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Box braids are a type of hair-braiding style that is predominantly popular among Black Africans and the African diaspora. This type of hairstyle is a “protective style” (a style which can be worn for a long period of time to let natural hair grow and protect the ends of the hair) and is “boxy”, consisting of square-shaped hair divisions. Box braids are generally installed by using synthetic hair which helps to add thickness as well as helping the natural hair that is in the braid. Because they are not attached to the scalp like other similar styles such as cornrows, box braids can be styled in a number of different ways. The installation process of box braids can be lengthy, but once installed they can last for six to eight weeks. They are known for being easy to maintain.^[1][2]

Hair-braiding styles were used to help differentiate tribes, locations, and also possibly a symbol of wealth and power due to the amount of effort that went into styling braids.^[3] Box braids were not given a specific name until the 1990s when popularized by R&B musician Janet Jackson, but have been used for years. This style of braiding comes from the Eembuvi braids of Namibia or the chin-length bob braids of the women of the Nile Valley from over 3,000 years ago.^[3] In the Mbalantu tribe of Namibia, braiding was an important social practice. Older women would gather with their girls and teach them how to braid.^[4] Box braids are also commonly worn by the Khoisan people of South Africa^[5] and the Afar people in the horn of Africa.^[6][7] In Africa, braid styles and patterns have been used to distinguish tribal membership, marital status, age, wealth, religion and social ranking.^[8] In some countries of Africa, the braids were used for communication.^[9] In some Caribbean islands, braid patterns were used to map routes to escape slavery.^[10][11] Layers of finely chopped tree bark and oils can be used to support the hairstyle. Human hair was at one point wefted into fiber wig caps made of durable materials like wool and felt for reuse in traditional clothing as well as different rituals.^[3] Cowry shells, jewels, beads and other material items adorned box braids of older women alluding to their readiness to have daughters, emulation of wealth, high priesthood and any other classifications.^[3]

Hair was and is a very important and symbolic part of different African communities. Africans believed that hair could help with divine communication as it was the elevated part of one’s body. Hair styling was entrusted only to close relatives, as it was explained that if a strand fell into the hands of an enemy, harm could come to the hair’s owner.^[12] Members of royalty would often wear elaborate hairstyles as a symbol of their stature, and those in mourning, usually women, would pay some attention to their hair during the period of grieving. Hair was seen as a symbol of fertility, as thick, long tresses and neat, clean hair symbolised ability to bear healthy children.^[12] Elaborate patterns were done for special occasions like weddings, social ceremonies or war preparations. People belonging to a tribe could easily be identified by another tribe member with the help of a braid pattern or style.^[13]

The U.S. Army has strong regulations and restrictions on hairstyles for both men and women. In 2014, the army updated its policies because the old regulations were too restrictive for African-American women. Army policy originally considered African American women’s natural hair “not neat” and deemed protective hairstyles “unprofessional”. In the newer regulations, “twists, cornrows and braids can be up to 1⁄2 inch [13 mm] in diameter. The previous maximum was a diameter of approximately 1⁄4 inch [6 mm]“.^[14] This gives more opportunity to wear protective styles.

Box braids can be worn by members of the US Army as long as they show no more than 3⁄8 of the scalp. The parting must be square or rectangular shape. The ends of the braids must be secured. Once the newly grown natural hair outside of the braid, also known as new growth, reaches 1⁄2 inch [13 mm], the style must be redone.^[15]

Similar regulations apply for styles like dreadlocks, flat twists, and braids with natural hair. The hairstyles must not interfere with the wear of uniform or covers (uniform hats).^[16] Though synthetic hair for box braids exists in multiple colors, the military dictates that enlisted women must have box braids in natural hair colors without any additional jewelry like hairclips or beads.

Medium box braids are a popular hairstyle within the African and African American communities. They involve parting the hair into individual square-shaped sections, and then each section is braided from the scalp to the ends. These braids are termed ‘medium’ due to their thickness, which is typically about the width of a pencil to that of a felt tip marker.^[17]

Tight or heavy hairstyles, such as long box braids, can also cause an external-traction headache, previously called a ponytail headache.^[18] Overly tight braids may cause traction alopecia.^[19] Looser braids have a lower risk than tight braids or other styles, such as cornrows and dreadlocks.^[20]

• African hair threading
• Braid (hairstyle)
• Cornrows
• Shuku
• koroba
• Dreadlocks
• French braid
• List of hairstyles

• “The Ultimate Guide to Medium Box Braids”. Meechi. Retrieved 2023-12-13.

