752 research outputs found
Why Philosophers Should Care About Computational Complexity
One might think that, once we know something is computable, how efficiently
it can be computed is a practical question with little further philosophical
importance. In this essay, I offer a detailed case that one would be wrong. In
particular, I argue that computational complexity theory---the field that
studies the resources (such as time, space, and randomness) needed to solve
computational problems---leads to new perspectives on the nature of
mathematical knowledge, the strong AI debate, computationalism, the problem of
logical omniscience, Hume's problem of induction, Goodman's grue riddle, the
foundations of quantum mechanics, economic rationality, closed timelike curves,
and several other topics of philosophical interest. I end by discussing aspects
of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and
beyond," MIT Press, 2012. Some minor clarifications and corrections; new
references adde
NP-complete Problems and Physical Reality
Can NP-complete problems be solved efficiently in the physical universe? I
survey proposals including soap bubbles, protein folding, quantum computing,
quantum advice, quantum adiabatic algorithms, quantum-mechanical
nonlinearities, hidden variables, relativistic time dilation, analog computing,
Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and
"anthropic computing." The section on soap bubbles even includes some
"experimental" results. While I do not believe that any of the proposals will
let us solve NP-complete problems efficiently, I argue that by studying them,
we can learn something not only about computation but also about physics.Comment: 23 pages, minor correction
Non-classical computing: feasible versus infeasible
Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are a range of possible architectures that could be implemented on silicon that are distinctly different from the von Neumann model. Beyond this, quantum simulators, which are the quantum equivalent of analogue computers, may be constructable in the near future
Effective Physical Processes and Active Information in Quantum Computing
The recent debate on hypercomputation has arisen new questions both on the
computational abilities of quantum systems and the Church-Turing Thesis role in
Physics. We propose here the idea of "effective physical process" as the
essentially physical notion of computation. By using the Bohm and Hiley active
information concept we analyze the differences between the standard form
(quantum gates) and the non-standard one (adiabatic and morphogenetic) of
Quantum Computing, and we point out how its Super-Turing potentialities derive
from an incomputable information source in accordance with Bell's constraints.
On condition that we give up the formal concept of "universality", the
possibility to realize quantum oracles is reachable. In this way computation is
led back to the logic of physical world.Comment: 10 pages; Added references for sections 2 and
Do we live in a [quantum] simulation? Constraints, observations, and experiments on the simulation hypothesis
The question "What is real?" can be traced back to the shadows in Plato's
cave. Two thousand years later, Rene Descartes lacked knowledge about arguing
against an evil deceiver feeding us the illusion of sensation. Descartes'
epistemological concept later led to various theories of sensory experiences.
The concept of "illusionism", proposing that even the very conscious experience
we have is an illusion, is not only a red-pill scenario found in the 1999
science fiction movie "The Matrix" but is also a philosophical concept promoted
by modern tinkers, most prominently by Daniel Dennett. Reflection upon a
possible simulation and our perceived reality was beautifully visualized in
"The Matrix", bringing the old ideas of Descartes to coffee houses around the
world. Irish philosopher Bishop Berkeley was the father of what was later
coined as "subjective idealism", basically stating that "what you perceive is
real". With the advent of quantum technologies based on the control of
individual fundamental particles, the question of whether our universe is a
simulation isn't just intriguing. Our ever-advancing understanding of
fundamental physical processes will likely lead us to build quantum computers
utilizing quantum effects for simulating nature quantum-mechanically in all
complexity, as famously envisioned by Richard Feynman. In this article, we
outline constraints on the limits of computability and predictability in/of the
universe, which we then use to design experiments allowing for first
conclusions as to whether we participate in a simulation chain. Eventually, in
a simulation in which the computer simulating a universe is governed by the
same physical laws as the simulation, the exhaustion of computational resources
will halt all simulations down the simulation chain unless an external
programmer intervenes, which we may be able to observe.Comment: 27 pages, 5 figure
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