The Shape of Space

by Graham Nerlich

This is a revised and updated edition of Graham Nerlich's classic book (1976). It develops a metaphysical account of space that treats it as a real and concrete entity, showing that shape plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument and investigates how different spaces would affect perception differently. Along the way Professor Nerlich criticizes and rejects conventionalism as a non-realist metaphysics of space, concluding that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, while offering an extensive discussion of the relativity of motion.

308 pages, Paperback

First published August 26, 1976

Reviews

[J.D. Steens · Rating 2 out of 5]

The book was generally too technical for me, but there was this:

Nerlich states that there is no consensus on the notion of causes and forces. For Galileo, “uniform motion in a straight line is not caused, not forced. There is no causal explanation of it.” Newton’s first law is a “non-causal explanation” since motion is internal to a particle/object, not external. Then there’s Einstein whose General Relativity provides a “geometric explanation,” which is “a kind of explanation all its own” as the shape of space, when concentrated around a massive gravitational center, directs in incoming object-particle toward that center and conforms to its shape. Nerlich then adds that General Relativity is a theory of gravitation, not of rest and motion. It says that gravity “is space-time curvature, not a force acting among bodies across space and in time.”

Nerlich throws a curveball when he says that Newton’s first law “is an essentially geometric statement.” I think what he must mean here is that inertial bodies (Newton’s first law of motion) follow spacetime curvature toward the gravitational center. Then he adds this important qualification: Motion in spacetime comes from within a particle or object and that such motion affects (accelerates) the motion of other bodies.

These are interesting observations in three respects. First, it seems that the aura of classical physics hangs over our understanding of the cosmic world. While in that view movement in the world comes from external causation (i.e. the force of gravity), movement is also inertial - coming from the body-particle itself, though why that’s the case seems to be, for Nerlich and others, a mystery. Second, does inertial movement come from the outward trajectories of the big bang and supernova type explosions, or from the emission of photons via the interactions of matter? So, inertia is a self-caused force that also has (accelerating) effects: When matter-energy concentrates into gravitational centers, those centers affect (accelerate) other matter-energy.

Then, third, there is this notion of gravity as an attractive force which persists in all of the popularization accounts of gravity, despite Einstein saying that gravity is not a force and, therefore, gravity is not attraction. Seen this way, it could be argued that the cause of motion in the cosmos is inertia (Newton’s first law), and that straight-line motion follows spacetime curvature shaped by a gravitational center (noting Wheeler’s observation: Mass forms gravitational centers that shape spacetime, and that the inertial motion of matter-energy follows that shape, thereby adding mass to the gravitational center).