The computational landscape of general physical theories

There is good evidence that quantum computers are more powerful than classical computers, and that various simple modifications of quantum theory yield computational power that is dramatically greater still. However, these modifications also violate fundamental physical principles. This raises the question of whether there exists a physical theory, allowing computation more powerful than quantum, but which still respects those fundamental physical principles. Prior work by two of us introduced this question within a suitable framework for theories that make good operational sense, and showed that in any theory satisfying tomographic locality, the class of problems that can be solved efficiently is contained in the complexity class AWPP. Here, we show that this bound is tight, in the sense that there exists a theory, satisfying tomographic locality, as well as a basic principle of causality, which can efficiently decide everything in AWPP. Hence this theory can efficiently simulate any computation in this framework, including quantum computation

Computational complexity of the landscape I

We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard. In particular, we prove that in the Bousso-Polchinski model, the problem is NP complete. We discuss the issues this raises and the possibility that, even if we were to find compelling evidence that some vacuum of string theory describes our universe, we might never be able to find that vacuum explicitly. In a companion paper, we apply this point of view to the question of how early cosmology might select a vacuum.Comment: JHEP3 Latex, 53 pp, 2 .eps figure

Connectionism, Analogicity and Mental Content

In Connectionism and the Philosophy of Psychology, Horgan and Tienson (1996) argue that cognitive processes, pace classicism, are not governed by exceptionless, “representation-level” rules; they are instead the work of defeasible cognitive tendencies subserved by the non-linear dynamics of the brain’s neural networks. Many theorists are sympathetic with the dynamical characterisation of connectionism and the general (re)conception of cognition that it affords. But in all the excitement surrounding the connectionist revolution in cognitive science, it has largely gone unnoticed that connectionism adds to the traditional focus on computational processes, a new focus – one on the vehicles of mental representation, on the entities that carry content through the mind. Indeed, if Horgan and Tienson’s dynamical characterisation of connectionism is on the right track, then so intimate is the relationship between computational processes and representational vehicles, that connectionist cognitive science is committed to a resemblance theory of mental content

"So what will you do if string theory is wrong?"

I briefly discuss the accomplishments of string theory that would survive a complete falsification of the theory as a model of nature and argue the possibility that such a survival may necessarily mean that string theory would become its own discipline, independently of both physics and mathematics