A supertask is a process in which an infinite number of individuated actions are performed in a finite time. A Newtonian supertask is one that obeys Newton''s laws of motion. Such supertasks can violate energy and momentum conservation and can exhibit indeterministic behavior. Perez Laraudogoitia, who proposed several Newtonian supertasks, uses a local, i.e., particle-by-particle, analysis to obtain these and other paradoxical properties of Newtonian supertasks. Alper and Bridger use a global analysis, embedding the system of particles in a Banach (...) space, to determine the origin of the strange behavior. This paper provides a common framework for the discussion of both the local and global methods of analysis. Using this single framework, the areas of disagreement and agreement are made explicit. Further examples of supertasks are proposed to illuminate various aspects of the discussion. (shrink)
The supertasks described by Perez Laraudogoitia, involving the dynamics of a system containing an infinite number of particles in a bounded region of space, are characterized by the nonconservation of energy and by the spontaneous motion of particles (“self-excitation”'). We argue that these features arise from the inadequacy of the local, particle-by-particle description used to analyze the supertasks. A global analysis, involving embeddings in Hilbert spaces, clarifies these supertasks and avoids what we regard as their nonphysical features.
Genetic discrimination is becoming an increasingly important problem in the United States. Information acquired from genetic tests has been used by insurance companies to reject applications for insurance policies and to refuse payment for the treatment of illnesses. Numerous states and the United States Congress have passed or are considering passage of laws that would forbid such use of genetic information by health insurance companies. Here we argue that much of this legislation is severely flawed because of the difficulty in (...) distinguishing genetic from nongenetic tests. In addition, barring the use by insurance companies of a genetic test but not a nongenetic test (conceivably for the same multifactorial disease) raises issues of fairness in health insurance. These arguments suggest that ultimately the problems arising from genetic discrimination cannot be solved by narrowly focused legislation but only by a modification of the entire health care system. (shrink)
In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at (...) the time the supertask is due to be completed, or else they rely on the application of the time-reversal transformation to states which are not well-defined. Consequently, it is unjustified to conclude that the paradoxical results are arising from within the framework of Newtonian mechanics. In the last part of this article, we discuss various aspects of the physics of these supertasks. (shrink)
A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...) discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time. (shrink)
Background. As the development and use of genetic tests have increased, so have concerns regarding the uses of genetic information. Genetic discrimination, the differential treatment of individuals based on real or perceived differences in their genomes, is a recently described form of discrimination. The range and significance of experiences associated with this form of discrimination are not yet well known and are investigated in this study. Methods. Individuals at-risk to develop a genetic condition and parents of children with specific genetic (...) conditions were surveyed by questionnaire for reports of genetic discrimination. A total of 27,790 questionnaires were sent out by mail. Of 917 responses received, 206 were followed up with telephone interviews. The responses were analyzed regarding circumstances of the alleged discrimination, the institutions involved, issues relating to the redress of grievances, and strategies to avoid discrimination. (shrink)