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Monday, December 16, 2019

Numeral system

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Numeral_system
 
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number eleven in the decimal numeral system (used in common life), the number three in the binary numeral system (used in computers), and the number two in the unary numeral system (e.g. used in tallying scores).

The number the numeral represents is called its value.

Ideally, a numeral system will:
  • Represent a useful set of numbers (e.g. all integers, or rational numbers)
  • Give every number represented a unique representation (or at least a standard representation)
  • Reflect the algebraic and arithmetic structure of the numbers.
For example, the usual decimal representation of whole numbers gives every nonzero whole number a unique representation as a finite sequence of digits, beginning with a non-zero digit. However, when decimal representation is used for the rational or real numbers, such numbers, in general, have an infinite number of representations, for example 2.31 can also be written as 2.310, 2.3100000, 2.309999999..., etc., all of which have the same meaning except for some scientific and other contexts where greater precision is implied by a larger number of figures shown.

Numeral systems are sometimes called number systems, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of real numbers, the system of complex numbers, the system of p-adic numbers, etc. Such systems are, however, not the topic of this article.

Main numeral systems

The most commonly used system of numerals is the Hindu–Arabic numeral system. Two Indian mathematicians are credited with developing it. Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero. The numeral system and the zero concept, developed by the Hindus in India, slowly spread to other surrounding countries due to their commercial and military activities with India. The Arabs modified it into simple numeral symbols as the hindi version was texts rather than symbols. The Arabic numeral system then spread to Europe along with many other science knowledge and due to merchants trading and using a stable simple numeral system. The Western world modified them and called them the Arabic numerals, as they learned them from the Arabs. Hence the current western numeral system is the modified version of the Hindu numeral system developed in India. It also exhibits a great similarity to the Sanskrit–Devanagari notation, which is still used in India and neighbouring Nepal. 

The simplest numeral system is the unary numeral system, in which every natural number is represented by a corresponding number of symbols. If the symbol / is chosen, for example, then the number seven would be represented by ///////. Tally marks represent one such system still in common use. The unary system is only useful for small numbers, although it plays an important role in theoretical computer science. Elias gamma coding, which is commonly used in data compression, expresses arbitrary-sized numbers by using unary to indicate the length of a binary numeral. 

The unary notation can be abbreviated by introducing different symbols for certain new values. Very commonly, these values are powers of 10; so for instance, if / stands for one, − for ten and + for 100, then the number 304 can be compactly represented as +++ //// and the number 123 as + − − /// without any need for zero. This is called sign-value notation. The ancient Egyptian numeral system was of this type, and the Roman numeral system was a modification of this idea. 

More useful still are systems which employ special abbreviations for repetitions of symbols; for example, using the first nine letters of the alphabet for these abbreviations, with A standing for "one occurrence", B "two occurrences", and so on, one could then write C+ D/ for the number 304. This system is used when writing Chinese numerals and other East Asian numerals based on Chinese. The number system of the English language is of this type ("three hundred [and] four"), as are those of other spoken languages, regardless of what written systems they have adopted. However, many languages use mixtures of bases, and other features, for instance 79 in French is soixante dix-neuf (60 + 10 + 9) and in Welsh is pedwar ar bymtheg a thrigain (4 + (5 + 10) + (3 × 20)) or (somewhat archaic) pedwar ugain namyn un (4 × 20 − 1). In English, one could say "four score less one", as in the famous Gettysburg Address representing "87 years ago" as "four score and seven years ago". 

More elegant is a positional system, also known as place-value notation. Again working in base 10, ten different digits 0, ..., 9 are used and the position of a digit is used to signify the power of ten that the digit is to be multiplied with, as in 304 = 3×100 + 0×10 + 4×1 or more precisely 3×102 + 0×101 + 4×100. Zero, which is not needed in the other systems, is of crucial importance here, in order to be able to "skip" a power. The Hindu–Arabic numeral system, which originated in India and is now used throughout the world, is a positional base 10 system. 

Arithmetic is much easier in positional systems than in the earlier additive ones; furthermore, additive systems need a large number of different symbols for the different powers of 10; a positional system needs only ten different symbols (assuming that it uses base 10).

The positional decimal system is presently universally used in human writing. The base 1000 is also used (albeit not universally), by grouping the digits and considering a sequence of three decimal digits as a single digit. This is the meaning of the common notation 1,000,234,567 used for very large numbers. 

In computers, the main numeral systems are based on the positional system in base 2 (binary numeral system), with two binary digits, 0 and 1. Positional systems obtained by grouping binary digits by three (octal numeral system) or four (hexadecimal numeral system) are commonly used. For very large integers, bases 232 or 264 (grouping binary digits by 32 or 64, the length of the machine word) are used, as, for example, in GMP

In certain biological systems, the unary coding system is employed. Unary numerals used in the neural circuits responsible for birdsong production. The nucleus in the brain of the songbirds that plays a part in both the learning and the production of bird song is the HVC (high vocal center). The command signals for different notes in the birdsong emanate from different points in the HVC. This coding works as space coding which is an efficient strategy for biological circuits due to its inherent simplicity and robustness. 

The numerals used when writing numbers with digits or symbols can be divided into two types that might be called the arithmetic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the geometric numerals (1, 10, 100, 1000, 10000 ...), respectively. The sign-value systems use only the geometric numerals and the positional systems use only the arithmetic numerals. A sign-value system does not need arithmetic numerals because they are made by repetition (except for the Ionic system), and a positional system does not need geometric numerals because they are made by position. However, the spoken language uses both arithmetic and geometric numerals.

In certain areas of computer science, a modified base k positional system is used, called bijective numeration, with digits 1, 2, ..., k (k ≥ 1), and zero being represented by an empty string. This establishes a bijection between the set of all such digit-strings and the set of non-negative integers, avoiding the non-uniqueness caused by leading zeros. Bijective base-k numeration is also called k-adic notation, not to be confused with p-adic numbers. Bijective base 1 is the same as unary. 

Positional systems in detail

In a positional base b numeral system (with b a natural number greater than 1 known as the radix), b basic symbols (or digits) corresponding to the first b natural numbers including zero are used. To generate the rest of the numerals, the position of the symbol in the figure is used. The symbol in the last position has its own value, and as it moves to the left its value is multiplied by b.

For example, in the decimal system (base 10), the numeral 4327 means (4×103) + (3×102) + (2×101) + (7×100), noting that 100 = 1.

