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Thursday, October 19, 2023

Perpendicular

From Wikipedia, the free encyclopedia
The segment AB is perpendicular to the segment CD because the two angles it creates (indicated in orange and blue) are each 90 degrees. The segment AB can be called the perpendicular from A to the segment CD, using "perpendicular" as a noun. The point B is called the foot of the perpendicular from A to segment CD, or simply, the foot of A on CD.

In elementary geometry, two geometric objects are perpendicular if their intersection forms right angles (angles that are 90 degrees or π/2 radians wide) at the point of intersection called a foot. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂. Perpendicular intersections can happen between two lines (or two line segments), between a line and a plane, and between two planes.

Perpendicularity is one particular instance of the more general mathematical concept of orthogonality; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as that between a surface and its normal vector.

A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order. A great example of perpendicularity can be seen in any compass, note the cardinal points; North, East, South, West (NESW) The line N-S is perpendicular to the line W-E and the angles N-E, E-S, S-W and W-N are all 90° to one another.

Perpendicularity easily extends to segments and rays. For example, a line segment is perpendicular to a line segment if, when each is extended in both directions to form an infinite line, these two resulting lines are perpendicular in the sense above. In symbols, means line segment AB is perpendicular to line segment CD.

A line is said to be perpendicular to a plane if it is perpendicular to every line in the plane that it intersects. This definition depends on the definition of perpendicularity between lines.

Two planes in space are said to be perpendicular if the dihedral angle at which they meet is a right angle.

Foot of a perpendicular

The word foot is frequently used in connection with perpendiculars. This usage is exemplified in the top diagram, above, and its caption. The diagram can be in any orientation. The foot is not necessarily at the bottom.

More precisely, let A be a point and m a line. If B is the point of intersection of m and the unique line through A that is perpendicular to m, then B is called the foot of this perpendicular through A.

Construction of the perpendicular

Construction of the perpendicular (blue) to the line AB through the point P.
Construction of the perpendicular to the half-line h from the point P (applicable not only at the end point A, M is freely selectable), animation at the end with pause 10 s

To make the perpendicular to the line AB through the point P using compass-and-straightedge construction, proceed as follows (see figure left):

  • Step 1 (red): construct a circle with center at P to create points A' and B' on the line AB, which are equidistant from P.
  • Step 2 (green): construct circles centered at A' and B' having equal radius. Let Q and P be the points of intersection of these two circles.
  • Step 3 (blue): connect Q and P to construct the desired perpendicular PQ.

To prove that the PQ is perpendicular to AB, use the SSS congruence theorem for QPA' and QPB' to conclude that angles OPA' and OPB' are equal. Then use the SAS congruence theorem for triangles OPA' and OPB' to conclude that angles POA and POB are equal.

To make the perpendicular to the line g at or through the point P using Thales's theorem, see the animation at right.

The Pythagorean theorem can be used as the basis of methods of constructing right angles. For example, by counting links, three pieces of chain can be made with lengths in the ratio 3:4:5. These can be laid out to form a triangle, which will have a right angle opposite its longest side. This method is useful for laying out gardens and fields, where the dimensions are large, and great accuracy is not needed. The chains can be used repeatedly whenever required.

In relationship to parallel lines

The arrowhead marks indicate that the lines a and b, cut by the transversal line c, are parallel.

If two lines (a and b) are both perpendicular to a third line (c), all of the angles formed along the third line are right angles. Therefore, in Euclidean geometry, any two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate. Conversely, if one line is perpendicular to a second line, it is also perpendicular to any line parallel to that second line.

In the figure at the right, all of the orange-shaded angles are congruent to each other and all of the green-shaded angles are congruent to each other, because vertical angles are congruent and alternate interior angles formed by a transversal cutting parallel lines are congruent. Therefore, if lines a and b are parallel, any of the following conclusions leads to all of the others:

  • One of the angles in the diagram is a right angle.
  • One of the orange-shaded angles is congruent to one of the green-shaded angles.
  • Line c is perpendicular to line a.
  • Line c is perpendicular to line b.
  • All four angles are equal.

In computing distances

In geometry, the perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both.

The distance from a point to a line is the distance to the nearest point on that line. That is the point at which a segment from it to the given point is perpendicular to the line.

Likewise, the distance from a point to a curve is measured by a line segment that is perpendicular to a tangent line to the curve at the nearest point on the curve.

The distance from a point to a plane is measured as the length from the point along a segment that is perpendicular to the plane, meaning that it is perpendicular to all lines in the plane that pass through the nearest point in the plane to the given point.

Other instances include:

Perpendicular regression fits a line to data points by minimizing the sum of squared perpendicular distances from the data points to the line. Other geometric curve fitting methods using perpendicular distance to measure the quality of a fit exist, as in total least squares.

The concept of perpendicular distance may be generalized to

Graph of functions

In the two-dimensional plane, right angles can be formed by two intersected lines if the product of their slopes equals −1. Thus defining two linear functions: y1 = a1x + b1 and y2 = a2x + b2, the graphs of the functions will be perpendicular and will make four right angles where the lines intersect if a1a2 = −1. However, this method cannot be used if the slope is zero or undefined (the line is parallel to an axis).

