16 research outputs found
How to Build an Infinite Lottery Machine
An infinite lottery machine is used as a foil for testing the reach of inductive inference, since inferences concerning it require novel extensions of probability. Its use is defensible if there is some sense in which the lottery is physically possible, even if exotic physics is needed. I argue that exotic physics is needed and describe several proposals that fail and at least one that succeeds well enough
How to Build an Infinite Lottery Machine
An infinite lottery machine is used as a foil for testing the reach of inductive inference, since inferences concerning it require novel extensions of probability. Its use is defensible if there is some sense in which the lottery is physically possible, even if exotic physics is needed. I argue that exotic physics is needed and describe several proposals that fail and at least one that succeeds well enough
Generating Ambiguity in the Laboratory
This article develops a method for drawing samples from which it is impossible to infer any quantile or moment of the underlying distribution. The method provides researchers with a way to give subjects the experience of ambiguity. In any experiment, learning the distribution from experience is impossible for the subjects, essentially because it is impossible for the experimenter. We describe our method mathematically, illustrate it in simulations, and then test it in a laboratory experiment. Our technique does not withhold sampling information, does not assume that the subject is incapable of making statistical inferences, is replicable across experiments, and requires no special apparatus. We compare our method to the techniques used in related experiments that attempt to produce an ambiguous experience for the subjects
Quantum Nonlocality without Entanglement
We exhibit an orthogonal set of product states of two three-state particles
that nevertheless cannot be reliably distinguished by a pair of separated
observers ignorant of which of the states has been presented to them, even if
the observers are allowed any sequence of local operations and classical
communication between the separate observers. It is proved that there is a
finite gap between the mutual information obtainable by a joint measurement on
these states and a measurement in which only local actions are permitted. This
result implies the existence of separable superoperators that cannot be
implemented locally. A set of states are found involving three two-state
particles which also appear to be nonmeasurable locally. These and other
multipartite states are classified according to the entropy and entanglement
costs of preparing and measuring them by local operations.Comment: 27 pages, Latex, 6 ps figures. To be submitted to Phys. Rev. A.
Version 2: 30 pages, many small revisions and extensions, author added.
Version 3: Proof in Appendix D corrected, many small changes; final version
for Phys. Rev. A Version 4: Report of Popescu conjecture modifie
The Material Theory of Induction
The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it.The content of that logic and where it can be applied are determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference