Religion chapter
Buddhism chapter
Christianity chapter
Islam chapter
QMRIslam considers extramarital sex to be sinful and forbidden.[4] Though Islamic law prescribes punishments for Muslim men and women for the act of zinā, in practice it is an extremely difficult offense to prove, requiring four respectable witnesses to the actual act of penetration. Though in Western cultures premarital sex and loss of virginity may be considered shameful to the individual, in some Muslim societies an act of premarital sex, even if not falling within the legal standards of proof, may result in personal shame and loss of family honor.[4]
QMRIslamic holy books are the texts which Muslims believe were authored by God to various prophets throughout humanity's history. All these books, in Muslim belief, promulgated the code and laws that God ordained for those people.
Muslims believe the Quran to be the final revelation of God's word to man, and a completion and confirmation of previous scriptures.[1] Despite the primacy that Muslims place upon the Qur'an as God's final word, Islam speaks of respecting all the previous scriptures, and belief in all the revealed books is an article of faith in Islam.
Among the books considered to be revealed, the four mentioned by name in the Qur'an are the Torah (revealed to Moses), the Psalms (Zabur) (revealed to David), the Injil (Gospel) (revealed to Jesus), and the Qur'an itself.
QMRShia Muslims do not use the Kutub al-Sittah (six major hadith collections) followed by the Sunni. Instead, their primary collections were written by three authors known as the 'Three Muhammads'.[32] They are: Kitab al-Kafi by Muhammad ibn Ya'qub al-Kulayni al-Razi (329 AH), Man la yahduruhu al-Faqih by Ibn Babawayh and Tahdhib al-Ahkam and Al-Istibsar both by Shaykh Tusi. Unlike Akhbari Twelver Shia, Usuli Twelver Shia scholars do not believe that everything in the four major books is authentic. In Shia hadith one often finds sermons attributed to Ali in The Four Books or in the Nahj al-Balagha.
Direct sum[edit]
For any arbitrary matrices A (of size m × n) and B (of size p × q), we have the direct sum of A and B, denoted by A \oplus B and defined as
\mathbf{A} \oplus \mathbf{B} =
\begin{bmatrix}
a_{11} & \cdots & a_{1n} & 0 & \cdots & 0 \\
\vdots & \cdots & \vdots & \vdots & \cdots & \vdots \\
a_{m 1} & \cdots & a_{mn} & 0 & \cdots & 0 \\
0 & \cdots & 0 & b_{11} & \cdots & b_{1q} \\
\vdots & \cdots & \vdots & \vdots & \cdots & \vdots \\
0 & \cdots & 0 & b_{p1} & \cdots & b_{pq}
\end{bmatrix}.
For instance,
\begin{bmatrix}
1 & 3 & 2 \\
2 & 3 & 1
\end{bmatrix}
\oplus
\begin{bmatrix}
1 & 6 \\
0 & 1
\end{bmatrix}
=
\begin{bmatrix}
1 & 3 & 2 & 0 & 0 \\
2 & 3 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 6 \\
0 & 0 & 0 & 0 & 1
\end{bmatrix}.
This operation generalizes naturally to arbitrary dimensioned arrays (provided that A and B have the same number of dimensions).
Note that any element in the direct sum of two vector spaces of matrices could be represented as a direct sum of two matrices.
Notation[edit]
Some textbooks have the ones on the subdiagonal, i.e., immediately below the main diagonal instead of on the superdiagonal. The eigenvalues are still on the main diagonal.[8][9]
Motivation[edit]
An n × n matrix A is diagonalizable if and only if the sum of the dimensions of the eigenspaces is n. Or, equivalently, if and only if A has n linearly independent eigenvectors. Not all matrices are diagonalizable. Consider the following matrix:
A=
\left[\!\!\!\begin{array}{*{20}{r}}
5 & 4 & 2 & 1 \\[2pt]
0 & 1 & -1 & -1 \\[2pt]
-1 & -1 & 3 & 0 \\[2pt]
1 & 1 & -1 & 2
\end{array}\!\!\right].
Including multiplicity, the eigenvalues of A are λ = 1, 2, 4, 4. The dimension of the eigenspace corresponding to the eigenvalue 4 is 1 (and not 2), so A is not diagonalizable. However, there is an invertible matrix P such that A = PJP−1, where
J = \begin{bmatrix}
1 & 0 & 0 & 0 \\[2pt]
0 & 2 & 0 & 0 \\[2pt]
0 & 0 & 4 & 1 \\[2pt]
0 & 0 & 0 & 4 \end{bmatrix}.
The matrix J is almost diagonal. This is the Jordan normal form of A. The section Example below fills in the details of the computation.
