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In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. [1] Supertasks are called hypertasks when the number of operations becomes uncountably infinite .
The thought experiment concerns a lamp that is toggled on and off with increasing frequency. Thomson's lamp is a philosophical puzzle based on infinites. It was devised in 1954 by British philosopher James F. Thomson, who used it to analyze the possibility of a supertask, which is the completion of an infinite number of tasks.
A graph that shows the number of balls in and out of the vase for the first ten iterations of the problem. The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity.
Thomson's conditions for the experiment are insufficiently complete, since only instants of time before t≡1 are considered. Benacerraf's essay led to a renewed interest in infinity-related problems, set theory and the foundation of supertask theory.
Besides the cardinality, which describes the size of a set, ordered sets also form a subject of set theory. The axiom of choice guarantees that every set can be well-ordered, which means that a total order can be imposed on its elements such that every nonempty subset has a first element with respect to that order.
Phrenology – a theory of highly localised brain function popular in 19th century medicine. Homeopathy – a theory according to which a disease can be cured by infinitesimal doses of the substance that caused it; Eclectic medicine – transformed into alternative medicine, and is no longer considered a scientific theory
Agreed! After seeing the PDF I still don't know what a supertask (or any of the other things mentioned there) is! Brianjd 06:08, 2004 Dec 12 (UTC) The meaning of the term supertask in popular computer science and in hypercomputing agrees with the one from mathematics and philosophy.
David Landes similarly condemns of what he terms the unscientific moral geography of Ellsworth Huntington. He argues that Huntington undermined geography as a science by attributing all human activity to physical influences so that he might classify civilizations hierarchically – favoring those civilizations he considered best. [23]