For another method, let the two linear functions be: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. The lines will be perpendicular if and only if a1a2 + b1b2 = 0. This method is simplified from the dot product (or, more generally, the inner product) of vectors. In particular, two vectors are considered orthogonal if their inner product is zero.

In circles and other conics

Circles

Each diameter of a circle is perpendicular to the tangent line to that circle at the point where the diameter intersects the circle.

A line segment through a circle's center bisecting a chord is perpendicular to the chord.

If the intersection of any two perpendicular chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then a2 + b2 + c2 + d2 equals the square of the diameter.

The sum of the squared lengths of any two perpendicular chords intersecting at a given point is the same as that of any other two perpendicular chords intersecting at the same point, and is given by 8r2 – 4p2 (where r is the circle's radius and p is the distance from the center point to the point of intersection).

Thales' theorem states that two lines both through the same point on a circle but going through opposite endpoints of a diameter are perpendicular. This is equivalent to saying that any diameter of a circle subtends a right angle at any point on the circle, except the two endpoints of the diameter.

Ellipses

The major and minor axes of an ellipse are perpendicular to each other and to the tangent lines to the ellipse at the points where the axes intersect the ellipse.

The major axis of an ellipse is perpendicular to the directrix and to each latus rectum.

Parabolas

In a parabola, the axis of symmetry is perpendicular to each of the latus rectum, the directrix, and the tangent line at the point where the axis intersects the parabola.

From a point on the tangent line to a parabola's vertex, the other tangent line to the parabola is perpendicular to the line from that point through the parabola's focus.

The orthoptic property of a parabola is that If two tangents to the parabola are perpendicular to each other, then they intersect on the directrix. Conversely, two tangents which intersect on the directrix are perpendicular. This implies that, seen from any point on its directrix, any parabola subtends a right angle.

Hyperbolas

The transverse axis of a hyperbola is perpendicular to the conjugate axis and to each directrix.

The product of the perpendicular distances from a point P on a hyperbola or on its conjugate hyperbola to the asymptotes is a constant independent of the location of P.

A rectangular hyperbola has asymptotes that are perpendicular to each other. It has an eccentricity equal to

In polygons

Triangles

The legs of a right triangle are perpendicular to each other.

The altitudes of a triangle are perpendicular to their respective bases. The perpendicular bisectors of the sides also play a prominent role in triangle geometry.

The Euler line of an isosceles triangle is perpendicular to the triangle's base.

The Droz-Farny line theorem concerns a property of two perpendicular lines intersecting at a triangle's orthocenter.

Harcourt's theorem concerns the relationship of line segments through a vertex and perpendicular to any line tangent to the triangle's incircle.

Quadrilaterals

In a square or other rectangle, all pairs of adjacent sides are perpendicular. A right trapezoid is a trapezoid that has two pairs of adjacent sides that are perpendicular.

Each of the four maltitudes of a quadrilateral is a perpendicular to a side through the midpoint of the opposite side.

An orthodiagonal quadrilateral is a quadrilateral whose diagonals are perpendicular. These include the square, the rhombus, and the kite. By Brahmagupta's theorem, in an orthodiagonal quadrilateral that is also cyclic, a line through the midpoint of one side and through the intersection point of the diagonals is perpendicular to the opposite side.

By van Aubel's theorem, if squares are constructed externally on the sides of a quadrilateral, the line segments connecting the centers of opposite squares are perpendicular and equal in length.

Lines in three dimensions

Up to three lines in three-dimensional space can be pairwise perpendicular, as exemplified by the x, y, and z axes of a three-dimensional Cartesian coordinate system.

Religion and drugs

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Religion_and_drugs

Many religions have expressed positions on what is acceptable to consume as a means of intoxication for spiritual, pleasure, or medicinal purposes. Psychoactive substances may also play a significant part in the development of religion and religious views as well as in rituals.

The most common drugs in the historical religions are cannabis and alcohol.

Neolithic

In the book Inside the Neolithic Mind, the authors, archaeologists David Lewis-Williams and David Pearce argue that hallucinogenic drugs formed the basis of neolithic religion and rock art.

Ancient Greece

Some scholars have suggested that Ancient Greek mystery religions employed entheogens, such as the ergot-spiked Kykeon central to the Eleusinian Mysteries, which contained LSD-like compounds to induce a trance or dream state. Research conducted by John R. Hale, Jelle Zeilinga de Boer, Jeffrey P. Chanton and Henry A. Spiller suggests that the prophecies of the Delphic Oracle were uttered by Priestesses under the influence of ethylene gas exuded from the ground.

Ancient Mesoamerica

Psilocybe Mushrooms statues

Archaeological, ethnohistorical, and ethnographic data show that Mesoamerican cultures used psychedelic substances in therapeutic and religious rituals. The ancient Aztecs used a variety of entheogenic plants and animals within their society, including ololiuqui (Rivea corymbosa), teonanácatl (Psilocybe spp.), and peyotl (Lophophora williamsii). Goals for the usage of entheogenics by the Maya were spiritual healing, wisdom gain, and religious ceremonies. The effects of psychedelic plants during religious rituals is believed to have had an impact on the development and creation of statues, and sacred images.