Complex matrices[edit]
In general, a square complex matrix A is similar to a block diagonal matrix
J = \begin{bmatrix}
J_1 & \; & \; \\
\; & \ddots & \; \\
\; & \; & J_p\end{bmatrix}
where each block Ji is a square matrix of the form
J_i =
\begin{bmatrix}
\lambda_i & 1 & \; & \; \\
\; & \lambda_i & \ddots & \; \\
\; & \; & \ddots & 1 \\
\; & \; & \; & \lambda_i
\end{bmatrix}.
So there exists an invertible matrix P such that P−1AP = J is such that the only non-zero entries of J are on the diagonal and the superdiagonal. J is called the Jordan normal form of A. Each Ji is called a Jordan block of A. In a given Jordan block, every entry on the superdiagonal is 1.
Assuming this result, we can deduce the following properties:
Counting multiplicity, the eigenvalues of J, therefore A, are the diagonal entries.
Given an eigenvalue λi, its geometric multiplicity is the dimension of Ker(A − λi I), and it is the number of Jordan blocks corresponding to λi.[10]
The sum of the sizes of all Jordan blocks corresponding to an eigenvalue λi is its algebraic multiplicity.[10]
A is diagonalizable if and only if, for every eigenvalue λ of A, its geometric and algebraic multiplicities coincide.
The Jordan block corresponding to λ is of the form λ I + N, where N is a nilpotent matrix defined as Nij = δi,j−1 (where δ is the Kronecker delta). The nilpotency of N can be exploited when calculating f(A) where f is a complex analytic function. For example, in principle the Jordan form could give a closed-form expression for the exponential exp(A).
The number of Jordan blocks corresponding to λ of size at least j is dim Ker(A - λI)j - dim Ker(A - λI)j-1. Thus, the number of Jordan blocks of size exactly j is
2 \dim \ker (A - \lambda_i I)^j - \dim \ker (A - \lambda_i I)^{j+1} - \dim \ker (A - \lambda_i I)^{j-1}
Given an eigenvalue λi, its multiplicity in the minimal polynomial is the size of its largest Jordan block.
A proof[edit]
We give a proof by induction. The 1 × 1 case is trivial. Let A be an n × n matrix. Take any eigenvalue λ of A. The range of A − λ I, denoted by Ran(A − λ I), is an invariant subspace of A. Also, since λ is an eigenvalue of A, the dimension Ran(A − λ I), r, is strictly less than n. Let A' denote the restriction of A to Ran(A − λ I), By inductive hypothesis, there exists a basis {p1, ..., pr} such that A' , expressed with respect to this basis, is in Jordan normal form.
Next consider the subspace Ker(A − λ I). If
\mathrm{Ran}(A - \lambda I) \cap \mathrm{Ker}(A - \lambda I) = \{0\},
the desired result follows immediately from the rank–nullity theorem. This would be the case, for example, if A was Hermitian.
Otherwise, if
Q = \mathrm{Ran}(A - \lambda I) \cap \mathrm{Ker}(A - \lambda I) \neq \{0\},
let the dimension of Q be s ≤ r. Each vector in Q is an eigenvector of A' corresponding to eigenvalue λ. So the Jordan form of A' must contain s Jordan chains corresponding to s linearly independent eigenvectors. So the basis {p1, ..., pr} must contain s vectors, say {pr−s+1, ..., pr}, that are lead vectors in these Jordan chains from the Jordan normal form of A'. We can "extend the chains" by taking the preimages of these lead vectors. (This is the key step of argument; in general, generalized eigenvectors need not lie in Ran(A − λ I).) Let qi be such that
\; (A - \lambda I) q_i = p_i \mbox{ for } i = r-s+1, \ldots, r.
Clearly no non-trivial linear combination of the qi can lie in Ker(A − λ I). Furthermore, no non-trivial linear combination of the qi can be in Ran(A − λ I), for that would contradict the assumption that each pi is a lead vector in a Jordan chain. The set {qi}, being preimages of the linearly independent set {pi} under A − λ I, is also linearly independent.
Finally, we can pick any linearly independent set {z1, ..., zt} that spans
\; \mathrm{Ker}(A - \lambda I) / Q.
By construction, the union of the three sets {p1, ..., pr}, {qr−s +1, ..., qr}, and {z1, ..., zt} is linearly independent. Each vector in the union is either an eigenvector or a generalized eigenvector of A. Finally, by rank–nullity theorem, the cardinality of the union is n. In other words, we have found a basis that consists of eigenvectors and generalized eigenvectors of A, and this shows A can be put in Jordan normal form.
Uniqueness[edit]
It can be shown that the Jordan normal form of a given matrix A is unique up to the order of the Jordan blocks.
