Infinity
From The Art and Popular Culture Encyclopedia
"Nature is an infinite sphere, whose center is everywhere and whose circumference is nowhere" "I remembered too that night which is at the middle of the Thousand and One Nights when Scheherazade (through a magical oversight of the copyist) begins to relate word for word the story of the Thousand and One Nights, establishing the risk of coming once again to the night when she must repeat it, and thus on to infinity…" --"The Garden of Forking Paths", Jorge Luis Borges |
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Infinity (symbol: ∞) refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin infinitas, which can be translated as "unboundedness", itself calqued from the Greek word apeiros, meaning "endless".
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History
Ancient cultures had various ideas about the nature of infinity. The ancient Indians and Greeks, unable to codify infinity in terms of a formalized mathematical system, approached infinity as a philosophical concept.
Early Greek
The earliest attestable accounts of mathematical infinity come from Zeno of Elea (c. 490 BCE? – c. 430 BCE?), a pre-Socratic Greek philosopher of southern Italy and member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, described by Bertrand Russell as "immeasurably subtle and profound".
In accordance with the traditional view of Aristotle, the Hellenistic Greeks generally preferred to distinguish the potential infinity from the actual infinity; for example, instead of saying that there are an infinity of primes, Euclid prefers instead to say that there are more prime numbers than contained in any given collection of prime numbers (Elements, Book IX, Proposition 20).
However, recent readings of the Archimedes Palimpsest have hinted that Archimedes at least had an intuition about actual infinite quantities.
Cosmology
In 1584, the Italian philosopher and astronomer Giordano Bruno proposed an unbounded universe in On the Infinite Universe and Worlds: "Innumerable suns exist; innumerable earths revolve around these suns in a manner similar to the way the seven planets revolve around our sun. Living beings inhabit these worlds."
Cosmologists have long sought to discover whether infinity exists in our physical universe: Are there an infinite number of stars? Does the universe have infinite volume? Does space "go on forever"? This is an open question of cosmology. Note that the question of being infinite is logically separate from the question of having boundaries. The two-dimensional surface of the Earth, for example, is finite, yet has no edge. By travelling in a straight line one will eventually return to the exact spot one started from. The universe, at least in principle, might have a similar topology. If so, one might eventually return to one's starting point after travelling in a straight line through the universe for long enough.
Logic
In logic an infinite regress argument is "a distinctively philosophical kind of argument purporting to show that a thesis is defective because it generates an infinite series when either (form A) no such series exists or (form B) were it to exist, the thesis would lack the role (e.g., of justification) that it is supposed to play."
See also