• Media related to Box braids at Wikimedia Commons

Radium Release Hitch
Category	Hitch
Efficiency	30kn
Releasing	Load releasing
Typical use	technical rope rescue

A radium release hitch is a load-releasing hitch using 3:1 mechanical advantage which is used in a two-rope technical rescue system.^[1] The Radium Release Hitch allows a load to be transferred from one rope to another and is commonly rigged into the belay line prior to the operation of a two-rope technical rescue system.^[2]

A radium release hitch is typically tied with 10 meters of 8mm rope and two locking carabiners. A reasonable length for the hitch (distance between the 2 carabiners) is 10 to 15 cm.^[3]

The Radium Release Hitch was developed by Kirk Mauthner (who lives near Radium Hot Springs, hence the name) as a result of the extensive comparative analysis of release devices undertaken during 1997 through 1999^[4]

• Passing knots
• Untensioning a locked lowering device or locked up prussiks.^[5]

• Tie a figure 8 on a bight at one end of the cord and clip it into the load carabiner on its spine side.
• Clip the standing part of the rope through the anchor carabiner and back down through the load carabiner; bring the rope back up to the anchor carabiner.
• Tie a Munter hitch on its gate side of the anchor carabiner. Ensure that the Munter hitch is in the release position with the in-feed rope toward the gate side of the carabiner
• Secure the Radium Release Hitch using a bight to tie a half hitch on a bight around the entire stem below the Munter hitch, and then back it up with an overhand on a bight knot again around the entire stem.
• Tie a figure 8 on a bight at the other end, and clip it to a secure anchor.^[3][6]

List of knots

Mountain Rescue

Bowline on a bight
Category	Loop
Related	Double bowline
Releasing	Non-jamming
Typical use	Forming a loop in the middle of a length of rope.
ABoK	#1080

The bowline on a bight is a knot which makes a pair of fixed-size loops in the middle of a rope. Its advantage is that it is reasonably easy to untie after being exposed to load. It is one of the two tie-in knots that are being taught by the German Alpine Club (DAV), generally being considered secure.^[1][2][3]

2011 testing shows that the knot might slip when only one loop is loaded. Cavers and canyoneers ought to fasten their cow-tail carabiner through both loops.^[4] European cavers widely advocate the use of a figure eight twisted version of the bowline on a bight.

This knot can be used to provide a toe hold in the middle of a rope; to make an emergency bosun’s chair;^[5][6] and to create an upper rope “block” to make a crude purchase by threading the rope round an anchor point and then back up through the loop. It is sometimes used in sport climbing to tie into two anchor bolts independently. This knot is convenient when a dependable loop is required but neither end of the line is available. It’s also commonly used as a seat while being hoisted as there are two secure loops as opposed to the traditional one loop bowline. In theory, this knot would make hoisting many people with one line possible. This knot is very popular in caving as it allows the load to be spread between two anchor points, reducing the stress placed on them and providing a backup should one fail. Commonly known as the Y-hang it allows for a free-hang descent and can be easily adjusted to avoid waterfalls or rub points.

As mentioned earlier, this knot can replace the figure-eight knot when tying into a climbing harness by tying a regular bowline knot and then re-threading it, such as is done with a figure eight knot. However, it is critical to use a strong backup knot with plenty of tail beyond the knot, as the knot may untie during long climbs. The advantage of using this knot instead of the figure eight knot is that it can be easily untied after a severe fall.

The bight of rope is initially used to make a bowline in the usual way (picture on right). However, the bowline is not completed by going on round the standing end(s) and tucking the bight back down beside itself. Instead, the bight is opened up to allow the whole knot to pass through it (see picture on right). When tightened, the bight now embraces the pair of standing ends (see top picture)

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  2
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  3
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  4
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  1
• 
  2
• 
  3

• Double bowline
• List of knots

• Grog. “Bowline on a bight using rope”. Animated Knots.
• Little Campfires (2020-08-01). “How to Tie a Bowline Knot (Plus Variations): Bowline on the Bight”. YouTube.
• TheTautLine (2023-09-11). “Complete Guide to the Bowline Knot and its Most Important Variants: Bowline on a Bight”. YouTube.

In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams.

While mainly used to obtain invariants of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle axiomatizes the properties of conjugation in a group.

In 1942, Mituhisa Takasaki introduced an algebraic structure which he called a kei (圭),^[1][2] which would later come to be known as an involutive quandle.^[3] His motivation was to find a nonassociative algebraic structure to capture the notion of a reflection in the context of finite geometry.^[2][3] The idea was rediscovered and generalized in an unpublished 1959 correspondence between John Conway and Gavin Wraith, who at the time were undergraduate students at the University of Cambridge. It is here that the modern definitions of quandles and of racks first appear. Wraith had become interested in these structures (which he initially dubbed sequentials) while at school.^[4] Conway renamed them wracks, partly as a pun on his colleague’s name, and partly because they arise as the remnants (or ‘wrack and ruin’) of a group when one discards the multiplicative structure and considers only the conjugation structure. The spelling ‘rack’ has now become prevalent.

These constructs surfaced again in the 1980s: in a 1982 paper by David Joyce^[5] (where the term quandle, an arbitrary nonsense word, was coined),^[6] in a 1982 paper by Sergei Matveev (under the name distributive groupoids)^[7] and in a 1986 conference paper by Egbert Brieskorn (where they were called automorphic sets).^[8] A detailed overview of racks and their applications in knot theory may be found in the paper by Colin Rourke and Roger Fenn.^[9]

A rack may be defined as a set ${\displaystyle \mathrm {R} }$ with a binary operation ${\displaystyle \triangleleft }$ such that for every ${\displaystyle a,b,c\in \mathrm {R} }$ the self-distributive law holds:
$${\displaystyle a\triangleleft (b\triangleleft c)=(a\triangleleft b)\triangleleft (a\triangleleft c)}$$

and for every ${\displaystyle a,b\in \mathrm {R} }$, there exists a unique ${\displaystyle c\in \mathrm {R} }$ such that
$${\displaystyle a\triangleleft c=b.}$$

