Posts tagged ‘Law’

February 7, 2013

Sturgeon’s Law

Sturgeon’s revelation, commonly referred to as Sturgeon’s law, is an adage commonly cited as ‘ninety percent of everything is crap.’ It is derived from quotations by Theodore Sturgeon, an American science fiction author.

The phrase was derived from Sturgeon’s observation that while science fiction was often derided for its low quality by critics, it could be noted that the majority of examples of works in other fields could equally be seen to be of low quality and that science fiction was thus no different in that regard to other art.

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March 13, 2012

Amdahl’s Law

amdahls law

Amdahl’s law, named after computer architect Gene Amdahl, is used to find the maximum expected improvement to an overall system when only part of the system is improved. It is often used in parallel computing to predict the theoretical maximum speedup using multiple processors. The speedup of a program using multiple processors in parallel computing is limited by the time needed for the sequential fraction of the program. For example, if a program needs 20 hours using a single processor core, and a particular portion of 1 hour cannot be parallelized, while the remaining promising portion of 19 hours (95%) can be parallelized, then regardless of how many processors we devote to a parallelized execution of this program, the minimum execution time cannot be less than that critical 1 hour. Hence the speedup is limited up to 20x.

Amdahl’s law is often conflated with the law of diminishing returns (the tendency for a continuing application of effort or skill toward a particular project or goal to decline in effectiveness after a certain level of result has been achieved). Amdahl’s law does represent the law of diminishing returns if you are considering what sort of return you get by adding more processors to a machine, if you are running a fixed-size computation that will use all available processors to their capacity. Each new processor you add to the system will add less usable power than the previous one. Each time you double the number of processors the speedup ratio will diminish, as the total throughput heads toward the limit. This analysis neglects other potential bottlenecks such as memory bandwidth and I/O bandwidth, if they do not scale with the number of processors; however, taking into account such bottlenecks would tend to further demonstrate the diminishing returns of only adding processors.

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February 3, 2012

Indiana Pi Bill

3.2

The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most famous attempts to establish scientific truth by legislative fiat. Despite that name, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for the mathematical constant π (pi), the ratio of the circumference of a circle to its diameter. However, the bill does contain text that appears to dictate various incorrect values of π, such as 3.2.

The bill never became law, due to the intervention of a mathematics professor who happened to be present in the legislature. The impossibility of squaring the circle using only compass and straightedge, suspected since ancient times, was rigorously proved in 1882 by Ferdinand von Lindemann. Better approximations of π than those inferred from the bill have been known since ancient times.

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