Hinduism

Soma

Hinduism has a history of psychedelic usage going back to the Vedic period. The oldest scriptures of Hinduism Rigveda(1500 BCE), mentions ritualistic consumption of a divine psychedelic known as soma. There are many theories about the recipe of Soma. Non-Indian researchers have proposed candidates including Amanita muscaria, Psilocybe cubensis, Peganum harmala and Ephedra sinica. According to recent philological and archaeological studies, and in addition, direct preparation instructions confirm in the Rig Vedic Hymns (Vedic period) Ancient Soma most likely consisted of Poppy, Phaedra/Ephedra (plant) and Cannabis.

In the Vedas, the same word soma is used for the drink, the plant, and its deity. Drinking soma produces immortality (Amrita, Rigveda 8.48.3). Indra and Agni are portrayed as consuming soma in copious quantities. In the vedic mythology, Indra drank large amounts of soma while fighting the serpent demon Vritra. The consumption of soma by human beings is well attested in Vedic ritual.

The Rigveda (8.48.3) says:

ápāma sómam amŕ̥tā abhūma
áganma jyótir ávidāma devā́n
kíṃ nūnám asmā́n kr̥ṇavad árātiḥ
kím u dhūrtír amr̥ta mártiyasya

Ralph T.H. Griffith translates this as:

We have drunk soma and become immortal; we have attained the light, the Gods discovered.
Now what may foeman's malice do to harm us? What, O Immortal, mortal man's deception?

Cannabis

The plant Cannabis is also mentioned in the Atharvaveda-Samhita (1200BCE) & Puranas (circa 200BCE) as one of the 5 of the holy plants.

The Atharvaveda 11.6.15 :

पञ्च राज्यानि वीरुधां सोमश्रेष्ठानि ब्रूमः।
दर्भो भङ्गो (bhang) यवः सह ते नो मुञ्चन्त्व् अंहसः॥

“To the five kingdoms of the plants which Soma rules as Lord we speak.
Darbha, hemp, barley, mighty power: may these deliver us from woe.”

‘भङ्ग’ (bhang) refers to the cannabis plant.

Datura

The hallucinogenic Datura plant has also been used in Ayurvedic contexts & are often used to adorn the Lingam in many Shiva temples & festivals like Navarathri. The plant goes through a detoxification process to remove the psychoactive elements when utilized in standard Ayurveda practice. In the Vamana Purana, it is mentioned that the Datura flower appeared from the chest of Shiva & offering it the will remove evil, suffering & wrongdoings. There are also Sadhus who are worshipers of Shiva & sometimes smoke the leaves and seeds of Datura plant, though is done with caution because it can be poisonous & cause very vivid hallucinations (delirium).

Buddhism

In Buddhism the Right View (samyag-dṛṣṭi / sammā-diṭṭhi) can also be translated as "right perspective", "right outlook" or "right understanding", is the right way of looking at life, nature, and the world as they really are for us. It is to understand how our reality works. It acts as the reasoning with which someone starts practicing the path. It explains the reasons for our human existence, suffering, sickness, aging, death, the existence of greed, hatred, and delusion. Right view gives direction and efficacy to the other seven path factors. It begins with concepts and propositional knowledge, but through the practice of right concentration, it gradually becomes transmuted into wisdom, which can eradicate the fetters of the mind. An understanding of right view will inspire the person to lead a virtuous life in line with right view. In the Pāli and Chinese canons, it is explained thus:

Right livelihood

Right livelihood (samyag-ājīva / sammā-ājīva). This means that practitioners ought not to engage in trades or occupations which, either directly or indirectly, result in harm for other living beings. In the Chinese and Pali Canon, it is explained thus:

And what is right livelihood? There is the case where a disciple of the noble ones, having abandoned dishonest livelihood, keeps his life going with right livelihood: This is called right livelihood.

More concretely today interpretations include "work and career need to be integrated into life as a Buddhist," it is also an ethical livelihood, "wealth obtained through rightful means" (Bhikku Basnagoda Rahula) – that means being honest and ethical in business dealings, not to cheat, lie or steal. As people are spending most of their time at work, it’s important to assess how our work affects our mind and heart. So important questions include "How can work become meaningful? How can it be a support, not a hindrance, to spiritual practice — a place to deepen our awareness and kindness?"

The five types of businesses that should not be undertaken:

  1. Business in weapons: trading in all kinds of weapons and instruments for killing.
  2. Business in human beings: slave trading, prostitution, or the buying and selling of children or adults.
  3. Business in meat: "meat" refers to the bodies of beings after they are killed. This includes breeding animals for slaughter.
  4. Business in intoxicants: manufacturing or selling intoxicating drinks or addictive drugs.
  5. Business in poison: producing or trading in any kind of poison or a toxic product designed to kill.

The fifth precept

According to the fifth precept of the Pancasila, Buddhists are meant to refrain from any quantity of "fermented or distilled beverages" which would prevent mindfulness or cause heedlessness. In the Pali Tipitaka the precept is explicitly concerned with alcoholic beverages:

"I undertake the training rule to abstain from fermented drink that causes heedlessness."
Surāmerayamajjapamādaṭṭhānā veramaṇī sikkhāpadaṃ samādiyāmi.