Knowing the algebraic and geometric multiplicities of the eigenvalues is not sufficient to determine the Jordan normal form of A. Assuming the algebraic multiplicity m(λ) of an eigenvalue λ is known, the structure of the Jordan form can be ascertained by analyzing the ranks of the powers (A − λ I)m(λ). To see this, suppose an n × n matrix A has only one eigenvalue λ. So m(λ) = n. The smallest integer k1 such that
(A - \lambda I)^{k_1} = 0
is the size of the largest Jordan block in the Jordan form of A. (This number k1 is also called the index of λ. See discussion in a following section.) The rank of
(A - \lambda I)^{k_1 - 1}
is the number of Jordan blocks of size k1. Similarly, the rank of
(A - \lambda I)^{k_1 - 2}
is twice the number of Jordan blocks of size k1 plus the number of Jordan blocks of size k1−1. The general case is similar.
This can be used to show the uniqueness of the Jordan form. Let J1 and J2 be two Jordan normal forms of A. Then J1 and J2 are similar and have the same spectrum, including algebraic multiplicities of the eigenvalues. The procedure outlined in the previous paragraph can be used to determine the structure of these matrices. Since the rank of a matrix is preserved by similarity transformation, there is a bijection between the Jordan blocks of J1 and J2. This proves the uniqueness part of the statement.
Invariant subspace decompositions[edit]
The Jordan form of a n × n matrix A is block diagonal, and therefore gives a decomposition of the n dimensional Euclidean space into invariant subspaces of A. Every Jordan block Ji corresponds to an invariant subspace Xi. Symbolically, we put
\mathbb{C}^n = \bigoplus_{i = 1}^k X_i
where each Xi is the span of the corresponding Jordan chain, and k is the number of Jordan chains.
One can also obtain a slightly different decomposition via the Jordan form. Given an eigenvalue λi, the size of its largest corresponding Jordan block si is called the index of λi and denoted by ν(λi). (Therefore the degree of the minimal polynomial is the sum of all indices.) Define a subspace Yi by
\; Y_i = \operatorname{Ker} (\lambda_i I - A)^{\nu(\lambda_i)}.
This gives the decomposition
\mathbb{C}^n = \bigoplus_{i = 1}^l Y_i
where l is the number of distinct eigenvalues of A. Intuitively, we glob together the Jordan block invariant subspaces corresponding to the same eigenvalue. In the extreme case where A is a multiple of the identity matrix we have k = n and l = 1.
The projection onto Yi and along all the other Yj ( j ≠ i ) is called the spectral projection of A at λi and is usually denoted by P(λi ; A). Spectral projections are mutually orthogonal in the sense that P(λi ; A) P(λj ; A) = 0 if i ≠ j. Also they commute with A and their sum is the identity matrix. Replacing every λi in the Jordan matrix J by one and zeroising all other entries gives P(λi ; J), moreover if U J U−1 is the similarity transformation such that A = U J U−1 then P(λi ; A) = U P(λi ; J) U−1. They are not confined to finite dimensions. See below for their application to compact operators, and in holomorphic functional calculus for a more general discussion.
Comparing the two decompositions, notice that, in general, l ≤ k. When A is normal, the subspaces Xi's in the first decomposition are one-dimensional and mutually orthogonal. This is the spectral theorem for normal operators. The second decomposition generalizes more easily for general compact operators on Banach spaces.
It might be of interest here to note some properties of the index, ν(λ). More generally, for a complex number λ, its index can be defined as the least non-negative integer ν(λ) such that
\mathrm{Ker}(\lambda - A)^{\nu(\lambda)} = \operatorname{Ker} (\lambda - A)^m, \; \forall m \geq \nu(\lambda) .
So ν(λ) > 0 if and only if λ is an eigenvalue of A. In the finite-dimensional case, ν(λ) ≤ the algebraic multiplicity of λ.
The word basmala was derived from a slightly unusual procedure, in which the first four pronounced consonants of the phrase bismi-llāhi... were used as a quadriliteral consonantal root:[16] b-s-m-l (ب س م ل). This abstract consonantal root was used to derive the noun basmala and its related verb forms, meaning "to recite the basmala". Other oft-repeated phrases in Islam given their own names include "Allāhu Akbar" (الله أكبر, called the Takbir and usually translated as "God is [the] Greatest" or "God is Great") and the phrase beginning "A`ūdhu billāhi..." called the Ta'awwudh. The method of coining a quadriliteral name from the consonants of a phrase is paralleled by the name Hamdala for Alhamdulillah.[16]
Recitation of the Basmala is known as tasmiyya (تسمية).
Hinduism chapter
QMRTypes and classifications[edit]
Bhakti can be practiced in four ways:[59][60]
To the Supreme Self (Atma-Bhakti)
To God or the Cosmic Lord as a formless being (Ishvara-Bhakti)
To God in the form of various Gods or Goddesses (Ishta Devata-Bhakti)
To God in the form of the Guru (Guru-Bhakti)
There are four types of Latin suits: Italian, Spanish, Portuguese,[note 1] and an extinct archaic type.[3][4] They can be distinguished by the pips of their long suits (swords and clubs). Italian swords and curved and clubs appear to be batons and they intersect one another. Spanish swords are straight and clubs appear to be cudgels and they don't cross each other. Portuguese pips are like the Spanish but they intersect like Italian ones. The archaic system is like the Italian one but the curve swords only touching each other without intersecting.[5] Minchiate used a mixed system of Italian clubs and Portuguese swords. The archaic system did not survive the 15th century. The Portuguese system lingers on only in the Tarocco Siciliano and the Unsun Karuta of Japan.
