|Infinity, infinite, philosophy: infinity is a result of a not stopping procedure, e.g. counting or dividing, or e.g. the continued description of a circular motion. In life-related contexts, infinitely continuous processes, e.g. infinite repetition, or never ending waiting are at least logically not contradictory. A construction rule does not have to exist to give an infinite continuation, such as e.g. in the development of the decimal places of real numbers. See also boundaries, infinity axiom, repetition, finitism, numbers, complex/complexity._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
W. Poundstone on Infinity - Dictionary of Arguments
Thomson's lamp/Poundstone: light turns on for 1/2 minutes, then off for 1/4 minutes, then 1/8 on ... Total: 1 - question: is it on or off after 1 min? (Sum of infinite elements) -
wrong question - analog: if the greatest number is odd/even.
I 228 ultimately physical limits: frequency, energy, switches.
Zenon/Achilles/Poundstone: Solution: overtaking after 111,111 ... cm - the "infinity" lies in Zeno's analysis, not in physics - Arrow paradox: even in the relativity theory the moment remains vague - here we also believe in cause and effect: the present determines the future - how does the arrow know, where it must go? - No physical problem, row term no solution.
Infinity/border/Lukrez: wanted to prove infinity of the space: if someone hurls an arrow towards the border, it will either fly over the border, or something stops it - so no border - PoundstoneVsLukrez: error, to accept a "something".
Olbers Paradox: four times the area balances like four times weaker radiation - it would heat up on earth to the average temperature of stars - solution: shift of red.
Multiplicity/ZenonVs: even the shortest line contains an infinite number of points, then the whole universe in a nutshell - also hierarchy of even smaller particles - containing mostly nothing, so there was nothing in 99.99% ... - solution/Poundstone: Blur effect by electrons - we needed X-ray vision, which would be switched on only when straightforward connection - then myriads of electrons and quarks - because you cannot see an infinitly small point, everything would be invisible._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Labyrinths of Reason, NY, 1988
Im Labyrinth des Denkens Hamburg 1995