However, caffeine and tea are permitted, even encouraged for monks of most traditions, as it is believed to promote wakefulness.

Generally speaking, the vast majority of Buddhists and Buddhist sects denounce and have historically frowned upon the use of any intoxicants by an individual who has taken the five precepts. Most Buddhists view the use and abuse of intoxicants to be a hindrance in the development of an enlightened mind. However, there are a few historical and doctrinal exceptions.

Vajrayana

Many modern Buddhist schools have strongly discouraged the use of psychoactive drugs of any kind; however, they may not be prohibited in all circumstances in all traditions. Some denominations of tantric or esoteric Buddhism especially exemplify the latter, often with the principle skillful means:

Alcohol

For example, as part of the ganachakra tsok ritual (as well as Homa, abhisheka and sometimes drubchen) some Tibetan Buddhists and Bönpos have been known to ingest small amounts of grain alcohol (called amrit or amrita) as an offering. If a member is an alcoholic, or for some other reason does not wish to partake in the drinking of the alcoholic offering, then he or she may dip a finger in the alcohol and then flick it three times as part of the ceremony.

Amrita is also possibly the same as, or at least in some sense a conceptual derivative of the ancient Hindu soma. (The latter which historians often equate with Amanita muscaria or other Amanita psychoactive fungi.) Crowley (1996) states:

"Undoubtedly, the striking parallels between "The legend about Chakdor" and the Hindu legend of the origin of soma show that the Buddhist amrita and the Hindu soma were at one time understood to be identical. Moreover, the principal property of amrita is, to this day, perceived by Buddhists as being a species of inebriation, however symbolically this inebriation may be interpreted. Why else would beer (Tibetan chhang, "barley beer") be used by yogins as a symbolic substitute for amrita [Ardussi]? Conversely, why else would the term bDud.rTsi be used as a poetic synonym for beer?

Conversely, in Tibetan and Sherpa lore there is a story about a monk who came across a woman who told him that he must either:

  • a. kill her goat,
  • b. sleep with her, or
  • c. drink a mug of beer.
  • d. All of the above.

The monk thought to himself, "well, surely if I kill the goat then I will be causing great suffering since a living being will die. If I sleep with the woman then I will have broken another great vow of a monk and will surely be lost to the ways of the world. Lastly, if I drink the beer then perhaps no great harm will come and I will only be intoxicated for a while, and most importantly I will only be hurting myself." (In the context of the story this instance is of particular importance to him because monks in the Mahayana and Vajrayana try to bring all sentient beings to enlightenment as part of their goal.)

So the monk drank the mug of beer and then he became very drunk. In his drunkenness he proceeded to kill the goat and sleep with the woman, breaking all three vows and, at least in his eyes, doing much harm in the world. The lesson of this story is meant to be that, at least according to the cultures from which it delineates, alcohol causes one to break all of one's vows, in a sense that one could say it is the cause of all other harmful deeds.

The Vajrayana teacher Drupon Thinley Ningpo Rinpoche has said that as part of the five precepts which a layperson takes upon taking refuge, that although they must refrain from taking intoxicants, they may drink enough so as they do not become drunk. Bhikkus and Bhikkunis (monks and nuns, respectively), on the other hand, who have taken the ten vows as part of taking refuge and becoming ordained, cannot imbibe any amount of alcohol or other drugs, other than pharmaceuticals taken as medicine.

Tenzin Gyatso, the 14th Dalai Lama of Tibet, is known as teetotaler and non-smoker.

Hallucinogens

There is some evidence regarding the use of deliriant Datura seeds (known as candabija) in Dharmic rituals associated with many tantras – namely the Vajramahabhairava, Samputa, Mahakala, Guhyasamaja, Tara and Krsnayamari tantras – as well as cannabis and other entheogens in minority Vajrayana sanghas. Ronald M Davidson says that in Indian Vajrayana, Datura was:

“employed as a narcotic paste or as wood in a fire ceremony and could be easily absorbed through the skin or the lungs. The seeds of this powerful narcotic, termed "passion seeds" (candabija), are the strongest elements and contain the alkaloids hyoscine, hyoscyamine, and atropine in forms that survive burning or boiling. In even moderate doses, datura can render a person virtually immobile with severe belladonna-like hallucinations.”

In the Profound Summarizing Notes on the Path Presented as the Three Continua, a Sakya Lamdre text, by Jamyang Khyentse Wangchuk (1524-1568), the use of Datura in combination with other substances, is prescribed as part of a meditation practice meant to establish that "All the phenomena included in apparent existence, samsara and nirvana, are not established outside of one's mind."

Ian Baker writes that Tibetan terma literature such as the Vima Nyingtik describes "various concoctions of mind altering substances, including datura and oleander, which can be formed into pills or placed directly in the eyes to induce visions and illuminate hidden contents of the psyche."

A book titled Zig Zag Zen: Buddhism and Psychedelics (2002), details the history of Buddhism and the use of psychedelic drugs, and includes essays by modern Buddhist teachers on the topic.

Zen

Zen Buddhism is known for stressing the precepts. In Japan, however, where Zen flourished historically, there are a number of examples of misconduct on the part of monks and laypeople alike. This often involved the use of alcohol, as sake drinking has and continues to be a well known aspect of Japanese culture.

The Japanese Zen monk and abbot, shakuhachi player and poet Ikkyu was known for his unconventional take on Zen Buddhism: His style of expressing dharma is sometimes deemed "Red Thread Zen" or "Crazy Cloud Zen" for its unorthodox characteristics. Ikkyu is considered both a heretic and saint in the Rinzai Zen tradition, and was known for his derogatory poetry, open alcoholism and for frequenting the services of prostitutes in brothels. He personally found no conflict between his lifestyle and Buddhism.

There are several koans (Zen riddles) referencing the drinking of sake (rice wine); for instance Mumonkan's tenth koan titled Seizei Is Utterly Destitute:

'Seizei said to Sozan, "Seizei is utterly destitute. Will you give him support?" Sozan called out: "Seizei!" Seizei responded, "Yes sir?!" Sozan said, "You have finished three cups of the finest wine in China, and still you say you have not yet moistened your lips!"'

Another monk, Gudo, is mentioned in a koan called Finding a Diamond on a Muddy Road buying a gallon of sake.

Judaism

Judaism maintains that people do not own their bodies – they belong to God. As a result, Jews are not permitted to harm, mutilate, destroy or take risks with their bodies, life or health with activities such as taking life-threatening drugs. For these reasons, rabbis generally prohibit the use of drugs except in controlled medical situations. Even without a risk to life or health, addictive drugs are discouraged due to their negative social effects.

When issues of physical, mental, and social harm are not present, it is debated whether drugs can have any positive spiritual value. According to Rabbi Walter Wurzburger, "Proximity to God cannot be reached by putting oneself into a trance either through physical or chemical means".

Rabbi Aryeh Kaplan suggested that some medieval kabbalists may have used some psychedelic drugs. Indeed, one can find in Kabbalistic medical manuals cryptic references to the hidden powers of mandrake, harmal and other psychoactive plants, though the exact usage of these powers is hard to decipher. Some kabbalists, including Isaac of Acco and Abraham Abulafia, mention a method of "philosophical meditation", which involves drinking a cup of "strong wine of Avicenna", which would induce a trance and would help the adept to ponder over difficult philosophical questions. The exact recipe of this wine remains unknown; Avicenna refers in his works to the effects of opium and datura extracts.

According to Aryeh Kaplan, some have translated kaneh-bosem (קְנֵה-בֹשֶׂם), an ingredient in the holy anointing oil (Exodus 30:23), as cannabis. However, the term kaneh-bosem literally translates to "sweet cane" (an association that is difficult to make with cannabis), and most lexicographers, botanists, and biblical commentators translate it as "calamus" (Acorus calamus), a species known throughout the Middle East for its fragrance since the mid-2nd millennium BCE.

Use of alcohol in moderation is an accepted part of Judaism. The Hebrew Bible states that "wine gladdens man's heart" (Psalms 104:15), and a single cup of wine is drunk for common rituals such as kiddush (though grape juice may be used instead). Nevertheless, excessive use of alcohol is condemned. Prayer and priestly service are forbidden while intoxicated, and numerous Biblical figures met their downfall through drunkenness. The Talmud states that wine received its Hebrew name (whose sound somewhat resembles a howl) because it "brings lament to the world". The holiday of Purim is exceptional in that on this date drunkenness is encouraged in some communities, in commemoration of the drunkenness which plays a significant role in the Book of Esther.

In Hasidic Judaism alcohol consumption is more common, especially at communal religious events like the farbrengen or tisch, where alcohol often accompanies singing and Torah study. If the drinking is moderate, for the purpose of Divine service, and done together with other chassidim, it is considered useful for expanding the mind and providing enthusiasm in the service of God. Nevertheless, excessive consumption is still discouraged; for example, the Lubavitcher Rebbe forbade his Chassidim under the age of 40 to consume more than 4 small shots of hard liqueurs.

The use of nicotine is well known in Hasidic communities. Stories are told about miracles and spiritual journeys performed by the Baal Shem Tov and other Tzaddikim with the help of their smoking pipe. Hasidim valued smoking both as part of their general goal to raise the spiritual "sparks" that are allegedly present in base physical phenomena, and for the practical goal of experiencing better concentration while under its influence. Nevertheless, since the health impacts of smoking have become understood by modern medicine, there has been a strong movement to discourage and prohibit smoking.

Caffeine use is accepted in Judaism, and played a significant role in the spread of nighttime rituals such as Tikkun Chatzot. Nevertheless, there was initially some opposition from rabbis who were concerned that nighttime gatherings or the coffeehouse atmosphere could lead to illicit behavior.

Christianity

Many Christian denominations disapprove of the use of most illicit drugs. Many denominations permit the moderate use of socially and legally acceptable drugs like alcohol, caffeine and tobacco. Some Christian denominations permit smoking tobacco, while others disapprove of it. Many denominations do not have any official stance on drug use, some more-recent, Pseudo-Christian denominations (e.g. Mormons, and Jehovah’s Witnesses) discourage or prohibit the use of any of these substances.