QMRFour-color suits[edit]
The aces of a four-color deck
See also: Four-color deck
Some decks, while using the French suits, give each suit a different color to make the suits more distinct from each other. In bridge, such decks are known as no-revoke decks, and the most common colors are black spades, red hearts, blue diamonds and green clubs, although in the past the diamond suit usually appeared in a golden yellow-orange. A related set occasionally used in Germany uses green spades (compare to leaves), red hearts, yellow diamonds (compare to bells) and black clubs (compare to acorns). This is a compromise deck devised to allow players from East Germany (who used German suits) and West Germany (who adopted the French suits) to be comfortable with the same deck when playing tournament Skat after the German reunification.[30]
Numerous variations of the 52-card French deck have existed over the years. Most notably, the tarot deck has a separate trump series in addition to the four suits; however this fifth suit is a series of cards of a different number and style than the suited cards. Various people have independently suggested expanding the French deck to five, six or even more suits where the additional suits have the same number and style of cards as the French suits, and have proposed rules for expanded versions of popular games such as rummy, hearts, bridge, and poker that could be played with such a deck.
If commercially-made decks are not readily available, a deck with up to eight suits can be made from two identical decks by altering the suit symbols throughout one of them with a non-fading marker. R. Wayne Schmittberger in New Rules for Classic Games originated the idea of drawing an arrow through each heart to create valentines and a cross through each diamond to create kites. Clubs would have their stem rounded to create cloverleaves and spades would have horns and tail added to become devils.
QMRA four-color deck is identical to the standard French deck except for the color of the suits. In a typical four-color deck, hearts are red and spades are black as usual, but clubs are green and diamonds are blue.[1] However, other color combinations have been used over the centuries.
In 1819, J. Y. Humphreys created the "Seminole Wars Deck", which had four colored suits of blue spades, green clubs, red hearts and yellow diamonds. In 1876, for the American Centennial, Victor Mauger issued a deck that contained black spades, red hearts, yellow diamonds and blue clubs.
QMRŚrauta Sutras[edit]
The Śrautasutras (śrautasūtra) form a part of the corpus of Sanskrit sutra literature. Their topics include instructions relating to the use of the śruti corpus in ritual ('kalpa') and the correct performance of these rituals. Some early Śrautasutras were composed in the late Brahmana period (such as the Baudhyanana and Vadhula Sutras), but the bulk of the Śrautasutras are roughly contemporary to the Gṛhya corpus of domestic sutras, their language being late Vedic Sanskrit, dating to the middle of the first millennium BCE (generally predating Pāṇini).
Veda Śrautasūtra[3]
Ṛgveda Āśvalāyana Śrautasūtra[4]
Sāṅkhāyana Śrautasūtra
Sāmaveda Lātyāyana Śrautasūtra
Drāhyāyana Śrautasūtra
Jaiminiya Śrautasūtra
Kṛsna Yajurveda Baudhāyana Śrautasūtra
Vādhūla Śrautasūtra
Mānava Śrautasūtra
Bharadvāja Śrautasūtra
Āpastamba Śrautastūra
Hiraṅyakeśi Śrautasūtra
Vārāha Śrautasūtra
Vaikhānasa Śrautasūtra
Śukla Yajurveda Kātyāyana Śrautasūtra
Atharvaveda Vaitāna Śrautasũtra
Gṛhyasūtras[edit]
The Gṛhyasūtras "domestic sutras" are a category of Sanskrit texts prescribing Vedic ritual, mainly relating to rites of passage. Their language is late Vedic Sanskrit, and they date to around roughly 500 BCE, contemporary with the Śrautasūtras. They are named after Vedic shakhas.
