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Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version of the Church–Turing Thesis is unaffected by SAD computation. 1 SAD Computability 1.1 The basic idea of SAD computation 1.2 Avoiding supertasks 1.3 Davies's model of SAD computation 1.4 Hogarth's model of SAD computation 1.5 Generalizing SAD computers 2 Physical Computability 2.1 The Physical Church–Turing Thesis 2.2 Deterministic barriers to physical computation 2.3 Probabilistic barriers to physical computation 3 Effective Computability 3.1 The Effective Church–Turing Thesis 3.2 Hogarth's challenge to the Effective Church–Turing Thesis 3.3 Arguing from SAD computability is a non-sequitur 3.4 SAD computability is built from finitary computability 4 Concluding Remarks 1 SAD Computability 1.1 The basic idea of SAD computation 1.2 Avoiding supertasks 1.3 Davies's model of SAD computation 1.4 Hogarth's model of SAD computation 1.5 Generalizing SAD computers 1.1 The basic idea of SAD computation 1.2 Avoiding supertasks 1.3 Davies's model of SAD computation 1.4 Hogarth's model of SAD computation 1.5 Generalizing SAD computers 2 Physical Computability 2.1 The Physical Church–Turing Thesis 2.2 Deterministic barriers to physical computation 2.3 Probabilistic barriers to physical computation 2.1 The Physical Church–Turing Thesis 2.2 Deterministic barriers to physical computation 2.3 Probabilistic barriers to physical computation 3 Effective Computability 3.1 The Effective Church–Turing Thesis 3.2 Hogarth's challenge to the Effective Church–Turing Thesis 3.3 Arguing from SAD computability is a non-sequitur 3.4 SAD computability is built from finitary computability 3.1 The Effective Church–Turing Thesis 3.2 Hogarth's challenge to the Effective Church–Turing Thesis 3.3 Arguing from SAD computability is a non-sequitur 3.4 SAD computability is built from finitary computability 4 Concluding Remarks

SAD Computers and Two Versions of the Church–Turing Thesis