In general, if b is the base, one writes a number in the numeral system of base b by expressing it in the form anbn + an − 1bn − 1 + an − 2bn − 2 + ... + a0b0 and writing the enumerated digits anan − 1an − 2 ... a0 in descending order. The digits are natural numbers between 0 and b − 1, inclusive.

If a text (such as this one) discusses multiple bases, and if ambiguity exists, the base (itself represented in base 10) is added in subscript to the right of the number, like this: numberbase. Unless specified by context, numbers without subscript are considered to be decimal.

By using a dot to divide the digits into two groups, one can also write fractions in the positional system. For example, the base 2 numeral 10.11 denotes 1×21 + 0×20 + 1×2−1 + 1×2−2 = 2.75.

In general, numbers in the base b system are of the form:
The numbers bk and bk are the weights of the corresponding digits. The position k is the logarithm of the corresponding weight w, that is . The highest used position is close to the order of magnitude of the number.

The number of tally marks required in the unary numeral system for describing the weight would have been w. In the positional system, the number of digits required to describe it is only , for k ≥ 0. For example, to describe the weight 1000 then four digits are needed because . The number of digits required to describe the position is (in positions 1, 10, 100,... only for simplicity in the decimal example).
A number has a terminating or repeating expansion if and only if it is rational; this does not depend on the base. A number that terminates in one base may repeat in another (thus 0.310 = 0.0100110011001...2). An irrational number stays aperiodic (with an infinite number of non-repeating digits) in all integral bases. Thus, for example in base 2, π = 3.1415926...10 can be written as the aperiodic 11.001001000011111...2

Putting overscores, n, or dots, , above the common digits is a convention used to represent repeating rational expansions. Thus:
14/11 = 1.272727272727... = 1.27   or
321.3217878787878... = 321.32178.
If b = p is a prime number, one can define base-p numerals whose expansion to the left never stops; these are called the p-adic numbers

Generalized variable-length integers

More general is using a mixed radix notation (here written little-endian) like for , etc.

This is used in punycode, one aspect of which is the representation of a sequence of non-negative integers of arbitrary size in the form of a sequence without delimiters, of "digits" from a collection of 36: a–z and 0–9, representing 0–25 and 26–35 respectively. A digit lower than a threshold value marks that it is the most-significant digit, hence the end of the number. The threshold value depends on the position in the number. For example, if the threshold value for the first digit is b (i.e. 1) then a (i.e. 0) marks the end of the number (it has just one digit), so in numbers of more than one digit, range is only b–9 (1–35), therefore the weight b1 is 35 instead of 36. Suppose the threshold values for the second and third digits are c (2), then the third digit has a weight 34 × 35 = 1190 and we have the following sequence:

a (0), ba (1), ca (2), .., 9a (35), bb (36), cb (37), .., 9b (70), bca (71), .., 99a (1260), bcb (1261), etc.

Unlike a regular based numeral system, there are numbers like 9b where 9 and b each represents 35; yet the representation is unique because ac and aca are not allowed – the a would terminate the number. 

The flexibility in choosing threshold values allows optimization depending on the frequency of occurrence of numbers of various sizes.

The case with all threshold values equal to 1 corresponds to bijective numeration, where the zeros correspond to separators of numbers with digits which are non-zero.

The Bible and homosexuality

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/The_Bible_and_homosexuality
 
Several passages in the Hebrew Bible and New Testament have been interpreted as involving same-sex sexual acts and desires.

Hebrew Bible

Leviticus 18 and 20

Chapters 18 and 20 of Leviticus form part of the Holiness code and list prohibited forms of intercourse, including the following verses:
  • "You shall not lie with a male as with a woman; it is an abomination." Chapter 18 verse 22
  • "If a man lies with a male as with a woman, both of them have committed an abomination; they shall surely be put to death; their blood is upon them." Chapter 20 verse 13
These two verses have historically been interpreted by Jews and Christians as clear overall prohibitions against homosexual acts in general. More recent interpretations focus more on its context as part of the Holiness Code, a code of purity meant to distinguish the behavior of Israelites from the polytheistic Canaanites. One of those interpretations is from Janet Edmonds, which says:
"To interpret these passages of Leviticus, it’s important to know that this book of the Bible focuses on ritual purity for the Israelites, and setting guidelines for the Israelites to distinguish themselves from their pagan neighbors, the Egyptians and Canaanites, who lived in the lands before they were settled by the Jews. This is shown in Leviticus Chapters 18 and 20 by three specific scripture passages (Leviticus 18:2-3, 18:24 and 20:23) that state that the Israelites should never do what the Egyptians and Canaanites did." 
Other interpreters state that God was commanding the Israelites to not to imitate anal sex between men practiced at the temples of Molech

Daniel A. Helminiak, a Christian author and theologian says "the anti-gay 'unnatural' hullabaloo rests on a mistranslation." and that "nowhere does the Bible actually oppose homosexuality" 

Sodom and Gomorrah

Lot prevents Sodomites from raping the angels, painting by Heinrich Aldegrever, 1555
 
The story of the destruction of Sodom and Gomorrah in Genesis does not explicitly identify homosexuality as the sin for which they were destroyed. Some interpreters find the story of Sodom and a similar one in Judges 19 to condemn the violent rape of guests more than homosexuality, but the passage has historically been interpreted within Judaism and Christianity as a punishment for homosexuality due to the interpretation that the men of Sodom wished to rape, or have sex with, the angels who retrieved Lot.

While the Jewish prophets spoke only of lack of charity as the sin of Sodom, the exclusively sexual interpretation became so prevalent among Christian communities that the name "Sodom" became the basis of the word "sodomy", still a legal synonym for homosexual and non-procreative sexual acts, particularly anal or oral sex.

While the Jewish prophets Isaiah, Jeremiah, Amos and Zephaniah refer vaguely to the sin of Sodom, Ezekiel specifies that the city was destroyed because of its commission of social injustice as well as its commission of 'abomination':
Behold, this was the iniquity of thy sister Sodom, pride, fullness of bread, and abundance of idleness was in her and in her daughters, neither did she strengthen the hand of the poor and needy. And they were haughty, and committed abomination before me: therefore I took them away as I saw good.
The Talmudic tradition as written between c. 370 and 500 also interprets the sin of Sodom as lack of charity, with the attempted rape of the angels being a manifestation of the city's violation of the social order of hospitality; as does Jesus in the New Testament, for instance in Matthew 10:14–15 when he tells his disciples that the punishment for houses or towns that will not welcome them will be worse than that of Sodom and Gomorrah.

