Moore bound

An upper limit on the number of nodes in a regular graph of degree d>2 and diameter k:

	N(d,k) <= d(d-1)^k - 2
		  ------------
		      d-2

<2001-03-16>

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Moore George Edward

<biography, history of philosophy> during his long career at Cambridge University and as Editor of the premier British philosophical journal, Mind, G. E. Moore (1873-1958) made an enormous contribution to the development of twentieth-century Anglo-American thought. Although he had studied with Bradley and McTaggart, Moore was an early leader in the revolt against absolute idealism. Amazed by the peculiar character of philosophical controversy, Moore supposed that common-sense beliefs about the world are correct as they are. The purpose of philosophy is not to debate their truth, but rather to seek an appropriate analysis of their significance. Moore was a significant influence on Russell, Wittgenstein, Ryle. Moore's departure from idealistic philosophy began with a criticism of internal relations in the careful analysis of truth and falsity in "The Nature of Judgment" (1899). In "The Refutation of Idealism" (1903) he also drew a sharp distinction between consciousness and its objects and argued explicitly against the idealistic belief that esse est percipi. Continuing to develop his realistic convictions, Moore argued in "A Defence of Common Sense" (1925) that we all certainly know the truth of many propositions about ourselves, bodies, and other people, even though we may be uncertain about the correct analysis of these propositions. Both idealists and skeptics, Moore argued, implausibly deny this simple, everyday knowledge. Moore's preoccupation with these issues is evident even in Some Main Problems of Philosophy (1953). Moore applied similar methods of analysis to moral philosophy in Principia Ethica (1903) and Ethics (1912). There he used the open question argument to reject the "naturalistic fallacy" of identifying good with anything else. On Moore's view, good is a simple, non-natural, indefinable quality of certain things, including especially personal friendship and aesthetics appreciation. This conception of the possibilities for human life was a significant influence on John Maynard Keynes and other members of the Bloomsbury group. Recommended Reading: Primary sources: G. E. Moore, Philosophical Studies (Routledge, 1965); G. E. Moore, Principia Ethica (Prometheus, 1988); G. E. Moore, Some Main Problems of Philosophy (Collier, 1962). Secondary sources: E. D. Klemke, A Defense of Realism: Reflections on the Metaphysics of G. E. Moore (Humanity, 1999); Philosophy of G. E. Moore, ed. by Paul A. Schlipp (Open Court, 1993). Additional on-line information about Moore includes: Geoffrey J. Warnock's article in The Oxford Companion to Philosophy. Also see: analysis, analytic philosophy, Cambridge philosophy, English philosophy, linguistic philosophy, moral philosophy, the naturalistic fallacy, non-natural properties, the open question argument, and internal and external relations. The article in the Columbia Encyclopedia at Bartleby.com. The thorough collection of resources at EpistemeLinks.com. A short article in Oxford's Who's Who in the Twentieth Century. A brief entry in The Macmillan Encyclopedia 2001.

[A Dictionary of Philosophical Terms and Names]

<2002-03-10>

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Moore graph

A graph which achieves the Moore bound. These are complete graphs, polygon graphs (regular graphs of degree 2) and three others: (nodes, degree, diameter) = (10,3,2), (50,7,2) and the possible but undiscovered (3250,57,2).

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Moore's Law

<architecture> /morz law/ The observation, made in 1965 by Intel co-founder Gordon Moore while preparing a speech, that each new memory integrated circuit contained roughly twice as much capacity as its predecessor, and each chip was released within 18-24 months of the previous chip. If this trend continued, he reasoned, computing power would rise exponentially with time.

Moore's observation still holds in 1997 and is the basis for many performance forecasts. In 24 years the number of transistors on processor chips has increased by a factor of almost 2400, from 2300 on the Intel 4004 in 1971 to 5.5 million on the Pentium Pro in 1995 (doubling roughly every two years).

 Date      Chip     Transistors   MIPS clock/MHz
 -----------------------------------------------
 Nov 1971  4004       	   2300   0.06	 0.108
 Apr 1974  8080       	   6000   0.64	 2
 Jun 1978  8086       	  29000   0.75	10
 Feb 1982  80286      	 134000   2.66	12
 Oct 1985  386DX      	 275000   5   	16
 Apr 1989  80486      	1200000  20   	25
 Mar 1993  Pentium    	3100000 112   	66
 Nov 1995  Pentium Pro  5500000 428    200
 -----------------------------------------------

Moore's Law has been (mis)interpreted to mean many things over the years. In particular, microprocessor performance has increased faster than the number of transistors per chip. The number of MIPS has, on average, doubled every 1.8 years for the past 25 years, or every 1.6 years for the last 10 years. While more recent processors have had wider data paths, which would correspond to an increase in transistor count, their performance has also increased due to increased clock rates.

Chip density in transistors per unit area has increased less quickly - a factor of only 146 between the 4004 (12 mm^2) and the Pentium Pro (196 mm^2) (doubling every 3.3 years). Feature size has decreased from 10 to 0.35 microns which would give over 800 times as many transistors per unit. However, the automatic layout required to cope with the increased complexity is less efficient than the hand layout used for early processors.

http://www.intel.com/intel/museum/25anniv/html/hof/moore.htm.

Intel Microprocessor Quick Reference Guide.

"Birth of a Chip", Linley Gwennap, Byte, Dec 1996. See also March 1997 "inbox".

Chronology of Events in the History of Microcomputers, Ken Polsson.

See also Parkinson's Law of Data.

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