# From "Concepts of Determinism," Chapter 3, Section 11, p.

The separation of space-time structures into manifold and metric (orconnection) facilitates mathematical clarity in many ways, but alsoopens up Pandora's box when it comes to determinism. The indeterminismof the Earman and Norton hole argument is only the tip of the iceberg;singularities make up much of the rest of the berg. In general terms,a singularity can be thought of as a “place where things gobad” in one way or another in the space-time model. For example,near the center of a Schwarzschild black hole, curvature increaseswithout bound, and at the center itself it is undefined, which meansthat Einstein's equations cannot be said to hold, which means(arguably) that this point does not exist as a part of the space-timeat all! Some specific examples are clear, but giving a generaldefinition of a singularity, like defining determinism itself in GTR,is a vexed issue (see Earman (1995) for an extended treatment;Callender and Hoefer (2001) gives a brief overview). We will notattempt here to catalog the various definitions and types ofsingularity.

## See other uses of the term Compatibility

### The Concept of 'Determinism' in American Literature

In supertasks, one frequently encounters infinite numbers ofparticles, infinite (or unbounded) mass densities, and other dubiousinfinitary phenomena. Coupled with some of the other breakdowns ofdeterminism in CM, one begins to get a sense that most, if not all,breakdowns of determinism rely on some combination of the followingset of (physically) dubious mathematical notions: {infinite space;unbounded velocity; continuity; point-particles; singular fields}. Thetrouble is, it is difficult to imagine *any* recognizablephysics (much less CM) that eschews everything in the set.

### he concluded that the Hopi have an entirely different concept of ..

Any particular example of coping is classified as being primarily adhibitory, inhibitory, or explicatory, but each has the other two strategies represented as either secondary or tertiary, respectively.