gullible.adjective
easily deceived or duped
gullibility.noun
gullibly.adverb

Kurt Gödel 1906-78
known primarily for his research in philosophy and mathematics. He was born in Brünn, Austria-Hungary (now Brno, Czech Republic). He was educated at Vienna University and taught at that institution from 1933 to 1938. He immigrated to the United States in 1940 and became an American citizen in 1948.
   Gödel was a member of the Institute for Advanced Studies, Princeton, New Jersey, until 1953, when he became professor of mathematics at Princeton University.
   Gödel became prominent for a paper, published in 1931, setting forth what has become known as Gödel's proof.
   This proof states that the propositions on which the mathematical system is in part based are unprovable because it is possible, in any logical system using symbols, to construct an axiom that is neither provable nor disprovable within the same system. To prove the self-consistency of the system, methods of proof from outside the system are required. Gödel also wrote The Consistency of the Continuum Hypothesis (1940) and Rotating Universes in General Relativity Theory (1950). Microsoft® Encarta® Encyclopedia 99. © 1993-1998 Microsoft Corporation. All rights reserved.

Gödel's Theorem, also known as the Incompleteness Theorem two theorems proposed by Austrian-born American logician Kurt Gödel. These theorems state that some parts of mathematics are based on ideas that cannot be proven within the system of mathematics.
   Gödel's First Theorem states that any consistent mathematical theory that includes the natural numbers (the counting numbers 1, 2, 3, 4, ...) is incomplete. Gödel's Second Theorem states that such a theory cannot contain a proof of its own consistency; consistency may be provable within some larger theory, but proving consistency within the larger theory would require an even bigger theory, leading to a never-ending sequence of ever-larger theories. In mathematics, a theory is consistent when it is free from contradictions and complete when all statements or their opposites (negations) are provable within the theory.
   Gödel used an ingenious numbering system to translate statements about a mathematical theorem T into numerical statements within T. Then he used many applications of the rules of logic (called a proof) to show that a theorem could not be proven to be consistent or complete.
   To understand how Gödel's proof works, imagine a numerical statement within T that means "this statement has no proof in T". Call this statement S and treat it like any other statement in T.
   If this particular statement S is provable in T, then S is false, which would make T inconsistent, in that it's both true and false, so really, when are things true? Therefore, S must be unprovable and thus true. If S is true, then the negation of S (not S "this statement has proof in T") must be unprovable; otherwise S would be false. Because neither S or not S is unprovable, T is incomplete. If we try to prove that T is consistent, we prove S, which is impossible. Therefore, T cannot be proven to be consistent or complete.
   Gödel published his theorem in 1931, around the time when the German mathematician David Hilbert, leading the formalism movement, proposed that every mathematical theory should be given firm logical foundations.
   Formalism aimed to establish the completeness and consistency of each theory and to decide algorithmically whether any given statement belonged in the theory.
   This would reduce mathematics to a mechanical process. Gödel's theorem showed that the formalists' first two aims of establishing completeness and consistency must fail for any theory involving the natural numbers. Similarly, the Undecidability Theorems (1936) of American mathematician Alonso Church and British mathematician Alan Turing showed that the third, deciding whether any statement belongs in a theory, must fail. comprised with Microsoft® Encarta® Encyclopedia 99. © 1993-1998 Microsoft Corporation. All rights reserved.

Grebe
common name for any member of an order of water birds, superficially resembling ducks and loons, but entirely unrelated to either. The feet of grebes, unlike those of ducks and loons, have three unconnected, flattened, flaplike toes; the fourth toe is separate and very small. Their legs are placed far back on their bodies and are not suitable for walking but enable the birds to swim powerfully. The plumage, especially on the breast, is dense and silky. The body color of most grebes is brown or gray. In spring and summer, many have tufts of feathers on the head and reddish brown patches on head and neck. In winter, most assume a plumage much like that of immature grebes gray above and white below. Grebes are about 13 to 29 inches (33 to 74 cm) long. The majority nest in swamps and on the edges of ponds. Some birds nest on plant matter floating near the edge of the water. The nests of all species are made of vegetation such as grass and reeds and lined with softer material. The eggs usually number from three to five.
   Grebes not only eat feathers, apparently their own, but also feed them to their young. Ornithologists have speculated that the feathers perform a straining function for hard, ingested substances, such as fish bones.
   Of the 21 species of grebes, seven breed in North America. The most widely distributed is the pied billed grebe, which nests from central Canada to southern South America. It is named for the black band across its short, thick bill. The largest North American species are the western and Clark's grebes, which are so similar that they were long thought to be color phases of a single species. The graceful western grebe, is well suited for life in water but cannot walk on dry land. The bird uses a variety of elaborate dances during courtship. The mating pair, shown here, race side by side across the water with their heads erect and their bodies pushed up out of the water. Microsoft® Encarta® Encyclopedia 99. © 1993-1998 Microsoft Corporation. All rights reserved.