In the Eucharist, wine represents (or among Christians who believe in some form of Real Presence, like the Catholic, Lutheran and Orthodox churches, actually is) the blood of Christ. Lutherans believe in the real presence of the body and blood of Christ in the Eucharist, that the body and blood of Christ are "truly and substantially present in, with and under the forms." of the consecrated bread and wine (the elements), so that communicants orally eat and drink the holy body and blood of Christ Himself as well as the bread and wine (cf. Augsburg Confession, Article 10) in this Sacrament. The Lutheran doctrine of the Real Presence is more accurately and formally known as "the Sacramental Union." It has been inaccurately called "consubstantiation", a term which is specifically rejected by most Lutheran churches and theologians.

On the other hand, some Protestant Christian denominations, such as Baptists and Methodists associated with the temperance movement, encourage or require teetotalism, as well as abstinence from cultivating and using tobacco. In some Protestant denominations, grape juice or non-alcoholic wine is used in place of wine in the administration of Holy Communion.

Conservative Anabaptist denominations, such as the Dunkard Brethren Church, teach:

Members of the Dunkard Brethren Church shall abstain from the use of intoxicating or addictive substances, such as narcotics, nicotine, marijuana, or alcoholic beverages (except as directed by a physician). Using, raising, manufacturing, buying or selling them by Christians is inconsistent with the Christian lifestyle and testimony. Members of the Dunkard Brethren Church who do so should be counseled in love and forbearance. If they manifest an unwilling or arbitrary spirit, they subject themselves to the discipline of the church, even to expulsion in extreme cases. We implore members to accept the advice and counsel of the church and abstain from all of the above. Since members are to be examples to the world (Romans 14:20-21) indulgence in any of these activities disqualifies then for Church or Sunday School work or as delegates to District or General Conference.

The best-known Western prohibition against alcohol happened in the United States in the 1920s, where concerned prohibitionists were worried about its dangerous side effects. However, the demand for alcohol remained and criminals stepped in and created the supply. The consequences of organized crime and the popular demand for alcohol led to alcohol being legalized again.

The Seventh-day Adventist Church is supportive of scientific medicine. It promotes eradication of illicit drug use and promotes abstinence against tobacco and alcohol., and promotes a measured and balanced approach to use of both medicinal drugs as well as natural remedies (which it neither discourages or prohibits), promotes the control of medicines that may be abused, and promotes vaccination and immunization.

Islam

Alcohol, or just wine (in the views of some), are considered haram (unlawful).

The Muslim-Majority nations of Turkey and Egypt were instrumental in banning opium, cocaine, and cannabis when the League of Nations committed to the 1925 International Convention relating to opium and other drugs (later the 1934 Dangerous Drugs Act). The primary goal was to ban opium and cocaine, but cannabis was added to the list, and it remained there largely unnoticed due to the much more heated debate over opium and cocaine. The 1925 Act has been the foundation upon which every subsequent policy in the United Nations has been founded.

There are no prohibitions in Islam on alcohol for scientific, industrial or automotive use and cannabis is generally permitted for medicinal purposes.

In spite of these restrictions on substance use, the recreational use of cannabis still occurs widely throughout many Muslim nations.

Baháʼí Faith

Followers of the Baháʼí Faith are forbidden to drink alcohol or to take drugs, unless prescribed by doctors. Accordingly, the sale and trafficking of such substances is also forbidden. Smoking is discouraged but not prohibited.

Rastafari movement

Many Rastafari believe cannabis, which they call "ganja," "the herb," or "Kaya," is a sacred gift of Jah. It may be used for spiritual purposes to commune with God, but should not be used profanely. The use of other drugs, however, including alcohol, is frowned upon. Many believe that the wine Jesus/Iyesus drank was not an alcoholic beverage, but simply the juice of grapes or other fruits.

While some Rastafari suggest that the Hebrew Bible may refer to marijuana, it is generally held by academics specializing in the lexicography of the text that cannabis is not documented or mentioned. Some popular writers have argued that there is evidence for religious use of cannabis in the Hebrew Bible, although this hypothesis and some of the specific case studies (e.g., John Allegro in relation to Qumran, 1970) have been "widely dismissed as erroneous" (Merlin, 2003). The primary advocate of a religious use of cannabis plant in early Judaism was Sula Benet (1967), who claimed that the plant kaneh bosm קְנֵה-בֹשֶׂם mentioned five times in the Hebrew Bible, and used in the holy anointing oil of the Book of Exodus, was in fact cannabis, although lexicons of Hebrew and dictionaries of plants of the Bible such as by Michael Zohary (1985), Hans Arne Jensen (2004) and James A. Duke (2010) and others identify the plant in question as either Acorus calamus or Cymbopogon citratus.

Groundation

A "groundation" (also spelled "grounation") or "binghi" is a holy day; the name "binghi" is derived from "Nyabinghi" (literally "Nya" meaning "black" and "Binghi" meaning "victory"). Binghis are marked by much dancing, singing, feasting, and the smoking of "ganja", and can last for several days.

Bible verses which Rastas believe justify cannabis use

...thou shalt eat the herb of the field.

Genesis 3.18

...eat every herb of the land.

Exodus 10:12

Better is a dinner of herb where love is, than a stalled ox and hatred therewith.