Later traditions on Sodom's sin, such as Testaments of the Twelve Patriarchs, considered it to be an illicit form of heterosexual intercourse. In Jude 1:7 the inhabitants of Sodom and Gomorrah are stated to have been "giving themselves over to fornication, and going after strange flesh", which may refer to homosexuality or to the lust of mortals after angels. Jewish writers Philo (d. AD 50) and Josephus (37 – c. 100) were the first to assert unambiguously that homosexuality was among the sins of Sodom. By the end of the 1st century Jews commonly identified the sin of Sodom with homosexual practices.

David and Jonathan, Ruth and Naomi

The account of the friendship between David and Jonathan in the Books of Samuel has been interpreted by traditional and mainstream Christians as a relationship only of affectionate regard. Some sexual scholars have concluded, "There is nothing to show that such a relationship was sexual." It has also been interpreted by some authors as of a sexual nature. Michael Coogan addresses the claim of their homosexual relationship and explicitly rejects it.

One relevant Bible passage on this issue is 1 Samuel 18:1:
  • When David had finished talking with Saul, Jonathan and David became bound together in close friendship. Jonathan loved David as much as he did his own life. (NET)
Another relevant passage is 2 Samuel 1:26, where David says:
  • I grieve over you, my brother Jonathan. You were very dear to me. Your love was more special to me than the love of women. (NET)
The story of Ruth and Naomi in the Book of Ruth is also occasionally interpreted by contemporary scholars as the story of a lesbian couple. Coogan states that the Hebrew Bible does not even mention lesbianism.

New Testament


Romans 1:26-27


This passage has been debated by some 20th and 21st-century interpreters as to its relevance today and as to what it actually prohibits: although Christians of several denominations have historically maintained that this verse is a complete prohibition of all forms of homosexual activity, some 20th and 21st-century authors contend the passage is not a blanket condemnation of homosexual acts, suggesting, among other interpretations, that the passage condemned heterosexuals who experimented with homosexual activity or that Paul's condemnation was relative to his own culture, in which homosexuality was not understood as an orientation and in which being penetrated was seen as shameful. These interpretations are in a minority. Several scholars believe these verses are part of a much larger non-Pauline interpolation, a later addition to the letter.

1 Corinthians 6:9-11

In the context of the broader immorality of his audience, Paul the Apostle wrote in the First Epistle to the Corinthians, chapter 6 verses 9-11, 


The Greek word arsenokoitai (ἀρσενοκοῖται) in verse 9 has been debated for some time, and has been variously rendered as "abusers of themselves with mankind" (KJV), "sodomites" (YLT), or "men who have sex with men" (NIV). Greek ἄῤῥην / ἄρσην [arrhēn / arsēn] means "male", and κοίτην [koitēn] "bed", with a sexual connotation. Paul's use of the word in 1 Corinthians is the earliest example of the term; its only other usage is in a similar list of wrongdoers given (possibly by the same author) in 1 Timothy 1:8–11: In the letter to the Corinthians, within the list of people who will not inherit the kingdom of God, Paul uses two Greek words: malakoi and arsenokoitai. Malakoi is a common Greek word meaning, of things subject to touch, "soft" (used in Matthew 11:8 and Luke 7:25 to describe a garment); of things not subject to touch, "gentle"; and, of persons or modes of life, a number of meanings that include "pathic". Nowhere else in scripture is malakoi used to describe a person. 

Interpretation

Bishop Gene Robinson says the early church seemed to have understood it as a person with a "soft" or weak morality; later, it would come to denote (and be translated as) those who engage in masturbation, or "those who abuse themselves"; all that is factually known about the word is that it means "soft".


Most scholars hold that Paul had two passages of the Book of Leviticus, 18:22 and 20:13, in mind when he used the word ἀρσενοκοῖται (which may be of his coinage) with most commentators and translators interpreting it as a reference to male same-sex intercourse. However, John Boswell states that it "did not connote homosexuality to Paul or his early readers", and that in later Christian literature the word is used, for instance, by Aristides of Athens (c. 138) clearly not for homosexuality and possibly for prostitution, Eusebius (d. c. 340) who evidently used it in reference to women, and in the writings of 6th-century Patriarch John IV of Constantinople, known as John the Faster. In a passage dealing with sexual misconduct, John speaks of arsenokoitia as active or passive and says that "many men even commit the sin of arsenokoitia with their wives". Although the constituent elements of the compound word refer to sleeping with men, he obviously does not use it to mean homosexual intercourse and appears to employ it for anal intercourse, not generic homosexual activity. Particulars of Boswell's arguments are rejected by several scholars in a way qualified as persuasive by David F. Greenberg, who declares usage of the term arsenokoites by writers such as Aristides of Athens and Eusebius, and in the Sibylline Oracles, to be "consistent with a homosexual meaning". A discussion document issued by the House of Bishops of the Church of England states that most scholars still hold that the word arsenokoites relates to homosexuality. Another work attributed to John the Faster, a series of canons that for various sins provided shorter though stricter penances in place of the previous longer penances, applies a penance of eighty days for "intercourse of men with one another" (canon 9), explained in the Pedalion as mutual masturbation – double the penalty for solitary masturbation (canon 8) – and three years with xerophagy or, in accordance with the older canon of Basil the Great, fifteen without (canon 18) for being "so mad as to copulate with another man" – ἀρρενομανήσαντα in the original – explained in the Pedalion as "guilty of arsenocoetia (i.e., sexual intercourse between males)" – ἀρσενοκοίτην in the original. According to the same work, ordination is not to be conferred on someone who as a boy has been the victim of anal intercourse, but this is not the case if the semen was ejaculated between his thighs (canon 19). These canons are included, with commentary, in the Pedalion, the most widely used collection of canons of the Greek Orthodox Church, an English translation of which was produced by Denver Cummings and published by the Orthodox Christian Educational Society in 1957 under the title, The Rudder.

Some scholars consider that the term was not used to refer to a homosexual orientation, but argue that it referred instead to sexual activity.

Other scholars have interpreted arsenokoitai and malakoi (another word that appears in 1 Corinthians 6:9) as referring to weakness and effeminacy or to the practice of exploitative pederasty.

