Figure 1: Simple model of computation in an M-H space-time.
A hypercomputer is able to finish infinitely many computations in finite time. Any user could hence get all the answers to any computable question rather quickly, including for instance the greatest prime number. Given our laws of physics, such devices cannot be built. However, there are theories of hypercompuation that makes use of relativistic space-time curvature. These would have to operate though for an infinite amount of time in their little pocket of the universe. This requires a rather reliable machine. Here I argue against such reliability. I start by examining the physical Church-Turing (PhCT) thesis and its interplay with supertasks and hypercomputation. I will introduce Piccinini’s usability constraint for testing the viability of possible counterexamples to PhCT and will examine relativistic hypercomputation to that end. I propose that ontic pancomputationalism is a possible solution of an infinitely persisting computation, but note that instead of the machine, the observer now perishes and also the computing function becomes unusable. Quintessentially, I conclude that on the reliability constraint alone, all hypercomputation will fail in nomologically accessible worlds.
In his book chapter, Bourne introduces the layman reader to the basic non-mathematical postulates of special relativity. He begins by presenting our common-sense intuitions about the additivity of speeds between objects, which turns out to be violated, since no speed can be added to exceed the speed of light c. This has some counterintuitive consequences for concepts like simultaneity and the uniform passage of time.
JJC Smart: “Indeterminism does not confer freedom on us: I would feel that my freedom was impaired if I thought that a quantum mechanical trigger in my brain might cause me to leap into the garden and eat a slug.” (2003: 63)
Libertarian free will (FW) cannot be defended solely by looking at the implications of quantum mechanics (QM). However, the last century threw a lot of empirical evidence onto us, the implications of which for FW are not yet understood. I shall define FW as the ability to choose out of my own will between genuine alternatives. Alas I require the actions of an agent to be causae sui (CS) i.e. their own cause, or, for an agent to have the ability to originate actions. To achieve such a definition from QM implications, one ought to first look at what these implications are and establish that they can affect us. I shall then examine the trade-off between randomness and freedom and finally look for CS among their implications. I will finish by offering a partial solution to the problem. This post assumes a logical positivist point of view and ignores epistemic concerns over QM. For simplicity, it will furthermore employ a counterfactual account of causation.