This definition, while terse and commonly used, is suboptimal for certain purposes because it contains an existential quantifier which is not really necessary. To avoid this, we may write the unique ${\displaystyle c\in \mathrm {R} }$ such that ${\displaystyle a\triangleleft c=b}$ as ${\displaystyle b\triangleright a}$. We then have
$${\displaystyle a\triangleleft c=b\iff c=b\triangleright a,}$$

and thus
$${\displaystyle a\triangleleft (b\triangleright a)=b,}$$

and
$${\displaystyle (a\triangleleft b)\triangleright a=b.}$$

Using this idea, a rack may be equivalently defined as a set ${\displaystyle \mathrm {R} }$ with two binary operations ${\displaystyle \triangleleft }$ and ${\displaystyle \triangleright }$ such that for all ${\displaystyle a,b,c\in \mathrm {R} }$:

1. ${\displaystyle a\triangleleft (b\triangleleft c)=(a\triangleleft b)\triangleleft (a\triangleleft c)}$ (left self-distributive law)
2. ${\displaystyle (c\triangleright b)\triangleright a=(c\triangleright a)\triangleright (b\triangleright a)}$ (right self-distributive law)
3. ${\displaystyle (a\triangleleft b)\triangleright a=b}$
4. ${\displaystyle a\triangleleft (b\triangleright a)=b}$

It is convenient to say that the element ${\displaystyle a\in \mathrm {R} }$ is acting from the left in the expression ${\displaystyle a\triangleleft b}$, and acting from the right in the expression ${\displaystyle b\triangleright a}$. The third and fourth rack axioms then say that these left and right actions are inverses of each other. Using this, we can eliminate either one of these actions from the definition of rack. If we eliminate the right action and keep the left one, we obtain the terse definition given initially.

Many different conventions are used in the literature on racks and quandles. For example, many authors prefer to work with just the right action. Furthermore, the use of the symbols ${\displaystyle \triangleleft }$ and ${\displaystyle \triangleright }$ is by no means universal: many authors use exponential notation
$${\displaystyle a\triangleleft b={}^{a}b}$$

and
$${\displaystyle b\triangleright a=b^{a},}$$

while many others write
$${\displaystyle b\triangleright a=b\star a.}$$

Yet another equivalent definition of a rack is that it is a set where each element acts on the left and right as automorphisms of the rack, with the left action being the inverse of the right one. In this definition, the fact that each element acts as automorphisms encodes the left and right self-distributivity laws, and also these laws:

$${\displaystyle {\begin{aligned}a\triangleleft (b\triangleright c)&=(a\triangleleft b)\triangleright (a\triangleleft c)\\(c\triangleleft b)\triangleright a&=(c\triangleright a)\triangleleft (b\triangleright a)\end{aligned}}}$$

which are consequences of the definition(s) given earlier.

A quandle is defined as an idempotent rack, ${\displaystyle \mathrm {Q} }$, such that for all ${\displaystyle a\in \mathrm {Q} }$
$${\displaystyle a\triangleleft a=a,}$$
or equivalently
$${\displaystyle a\triangleright a=a.}$$

Every group gives a quandle where the operations come from conjugation:
$${\displaystyle {\begin{aligned}a\triangleleft b&=aba^{-1}\\b\triangleright a&=a^{-1}ba\\&=a^{-1}\triangleleft b\end{aligned}}}$$

In fact, every equational law satisfied by conjugation in a group follows from the quandle axioms. So, one can think of a quandle as what is left of a group when we forget multiplication, the identity, and inverses, and only remember the operation of conjugation.

Every tame knot in three-dimensional Euclidean space (or more generally, a 3-sphere) has a ‘fundamental quandle’ ^[5] similarly to how every knot has a knot group. The knot group of a tame knot has a Wirtinger presentation where generators of the group are given as conjugates, and thus this presentation can be used to give a presentation for the fundamental quandle: the generators are the arcs of an oriented diagram of the knot, and for each crossing in that diagram, labeling the overstrand ${\displaystyle x}$ and the left and right understrands (relative to ${\displaystyle x}$‘s orientation) ${\displaystyle u,v}$ respectively, the relation

$${\displaystyle u\triangleright x=v}$$

holds. Note that this resulting quandle need not be the same as the conjugation quandle of the knot group.

The fundamental quandle is a very powerful invariant of knots. In particular, if two tame knots have isomorphic fundamental quandles then there is a homeomorphism of three-dimensional Euclidean space, which may be orientation reversing, taking one knot to the other.

Less powerful but more easily computable invariants of knots may be obtained by counting the homomorphisms from the knot quandle to a fixed quandle ${\displaystyle \mathrm {Q} }$. Since the knot quandle has a presentation with one generator per strand in a knot diagram, these invariants can be computed by counting ways of labelling each strand by an element of ${\displaystyle \mathrm {Q} }$, subject to certain constraints. More sophisticated invariants of this sort can be constructed with the help of quandle cohomology.