Jesus's discussion of marriage

In Matthew 19:3, Jesus is asked if a man can divorce his wife. In that context,


(Matthew 19:4-6, NRSV translation; Mark 10:6-9 is a parallel text)

Robert Gagnon, an associate professor of New Testament studies, argues that Jesus's back-to-back references to Genesis 1 and Genesis 2 show that he "presupposed a two-sex requirement for marriage".

Matthew 8; Luke 7

In Matthew 8:5–13 and Luke 7:1–10, Jesus heals a centurion's servant who is dying. Daniel A. Helminiak writes that the Greek word pais, used in this account, was sometimes given a sexual meaning. Donald Wold states that its normal meaning is "boy", "child" or "slave" and its application to a boy lover escapes notice in the standard lexica of Liddell and Scott and Bauer. The Greek-English Lexicon of Liddell and Scott registers three meanings of the word παῖς (pais): a child in relation to descent (son or daughter); a child in relation to age (boy or girl); a slave or servant (male or female). In her detailed study of the episode in Matthew and Luke, Wendy Cotter dismisses as very unlikely the idea that the use of the Greek word "pais" indicated a sexual relationship between the centurion and the young slave.

Matthew's account has parallels in Luke 7:1–10 and John 4:46–53. There are major differences between John's account and those of the two synoptic writers, but such differences exist also between the two synoptic accounts, with next to nothing of the details in Luke 7:2–6 being present also in Matthew. The Commentary of Craig A. Evans states that the word pais used by Matthew may be that used in the hypothetical source known as Q used by both Matthew and Luke and, since it can mean either son or slave, it became doulos (slave) in Luke and huios (son) in John. Writers who admit John 4:46–53 as a parallel passage generally interpret Matthew's pais as "child" or "boy", while those who exclude it see it as meaning "servant" or "slave".

Theodore W. Jennings Jr. and Tat-Siong Benny Liew write that Roman historical data about patron-client relationships and about same-sex relations among soldiers support the view that the pais in Matthew's account is the centurion's "boy-love" and that the centurion did not want Jesus to enter his house for fear the boy would be enamoured of Jesus instead. D.B. Saddington writes that while he does not exclude the possibility, the evidence the two put forward supports "neither of these interpretations", with Stephen Voorwinde saying of their view that "the argument on which this understanding is based has already been soundly refuted in the scholarly literature" and Wendy Cotter saying that they fail to take account of Jewish condemnation of pederasty. Others interpret Matthew's pais merely as a boy servant, not a male lover, and read nothing sexual into Luke's "valued highly". 

Matthew 19:12

In Matthew 19:12, Jesus speaks of eunuchs who were born as such, eunuchs who were made so by others, and eunuchs who choose to live as such for the kingdom of heaven. Jesus's reference to eunuchs who were born as such has been interpreted by some commentators as having to do with homosexual orientation; Clement of Alexandria, for instance, cites in his book "Stromata" (chapter III,1,1) an earlier interpretation from Basilides that some men, from birth, are naturally averse to women and should not marry. "The first category – those eunuchs who have been so from birth – is the closest description we have in the Bible of what we understand today as homosexual."

Acts 8

The Ethiopian eunuch, an early gentile convert described in Acts 8, has been interpreted by some commentators as an early gay Christian, based on the fact that the word "eunuch" in the Bible was not always used literally, as in Matthew 19:12. Religious commentators generally suggest that the combination of "eunuch" together with the title "court official" indicates a literal eunuch — not a homosexual — who would have been excluded from the Temple by the restriction in Deuteronomy 23:1.

Sodom and Gomorrah

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Sodom_and_Gomorrah
 
The Destruction of Sodom and Gomorrah, John Martin, 1852
 
Sodom and Gomorrah were two cities mentioned in the Book of Genesis and throughout the Hebrew Bible, the New Testament, and in the deuterocanonical books, as well as in the Quran and the hadith.

According to the Torah, the kingdoms of Sodom and Gomorrah were allied with the cities of Admah, Zeboim, and Bela. These five cities, also known as the "cities of the plain" (from Genesis in the Authorized Version), were situated on the Jordan River plain in the southern region of the land of Canaan. The plain was compared to the garden of Eden[Gen.13:10] as being well-watered and green, suitable for grazing livestock. Divine judgment was passed upon Sodom and Gomorrah and two neighboring cities, which were consumed by fire and brimstone. Neighboring Zoar (Bela) was the only city to be spared. In Abrahamic religions, Sodom and Gomorrah have become synonymous with impenitent sin, and their fall with a proverbial manifestation of divine retribution.

Sodom and Gomorrah have been used historically and in modern discourse as metaphors for homosexuality, and are the origin of the English words, sodomite, a pejorative term for male homosexuals, and sodomy, which is used in a legal context to describe sexual crimes against nature, namely anal or oral sex (particularly homosexual) and bestiality. This is based upon exegesis of the biblical text interpreting divine judgement upon Sodom and Gomorrah as punishment for the sin of homosexuality, though some contemporary scholars dispute this interpretation. Some Islamic societies incorporate punishments associated with Sodom and Gomorrah into sharia.

Etymology

The etymology of both names is uncertain, and scholars disagree about them.

They are known in Hebrew as סְדֹם (Səḏōm) and עֲמֹרָה (‘Ămōrāh). In the Septuagint these became Σόδομα (Sódoma) and Γόμορρᾰ (Gómorrha; the Hebrew ayin is pronounced as a voiced uvular fricative in Mizrahi, which is rendered in Greek by a gamma, a voiced velar stop).

According to Bob Macdonald, the Hebrew term for Gomorrah was based on the Semitic root ʿ-m-r, which means "be deep", "copious (water)".

In the Book of Genesis

The Book of Genesis is the primary source that mentions the cities of Sodom and Gomorrah. 

Battle of Siddim

The Battle of Siddim is described in Genesis 14:1–17. Sodom and Gomorrah's political situation is described when Lot had encamped in Sodom's territory. At this time, "the men of Sodom [were] wicked and sinners before the Lord exceedingly". Sodom was ruled by King Bera while Gomorrah was ruled by King Birsha. Their kingship was not sovereign, because all of the river Jordan plain was under Elamite rule for 12 years. The kingdom of Elam was ruled by King Chedorlaomer. In the 13th year of subjugation to Elam, the five kings of the river Jordan plain allied to rebel against Elamite rule. These kings included those of Sodom and Gomorrah as well as their neighbors: King Shinab of Admah, King Shemeber of Zeboiim, and the unnamed king of Bela (later called Zoar). 