Veda Gr̥hyasūtra[3]
R̥gveda Âśvalāyana-Gṛhyasūtra [4]
Kausîtaki-Gṛhyasūtra (Bāṣkala śakha)
Śāṅkhāyana-Gr̥hyasūtra [1]
Sāmaveda Gobhila-Gṛhyasūtra
Khādira-Gṛhyasūtra (Drāhyāyana-Gṛhyasūtra)
Jaiminiya-Gṛhyasūtra
Kauthuma-Gṛhyasūtra
Kṛsna Yajurveda Baudhāyana-Gṛhyasūtra
Hiraṇyakeśi-Gṛhyasūtra (Satyāsādha-Gṛhyasūtra) [2]
Mānava-Gṛhyasūtra
Bhāradvāja-Gṛhyasūtra
Āpastamba-Gṛhyasūtra
Āgniveśya-Gṛhyasūtra
Vaikhānasa-Gṛhyasūtra
Kāthaka-Gṛhyasūtra (Laugāksi-Gṛhyasūtra)
Vārāha-Gṛhyasūtra
Vādhûla-Gṛhyasūtra
Kapisthala-Katha Gṛhyasūtra (unpublished)
Śukla Yajurveda
Pāraskara-Gṛhyasūtra
Katyayana-Gṛhyasūtra
Atharvaveda Kauśika Gṛhyasūtra
Dharmasūtras[edit]
The Dharmasūtras are texts dealing with custom, rituals, and law. They include the four surviving written works of the ancient Indian tradition on the subject of dharma, or the rules of behavior recognized by a community. Unlike the later Dharmaśāstra, the dharmasūtras are composed in prose. The oldest Dharmasūtra is generally believed to have been that of Apastamba, followed by the dharmasūtras of Gautama, Baudhayana, and an early version of Vasistha. It is difficult to determine exact dates for these texts, but the dates between 500–300 BCE have been suggested for the oldest Dharmasūtras. Later Dharmasūtras include those of Kashyapa, Bṛhaspati, and Ushanas.
Veda Dharmasūtra[3]
R̥gveda Vasishtha Dharmasūtra
Sāmaveda Gautama Dharmasūtra
Kr̥sna Yajurveda Baudhāyana Dharmasūtra
Āpastamba Dharmasūtra
Śukla Yajurveda Vishnu Dharmasūtra
Shulba Sutras[edit]
The Śulbasûtra deal with Shrauta ritual and altar geometries.
Veda Śulbasûtra[3]
Kr̥sna Yajurveda Baudhāyana Śulbasûtra
Mānava Śulbasûtra
Āpastamba Śulbasûtra
Śukla Yajurveda Kātyāyana Śulbasûtra
Other religion chapter
QMRSome post-conquest sources report that at the re-consecration of Great Pyramid of Tenochtitlan in 1487, the Aztecs sacrificed about 80,400 prisoners over the course of four days. This number is considered an exaggeration. According to Ross Hassig, author of Aztec Warfare, "between 10,000 and 80,400 persons" were sacrificed in the ceremony.[39] The higher estimate would average 14 sacrifices per minute during the four-day consecration. Four tables were arranged at the top so that the victims could be jettisoned down the sides of the temple.[40] Nonetheless, according to Codex Telleriano-Remensis, old Aztecs who talked with the missionaries told about a much lower figure for the reconsecration of the temple, approximately 4,000 victims in total.
The sacrificed people would walk to the four tables in four linesQMRMixcoatl was one of four children of Tonacatecutli, meaning "Lord of Sustenance," an aged creator god, and Cihuacoatl, a fertility goddess and the patroness of midwives
QMRAnthony F.C. Wallace proposes four categories of religion, each subsequent category subsuming the previous. These are, however, synthetic categories and do not necessarily encompass all religions.[19]
Individualistic: most basic; simplest. Example: vision quest.
Shamanistic: part-time religious practitioner, uses religion to heal, to divine, usually on the behalf of a client. The Tillamook have four categories of shaman. Examples of shamans: spiritualists, faith healers, palm readers. Religious authority acquired through one's own means.
Communal: elaborate set of beliefs and practices; group of people arranged in clans by lineage, age group, or some religious societies; people take on roles based on knowledge, and ancestral worship.
Ecclesiastical: dominant in agricultural societies and states; are centrally organized and hierarchical in structure, paralleling the organization of states. Typically deprecates competing individualistic and shamanistic cults.
QMRPhilosopher Lynne Rudder Baker has outlined four main contemporary approaches to belief in her controversial book Saving Belief:[9]
Our common-sense understanding of belief is correct - Sometimes called the "mental sentence theory," in this conception, beliefs exist as coherent entities, and the way we talk about them in everyday life is a valid basis for scientific endeavour. Jerry Fodor is one of the principal defenders of this point of view.
Our common-sense understanding of belief may not be entirely correct, but it is close enough to make some useful predictions - This view argues that we will eventually reject the idea of belief as we use it now, but that there may be a correlation between what we take to be a belief when someone says "I believe that snow is white" and how a future theory of psychology will explain this behaviour. Most notably, philosopher Stephen Stich has argued for this particular understanding of belief.
Our common-sense understanding of belief is entirely wrong and will be completely superseded by a radically different theory that will have no use for the concept of belief as we know it - Known as eliminativism, this view (most notably proposed by Paul and Patricia Churchland) argues that the concept of belief is like obsolete theories of times past such as the four humours theory of medicine, or the phlogiston theory of combustion. In these cases science hasn't provided us with a more detailed account of these theories, but completely rejected them as valid scientific concepts to be replaced by entirely different accounts. The Churchlands argue that our common-sense concept of belief is similar in that as we discover more about neuroscience and the brain, the inevitable conclusion will be to reject the belief hypothesis in its entirety.
Our common-sense understanding of belief is entirely wrong; however, treating people, animals, and even computers as if they had beliefs is often a successful strategy - The major proponents of this view, Daniel Dennett and Lynne Rudder Baker, are both eliminativists in that they hold that beliefs are not a scientifically valid concept, but they don't go as far as rejecting the concept of belief as a predictive device. Dennett gives the example of playing a computer at chess. While few people would agree that the computer held beliefs, treating the computer as if it did (e.g. that the computer believes that taking the opposition's queen will give it a considerable advantage) is likely to be a successful and predictive strategy. In this understanding of belief, named by Dennett the intentional stance, belief-based explanations of mind and behaviour are at a different level of explanation and are not reducible to those based on fundamental neuroscience, although both may be explanatory at their own level.
QMRA question by the monk Subhadda to the Buddha:
"O Gotama, there are Samanas (wandering monks) and Brahmanas (religious leaders) who are leaders of their sects, who are well-esteemed by many people, such as Purana Kassapa, Makkhali Gosala, Ajita Kesakambala, Pakudha Kaccayana, Sancaya Belatthaputta and Nigantha Nataputta. Do all of them have knowledge and understanding as they themselves have declared? Or do all of them have no knowledge and understanding?"
The reply by Buddha was:
"Subhadda, in whatever teaching is not found the Noble Eightfold Path, neither in it is there found a Samana of the first stage, nor a Samana of the second stage, nor a Samana of the third stage, nor a Samana of the fourth stage."
QMRTryon Edwards (7 August 1809, Hartford, Conn.; 4 January 1894, Detroit, Mich.)[1] was an American theologian, best known for compiling A Dictionary of Thoughts,[2] a book of quotations. He published the works of Jonathan Edwards (the younger) in 1842. He also compiled and published the sixteen sermons of his great grandfather, Jonathan Edwards, on 1 Corinthians 13, the "Love Chapter", titling the book "Charity And Its Fruits; Christian love as manifested in the heart and life", which was thought by some[citation needed] to be the most thorough analysis of the text of 1 Corinthians 13 ever written. An original quote of Tryon Edwards is: “Thoughts lead on to purposes; purposes go forth in action; actions form habits; habits decide character; and character fixes our destiny.” ~ Tyrone Edwards
QMRIn their shamanic ceremonies, Manchus worshipped a number of gods, including non-Tungusic deities. Guandi and the bodhisattva (Buddhist "enlightened being") Guanyin were two of a "handful of Chinese gods" who were integrated into the rituals of the state tangse and Kunning Palace.[64] One of the four ritual sites in the tangse was a large hall where the Buddha, Guanyin, and Guandi received offerings several times a year, including at the New Year.[65] Ordinary Manchu households rarely sacrificed to Buddhist deities, but almost all of them worshipped Guandi because of his association with war.[66]
QMRPaul Offit has proposed four ways that "alternative medicine becomes quackery":[80]
"...by recommending against conventional therapies that are helpful."
"...by promoting potentially harmful therapies without adequate warning."
"...by draining patients' bank accounts,..."
"...by promoting magical thinking,..."[80
QMRTezcatlipoca (/ˌtɛzˌkætliˈpoʊkə/; Classical Nahuatl: Tezcatlipōca pronounced [teskatɬiˈpoːka][1]) was a central deity in Aztec religion, and his main festival was the Toxcatl ceremony celebrated in the month of May. One of the four sons of Ometeotl,
QMRIn later myths, the four gods who created the world, Tezcatlipoca, Quetzalcoatl, Huitzilopochtli and Xipe Totec were referred to respectively as the Black, the White, the Blue and the Red Tezcatlipoca. The four Tezcatlipocas were the sons of Ometecuhtli and Omecihuatl, lady and lord of the duality, and were the creators of all the other gods, as well as the world and all humanity.
QMRTezcatlipoca was also worshipped in many other Nahua cities such as Texcoco, Tlaxcala and Chalco. Each temple had a statue of the god for which copal incense was burned four times a day.
QMRChālco [ˈt͡ʃaːɬko] was a complex pre-Columbian Nahua altepetl or confederacy in central Mexico. It was divided into the four sub-altepetl of Tlalmanalco/Tlacochcalco, Amaquemecan, Tenanco Texopalco Tepopolla and Chimalhuacan-Chalco, which were themselves further subdivided into altepetl tlayacatl, each with its own tlatoani (king). Its inhabitants were known as the Chālcatl [ˈt͡ʃaːɬkat͡ɬ] (singular) or Chālcah [ˈt͡ʃaːɬkaʔ] (plural).