The Alexander quandles are also important, since they can be used to compute the Alexander polynomial of a knot. Let ${\displaystyle \mathrm {A} }$ be a module over the ring ${\displaystyle \mathbb {Z} [t,t^{-1}]}$ of Laurent polynomials in one variable (that is, ${\displaystyle \mathrm {A} }$ is an Abelian group equipped with an automorphism, which ${\displaystyle t}$ acts by). Then the Alexander quandle is ${\displaystyle \mathrm {A} }$ made into a quandle with the left action given by
$${\displaystyle a\triangleleft b=tb+(1-t)a.}$$

Racks are a useful generalization of quandles in topology, since while quandles can represent knots on a round linear object (such as rope or a thread), racks can represent ribbons, which may be twisted as well as knotted.

A quandle ${\displaystyle \mathrm {Q} }$ is said to be involutory if for all ${\displaystyle a,b\in \mathrm {Q} }$,
$${\displaystyle a\triangleleft (a\triangleleft b)=b}$$

or equivalently,
$${\displaystyle (b\triangleright a)\triangleright a=b.}$$

This may be stated more simply as
$${\displaystyle a\triangleleft b=b\triangleright a,}$$
which allows an equational definition with only one operation.

Any symmetric space gives an involutory quandle, where ${\displaystyle a\triangleleft b}$ is the result of ‘reflecting ${\displaystyle b}$ through ${\displaystyle a}$‘.

• Biracks and biquandles
• Laver table

• Knot Quandaries Quelled by Quandles – An undergraduate introduction to quandles and another knot invariants
• A Survey of Quandle Ideas by Scott Carter
• Knot Invariants Derived from Quandles and Racks by Seiichi Kamada
• Shelves, Racks, Spindles and Quandles, p. 56 of Lie 2-Algebras by Alissa Crans
• https://ncatlab.org/nlab/show/quandle

Bowline
Names	Bowline, Boling knot (archaic)
Category	Loop
Origin	Ancient
Related	Sheet bend, double bowline, water bowline, Yosemite bowline, Spanish bowline, Portuguese bowline, triple bowline, bowline on a bight, running bowline, Poldo tackle, Eskimo bowline, cowboy bowline, cossack knot, Kalmyk loop
Releasing	Non-jamming[1]
Typical use	Making a fixed loop at the end of a line.
Caveat	While widely considered a reliable knot, when tied in certain materials or loading conditions it may not hold. Tends to work itself loose when not under tension.
ABoK	#1010, #1716
Instructions

The bowline (/ˈboʊlɪn/) is an ancient and simple knot used to form a fixed loop at the end of a rope. It has the virtues of being both easy to tie and untie; most notably, it is easy to untie after being subjected to a load. The bowline is sometimes referred to as king of the knots because of its importance. Along with the sheet bend and the clove hitch, the bowline is often considered one of the most essential knots.^[2]

The common bowline shares some structural similarity with the sheet bend. Virtually all end-to-end joining knots (i.e., bends) have a corresponding loop knot.

Although the bowline is generally considered a reliable knot, its main deficiencies are a tendency to work loose when not under load (or under cyclic loading),^[3][4] to slip when pulled sideways,^[5] and the bight portion of the knot to capsize in certain circumstances.^[6] To address these shortcomings, a number of more secure variations of the bowline have been developed for use in safety-critical applications, or by securing the knot with an overhand knot backup.

The bowline’s name has an earlier meaning, dating to the Age of Sail. On a square-rigged ship, a bowline (sometimes spelled as two words, bow line) is a rope that holds the edge of a square sail towards the bow of the ship and into the wind, preventing it from being taken aback.^[7] A ship is said to be on a “taut bowline” when these lines are made as taut as possible in order to sail close-hauled to the wind.^[8]

The bowline knot is thought to have been first mentioned in John Smith’s 1627 work A Sea Grammar under the name Boling knot. Smith considered the knot to be strong and secure, saying, “The Boling knot is also so firmly made and fastened by the bridles into the cringles of the sails, they will break, or the sail split before it will slip.”^[9][a]

Another possible finding was discovered on the rigging of the Ancient Egyptian Pharaoh Khufu’s solar ship (26th century B.C.) during an excavation in 1954.^[10]

The bowline is used to make a loop at one end of a line. It is tied with the rope’s working end also known as the “tail” or “end”. The loop may pass around or through an object during the making of the knot. The knot tightens when loaded at (pulled by) the standing part of the line.

The bowline is commonly used in sailing small craft, for example to fasten a halyard to the head of a sail or to tie a jib sheet to a clew of a jib. The bowline is well known as a rescue knot for such purposes as rescuing people who might have fallen down a hole, or off a cliff onto a ledge. This knot is particularly useful in such a situation because it is possible to tie with one hand. As such, a person needing rescue could hold onto the rope with one hand and use the other to tie the knot around their waist before being pulled to safety by rescuers. The Federal Aviation Administration recommends the bowline knot for tying down light aircraft.^[11]

A rope with a bowline retains approximately 2/3 of its strength, with variances depending upon the nature of the rope, as in practice the exact strength depends on a variety of factors.

In the United Kingdom, the knot is listed as part of the training objectives for the Qualified Firefighter Assessment.^[12]

A mnemonic used to teach the tying of the bowline is to imagine the working end of the rope as a rabbit.

