physical space of our universe. Other formulas, some employing vector calculus, treat these contingencies. Lakoff and Núñez argue that the concept of infinity itself is a metaphor: ‘processes that go on indefinitely are conceptualized as having an end and ultimate result, an infinite thing’. The infinite ‘thing’ here is a container that holds an indefinite sequence of processes. In the case of Newtonian mechanics, the indefinite sequence of processes would be the motion of rigid bodies: presumably, they could travel indefinitely across the expanse of space. See Lakoff and Núñez, Where Mathematics Comes From, p. 158. [6] ‘Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably and without relation to anything external.’ From Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World, trans. by Andrew Motte and Florian Cajori. (Berkeley, CA: U. of California Press, 1962), vol.1, p. 6. [7] Lakoff and Johnson, Philosophy in the Flesh, p. 184-7. [8] Lakoff and Johnson, Philosophy in the Flesh, p. 212.
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The independent variables here are ‘m’ and ‘r’. G is a metric that formalizes the smallest possible increments at which the force of gravity operates—around the scale of 10-11 meters cubed. The force of gravity, as such, is relatively weak compared to the other forces, electromagnetism, and the weak and strong nuclear forces. Consequently, gravity becomes noticeable on large scales but has relatively little effect on the dynamics of individual subatomic particles at low energies and microscopic scales. Note that while describing with great precision a set of relationships between two rigid bodies in terms of the square of the distance between them, the formula is not purely differential. Embodied human agents are required to intervene to give the formula its meaning: they must physically measure out conventionally established grounding units: metres, seconds, and kilograms. As such, the formula only has significance within the enveloping context of embodied experience, of the work of grounding it, through the sensorimotor system, to the environment.
The variable m metonymically embodies the basic-level metaphor at work in 
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