In response, Elam's King Chedorlaomer, gathered additional forces from Shinar, Ellasar and Goyim to suppress this rebellion from the cities of the plain. They waged war in the Vale of Siddim in the 14th year. The battle was brutal with heavy losses in the cities of the plain, with their resultant defeat, Genesis 14:10. Sodom and Gomorrah were spoiled of their goods, and captives were taken, including Lot. The tide of war turned when Lot's uncle, Abraham, gathered an elite force that slaughtered King Chedorlaomer's forces in Hobah, north of Damascus. The success of his mission freed the cities of the plain from under Elam's rule. 

The Judgment upon Sodom and Gomorrah

Sodom and Gomorrah being destroyed in the background of Lucas van Leyden's 1520 painting Lot and his Daughters
 
The story of the judgment of Sodom and Gomorrah is told in Genesis 18–19. Three men came to Abraham in the plains of Mamre. After the angels received the hospitality of Abraham and Sarah, the Lord revealed to Abraham that he would confirm what he had heard against Sodom and Gomorrah, "and because their sin is very grievous." 

In response, Abraham inquired of the Lord if he would spare the city if 50 righteous people were found in it, to which the Lord agreed he would not destroy it for the sake of the righteous yet dwelling therein. Abraham then inquired of God for mercy at lower numbers (first 45, then 40, then 30, then 20, and finally at 10), with the Lord agreeing each time. Two angels were sent to Sodom to investigate and were met by Abraham's nephew Lot, who convinced the angels to lodge with him, and they ate with Lot.

Genesis 19:4–5 described what followed, which confirmed its end:
4 But before they lay down, the men of the city, even the men of Sodom, compassed the house round, both young and old, all the people from every quarter.
5 And they called unto Lot, and said unto him: 'Where are the men that came in to thee this night? bring them out unto us, that we may know them.'

(NRSV: know them, NIV: can have sex with them, NJB: can have intercourse with them).
Sodom and Gomorrah from the Nuremberg Chronicle by Hartmann Schedel, 1493. Lot's wife, already transformed into a salt pillar, is in the center.
 
Lot refused to give his guests to the inhabitants of Sodom and, instead, offered them his two virgin daughters "which have not known man" and to "do ye to them as [is] good in your eyes". They refused this offer, complained about this alien, namely Lot, judging them, and then came near to break down the door. Lot's angelic guests rescued him and struck the men with blindness and they informed Lot of their mission to destroy the city. Then (not having found even 10 righteous people in the city), they commanded Lot to gather his family and leave. As they made their escape, one angel commanded Lot to "look not behind thee" (singular "thee"). As Sodom and Gomorrah were being destroyed with brimstone and fire from the Lord, Lot's wife looked back at the city, and she became a pillar of salt.

Other biblical references

The Hebrew Bible refers to Sodom and Gomorrah. The New Testament also contains passages of parallels to the destruction and surrounding events that pertained to these cities and those who were involved. Later deuterocanonical texts attempt to glean additional insights about these cities of the Jordan Plain and their residents.

Hebrew Bible

Moses referred to the destruction of Sodom and Gomorrah in Deuteronomy 29:22–23:
Your children who follow you in later generations and foreigners who come from distant lands will see the calamities that have fallen on the land and the diseases with which the LORD has afflicted it. The whole land will be a burning waste of salt and sulfur—nothing planted, nothing sprouting, no vegetation growing on it. It will be like the destruction of Sodom and Gomorrah, Admah and Zeboyim, which the Lord overthrew in fierce anger.—NIV
Isaiah 1:9–10, Isaiah 3:9 and Isaiah 13:19–22 addresses people as from Sodom and Gomorrah, associates Sodom with shameless sinning and tells Babylon that it will end like those two cities. 

Jeremiah 23:14, Jeremiah 49:17–18, Jeremiah 50:39–40 and Lamentations 4:6 associate Sodom and Gomorrah with adultery and lies, prophesies the fate of Edom, south of the Dead Sea, predicts the fate of Babylon and uses Sodom as a comparison.

In Ezekiel 16:48–50, God compares Jerusalem to Sodom, saying "Sodom never did what you and your daughters have done." He explains that the sin of Sodom was that "She and her daughters were arrogant, overfed and unconcerned; they did not help the poor and needy. They were haughty and did detestable things before me."

In Amos 4:1–11, God tells the Israelites that although he treated them like Sodom and Gomorrah, they still did not repent. 

In Zephaniah 2:9, Zephaniah tells Moab and Ammon, southeast and northeast of the Dead Sea, that they will end up like Sodom and Gomorrah. 

New Testament

In Matthew 10:1–15, cf. Luke 10:1–12, Jesus declares certain cities more damnable than Sodom and Gomorrah, due to their response to Jesus' disciples, in the light of greater grace (RSV):
And if any one will not receive you or listen to your words, shake off the dust from your feet as you leave that house or town. Truly, I say to you, it shall be more tolerable on the day of judgment for the land of Sodom and Gomor'rah than for that town.
In Matthew 11:20–24, Jesus prophesies the fate of some cities where he did some of his works (RSV):
And you, Caper'na-um, will you be exalted to heaven? You shall be brought down to Hades. For if the mighty works done in you had been done in Sodom, it would have remained until this day. But I tell you that it shall be more tolerable on the day of judgment for the land of Sodom than for you.
In Luke 17:28–30, Jesus compares his second-coming to the judgment of Sodom and Gomorrah (RSV):
Likewise as it was in the days of Lot—they ate, they drank, they bought, they sold, they planted, they built, but on the day when Lot went out from Sodom fire and sulphur rained from heaven and destroyed them all—so will it be on the day when the Son of man is revealed.
In Romans 9:29, Paul the Apostle quotes Isaiah 1:9 (RSV): "And as Isaiah predicted, 'If the Lord of hosts had not left us children, we would have fared like Sodom and been made like Gomor'rah.'" 

In 2 Peter 2:4–10, Saint Peter says that just as God destroyed Sodom and Gomorrah and saved Lot, he will deliver godly people from temptations and punish the wicked on Judgement Day.