• 1,2 – a loop is made into the standing part which will act as the rabbit’s hole
• 3 – the “rabbit” comes up the hole,
• 4 – goes round the tree (standing part) right to left
• 5 – and back down the hole

This can be taught to children with the rhyme: “Up through the rabbit hole, round the big tree; down through the rabbit hole and off goes he.”

There is a potential with beginners to wrongly tie the bowline. This faulty knot stems from an incorrect first step while tying the rabbit hole. If the loop is made backwards so that the working end of the rope is on the bottom, the resulting knot will be the Eskimo bowline, looking like a sideways bowline, which is also a stable knot.

As noted above, the simplicity of the bowline makes it a good knot for a general purpose end-of-line loop. However, in situations that require additional security, several variants have been developed:

The cowboy bowline (also called Dutch bowline), French bowline, and Portuguese bowline are variations of the bowline, each of which makes one loop. (Names of knots are mostly traditional and may not reflect their origins.) A running bowline can be used to make a noose which draws tighter as tension is placed on the standing part of the rope. The Birmingham bowline has two loops; the working part is passed twice around the standing part (the “rabbit” makes two trips out of the hole and around the tree). Other two-loop bowline knots include the Spanish bowline and the bowline on the bight; these can be tied in the middle of a rope without access to the ends. A triple bowline is used to make three loops.^[13] An Eskimo bowline or Cossack knot is a bowline where the running end goes around the loop-start rather than the main part and has a more symmetric triangular shaped knot. A slipped version of the Cossack knot is called Kalmyk loop.^[14][15]

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  Two-loop Birmingham bowline before tightening and dressing the knot. Two turns taken around the standing part of the line form two loops.
• 
  Variants:

  1. Bowline
  2. Cowboy bowline
  3. Eskimo bowline
  4. Left-hand Eskimo bowline
• 
  If a bowline is tied and the two free ends of the rope are brought together in the simplest way, the mathematical knot obtained is the so-called 6₂ knot. The sequence of necessary moves is depicted here.

• List of knots
• Karash double loop
• Eye splice
• Bowline on a bight

• Dickey, Glenn A. (n.d.). “Bowline Knots and Variations”. More Than Knots.

• Video of the Lightning Method
• YouTube animation of a Bowline knot

Bowen knot
Information
Family	Bowen Family
Region	Wales

The Bowen knot is an unknot design used as a heraldic charge. It is named after the Welshman James Bowen (died 1629)^[1] and is also called the true lover’s knot.^[1] It consists of a rope in the form of a continuous loop laid out as an upright square shape with loops at each of the four corners.^[2] Since the design readily unwinds to an ordinary loop, it is not a proper topological knot.

In Norwegian heraldry, a Bowen knot is called a valknute (valknut), and the municipal coat of arms of Lødingen Municipality used since 1984 has a femsløyfet valknute, which means a Bowen knot with five loops.^[3]

An angular Bowen knot is such a knot with no rounded sides so that it appears to be made of five squares. A Bowen knot with lozenge-shaped loops is called a bendwise Bowen knot or a Bowen cross.

The Dacre, Hungerford, Lacy, Shakespeare and Tristram knots are all considered variations of the Bowen knot and are sometimes blazoned as such.

The Bowen knot resembles the symbol ⌘ (looped square), which is used on Apple keyboards as the symbol of the Command key. However, the origin of this use is not related to the use of the Bowen knot in heraldic designs.

• 
  Bowen knot in a book from 1827^[4]
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  Angular Bowen knot
• 
  Bowen cross
• 
  Arms of the Norwegian municipality Lødingen
• 
  Schildknoten
• 
  Totem sign as a symbol of the ancient culture of the region in the coat of arms of Kostomuksha, Russia
• 
  Fensterrautenkreuz
• 
  Coat of arms from Hausgereut (Rheinau, Baden):^[5] Hausmarke with triangles instead of loops

• “Lord Kyl’s Heraldry – Glossary – Bo… – Entry: Bowen’s Knot”. Lord Padraig MacKay of Kyle. Archived from the original on 2008-10-15. Retrieved 2013-02-15.
• Heraldic Templates — Knots.

• Endless knot

Racking bend
Category	Bend
Typical use	Joining two ropes of widely different diameter
ABoK	#1462[1]

The racking bend is a knot for joining two ropes of different diameter.^[2] “Racking” refers to the figure eight weaving that binds the bight of the larger rope together.

It serves a somewhat similar purpose as a Sheet bend, a Double sheet bend or a Heaving line bend, and may be used to throw a thick line over with the help of a thinner line at the end of which there may be a weight such as a Monkey fist or a Heaving line knot.

• List of bend knots
• List of knots

The Bourchier knot is a variety of heraldic knot. It was used as a heraldic badge by the Bourchier family, whose earliest prominent ancestor in England was John de Bourchier (alias Boucher, Boussier, etc., d. c. 1330), a Judge of the Common Pleas, seated at Stanstead Hall in the parish of Halstead, Essex. He was the father of Robert Bourchier, 1st Baron Bourchier (d.1349), Lord Chancellor of England. The various branches of his descendants held the titles Baron Bourchier, Count of Eu, Viscount Bourchier, Earl of Essex, Baron Berners, Baron FitzWarin and Earl of Bath. The knot should perhaps have been called the “FitzWarin knot” as according to Boutell (1864) the device was first used by the FitzWarin family,^[2] whose heir was the Bourchier family.

The Bourchier knot is shown in two forms: as a reef knot and as a granny knot.

• Beningbrough Hall, North Yorkshire, owned at one time by a branch of the Bourchier family. A large Bourchier knot is cut into a lawn adjoining the house.
• On the tomb of Thomas Bourchier (c.1404-1486), Archbishop of Canterbury in Canterbury Cathedral
• Sculpted on the Tudor gatehouse of Tawstock Court in North Devon, seat of the Bourchier Earls of Bath.
• Tawstock Church in North Devon, visible on monuments to Bourchiers and Wrey baronets.

• Aveling, S.T. Heraldry: Ancient and Modern, New York, 1891. (Illustration of granny-knot form)
• Mollett, J.W., Illustrated Dictionary of Art and Archeology by J W Mollett, 1883. (Fig.410, Illustration of reef-knot form)
• Arthur Charles Fox-Davies, Complete Guide to Heraldry, 1909, pp. 390, 469.

Media related to Bourchier knot at Wikimedia Commons

Quipu Khipu
An Inca quipu, from the Larco Museum in Lima, Peru.
Period	c. 2600 BCE – c. 1900 CE
Region	Central Andes Caral–Supe civilization Paracas culture Wari culture Inca

Quipu (/ˈkiːpuː/ KEE-poo), also spelled khipu (Ayacucho Quechua: kipu, [ˈkipu]; Cusco Quechua: khipu, [kʰipu]), are record-keeping devices fashioned from knotted cords. They were historically used by various cultures in the central Andes of South America, most prominently by the Inca Empire.^[1]

A quipu usually consists of cotton or camelid fiber cords, and contains categorized information based on dimensions like color, order, and number.^[2] The Inca, in particular, used knots tied in a decimal positional system to store numbers and other values in quipu cords. Depending on use and the amount of information stored, quipus can have anywhere from a few to several thousand cords.

Objects which can unambiguously be identified as quipus first appear in the archaeological record during the 1st millennium CE,^[3] likely attributable to the Wari Empire.^[4][5] Quipus subsequently played a key part in the administration of the Kingdom of Cusco of the 13th to 15th centuries, and later of the Inca Empire (1438–1533), flourishing across the Andes from c. 1100 to 1532. Inca administration used quipus extensively for a variety of uses: monitoring tax obligations, collecting census records, keeping calendrical information,^[6] military organization,^[7] and potentially for recording simple and stereotyped historical “annales”.^[2]

It is not known exactly how many intact quipus still remain, as many were deposited in ancient mausoleums^[3] or later destroyed by the Spanish. However, a recent survey of both museum and private collection inventories places the total number of known extant pre-Columbian quipus at just under 1,400.^[8]

After the Spanish conquest of the Inca Empire, quipus were slowly replaced by European writing and numeral systems. Many quipus were identified as idolatrous and destroyed, but some Spaniards promoted the adaptation of the quipu recording system to the needs of the colonial administration, and some priests advocated the use of quipus for ecclesiastical purposes.^[9] In some cases quipu technology was even fused with writing to form hybrid objects called quipu boards, which were often used to track religious duties.^[10] Today, quipus continue to serve as important items in several modern Andean villages.^[11]

Various other cultures have used knotted strings, unrelated to Andean quipus, to record information, such as Chinese knotting, also practiced by Tibetans, Japanese, and Polynesians.^{[12][13][14][15][16]}

The word quipu is derived from a Quechua word meaning ‘knot’.^[17] The terms quipu and khipu are spelling variations on the same word. Quipu is the traditional spelling based on the Spanish orthography, while khipu reflects the Quechuan and Aymaran spelling shift. Khipu (pronounced [ˈkʰipu]) comes from Cusco Quechua, while many other Quechua varieties use the term kipu. The hispanicized spelling of quipu is the form most commonly used in both Spanish and English.^[18]

Quipus held information, decipherable by officials called quipucamayocs (Cusco Quechua: khipu kamayuq, lit. ‘khipu specialist‘, [ˈkʰipu kaˈmajoχ]), classified in various categories, narrated from the most important to the least important category, according to color, number, and order.^[2]

To date, most of the information recorded on the quipus studied by researchers consists of numbers in a decimal system,^[20] such as “Indian chiefs ascertain[ing] which province had lost more than another and balanc[ing] the losses between them” after the Spanish invasion.^[21] In the early years of the Spanish conquest of Peru, Spanish officials often relied on the quipus to settle disputes over local tribute payments or goods production. The quipucamayocs could be summoned to court, where their bookkeeping was recognised as valid documentation of past payments.

Some knots — as well as other features, such as color, fiber type, cord attachments, etc. — are thought to compose an undeciphered non-numeric information system. The lack of a clear link between any indigenous Andean languages and the quipus has historically led to the supposition that quipus are not a glottographic writing system and have no phonetic referent.^[22] However, anthropologist Gary Urton has suggested that the quipus used a binary system that could record phonological or logographic data.^[23] According to Martti Pärssinen, quipucamayocs would learn specific oral texts, which in relation to the basic information contained in quipu, and pictorial representations, often painted on quiru vessels, similar to Aztec pictograms, related simple “episodes”.^[2] Frank Salomon, meanwhile, has argued that quipus are actually a semasiographic language, a system of representative symbols – such as music notation or numerals – that relay information but are not directly related to the speech sounds of a particular language,^[24] like ideograms and proto-writing.

