Retrocausality at no extra cost

One obstacle faced by proposals of retrocausal influences in quantum mechanics is the perceived high conceptual cost of making such a proposal. I assemble here a metaphysical picture consistent with the possibility of retrocausality and not precluded by the known physical structure of our reality. I conclude that given the right mix of some reasonable metaphysical and epistemological ingredients there is no conceptual cost to such a picture

Signal propagation and noisy circuits

The information carried by a signal decays when the signal is corrupted by random noise. This occurs when a message is transmitted over a noisy channel, as well as when a noisy component performs computation. We first study this signal decay in the context of communication and obtain a tight bound on the rate at which information decreases as a signal crosses a noisy channel. We then use this information theoretic result to obtain depth lower bounds in the noisy circuit model of computation defined by von Neumann. In this model, each component fails (produces 1 instead of 0 or vice-versa) independently with a fixed probability, and yet the output of the circuit is required to be correct with high probability. Von Neumann showed how to construct circuits in this model that reliably compute a function and are no more than a constant factor deeper than noiseless circuits for the function. We provide a lower bound on the multiplicative increase in circuit depth necessary for reliable computation, and an upper bound on the maximum level of noise at which reliable computation is possible

On the maximum tolerable noise of k-input gates for reliable computation by formulas

We determine the precise threshold of component noise below which formulas composed of odd degree components can reliably compute all Boolean functions

Information Theory and Noisy Computation

We report on two types of results. The first is a study of the rate of decay of information carried by a signal which is being propagated over a noisy channel. The second is a series of lower bounds on the depth, size, and component reliability of noisy logic circuits which are required to compute some function reliably. The arguments used for the circuit results are information-theoretic, and in particular, the signal decay result is essential to the depth lower bound. Our first result can be viewed as a quantified version of the data processing lemma, for the case of Boolean random variables

A Comparison of Approaches and Instruments for Evaluating a Geological Sciences Research Experiences Program

This article describes a study in which changes in knowledge of science and attitudes regarding science among participants in a summer Research Experiences for Undergraduates (REU) program were examined. It was discovered that existing survey instruments could not detect changes in participants' attitudes over the course of the program and also failed to detect differences between geoscience faculty and a group of college students with limited exposure to college level science. In response to this, researchers developed a new survey instrument based on clusters of statements representing a variety of philosophical positions, from which respondents must pick one statement. It was discovered that open-ended questions about the nature of science provide a potentially richer source of information and that a survey instrument designed to probe more subtle aspects of one's beliefs about science can be used to assess adults who have had a variety of different kinds of exposure to science. The pilot survey instrument may also be able, with modifications, to assess attitude and knowledge changes caused by participation in a scientific research experience. Educational levels: Graduate or professional

Extending du Bois-Reymond's Infinitesimal and Infinitary Calculus Theory

The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and little-o/big-O defined with the Gossamer number system, and the relations algebra is explored. A comparison of function algebra is developed. A transfer principle more general than Non-Standard-Analysis is developed, hence a two-tier system of calculus is described. Non-reversible arithmetic is proved, and found to be the key to this calculus and other theory. Finally sequences are partitioned between finite and infinite intervals.Comment: Resubmission of 6 other submissions. 99 page