QMRTlaxcala (Classical Nahuatl: Tlaxcallān [tɬaʃ.ˈká.lːaːn̥] "place of maize tortillas") was a pre-Columbian city and state in central Mexico.
Ancient Tlaxcala was a republic ruled by a council of between 50 and 200 chief political officials (teuctli [sg.], teteuctin [pl.]) (Fargher et al. 2010). These officials gained their positions through service to the state, usually in warfare, and as a result came from both the noble (pilli) and commoner (macehualli) classes. Following the Spanish Conquest, Tlaxcala was divided into four fiefdoms (señoríos) by the Spanish corregidor Gómez de Santillán in 1545 (26 years after the Conquest). These fiefdoms were Ocotelolco, Quiahuiztlan, Tepeticpac, and Tizatlan. At this time, four great houses or lineages emerged and claimed hereditary rights to each fiefdom and created fictitious genealogies extending back into the pre-Columbian era to justify their claims (Gibson 1952)
In Aztec mythology, the Centzonmimixcoa (Nahuatl pronunciation: [sentsonmiːmiʃˈkoːaʔ] or Centzon Mimixcoa, the "Four Hundred alike Mixcoatl") are the gods of the northern stars.
The Aztec gods of the southern stars are the Centzonuitznaua.
According to the Manuscript of 1558, section 6, these 400 'Cloud-Serpents' were divinely slain [= transformed into stars] in this wise :- of their protagonists 4,
Quauhtli-icohuauh ('Eagle's Twin') "hid inside a tree";
Mix-coatl ('Cloud Serpent') "hid within the earth";
Tlo-tepetl ('Hawk Mountain') "hid within a hill";
Apan-teuctli ('River Lord') "hid in the water";
their sister, Cuetlach-cihuatl, "hid in the ball court."
From this ambuscade these 4 slew the 400.[1]
Notice the repetitions of fours
In Aztec mythology, the Centzonuitznahua Nahuatl pronunciation: [sent͡sonwiːtsˈnaːwa] (or, in plural, Centzon Huitznauhtin Nahuatl pronunciation: [sent͡sonwiːtsˈnaːwtin]) were the gods of the southern stars. They are the evil elder sons of Coatlicue, and their sister is Coyolxauhqui. They and their sister tried to murder their mother upon learning of her pregnancy with Huitzilopochtli; their plan was thwarted when their brother sprang from the womb—fully grown and garbed for battle—and killed them all.
The Centzonhuitznaua are known as the "Four Hundred Southerners"; the gods of the northern stars are the Centzonmimixcoa.
Whether it is four or four hundred Amerindian myths are filled with fours. But so are mythologies throughout the world but it is kind of accentuated in Amerindian myths
QMRIn Aztec mythology, Coyolxauhqui (Classical Nahuatl: Coyolxāuhqui [kojoɬˈʃaːʍki], "Face painted with Bells") was a daughter of Coatlicue and Mixcoatl and is the leader of the Centzon Huitznahuas, the southern star gods. Coyolxauhqui ruled over her brothers, the Four Hundred Southerners, she led them in attack against their mother, Coatlicue, when they learned she was pregnant, convinced she dishonored them all.[1]
Contents [hide]
1 Attack on Coatlicue
2 Templo Mayor stone disk
3 Other associations
4 See also
5 References
6 External links
Attack on Coatlicue[edit]
The miraculous pregnancy of Coatlicue, the maternal Earth deity, made her other children embarrassed, including her oldest daughter Coyolxauhqui. As Coatlicue swept the temple, a few hummingbird feathers fell into her chest. Coatlicue’s child Huitzilopochtli sprang from her womb in full war armor and killed Coyolxauhqui and her other 400 brothers, who had been attacking their mother. He cut off her limbs, then tossed her head into the sky where it became the moon, so that his mother would be comforted in seeing her daughter in the sky every night
QMRThere are a handful of origin mythologies describing the deity’s beginnings. One story tells of the cosmic creation and Huitzilopochtli’s role. According to this legend, he was the smallest son of four—his parents being the creator couple Tonacateuctli and Tonacacihuatl while his brothers were Quetzalcoatl and the two Tezcatlipocas. His mother and father instructed both him and Quetzalcoatl to bring order to the world. And so, together they made fire, the first male and female humans, created the Earth, and manufactured a sun.[6]
Another origin story tells of a fierce goddess, Coatlicue, being impregnated as she was sweeping by a ball of feathers on Coatepec ("Serpent Hill").[7] Her other children, who were already fully grown, were the four hundred male Centzonuitznaua and the female deity Coyolxauhqui. These children, angered by the manner by which their mother became impregnated, conspired to kill her.[8] Huitzilopochtli burst forth from his mother’s womb in full armor and fully grown. He attacked his older brothers and sister, defending his mother by beheading his sister and casting her body from the mountain top. He also chased after his brothers, who fled from him and became scattered all over the sky. [9]
QMRIn Aztec cosmology, the four corners of the universe are marked by "the four Tlalocs" (Classical Nahuatl: Tlālōquê [tɬaːˈloːkeʔ]) which both hold up the sky and function as the frame for the passing of time. Tlaloc was the patron of the Calendar day Mazātl. In Aztec mythology, Tlaloc was the lord of the third sun which was destroyed by fire.
