Karma or "Karm"(Sanskrit: कर्म from the root kri, "to do", meaning deed) or Kamma (Pali: meaning action, effect, destiny) is a term in several eastern religions that comprises the entire cycle of cause and effect. Karma is a sum of all that an individual has done and is currently doing. The effects of those deeds actively create present and future experiences, thus making one responsible for one's own life. In religions that incorporate reincarnation, karma extends through one's present ...

Including:

Karma - Karma in the Dharma-based religions
Karma - Hinduism Karma - Buddhism
Karma - Analogs of Karma - God the judge Karma - Western interpretation
Karma - New Age and Theosophy Karma - Psychology

Read more here: » Karma: Encyclopedia - Karma

Zeno's paradoxes are a set of paradoxes devised by Zeno of Elea to support Parmenides' doctrine that "all is one" and that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. Several of Zeno's eight surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another; and most of them were regarded, even in ancient times, as very easy to refute. Three of the strongest and most famous—that of Achilles and the tortoise, the Dichotomy arg ...

Including:

Zeno's paradoxes - The Paradoxes of motion
Zeno's paradoxes - Achilles and the tortoise Zeno's paradoxes - The dichotomy paradox Zeno's paradoxes - The arrow paradox
Zeno's paradoxes - Proposed solutions
Zeno's paradoxes - Proposed solutions to the arrow paradox Zeno's paradoxes - Proposed solutions both to Achilles & the tortoise and to the Dichotomy Zeno's paradoxes - Problem with the calculus-based solution Zeno's paradoxes - Are space and time infinitely divisible? Zeno's paradoxes - Does motion involve a sequence of points? Zeno's paradoxes - Conceptual approaches
Zeno's paradoxes - Status of the paradoxes today Zeno's paradoxes - Two other paradoxes as given by Aristotle Zeno's paradoxes - The quantum Zeno effect

Read more here: » Zeno's paradoxes: Encyclopedia - Zeno's paradoxes

The Condon Committee was the informal name of the University of Colorado UFO Project, a study of unidentified flying objects, undertaken at the University of Colorado and directed by physicist Edward Condon from 1966 to 1968. The Condon Committee was instigated at the behest of the United States Air Force, which had studied UFOs since the 1940's. After examining many hundreds of UFO files from the Air Force’s Project Blue Book and from civilian UFO groups NICAP and APRO, the Committee selected 56 to analyze in detail f ...

Including:

Condon Committee - History
Condon Committee - Background Condon Committee - Enter Condon Condon Committee - The Trick Memo Condon Committee - The Study Begins Condon Committee - Internal Tensions Begin Condon Committee - Cracks in the Dam Condon Committee - The Trick Memo Exposed Condon Committee - Publicity Condon Committee - The Condon Report
Condon Committee - Sources

Read more here: » Condon Committee: Encyclopedia - Condon Committee

Cantor set - The Cantor set is uncountable. It can be shown that there are as many points left behind in this process as there were that were removed. To see this, we show that there is a function f from the Cantor set C to the closed interval [0,1] that is surjective (i.e. f maps from C onto [0,1]) so that the cardinality of C is no less than that of [0,1]. Since C is a subset of [0,1], its cardinality is also ...

See also:

Cantor set, Cantor set - What's in the Cantor set?, Cantor set - Non-endpoints in the Cantor set, Cantor set - Properties, Cantor set - The Cantor set is uncountable, Cantor set - The Cantor set is a fractal, Cantor set - Topological and analytical properties, Cantor set - Variants of the Cantor set, Cantor set - Historical remarks, Cantor set - Historical references, Cantor set - Modern references

Read more here: » Cantor set: Encyclopedia II - Cantor set - Properties

Gödel's second incompleteness theorem can be stated as follows: For any formal theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent. (Proof of the "if" part:) If T is inconsistent then anything can be proved, including that T is consistent. (Proof of the "only if" part:) If T is consistent then T does not i ...

