Alexander cuts the Gordian Knot, by Jean-Simon Berthélemy (1743–1811)

The Gordian Knot is a legend of Phrygian Gordium associated with Alexander the Great. It is often used as a metaphor for an intractable problem solved easily by cheating or "thinking outside the box". ("cutting the Gordian knot"):

"Turn him to any cause of policy,
The Gordian Knot of it he will unloose,
Familiar as his garter" (Shakespeare, Henry V, Act 1 Scene 1. 45–47)

Legend[link]

At one time the Phrygians were without a king. An oracle at Telmissus (the ancient capital of Phrygia) decreed that the next man to enter the city driving an ox-cart should become their king. A peasant farmer named Gordias drove into town on an ox-cart. His position had also been predicted earlier by an eagle landing on his cart, a sign to him from the gods, and on entering the city Gordias was declared king by the priests. Out of gratitude, his son Midas dedicated the ox-cart^[1] to the Phrygian god Sabazios (whom the Greeks identified with Zeus) and either tied it to a post or tied its shaft with an intricate knot of cornel (Cornus mas) bark. The ox-cart^[2] still stood in the palace of the former kings of Phrygia at Gordium in the fourth century BC when Alexander arrived, at which point Phrygia had been reduced to a satrapy, or province, of the Persian Empire.

Several themes of myth converged on the chariot, as Robin Lane Fox remarks:^[3] Midas was connected in legend with Alexander's native Macedonia, where the lowland "Gardens of Midas" still bore his name, and the Phrygian tribes were rightly remembered as having once dwelt in Macedonia. So, in 333 BC, while wintering at Gordium, Alexander the Great attempted to untie the knot. When he could not find the end to the knot to unbind it, he sliced it in half with a stroke of his sword, producing the required ends (the so-called "Alexandrian solution"). That night there was a violent thunderstorm. Alexander's prophet Aristander took this as a sign that Zeus was pleased and would grant Alexander many victories. Once Alexander had sliced the knot with a sword-stroke, his biographers claimed in retrospect^[4] that an oracle further prophesied that the one to untie the knot would become the king of Asia.^[5]

Status of the legend[link]

Alexander is a figure of outstanding celebrity and the dramatic episode with the Gordian Knot remains widely known. Literary sources are Alexander's propagandist Arrian (Anabasis Alexandri 2.3) Quintus Curtius (3.1.14), Justin's epitome of Pompeius Trogus (11.7.3), and Aelian's De Natura Animalium 13.1.^[6]

While sources from antiquity agree that Alexander was confronted with the challenge of the knot, the means by which he solved the problem are disputed. Both Plutarch and Arrian relate that according to Aristobulus,^[7] Alexander pulled the knot out of its pole pin, exposing the two ends of the cord and allowing him to untie the knot without having to cut through it. Some classical scholars regard this as more plausible than the popular account.^[8]

Alexander later went on to conquer Asia as far as the Indus and the Oxus thus, for Callisthenes, fulfilling the prophecy.

Interpretations[link]

The knot may have been a religious knot-cipher guarded by Gordian/Midas's priests and priestesses. Robert Graves suggested that it may have symbolized the ineffable name of Dionysus that, knotted like a cipher, would have been passed on through generations of priests and revealed only to the kings of Phrygia.^[9]

Unlike fable, true myth has few completely arbitrary elements. This myth taken as a whole seems designed to confer legitimacy to dynastic change in this central Anatolian kingdom: thus Alexander's "brutal cutting of the knot... ended an ancient dispensation."^[10] The ox-cart suggests a longer voyage, rather than a local journey, perhaps linking Gordias/Midas with an attested origin-myth in Macedon, of which Alexander is most likely to have been aware.^[11] Based on the myth, the new dynasty was not immemorially ancient, but had widely remembered origins in a local, but non-priestly "outsider" class, represented by Greek reports equally as an eponymous peasant "Gordias"^[12] or the locally-attested, authentically Phrygian "Midas"^[13] in his ox-cart.^[14] Other Greek myths legitimize dynasties by right of conquest (compare Cadmus), but the legitimizing oracle stressed in this myth suggests that the previous dynasty were a race of priest-kings allied to the unidentified oracle deity.