Tlaloc (Classical Nahuatl: Tlāloc [ˈtɬaːlok])[1] was an important deity in Aztec religion; as supreme god of the rains, he was also by extension a god of fertility and of water. He was widely worshiped as a beneficent giver of life and sustenance, but he was also feared for his ability to send hail, thunder, and lightning, and for being the lord of the powerful element of water.
QMRPage 46 of the pre-Columbian Codex Borgia depicts four smoking Xiuhcoatl serpents arranged around a burning turquoise mirror. A turquoise-rimmed mirror has been found at the Maya city of Chichen Itza, with four fire serpents circling the rim. The archaeological site of Tula has warrior columns on Mound B that bear mirrors on their backs, also surrounded by four Xiuhcoatl fire serpents.[
QMRThe Codex Borgia or Codex Yoalli Ehēcatl is a Mesoamerican ritual and divinatory manuscript. It is generally believed to have been written before the Spanish conquest of Mexico, somewhere within what is now southern or western Puebla. The Codex Borgia is a member of, and gives its name to, the Borgia Group of manuscripts.
14[edit]
Pages 9 to 13 are divided into four quarters. Each quarter contains one of the twenty day signs, its patron deity, and associated symbols.
Page 14 is divided into nine sections for each of the nine Lords of the Night. They are accompanied by a day sign and symbols indicating positive or negative associations.
Pages 15 to 17 depict deities associated with childbirth. Each of the twenty sections contains four day signs.
The bottom section of page 17 contains a large depiction of Tezcatlipoca, with day signs associated with different parts of his body.
Page 71 depicts Tonatiuh, the sun god, receiving blood from a decapitated bird. Surrounding the scene are the thirteen Birds of the Day, corresponding to each of the thirteen days of a trecena. Page 72 depicts four deities with day signs connected to parts of their bodies. Each deity is surrounded by a serpent. Page 73 depicts the gods Mictlantecuhtli and Quetzalcoatl seated back to back, similar to page 56. They likewise have day signs attached to various parts of their bodies, and the entire scene is encircled by day signs.
QMRThe Valley of Mexico can be subdivided into four basins, but the largest and most-studied is the area which contains Mexico City. This section of the valley in particular is colloquially referred to as the "Valley of Mexico".[3] The valley has a minimum altitude of 2,200 meters (7,200 ft) above sea level and is surrounded by mountains and volcanoes that reach elevations of over 5,000 meters (16,000 ft).[4] It is an enclosed valley with no natural outlet for water to flow and a gap to the north where there is a high mesa but no high mountain peaks. Within this vulnerable watershed all the native fishes were extinct by the end of the 20th century.[5] Hydrologically, the valley has three features. The first feature is the lakebeds of five now-extinct lakes, which are located in the southernmost and largest of the four sub-basins. The other two features are piedmont, and the mountainsides that collect the precipitation that eventually flows to the lake area. These last two are found in all four of the sub-basins of the valley.[1][3] Today, the Valley drains through a series of artificial canals to the Tula River, and eventually the Pánuco River and the Gulf of Mexico. Seismic activity is frequent here, and the valley is considered an earthquake prone zone.[6]
QMR Mexico cityIntercity buses[edit]
The city has four major bus stations (North, South, Observatorio, TAPO), which comprise one of the world's largest transportation agglomerations, with bus service to many cities across the country and international connections.
QMRThe capital city of the Aztec empire was Tenochtitlan, now the site of modern-day Mexico City. Built on a series of islets in Lake Texcoco, the city plan was based on a symmetrical layout that was divided into four city sections called campans. The city was interlaced with canals which were useful for transportation.
QMRThe Popol Vuh gives a sequence of four efforts at creation: First were animals, then wet clay, wood, then last, the creation of the first ancestors from maize dough. To this, the Lacandons add the creation of the main kind groupings and their 'totemic' animals.[3] The creation of humankind is concluded by the Mesoamerican tale of the opening of the Maize (or Sustenance) Mountain by the Lightning deities.[4]
QMRPage 11 reverse from Codex Magliabechiano, showing four day-symbols of the tonalpohualli: (Ce = one) Flint/Knife tecpatl, (Ome = two) Rain quiahuitl, (Yei = three) Flower xochitl, and (Nahui = four) Caiman/Crocodile (cipactli), with Spanish descriptions.
No comments:
Post a Comment