See also:

Gödel's incompleteness theorem, Gödel's incompleteness theorem - First incompleteness theorem, Gödel's incompleteness theorem - Second incompleteness theorem, Gödel's incompleteness theorem - Gentzen's theorem, Gödel's incompleteness theorem - Meaning of Gödel's theorems, Gödel's incompleteness theorem - Examples of undecidable statements, Gödel's incompleteness theorem - Misconceptions about Gödel's theorems, Gödel's incompleteness theorem - Discussion and implications, Gödel's incompleteness theorem - Minds and machines, Gödel's incompleteness theorem - Proof sketch for the first theorem, Gödel's incompleteness theorem - Proof sketch for the second theorem, Gödel's incompleteness theorem - Footnotes

Read more here: » Gödel's incompleteness theorem: Encyclopedia II - Gödel's incompleteness theorem - Second incompleteness theorem

There has been much scientific opposition to the irreducible complexity, with one science writer calling it a "full-blown intellectual surrender strategy." [9] It may be that irreducible complexity does not actually exist in nature: that the examples given by Behe and others are not in fact irreducibly complex, but can be explained in terms of simpler precursors. Thus they would either be merely very complex, or they would be misunderstood or misrepresented. The precursors of complex systems, when they are not useful in themsel ...

See also:

Irreducible complexity, Irreducible complexity - Definitions, Irreducible complexity - Stated examples, Irreducible complexity - Flagella, Irreducible complexity - Blood clotting cascade, Irreducible complexity - Forerunners, Irreducible complexity - Criticisms of irreducible complexity, Irreducible complexity - Gradual replacement, Irreducible complexity - Handicaps and sexual selection, Irreducible complexity - Falsifiability and experimental evidence, Irreducible complexity - Behe's own Criticisms, Irreducible complexity - God and Irreducible Complexity, Irreducible complexity - Claimed significance

Read more here: » Irreducible complexity: Encyclopedia II - Irreducible complexity - Criticisms of irreducible complexity

Hindu-Arabic numerals system - Origins. Buddhist inscriptions from around 300 B.C. use the symbols which became 1, 4 and 6. One century later, their use of the symbols which became 2, 4, 6, 7 and 9 was recorded. These Brahmi numerals are the ancestors of the Hindu-Arabic glyphs 1 to 9, but they were not used as a positional system with a zero, and there were rather separate numerals for each of the tens (10, 20, 30, etc.). Hind ...

See also:

Hindu-Arabic numerals system, Hindu-Arabic numerals system - Positional notation, Hindu-Arabic numerals system - Symbols, Hindu-Arabic numerals system - History, Hindu-Arabic numerals system - Origins, Hindu-Arabic numerals system - Adoption by the Arabs, Hindu-Arabic numerals system - Adoption in Europe

Read more here: » Hindu-Arabic numerals system: Encyclopedia II - Hindu-Arabic numerals system - History

Gödel's second incompleteness theorem can be stated as follows: For any formal theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent. (Proof of the "if" part:) If T is inconsistent then anything can be proved, including that T is consistent. (Proof of the "only if" part:) If T is consistent then T does not i ...

See also:

Gödel's incompleteness theorem, Gödel's incompleteness theorem - First incompleteness theorem, Gödel's incompleteness theorem - Gödel's Theorem, Gödel's incompleteness theorem - Second incompleteness theorem, Gödel's incompleteness theorem - Gentzen's theorem, Gödel's incompleteness theorem - Meaning of Gödel's theorems, Gödel's incompleteness theorem - Examples of undecidable statements, Gödel's incompleteness theorem - Misconceptions about Gödel's theorems, Gödel's incompleteness theorem - Discussion and implications, Gödel's incompleteness theorem - Minds and machines, Gödel's incompleteness theorem - Proof sketch for the first theorem, Gödel's incompleteness theorem - Proof sketch for the second theorem, Gödel's incompleteness theorem - Footnotes

Read more here: » Gödel's incompleteness theorem: Encyclopedia II - Gödel's incompleteness theorem - Second incompleteness theorem

The first of these devices was conceived in 1786 by J. H. Mueller. It was never built. Difference engines were forgotten and then rediscovered in 1822 by Charles Babbage, who proposed it in a paper to the Royal Astronomical Society entitled "Note on the application of machinery to the computation of astronomical and mathematical tables."[1] This machine used the decimal number system and was powered by cranking a handle. The British government initially financed the project, but withdrew funding when Babbage repeatedly asked for more ...