Use of the phrase[link]

This section requires expansion.

• Brian Coless has suggested that Donald Wiseman "cut the Gordian knot" of "the intractable problem of identifying King Darius the Mede" in the Book of Daniel, by identifying Darius with Cyrus the Great.^[15]

• W. G. Sebald in The Rings of Saturn recounts the episode of Joseph Conrad who was shot or shot himself in the chest allowing him to "Cut the Gordian Knot" of a stormy love affair.^[16]

• In Tracy Letts' Pulitzer Prize-winning play August: Osage County, Bill Fordham uses the phrase to describe his marital problems with his wife Barbara when he says to her: "Just because you and I are struggling with this Gordian knot doesn't make me any less of a --"^[17]

• Lord Upjohn, speaking of the allocation of beneficial interests between the parties under a constructive trust in National Provincial Bank Ltd v Ainsworth ^[18], said that the parties' affairs are sometimes so inextricably intermixed that "an equitable knife must be used to sever the Gordian Knot".

• Gottfried Leibniz argues in his essay On Nature Itself that refusing to acknowledge an active force in things and instead "simply to absorb this force into a command of God’s - a command given just once in the past, having no effect on things and leaving no traces of itself in them - is so far from making the matter easier to grasp that it is more like abandoning the role of the philosopher altogether and cutting the Gordian knot with a sword."^[19]

See also[link]

Look up Gordian knot in Wiktionary, the free dictionary.

• Egg of Columbus
• Archimedean point
• Endless knot
• Hellenic Army IV Army Corps: Τώ ξιφεί τόν δεσμό λελύσθαι (Solve the knot with the sword.)
• Trefoil knot

Notes[link]

References[link]

Wikimedia Commons has media related to: Gordian knot

• Robert Graves, The Greek Myths, 1993. ISBN 0-14-017199-1
• Robin Lane Fox, Alexander the Great, 1973, pp 149–151. ISBN 0-14-008878-4
• Plutarch, Lives

Some knots

1. Yarn knot ABoK #2688
2. Manrope knot
3. Granny knot
4. Rosebud stopper knot (?)
5. Matthew Walker's knot
6. Shroud knot
7. Turks head knot
8. Overhand knot, Figure-of-eight knot
9. Reef knot, Square knot
10. Two half hitches

A knot is a method of fastening or securing linear material such as rope by tying or interweaving. It may consist of a length of one or several segments of rope, string, webbing, twine, strap, or even chain interwoven such that the line can bind to itself or to some other object—the "load". Knots have been the subject of interest for their ancient origins, their common uses, and the area of mathematics known as knot theory.

Use[link]

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There is a large variety of knots, each with properties that make it suitable for a range of tasks. Some knots are used to attach the rope (or other knotting material) to other objects such as another rope, cleat, ring, or stake. Some knots are used to bind or constrict objects. Decorative knots usually bind to themselves to produce attractive patterns.

Teaching[link]

Sailors learning knots and ropework in the early 20th century

While some people can look at diagrams or photos and tie the illustrated knots, others learn best by watching how a knot is tied. Knot tying skills are often transmitted by sailors, scouts, climbers, cavers, arborists, rescue professionals, fishermen, linemen and surgeons.

Applications[link]

Truckers in need of securing a load may use a trucker's hitch, gaining mechanical advantage. Knots can save a spelunker from finding himself buried under rock. Many knots can also be used as makeshift tools, for example, the Bowline can be used as a rescue loop, and the Munter hitch can be used as a belay. The Diamond hitch was widely used to tie packages on to donkeys and mules.

In hazardous environments such as mountains, knots are very important. In the event of someone falling into a ravine or a similar terrain feature, with a rope or two, some carabineers, and knowledge of knots you can set up a rappel system to lower yourself down to the individual and set up a hauling system to allow another individual to pull you and the injured person out of the ravine. Further application of knots includes developing a high line, which is basically equivalent to a zip line. Using the high line you can move supplies, injured people, or those lacking training in rappelling and rock climbing across a river or a large crevice or ravine. Note the systems mentioned typically require carabineers and the use of multiple useful knots. These knots include the bowline, double figure eight, munter hitch, munter mule, prusik, autoblock, and clove hitch. Thus any individual who goes into a mountainous environment should have basic knowledge of knots and knot systems to increase safety and the ability to do interesting activities such as rappelling.