Jude 1:7 records that both Sodom and Gomorrah were "giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire".

Revelation 11:7–8 makes an allegorical use of Sodom when it describes the places where the two witnesses will descend during the Apocalypse

Deuterocanon

Wisdom 10:6–8 refers to the Five Cities:
Wisdom rescued a righteous man when the ungodly were perishing; he escaped the fire that descended on the Five Cities. Evidence of their wickedness still remains: a continually smoking wasteland, plants bearing fruit that does not ripen, and a pillar of salt standing as a monument to an unbelieving soul. For because they passed wisdom by, they not only were hindered from recognizing the good, but also left for mankind a reminder of their folly, so that their failures could never go unnoticed.
Wisdom 19:17 says that the Egyptians who enslaved the Israelites were "struck with blindness, like the men of Sodom who came to the door of that righteous man Lot. They found themselves in total darkness, as each one groped around to find his own door."

Sirach 16:8 says "[God] did not spare the neighbors of Lot, whom he loathed on account of their insolence." 

In 3 Maccabees 2:5, the high priest Simon says that God "consumed with fire and sulphur the men of Sodom who acted arrogantly, who were notorious for their vices; and you made them an example to those who should come afterward".

2 Esdras 2:8–9 says "Woe to you, Assyria, who conceal the unrighteous in your midst! O wicked nation, remember what I did to Sodom and Gomor′rah, whose land lies in lumps of pitch and heaps of ashes. So will I do to those who have not listened to me, says the Lord Almighty."

2 Esdras 5:1–13 describes signs of the end times, one of which is that "the sea of Sodom shall cast up fish". 

In 2 Esdras 7:106, Ezra says that Abraham prayed for the people of Sodom.

In chapter 12 of 1 Meqabyan, a book considered canonical in the Ethiopian Orthodox Tewahedo Church.

Historicity

Painting from William Francis Lynch book The Narrative of the United States Expedition of the River Jordan and the Dead Sea. Published in 1849
 
There are other stories and historical names which bear a resemblance to the biblical stories of Sodom and Gomorrah. Some possible natural explanations for the events described have been proposed, but no widely accepted or strongly verified sites for the cities have been found.

Sites

The ancient Greek historiographer Strabo states that locals living near Moasada (as opposed to Masada) say that "there were once thirteen inhabited cities in that region of which Sodom was the metropolis”. Strabo identifies a limestone and salt hill at the southwestern tip of the Dead Sea, and Kharbet Usdum (Hebrew: הר סדום, Har Sedom or Arabic: جبل السدوم, Jabal(u) 'ssudūm) ruins nearby as the site of biblical Sodom. Archibald Sayce translated an Akkadian poem describing cities that were destroyed in a rain of fire, written from the view of a person who escaped the destruction; the names of the cities are not given. Sayce later mentions that the story more closely resembles the doom of Sennacherib's host.

The Jewish historian Josephus identifies the Dead Sea in geographic proximity to the ancient biblical city of Sodom. He refers to the lake by its Greek name, Asphaltites.

Southern Theory

In 1973, Walter E. Rast and R. Thomas Schaub discovered or visited a number of possible sites of the cities, including Bab edh-Dhra, which was originally excavated in 1965 by archaeologist Paul Lapp, and later finished by Rast and Schaub following his death. Other possibilities include Numeira, al-Safi, Feifa (or Fifa, Feifah), and Khirbet al-Khanazir, which were also visited by Schaub and Rast. However, in 1993 Nancy Lapp, from Pittsburgh Theological Seminary, reported that Feifa had no Bronze age occupation and merely an EB cemetery with Iron Age walls. She reports: "In the final season of the present series of excavations of the Expedition to the Dead Sea Plain (1990–1991), the walled site of Feifa was investigated and the EB cemetery that stretched to its east was excavated. The most recent surveys suggested that the visible structures of the walled site belonged to the Iron Age or Roman period." At khirbet al-Khanazir the walls which Rast and Schaub identified in 1973 as houses were in reality rectangular charnel burial houses marking EB IV shaft tombs and not occupational structures. According to Schaub, who dug at Bab edh-Dhra, Numeira was destroyed in 2600 BCE at a different time period than Bab edh-Dhra (2350–2067 BCE).

Northern Theory

Another candidate for Sodom is the Tall el-Hammam dig site which began in 2006 under the direction of Steven Collins.

Tall el-Hammam overlooking the Jordan Valley 2007
 
Tall el-Hammam is located in the southern Jordan river valley approximately 14 kilometres (9 mi) northeast of the Dead Sea, and according to Collins fits the biblical descriptions of the lands of Sodom. The ongoing dig is a result of joint cooperation between the unaccredited Trinity Southwest University and the Department of Antiquities of the Hashemite Kingdom of Jordan.

Professor Eugene H. Merrill believes that the identification of Tall el-Hammam with Sodom would require an unacceptable restructuring of the biblical chronology.

Natural disaster

Certain skeptics of the biblical account have theorized that, provided that the cities existed at all, they might have been destroyed by natural disaster. One such idea is that the Dead Sea was devastated by an earthquake between 2100 and 1900 BCE. This might have unleashed showers of steaming tar. It is possible that the towns were destroyed by an earthquake, especially if they lay along a major fault such as the Jordan Rift Valley. There is a lack of contemporary accounts of seismic activity within the necessary time frame to corroborate this theory.

In 2018, it was proposed that this ancient city was destroyed about 3700 years ago by a meteoritic explosion in the atmosphere equivalent to 10 megatonnes, laying waste to Tall el-Hammam and degrading the fertility of the local land.

Other hypotheses

In 1976 Giovanni Pettinato claimed that a cuneiform tablet that had been found in the newly discovered library at Ebla contained the names of all five of the cities of the plain (Sodom, Gomorrah, Admah, Zeboim, and Bela), listed in the same order as in Genesis. The names si-da-mu [TM.76.G.524] and ì-ma-ar [TM.75.G.1570 and TM.75.G.2233] were identified as representing Sodom and Gomorrah, which gained some acceptance at the time. However, Alfonso Archi states that, judging from the surrounding city names in the cuneiform list, si-da-mu lies in northern Syria and not near the Dead Sea, and ì-ma-ar is a variant of ì-mar, known to represent Emar, an ancient city located near Ebla. Today, the scholarly consensus is that "Ebla has no bearing on ... Sodom and Gomorra."