See also:

Difference engine, Difference engine - History, Difference engine - Method of differences

Read more here: » Difference engine: Encyclopedia II - Difference engine - History

These arguments can be refuted in various ways, for example by showing that the claimed ethical dilemma is only apparent and does not really exist (thus is not a paradox logically), or that the solution to the ethical dilemma involves choosing the greater good and lesser evil (as discussed in value theory), or that the whole framing of the problem is omitting creative alternatives (as in peacemaking), or (more recently) that situational ethics or situated ethics must apply because the case can't be removed from context and still be unde ...

See also:

Ethical dilemma, Ethical dilemma - Refuting ethical dilemmas, Ethical dilemma - Recurring struggles, Ethical dilemma - Roles within structures, Ethical dilemma - Division by Zero

Read more here: » Ethical dilemma: Encyclopedia II - Ethical dilemma - Refuting ethical dilemmas

The definition of the Lebesgue covering dimension can be used to build some unusual topological sets, such as the Sierpinski carpet. A construction can proceed as follows. Consider, for example, a finite open covering for the two-dimensional unit disk. This covering can always be refined so that no point in the disk belongs to more than three sets. Fixing this covering, remove all of the points in the disk that belong to three sets. Depending on the refinement, this will leave possibly one or more holes in the disk. The remaining obje ...

See also:

Lebesgue covering dimension, Lebesgue covering dimension - Some unusual topological constructions, Lebesgue covering dimension - History, Lebesgue covering dimension - Historical references, Lebesgue covering dimension - Modern references

Read more here: » Lebesgue covering dimension: Encyclopedia II - Lebesgue covering dimension - Some unusual topological constructions

There has been much scientific opposition to the irreducible complexity, with one science writer calling it a "full-blown intellectual surrender strategy." [11] It may be that irreducible complexity does not actually exist in nature: that the examples given by Behe and others are not in fact irreducibly complex, but can be explained in terms of simpler precursors. Thus they would either be merely very complex, or they would be misunderstood or misrepresented. The precursors of complex systems, when they are not useful in themse ...

See also:

Irreducible complexity, Irreducible complexity - Irreducible complexity IC, Irreducible complexity - Criticism, Irreducible complexity - Definitions, Irreducible complexity - Stated examples, Irreducible complexity - Flagella, Irreducible complexity - Blood clotting cascade, Irreducible complexity - Forerunners, Irreducible complexity - Criticisms of irreducible complexity, Irreducible complexity - Gradual replacement, Irreducible complexity - Handicaps and sexual selection, Irreducible complexity - Falsifiability and experimental evidence, Irreducible complexity - Behe's own Criticisms, Irreducible complexity - God and Irreducible Complexity, Irreducible complexity - Claimed significance

Read more here: » Irreducible complexity: Encyclopedia II - Irreducible complexity - Criticisms of irreducible complexity

Zeno's paradoxes - Proposed solutions to the arrow paradox. One objection to the arrow paradox is that the arrow paradox seems to be a play on words more than anything else. In particular, the premises state that at any instant, the arrow is at rest. However, being at rest is a relative term. One cannot judge, from observing any one instant, that the arrow is at rest. Rather, one requires other, adjacent instants to assert whether, compared to other instants, the arrow at one instant is at rest. Thus, compared to ...