Proverbs 15:17

Beliefs about other drugs

According to many Rastas, the illegality of cannabis in many nations is evidence of persecution of Rastafari. They are not surprised that it is illegal, viewing Cannabis as a powerful substance that opens people's minds to the truth – something the Babylon system, they reason, clearly does not want. Cannabis use is contrasted with the use of alcohol and other drugs, which they feel destroy the mind.

Asatru

Alcoholic drinks are commonly used during Asatru blóts but non-alcoholic drinks can be substituted.

Lead-based paint in the United States

Lead paint on a porch in 2018

Lead-based paint was widely used in the United States because of its durability. The United States banned the manufacture of lead-based house paint in 1978 due to health concerns.

Lead has long been considered to be a harmful environmental pollutant. Cited cases of lead poisoning date back to the early 20th century. In the July 1904 edition of its monthly publication, paint manufacturer, Sherwin-Williams, reported the dangers of paint containing lead, noting that a French expert had deemed lead paint "poisonous in a large degree, both for the workmen and for the inhabitants of a house painted with lead colors."

In 1971, Congress banned the use of lead-based paint in residential projects (including residential structures and environments) constructed by, or with the assistance of, the federal government. The Consumer Product Safety Commission followed with implementing regulations, effective in 1978. Additional regulations regarding lead abatement, testing and related issues have been issued by the Environmental Protection Agency (EPA).

Much of the government's response to the lead public health problems in the 1970s can be credited to the work of epidemiologist and pediatrician, Philip J. Landrigan, who conducted detailed studies of lead poisoning near lead refineries, as well as the effects of lead in gasoline.

In 1991, Secretary of the Department of Health and Human Services, Louis Wade Sullivan, called lead the "number one environmental threat to the health of children in the United States." Humans are exposed to lead through air, drinking water, food, contaminated soil, deteriorating paint, and dust. Airborne lead enters the body by breathing or swallowing lead particles or dust once it has settled. Old lead-based paint is the most significant source of lead exposure in the U.S. Most homes built before 1960 contain heavily leaded paint. Some homes built as recently as 1978 may also contain lead paint.

The U.S. Centers for Disease Control and Prevention’s (CDC) National Center for Health Statistics monitors blood lead levels in the United States. Experts use a new level based on the U.S. population of children ages 1-5 years who are in the top 2.5% of children when tested for lead in their blood (when compared to children who are exposed to more lead than most children). Currently that is 3.5 micrograms of lead per deciliter of blood.

Overview

Definition

The District of Columbia defines "lead-based paint" as any "paint, surface coating that contains lead equal to or exceeding one milligram per square centimeter (1.0 mg/cm2) or 0.5% by weight." Some states have adopted this or similar definitions of "lead-based paint." These definitions are used to enforce regulations that apply to certain activities conducted in housing constructed prior to 1978, such as abatement, or the permanent elimination of a "lead-based paint hazard."

The U.S. government and many states have regulations regarding lead-based paint. Many of them apply to evaluating a property for lead-based paint. There are two different testing procedures that are similar but yield different information. Lead-based paint inspections will evaluate all painted surfaces in a complex to determine where lead-based paint, if any, is present. The procedures for lead inspections is outlined in the United States Department of Housing and Urban Development (HUD) Guidelines, Chapter 7, 1997 Revision. The other testing is a lead-based paint risk assessment. In this testing, only deteriorated painted surfaces are tested and dust wipe samples are collected. This information will help the risk assessor determine if there are any lead hazards. Many property owners decided to get a combination of both tests to determine where the lead-based paint is present and what hazards are present as well. Risk assessments are outlined in the HUD Guidelines, Chapter 5. In addition, if a child is poisoned in a property, the owner may be required to perform abatement (permanent elimination of the lead hazard).

The Lead-Based Paint Disclosure Regulation

EPA flyer on lead-based paint disclosure

In 1996, the Department of Housing and Urban Development and the Environmental Protection Agency enacted the Lead-Based Paint Disclosure Regulation. It requires owners of pre-1978 "target housing" to disclose to potential buyers or renters all known information about the presence of lead-based paint and/or lead-based paint hazards in the property. It requires that the potential buyer or tenant be given the lead information pamphlet, "Protect Your Family From Lead In Your Home," or other EPA-approved pamphlet as well as a specific disclosure statement. The option of whether to test for the presence of lead-based paint is left to the owner, so long as a decision not to test is disclosed.

Renovation, Repair and Painting

The EPA issued a new regulation called 'Renovation, Repair and Painting' (RRP) regarding the renovation of residential housing and child-occupied buildings built before 1978 on April 22, 2008. The rule (Federal Register: July 15, 2009 (Volume 74, Number 134)) became effective April 22, 2010. Under the rule, contractors performing renovation, repair and painting projects that disturb lead-based coatings (including lead paint, shellac or varnish) in child-occupied facilities built before 1978 must be certified and must follow specific work practices to prevent lead contamination. EPA’s RRP rule impacts many construction trades, including general contractors and special trade contractors, painters, plumbers, carpenters, glaziers, wood floor refinishers and electricians. Activities performed by all of these trades can disturb lead-based paint and have the potential to create hazardous lead dust. For most individuals, eight hours of training is required. However, individuals who have successfully completed renovation courses developed by HUD or EPA, or an abatement worker or supervisor course accredited by EPA or an authorized State or Tribal program, can become certified renovators by taking a four-hour EPA-accredited renovator refresher training.