In 1990, Ron Wyatt, and Richard Rives explored the area around Masada and uncovered large sulfur chunks embedded within natural rock. These sulfuric deposits are most likely the result of calcite and gypsum reacting with the local strata following a seismic event. Wyatt's reliability is discredited by many scholars, historians, historical organizations, the Israel Antiquities Authority and even religious institutions, including Answers in Genesis.

Religious views


Jewish

Rabbi Basil Herring, who served as head of the Rabbinical Council of America from 2003 to 2012, writes that both the Rabbinic tradition and modern orthodox position consider the Torah to condemn homosexuality as an abomination. Moreover, that it "conveys its abhorrence of homosexuality through a variety of narrative settings", God's judgment of Sodom and Gomorrah being a "paradigmatic" instance of such condemnation.

Rictor Norton views classical Jewish texts as stressing the cruelty and lack of hospitality of the inhabitants of Sodom to the "stranger". The people of Sodom were seen as guilty of many other significant sins. Rabbinic writings affirm that the Sodomites also committed economic crimes, blasphemy and bloodshed.

Other extrabiblical crimes committed by Sodom and Gomorrah included extortion on crossing a bridge/or swimming a river; harshly punishing victims for crimes that the perpetrator committed, forcing an assault victim to pay for the perpetrator's "bleeding" and forcing a woman to marry a man who intentionally caused her miscarriage to compensate for the lost child. Because of this, the judges of the two cities were referred to as Shakrai ("Liar"), Shakurai ("Awful Liar"), Zayyafi ("Forger") and Mazle Dina ("Perverter of Justice"). Eliezer was reported to be a victim of such legally unjust conduct, after Sarah sent him to Sodom to report on Lot's welfare. The citizens also regularly tortured foreigners who sought lodging. They did this by providing the foreigners a standard-sized beds and if they saw that the foreigner was too short for the bed, they would forcibly stretch their limbs but if the foreigner was too tall, they would cut off their legs; As a result, many people refrained from visiting Sodom and Gomorrah. Beggars who settled into the two cities for refuge were similarly mistreated. The citizens would give them marked coins (presumably used to purchase food) but were nonetheless forbidden, by proclamation, to provide these necessary services. Once the beggar died of starvation, citizens who initially gave the beggar the coins were permitted to retrieve them, provided that they could recognize it. The beggar's clothing was also provided as a reward for any citizen who could successfully overcome their opponent in a street fight.

The provision of bread and water to the poor was also a capital offense (Yalḳ., Gen. 83). Two girls, one poor and the other rich, went to a well; and the former gave the latter her jug of water, receiving in return a vessel containing bread. When this became known, both were burned alive (ib.). According to the Book of Jasher, Paltith, one of Lot's daughters, was burnt alive (in some versions, on a pyre) for giving a poor man bread. Her cries went to the heavens. Another woman was similarly executed in Admah for giving a traveler, who intended to leave the town the next day, water. When the scandal was revealed, the woman was stripped naked and covered with honey. This attracted bees as the woman was slowly stung to death. Her cries then went up into the heavens, the turning point that was revealed to have provoked God to enact judgement upon Sodom and Gomorrah in the first place in Genesis 18:20.

Jon D. Levenson views a rabbinic tradition described in the Mishnah as postulating that the sin of Sodom was a violation of conventional hospitality in addition to homosexual conduct, describing Sodom's lack of generosity with the saying, "What is mine is mine; what is yours is yours" (m. Avot 5.10).

Jay Michaelson proposes a reading of the story of Sodom that emphasizes the violation of hospitality as well as the violence of the Sodomites. "Homosexual rape is the way in which they violate hospitality—not the essence of their transgression. Reading the story of Sodom as being about homosexuality is like reading the story of an ax murderer as being about an ax." Michaelson places the story of Sodom in context with other Genesis stories regarding Abraham's hospitality to strangers, and argues that when other texts in the Hebrew Bible mention Sodom, they do so without commentary on homosexuality. The verses cited by Michaelson include Jeremiah 23:14,[Jeremiah 23:14] where the sins of Jerusalem are compared to Sodom and are listed as adultery, lying, and strengthening the hands of evildoers; Amos 4:1–11 (oppressing the poor and crushing the needy);[Amos 4:1–11] and Ezekiel 16:49–50,[Ezekiel 16:49–50] which defines the sins of Sodom as "pride, fullness of bread, and abundance of idleness was in her and in her daughters, neither did she strengthen the hand of the poor and needy. And they were haughty, and did toevah before me, and I took them away as I saw fit." Michaelson uses toevah in place of abomination to emphasize the original Hebrew, which he explains as being more correctly translated as "taboo".

Christian

Two areas of contention have arisen in modern Christian scholarship concerning the story of Sodom and Gomorrah.
  1. Whether the violent mob surrounding Lot's house were demanding to engage in sexual violence against Lot's guests.
  2. Whether it was homosexuality or another transgression, such as the act of inhospitability towards visitors, that was the principal reason for God's destruction of Sodom and Gomorrah.
The first contention focuses primarily upon the meaning of the Hebrew verb Hebrew: ידע (yada), translated as "know" in the King James Version:
And they called unto Lot, and said unto him, Where [are] the men which came in to thee this night? bring them out unto us, that we may know them. —Genesis 19:5
Yada is used to refer to sexual intercourse in various instances, such as in Genesis 4:1 between Adam and Eve:
And Adam knew Eve his wife; and she conceived, and bare Cain, and said, I have gotten a man from the LORD.—Genesis 4:1
Some Hebrew scholars believe that yada, unlike the English word "know", requires the existence of a "personal and intimate relationship". For this reason, many of the most popular of the 20th century translations, including the New International Version, the New King James Version, and the New Living Translation, translate yada as "have sex with" or "know ... carnally" in Gen 19:5.

Those who favor the non-sexual interpretation argue against a denotation of sexual behavior in this context, noting that while the Hebrew word for "know" appears over 900 times in the Hebrew Scriptures, only 1% (13–14 times) of those references are clearly used as a euphemism for realizing sexual intimacy. Instead, those who hold to this interpretation see the demand to know as demanding the right to interrogate the strangers.