In 2011, a potential match between six colonial-era Santa Valley Quipus and a Spanish colonial document from the same region was identified.^[3] Researchers believe this possible quipu-document match is the strongest Rosetta Stone-like connection currently known, which could offer key clues needed to unlock the full extent of the quipu code. Subsequent studies have built on the proposed quipu-document connection, suggesting that the binary manner by which cords can be attached to the main body of the six quipus may encode moiety affiliation,^[25][26] and uncovering detailed Andean social structures encoded within the six quipus.^[27]

Sabine Hyland claims to have made the first phonetic decipherment through her analysis of epistolary quipus from San Juan de Collata, Peru, challenging the assumption that quipus do not represent information phonetically.^[28] However, the quipus in question date to the colonial period and are believed to have been exchanged during an 18th-century rebellion against the Spanish government, suggesting that their encoding may have been influenced by the introduction of European writing systems. With the help of local leaders, Hyland argues that the names of the two ayllus, or family lineages, who received and sent the quipus can be translated using phonetic references to the animal fibers and colors of the relevant quipu cords.^[29][30]

The total number of quipus is unknown. Their whereabouts range from Europe to North and South America. Most are housed in museums outside of their native countries, but some reside in their native locations under the care of the descendants of those who made the knot records.

The archaeologist Gary Urton noted in his 2003 book Signs of the Inka Khipu that he estimated “from my own studies and from the published works of other scholars that there are about 600 extant quipu in public and private collections around the world.”^[70]

The Khipu Database Project was started by Urton and Carrie Brezine with funding from Harvard University and the National Science Foundation with the aim of centralizing data about known quipus.^[71][72] The project later became the Open Khipu Repository, which introduced a new “KH” numbering system to distinguish between quipus, moving away from naming systems based on archaeologists’ names.^[73] As of January 2026, the Open Khipu Repository records 702 quipus with publicly available data.^[74]

A 2021 survey of both museum and private collection inventories places the total number of known extant pre-Columbian quipus at just under 1,400.^[75]

Quipus are made of fibers, either spun and plied thread such as wool or hair from alpaca, llama, guanaco or vicuña, though are also commonly made of cellulose like cotton. Archaeological evidence has also shown that, in some cases, finely carved wood was used as a supplemental base to which the color-coded cords could be attached.^[81] The knotted strings of quipus were often made with an “elaborate system of knotted cords, dyed in various colors, the significance of which was known to the magistrates”.^[82] Fading of color, natural or dyed, cannot be reversed, and may indicate further damage to the fibers. Colors can darken if damaged by dust or by certain dyes and mordants.^[83] Quipus have been found with adornments, such dried potatoes and beans, attached to the cords, and these non-textile materials may require additional preservation measures.^[84]

Quipus are now preserved using techniques that aim to minimize their future degradation. Museums, archives and special collections have adopted preservation guidelines from textile practices.^[85]

Environmental controls are used to monitor and control temperature, humidity and light exposure of storage areas. As with all textiles, cool, clean, dry and dark environments are most suitable. The heating, ventilating and air conditioning, or HVAC systems, of buildings that house quipu knot records are usually automatically regulated. Relative humidity should be 60% or lower, with low temperatures, as high temperatures can damage the fibres and make them brittle. Damp conditions and high humidity can damage protein-rich material. Textiles suffer damage from ultraviolet (UV) light, which can include fading and weakening of the fibrous material. When quipus are on display, their exposure to ambient conditions is usually minimized and closely monitored.^[83][86]

Despite best efforts, damage can occur during storage, or be from the result of earlier conservation efforts.^[87] The more accessible the items are during storage, the greater the chance of early detection.^[86] Storing quipus horizontally on boards covered with a neutral pH paper (paper that is neither acid or alkaline) to prevent potential acid transfer is a preservation technique that extends the life of a collection. The fibers can be abraded by rubbing against each other or, for those attached to sticks or rods, by their own weight if held in an upright position. Extensive handling of quipus can also increase the risk of further damage.^[88]

Quipus are also closely monitored for mold, as well as insects and their larvae. As with all textiles, these are major problems. Fumigation may not be recommended for fiber textiles displaying mold or insect infestations, although it is common practice for ridding paper of mold and insects.

Conservators in the field of library science have the skills to handle a variety of situations. Even though some quipus have hundreds of cords, each cord should be assessed and treated individually. Quipu cords can be “mechanically cleaned with brushes, small tools and light vacuuming”.^[89] Just as the application of fungicides is not recommended to rid quipus of mold, neither is the use of solvents to clean them.