The RRP rule is controversial, primarily due to the increased cost remodelers incur as a result of having to set up dust containment apparatuses, including sealing off doorways and HVAC ducts with plastic. Various national trade associations have been very vocal in their opposition, some going so far as to sue the EPA. Though the EPA considered expanding the rule to require contractors to pass a third-party dust wipe clearance exam these revisions were rejected in July, 2011.

Although the rule was not fully implemented until April 2010, certain elements were required before, and others required attention well before April 2010.

  • Before April 2009, contractors that disturb paint in homes, residential buildings, schools and child care facilities built prior to 1978 had to provide lead hazard information prior to the start of the job to building owners, occupants, and to the families of children using the facilities by distributing EPA’s new Renovate Right brochure.
  • As of April 2009, trainers could begin to apply to EPA or an EPA-approved state for accreditation, and, once approved, contractors and construction trade workers could begin to take the training to become certified.
  • Beginning October 2009, firms could apply for EPA or state certification.
  • Beginning April 2010, all businesses engaged in renovation, repair or painting activities in homes, residential buildings, schools and child care facilities built prior to 1978 must be certified, use certified workers, and follow specific lead-safe work practices to prevent lead contamination.

State action against the lead paint industry

The state of Rhode Island filed a public nuisance lawsuit in 1999 (State of Rhode Island v. Lead Industries Association) to force the former manufacturers of lead paint to pay for the cleanup of current lead hazards in Rhode Island. After a trial that ended in a hung jury in 2002, the state refiled the case. In February 2006, the jury decided in favor of the state and said that Sherwin-Williams, NL Industries and Millennium Holdings would have to pay for the clean-up of lead paint in the state. On July 1, 2008, the Rhode Island Supreme Court in a landmark decision overturned the verdict, dismissing the case stating that "the State of Rhode Island 'cannot allege' facts sufficient to state a claim for common law public nuisance against lead pigment manufacturers."

In 2007, the Missouri Supreme Court and the New Jersey Supreme Court also rejected the use of the public nuisance theory in lead paint lawsuits, leaving Ohio and California as the only two remaining public nuisance cases.

The California Supreme Court has reviewed the contingency fee agreement between the municipalities and private counsel. A briefing schedule is currently being set. In recent rulings, the Supreme Court held the contingent fee agreement was improper, stating that “When a government attorney has a personal interest in the litigation, the neutrality so essential to the system is violated.”

While the City of Columbus, Ohio voluntarily dropped its lawsuit against the paint industry after the Rhode Island decision, the State of Ohio's suit remains.

Real estate maintenance and renovation

Humans can be poisoned during unsafe renovations or repainting jobs on housing that has lead paint. Therefore, homeowners are encouraged to carefully stabilize any deteriorated (peeling, chipping, cracking, etc.) paint in a lead-safe manner. More than 250,000 children in the United States have significantly harmful levels of lead in their bodies. There is no safe level of exposure.

Dry sanding, dry scraping, removing paint by torching and burning, the use of heat guns over 1100°F, and machine-sanding or grinding without a HEPA filtered dust collection system or a HEPA-filtered vacuum are all prohibited by the United States Department of Housing and Urban Development (HUD) as methods of removing lead-based-paint. HUD prohibits these methods because they have been proven to create significant levels of lead dust during remodeling, renovation and painting. The use of these methods should be avoided because they significantly increase the chance to become lead poisoned.

Man removing lead paint
A man wearing coveralls while removing lead paint.

Paint strippers are also often used to remove lead-based-paint from walls. There are specialized paint strippers for use with lead paint which render lead non-hazardous decreasing the risks associated with lead paint removal.

HUD requires a dust test for "clearance" at the end of any remodeling or repainting job be performed by a third-party professional who is independent of the entity performing the work.

Lead evaluations of paint are usually performed by a field testing method known as X-Ray fluorescence (XRF) using equipment which can effectively detect lead. XRF is the preferred method because it is not destructive and a reading is usually obtained in about 4–8 seconds with a 95% accuracy at the 2-sigma level.

Instruments of this sort have an inconclusive range, and when a reading falls in this range (range is different for each instrument and model), a paint chip may be taken and sent for laboratory analysis. Testing for lead in dust, water, and air also require laboratory analysis. Although there are commercially available lead test kits, they are not reliable and are not authorized by HUD for the use of determining if a property is lead-based-paint free.

The home's year of construction can be a clue as to the likelihood that lead is present in its paint. As of April 2011, 87% of homes built before 1940 contain at least some lead paint, homes built between 1940 and 1960 have a 69% chance of containing such paint, homes built between 1960 and 1978 have a 24% chance of containing lead paint, while homes built after 1978 are unlikely to have lead-based paint. The U.S. Department of Housing and Urban Development's Office of Healthy Homes and Lead Hazard Control performs regular studies of housing-based health hazards in the U.S.

Inequality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Inequality...