Countering this is the observation that one of the examples of "know" meaning to know sexually occurs when Lot responds to the Gen 19:5 request, by offering his daughters for rape, only three verses later in the same narrative:
Behold now, I have two daughters which have not known man; let me, I pray you, bring them out unto you, and do ye to them as is good in your eyes: only unto these men do nothing.... —Genesis 19:8
The following is a major text in regard to these conflicting opinions:
Even as Sodom and Gomorrah, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire. —Jude 1:7
This reference to "going after strange flesh" is understood in different ways to include something akin to bestiality, having illicit sex with strangers, having sex with angels, but most often God's destruction of the populations of the four cities is interpreted to mean homosexual (same-sex) relations.

Many who interpret the stories in a non-sexual context contend that as the word for "strange" is akin to "another", "other", "altered" or even "next", the meaning is unclear, and if the condemnation of Sodom was the result of sexual activities perceived to be perverse, then it is likely that it was because women sought to commit fornication with "other than human" angels, perhaps referring to Genesis 6 or the apocryphal Book of Enoch. Countering this, it is pointed out that Genesis 6 refers to angels seeking women, not men seeking angels, and that both Sodom and Gomorrah were engaged in the sin Jude describes before the angelic visitation, and that, regardless, it is doubtful that the Sodomites knew they were angels. In addition, it is argued the word used in the King James Version of the Bible for "strange", can mean unlawful or corrupted (Rm. 7:3; Gal. 1:6), and that the apocryphal Second Book of Enoch condemns "sodomitic" sex (2 Enoch 10:3; 34:1), thus indicating that homosexual relations was the prevalent physical sin of Sodom.

Both the non-sexual and the homosexuality view invoke certain classical writings as well as other portions of the Bible.
Now this was the sin of Sodom: She and her daughters were arrogant, overfed and unconcerned; they did not help the poor and needy. They were haughty and did detestable things before me. Therefore I did away with them as you have seen. —Ezekiel 16:49–50
Here the nonsexual view focuses on the inhospitality aspect, while the other notes the description detestable or abomination, the Hebrew word for which often denotes moral sins, including those of a sexual nature.

In the Gospel of Matthew (and corresponding verse) when Jesus warns of a worse judgment for some cities than Sodom, inhospitality is perceived by some as the sin, while others see it fundamentally being impenitence:
If anyone will not welcome you or listen to your words, shake the dust off your feet when you leave that home or town. I tell you the truth, it will be more bearable for Sodom and Gomorrah on the day of judgment than for that town. —Matthew 10:14–15
The nonsexual view focuses on the cultural importance of hospitality, which this biblical story shares with other ancient civilizations, such as Ancient Greece and Ancient Rome, where hospitality was of singular importance and strangers were under the protection of the gods. James L. Kugel, Starr Professor of Hebrew Literature at Harvard University suggests the story encompasses the sexual and non-sexual: the Sodomites were guilty of stinginess, inhospitality and sexual license, homo- and heterosexual in contrast to the generosity of Abraham, and Lot whose behavior in protecting the visitors but offering his daughters suggests he was "scarcely better than his neighbors" according to some ancient commentators, The Bible As It Was, 1997, pp. 179–197.

Within the Christian Churches that agree on the possible sexual interpretation of "know" (yada) in this context, there is still a difference of opinion on whether homosexuality is important. On its website, the Anglican Communion presents the argument that the story is "not even vaguely about homosexual love or relationships", but is instead "about dominance and rape, by definition an act of violence, not of sex or love". This argument that the violence and the threat of violence towards foreign visitors is the true ethical downfall of Sodom (and not homosexuality), also observes the similarity between the Sodom and Gomorrah and the Battle of Gibeah Bible stories. In both stories, an inhospitable mob demands the homosexual rape of a foreigner or foreigners. As the mob instead settles for the rape and murder of the foreigner's female concubine in the Battle of Gibeah story, the homosexual aspect is generally seen as inconsequential, and the ethical downfall is understood to be the violence and the threat of violence towards foreigners by the mob. This Exodus 22:21–24 lesson is viewed by Anglicans as a more historically accurate way to interpret the Sodom and Gomorrah story.

Scholar in history and gender studies Lisa McClain has claimed that the association between Sodom and Gomorrah with homosexuality emerged from the writings of 1st century Jewish philosopher Philo, and that no prior exegesis of the text suggested such a linkage.

Islamic

Lut fleeing the city with his daughters; his wife is killed by a rock.
 
The Quran contains twelve references to "the people of Lut", the biblical Lot, but meaning the residents of Sodom and Gomorrah, and their destruction by God is associated explicitly with their sexual practices.

The 'people of Lot' transgressed consciously against the bounds of God. Lot only prayed to God to be saved from doing as they did. Then Gabriel met Lot and said that he must leave the city quickly, as God had given this command to Lot for saving his life. In the Quran it was written that Lot's wife stayed behind as she had transgressed. She met her fate in the disaster, and only Lot and his family were saved during the destruction of their city, with the understanding that the cities of Sodom and Gomorrah are identified in Genesis, but "the location remains unnamed in the Qur'an"

In the Quran, surah (chapter) 26 Ash-Shu`arā' (The Poets) –
So, We saved him and his family, all. Except an old woman among those who remained behind.
Commentary: This was his wife, who was a bad old woman. She stayed behind and was destroyed with whoever else was left. This is similar to what Allah says about them in Surat Al-A`raf and Surat Hud, and in Surat Al-Hijr, where Allah commanded him to take his family at night, except for his wife, and not to turn around when they heard the Sayhah as it came upon his people. So they patiently obeyed the command of Allah and persevered, and Allah sent upon the people a punishment which struck them all, and rained upon them stones of baked clay, piled up.
— Tafsir ibn Kathir (Commentary by Ibn Kathir)

Modern Sodom

The site of the present Dead Sea Works, a large operation for the extraction of Dead Sea minerals, is called "Sdom" (סדום) according to its traditional Arab name, Khirbet as-sudūm (خربت السدوم). Nearby is Mount Sodom (הר סדום in Hebrew and جبل السدوم in Arabic) which consists mainly of salt. In the Plain of Sdom (מישור סדום) to the south there are a few springs and two small agricultural villages, Neot Hakikar and Ein Tamar.

Second World War

"Operation Gomorrah" was the name given to the Bombing of Hamburg in July 1943, in which 42,600 civilians were killed, and where use of incendiaries caused a vortex and whirling updraft of super-heated air which created a 460 meter high tornado of fire.

Optimal tax

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