Even when people have tried to preserve quipus, corrective care may still be required. If quipus are to be conserved close to their place of origin, local camelid or wool fibres in natural colors can be obtained and used to mend breaks and splits in the cords.^[89] Rosa Choque Gonzales and Rosalia Choque Gonzales, conservators from southern Peru, worked to conserve the Rapaz patrimonial quipus in the Andean village of Rapaz, Peru. These quipus had undergone repair in the past, so this conservator team used new local camelid and wool fibers to spin around the area under repair in a similar fashion to the earlier repairs found on the quipu.^[89]

When Gary Urton, professor of Anthropology at Harvard, was asked “Are they [quipus] fragile?”, he answered, “some of them are, and you can’t touch them – they would break or turn into dust. Many are quite well preserved, and you can actually study them without doing them any harm. Of course, any time you touch an ancient fabric like that, you’re doing some damage, but these strings are generally quite durable.”^[90]

Ruth Shady, a Peruvian archeologist, has discovered what she argues resembles a proto-quipu dating to approximately 5,000 years old in the coastal city of Caral. It was in quite good condition, with “brown cotton strings wound around thin sticks”, along with “a series of offerings, including mysterious fiber balls of different sizes wrapped in ‘nets’ and pristine reed baskets. Piles of raw cotton – uncombed and containing seeds, though turned a dirty brown by the ages – and a ball of cotton thread” were also found preserved. The good condition of these articles can be attributed to the arid climate of Caral.^[91]

Bottle sling (Scoutcraft knot)
Names	Bottle sling (Scoutcraft knot), Bottle knot, jug sling, jug knot, jar knot, moonshiner’s knot, hackamore, hackamore knot, bridle knot, Beggarman’s knot
Category	Binding
Origin	Ancient
Related	Jury mast knot, miller’s knot, Fiador knot
Typical use	Suspending bottles and other similar objects
Caveat	Cord must be scaled to size of bottle’s flare or collar
ABoK	#260, #1142, #2007, #2186, #2300, #2554

The bottle sling (also called a jug sling, a Hackamore knot, or a Scoutcraft knot) is a knot which can be used to create a handle for a glass or ceramic container with a slippery narrow neck, as long as the neck widens slightly near the top.^[1]

While classed with binding knots, such as the reef knot and miller’s knot, the bottle sling is able to perform a function for which most other binding knots are unsuited. The bottle sling’s specific form allows it to grip a cylinder, assuming it has even a slight flare or collar, and lift it along its axis when the knot is loaded by all four strands.^[1] With appropriate size cord, most wine bottles can be reliably suspended with this knot.

The bottle sling was described in detail by the Greek physician Heraklas in his first century monograph on surgical knots and slings. It was included under the name diplous karkhesios brokhos (“double jug-sling noose”). Clearly familiar with the knot, Heraklas provided three distinct tying methods.^[2][3] Knot expert Cyrus L. Day believed the bottle sling was not described again in print until Craigin’s 1884 A Boy’s Workshop,^[4][5] although Clifford Ashley noted it was illustrated in Johann Röding’s 1795 Allgemeines Wörterbuch der Marine (“General Dictionary of the Navy”).^[1] More recently, the bottle sling has been nationally recognized by the Boy Scouts of America as the symbol of Outdoor Skills by scout camps throughout the country.

As the name suggests, the primary use for this knot is to suspend bottles, jugs, and other items with similar shapes. The space at the center of the knot is dropped over the top of a bottle or similar object. Firmly pulling on all four ends emerging from the knot tightens it against the neck of the bottle. Looping the running ends through the bight and tying them together will make a sling that grips and can be used to lift the bottle.^[6] This provides a convenient method of lowering a beverage bottle from a boat into the water to chill.

As mentioned above, the knot is believed to have been used medically in ancient Greece for applying traction in the reduction of fractures and dislocations. However it is not known to have any current medical application.^[3]

The knot is also said to have been used as an improvised emergency horse bridle when rope was the only material at hand. Its use is described with the central parts of the knot acting as a bit, one of the knot’s outer bights passing over the top of the animal’s muzzle, and the other passing under the jaw to form the noseband. The closed loop end of the knot would be placed over the animal’s head and behind the ears, as a crownpiece, and the two free ends coming off under the chin used as reins. It was intended only for temporary use.^[7] However, at least one author has disputed this as “nonsense” and suggests its only proper equestrian use is in a doubled form, in this context known as a hackamore knot, to secure the fiador to the bosal in some hackamore designs.^[8]

Perhaps not surprisingly—given three were already known to the ancient Greeks—there are many methods to tie the bottle sling. Swedish physiologist and knot researcher Hjalmar Öhrvall listed eight in his 1916 book Om Knutar (“About Knots”).^[9][10]

One method for tying the bottle sling is similar to the loop-and-weave method used to tie the jury mast knot and the trumpet knot. The knot is begun by making a bight in a piece of rope and folding the bight back on itself to make two separated loops that are mirror images of each other. Lay one loop on top of the other so that they overlap slightly and create a cat’s-eye-shaped hole above a triangular hole between the two loops. Make a bird’s beak with your index and thumb and weave them down through the loop, up through the cat’s eye and down through the bottom loop, bunching the coils of rope against your fingers. Pinch the section of rope that was the bottom of the triangle and flip the coils over the pinched section. The flip may take a little practice, but the pinched section should become a short bight hanging off a circular knot.

• 
  Overlapping the loops
• 
  Path the bight takes through the cat’s eye
• 
  Flipping the knot
• 
  Final configuration

• Bottle cage
• List of binding knots
• List of knots

• Brief video of one tying method
• Bottle sling discussed in relation to an alternative knot