See also:

Zeno's paradoxes, Zeno's paradoxes - The Paradoxes of motion, Zeno's paradoxes - Achilles and the tortoise, Zeno's paradoxes - The dichotomy paradox, Zeno's paradoxes - The arrow paradox, Zeno's paradoxes - Proposed solutions, Zeno's paradoxes - Proposed solutions to the arrow paradox, Zeno's paradoxes - Proposed solutions both to Achilles & the tortoise and to the Dichotomy, Zeno's paradoxes - Problem with the calculus-based solution, Zeno's paradoxes - Are space and time infinitely divisible?, Zeno's paradoxes - Does motion involve a sequence of points?, Zeno's paradoxes - Conceptual approaches, Zeno's paradoxes - Status of the paradoxes today, Zeno's paradoxes - Two other paradoxes as given by Aristotle, Zeno's paradoxes - The quantum Zeno effect

Read more here: » Zeno's paradoxes: Encyclopedia II - Zeno's paradoxes - Proposed solutions

In response to many Unidentified Flying Object sightings, the U.S. Air Force established Project Sign in 1948; this later became Project Grudge, which in turn became Project Blue Book in 1952. Hynek was contacted by Project Grudge to act as scientific consultant for their investigation of UFO reports. Hynek would study a UFO report and subsequently decide if its description of the UFO suggested a known astronomical object. When Project Grudge hired Hynek, he was initially skeptical of UFO reports. Hynek suspected that UFO reports were ...

See also:

J. Allen Hynek, J. Allen Hynek - Early Life and Career, J. Allen Hynek - Project Grudge and Project Blue Book, J. Allen Hynek - Final years, J. Allen Hynek - UFO books

Read more here: » J. Allen Hynek: Encyclopedia II - J. Allen Hynek - Project Grudge and Project Blue Book

Condon Committee - Background. Beginning in 1947 with Project Sign (which then became Project Grudge and finally Project Blue Book), the U.S. Air Force had undertaken a formal study of UFOs, which had become a subject of considerable public (and some governmental) interest. Yet Blue Book had come under increasing criticism in the 1960’s. Growing numbers of critics--including U.S. politicians, newspaper writers, UFO researchers, scientists and some the general public--were suggesting that Blue Book was co ...

See also:

Condon Committee, Condon Committee - History, Condon Committee - Background, Condon Committee - Enter Condon, Condon Committee - The Trick Memo, Condon Committee - The Study Begins, Condon Committee - Internal Tensions Begin, Condon Committee - Cracks in the Dam, Condon Committee - The Trick Memo Exposed, Condon Committee - Publicity, Condon Committee - The Condon Report, Condon Committee - Sources

Read more here: » Condon Committee: Encyclopedia II - Condon Committee - History

Karma - Hinduism. Main article: Karma in Hinduism Karma in Hinduism differs from karma in Buddhism and Jainism, and involves the role of God. Within Hinduism, Karma appears to function primarily as a means to explain the Problem of evil. One of the first and most dramatic illustrations of Karma can be found in the great Hindu epic, the Mahabharata. The original Hindu concept of karma was later enhanced by several other mov ...

See also:

Karma, Karma - Karma in the Dharma-based religions, Karma - Hinduism, Karma - Buddhism, Karma - Analogs of Karma - God the judge, Karma - Western interpretation, Karma - New Age and Theosophy, Karma - Psychology

Read more here: » Karma: Encyclopedia II - Karma - Karma in the Dharma-based religions

The first of these devices was conceived in 1786 by J. H. Mueller. It was never built. Difference engines were forgotten and then rediscovered in 1822 by Charles Babbage, who proposed it in a paper to the Royal Astronomical Society entitled "Note on the application of machinery to the computation of astronomical and mathematical tables."[1] This machine used the decimal number system and was powered by cranking a handle. The British government first financed the project but then later cut off support. Babbage went on to design his muc ...

See also:

Difference engine, Difference engine - History, Difference engine - Method of differences

Read more here: » Difference engine: Encyclopedia II - Difference engine - History

Gödel's first incompleteness theorem is perhaps the most celebrated result in mathematical logic. It basically says that: For any consistent formal theory including basic arithmetical truths, it is possible to construct an arithmetical statement that is true 1 but not included in the theory. That is, any consistent theory of a certain expressive strength is incomplete. Here, "theory" has the special sense of a set of statements closed under logical inference ru ...

