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137
The Speed Prior: A New Simplicity Measure Yielding NearOptimal Computable Predictions
 Proceedings of the 15th Annual Conference on Computational Learning Theory (COLT 2002), Lecture Notes in Artificial Intelligence
, 2002
"... Solomonoff's optimal but noncomputable method for inductive inference assumes that observation sequences x are drawn from an recursive prior distribution p(x). Instead of using the unknown p() he predicts using the celebrated universal enumerable prior M() which for all exceeds any recursive p() ..."
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Cited by 51 (20 self)
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Solomonoff's optimal but noncomputable method for inductive inference assumes that observation sequences x are drawn from an recursive prior distribution p(x). Instead of using the unknown p() he predicts using the celebrated universal enumerable prior M() which for all exceeds any recursive p(), save for a constant factor independent of x. The simplicity measure M() naturally implements "Occam's razor " and is closely related to the Kolmogorov complexity of . However, M assigns high probability to certain data that are extremely hard to compute. This does not match our intuitive notion of simplicity. Here we suggest a more plausible measure derived from the fastest way of computing data. In absence of contrarian evidence, we assume that the physical world is generated by a computational process, and that any possibly infinite sequence of observations is therefore computable in the limit (this assumption is more radical and stronger than Solomonoff's).
QuantumInspired Computing
, 1995
"... The paper identifies and demonstrates the feasibility of a novel computational paradigm which is inspired by the principles of quantum mechanics and quantum computing. A brief history of quantum computing and basic exposition of quantum mechanics are provided, followed by a detailed description of S ..."
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Cited by 36 (5 self)
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The paper identifies and demonstrates the feasibility of a novel computational paradigm which is inspired by the principles of quantum mechanics and quantum computing. A brief history of quantum computing and basic exposition of quantum mechanics are provided, followed by a detailed description of Shor's quantum `algorithm' for factoring very large numbers. An extension to Shor's method is described, and this leads to two further applications of `quantuminspired' methods: sorting, and the 15puzzle. In all cases, quantuminspired methods require the use of `classical' methods to determine whether the candidate answers provided by the quantuminspired methods are correct. Finally, some basic methodological principles and guidelines are provided for quantuminspired computing. The aim is not to provide a formal exposition of quantuminspired computing but to identify its novelty and potential use in tackling NPhard problems. 1 Introduction It has been estimated that every two years ...
Algorithmic Theories Of Everything
, 2000
"... The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong inductive bias. We show that P(x) is small for any universe x lac ..."
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Cited by 31 (15 self)
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The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong inductive bias. We show that P(x) is small for any universe x lacking a short description, and study the spectrum of TOEs spanned by two Ps, one reflecting the most compact constructive descriptions, the other the fastest way of computing everything. The former derives from generalizations of traditional computability, Solomonoff’s algorithmic probability, Kolmogorov complexity, and objects more random than Chaitin’s Omega, the latter from Levin’s universal search and a natural resourceoriented postulate: the cumulative prior probability of all x incomputable within time t by this optimal algorithm should be 1/t. Between both Ps we find a universal cumulatively enumerable measure that dominates traditional enumerable measures; any such CEM must assign low probability to any universe lacking a short enumerating program. We derive Pspecific consequences for evolving observers, inductive reasoning, quantum physics, philosophy, and the expected duration of our universe.
Everettian Rationality: defending Deutsch’s approach to probability in the Everett Interpretation
, 2002
"... ..."
Structural Issues in Quantum Gravity
, 1995
"... A discursive, nontechnical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the applicability of the conceptual and mathematical structures of bo ..."
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Cited by 23 (1 self)
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A discursive, nontechnical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the applicability of the conceptual and mathematical structures of both classical general relativity and standard quantum theory. This discussion is preceded by a short history of the last twentyfive years of research in quantum gravity, and concludes with speculations on what a future theory might look like.
Understanding Deutsch’s probability in a deterministic multiverse
 Studies in History and Philosophy of Modern Physics 35B
, 2004
"... Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from ‘probability ’ without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: ..."
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Cited by 23 (2 self)
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Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from ‘probability ’ without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular rationality principle. The decisiontheoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future Everettian measurement outcome is subjective uncertainty. I argue that subjective uncertainty is not to be had, but I offer an alternative interpretation that enables the Everettian to live without uncertainty: we can justify Everettian decision theory on the basis that an Everettian should care about all her future branches. The probabilities appearing in the decisiontheoretic representation theorem can then be interpreted as the degrees to which the rational agent cares about each future branch. This reinterpretation, however, reduces the intuitive plausibility of one of the DeutschWallace axioms (Measurement Neutrality).
On schizophrenic experiences of the neutron or why we should believe in the manyworlds interpretation of quantum theory
, 1998
"... The truth about physical objects must be strange. It may be unattainable, but if any philosopher believes that he has attained it, the fact that what he offers as the truth is strange ought not to be made a ground of objection to his opinion. – Bertrand Russell 1. ..."
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Cited by 22 (5 self)
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The truth about physical objects must be strange. It may be unattainable, but if any philosopher believes that he has attained it, the fact that what he offers as the truth is strange ought not to be made a ground of objection to his opinion. – Bertrand Russell 1.
Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems
 Am. J. Phys
, 2001
"... This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these cor ..."
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Cited by 20 (1 self)
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This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible
Decoherence, Einselection and the Existential Interpretation (The Rough Guide)
 PHIL. TRANS. R. SOC. LOND. A
, 1998
"... The roles of decoherence and environmentinduced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states ..."
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Cited by 19 (0 self)
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The roles of decoherence and environmentinduced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states were once thought to exist: there are ways of finding out what is the pointer state of the system which uses redundancy of its correlations with the environment, and which leave einselected states essentially unperturbed. This relatively objective existence of certain quantum states facilitates operational definition of probabilities in the quantum setting. Moreover, once there are states that ‘exist ’ and can be ‘found out’, a ‘collapse ’ in the traditional sense is no longer necessary—in effect, it has already happened. The role of the preferred states in the processing and storage of information is emphasized. The existential interpretation based on the relatively objective existence of stable correlations between the einselected states of observers’ memory and in the outside universe is formulated and discussed.
On the Common Structure of Bohmian Mechanics and the GhirardiRiminiWeber Theory
, 2006
"... Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonline ..."
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Cited by 18 (11 self)
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Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger’s equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about “matter” moving in space, represented by either particle trajectories, fields on spacetime, or a discrete set of spacetime points. The role of the wave function then is to govern the motion of the matter.