See also:

Gödel's incompleteness theorem, Gödel's incompleteness theorem - First incompleteness theorem, Gödel's incompleteness theorem - Gödel's Theorem, Gödel's incompleteness theorem - Second incompleteness theorem, Gödel's incompleteness theorem - Gentzen's theorem, Gödel's incompleteness theorem - Meaning of Gödel's theorems, Gödel's incompleteness theorem - Examples of undecidable statements, Gödel's incompleteness theorem - Misconceptions about Gödel's theorems, Gödel's incompleteness theorem - Discussion and implications, Gödel's incompleteness theorem - Minds and machines, Gödel's incompleteness theorem - Proof sketch for the first theorem, Gödel's incompleteness theorem - Proof sketch for the second theorem, Gödel's incompleteness theorem - Footnotes

Read more here: » Gödel's incompleteness theorem: Encyclopedia II - Gödel's incompleteness theorem - First incompleteness theorem

Instead of repeatedly removing the middle third of every piece as in the Cantor set, we could also keep removing any other fixed percentage (other than 0% and 100%) from the middle. The resulting sets are all homeomorphic to the Cantor set and also have Lebesgue measure 0. In the case where the middle 8/10 of the interval is removed, we get a remarkably accessible case — the set consists of all numbers in [0,1] that can be written as a decimal consisting entirely of 0's and 9's. By removing progressively smaller percentages of the r ...

See also:

Cantor set, Cantor set - What's in the Cantor set?, Cantor set - Non-endpoints in the Cantor set, Cantor set - Properties, Cantor set - The Cantor set is uncountable, Cantor set - The Cantor set is a fractal, Cantor set - Topological and analytical properties, Cantor set - Variants of the Cantor set, Cantor set - Historical remarks, Cantor set - Historical references, Cantor set - Modern references

Read more here: » Cantor set: Encyclopedia II - Cantor set - Variants of the Cantor set

Since the Cantor set is defined as the set of points not excluded, the proportion of the unit interval remaining can be found by total length removed. This total is the geometric series So that the proportion left is 1 – 1 = 0. Alternatively, it can be observed that each step leaves 2/3 of the length in the previous stage, so that the amount remaining is 2/3 × 2/3 × 2/3 ...

See also:

Cantor set, Cantor set - What's in the Cantor set?, Cantor set - Non-endpoints in the Cantor set, Cantor set - Properties, Cantor set - The Cantor set is uncountable, Cantor set - The Cantor set is a fractal, Cantor set - Topological and analytical properties, Cantor set - Variants of the Cantor set, Cantor set - Historical remarks, Cantor set - Historical references, Cantor set - Modern references

Read more here: » Cantor set: Encyclopedia II - Cantor set - What's in the Cantor set?

The term "irreducible complexity" was originally defined by Behe as: A single system which is composed of several interacting parts that contribute to the basic function, and where the removal of any one of the parts causes the system to effectively cease functioning". (Darwin's Black Box p9) Supporters of intelligent design use this term to refer to biological systems and organs that they believe could not have come about by any series of small changes. They argue that anything less than the complete ...

See also:

Irreducible complexity, Irreducible complexity - Irreducible complexity IC, Irreducible complexity - Criticism, Irreducible complexity - Definitions, Irreducible complexity - Stated examples, Irreducible complexity - Flagella, Irreducible complexity - Blood clotting cascade, Irreducible complexity - Forerunners, Irreducible complexity - Criticisms of irreducible complexity, Irreducible complexity - Gradual replacement, Irreducible complexity - Handicaps and sexual selection, Irreducible complexity - Falsifiability and experimental evidence, Irreducible complexity - Behe's own Criticisms, Irreducible complexity - God and Irreducible Complexity, Irreducible complexity - Claimed significance

Read more here: » Irreducible complexity: Encyclopedia II - Irreducible complexity - Definitions