Knots can be applied in combination to produce complex objects such as lanyards and netting. In ropework, the frayed end of a rope is held together by a type of knot called a whipping knot. Many types of textiles use knots to repair damage. Macrame, one kind of textile, is generated exclusively through the use of knotting, instead of knits, crochets, weaves or felting. Macramé can produce self-supporting three dimensional textile structures, as well as flat work, and is often used ornamentally or decoratively.

Properties[link]

Strength[link]

Knots weaken the rope in which they are made.^[1] When knotted rope is strained to its breaking point, it almost always fails at the knot or close to it, unless it is defective or damaged elsewhere. The bending, crushing, and chafing forces that hold a knot in place also unevenly stress rope fibers and ultimately lead to a reduction in strength. The exact mechanisms that cause the weakening and failure are complex and are the subject of continued study.

Relative knot strength, also called knot efficiency, is the breaking strength of a knotted rope in proportion to the breaking strength of the rope without the knot. Determining a precise value for a particular knot is difficult because many factors can affect a knot efficiency test: the type of fiber, the style of rope, the size of rope, whether it is wet or dry, how the knot is dressed before loading, how rapidly it is loaded, whether the knot is repeatedly loaded, and so on. The efficiency of common knots ranges between 40—80% of the rope's original strength.^[2]

In most situations forming loops and bends with conventional knots is far more practical than using rope splices, even though the latter can nearly maintain the rope's full strength. Prudent users allow for a large safety margin in the strength of rope chosen for a task due to the weakening effects of knots, aging, damage, shock loading, etc. The working load limit of a rope is generally specified with a significant safety factor, up to 15:1 for critical applications.^[3] For life-threatening applications, other factors come into play.

Security[link]

Even if the rope does not break, a knot may still fail to hold. Knots that hold firm under a variety of adverse conditions are said to be more secure than those that do not. The main ways knots fail to hold are:

Slipping[link]

The load creates tension that pulls the rope back through the knot in the direction of the load. If this continues far enough, the working end passes into the knot and the knot unravels and fails. This behavior can worsen when the knot is repeatedly strained and let slack, dragged over rough terrain, or repeatedly struck against hard objects such as a masts and flagpoles.

Even with secure knots, slippage may occur when the knot is first put under real tension. This can be mitigated by leaving plenty of rope at the working end outside of the knot, and by dressing the knot cleanly and tightening it as much as possible before loading. Sometimes, the use of a stopper knot or, even better, a backup knot can prevent the working end from passing through the knot; but if a knot is observed to slip, it is generally preferable to use a more secure knot. Life-critical applications often require backup knots to maximize safety.

Capsizing[link]

Bowline

Capsizing (or spilling) a knot refers to changing a knot's form and rearranging its parts, usually by pulling on specific ends in certain ways.^[2] When used inappropriately, some knots tend to capsize easily or even spontaneously. Often the capsized form of the knot offers little resistance to slipping or unraveling. A Reef Knot, when misused as a bend, can capsize dangerously.

Sometimes a knot is intentionally capsized as a method of tying another knot, as with the "lightning method" of tying a Bowline. Some knots, such as the Carrick Bend, are generally tied in one form then capsized to obtain a stronger or more stable form.

Sliding[link]

In knots that are meant to grip other objects, failure can be defined as the knot moving relative to the gripped object. While the knot itself does not fail, it ceases to perform the desired function. For instance, a simple Rolling Hitch tied around a railing and pulled parallel to the railing might hold up to a certain tension, then start sliding. Sometimes this problem can be corrected by working-up the knot tighter before subjecting it to load, but usually the problem requires either a knot with more wraps or a rope of different diameter or material.

Releasability[link]

Knots differ in the effort required to untie them after loading. Knots that are very difficult to untie, such as the water knot, are said to "jam". Knots that come untied with less difficulty, such as the Zeppelin bend, are referred to as "non-jamming".

Components[link]

Knot components

A	Turn
B	Round turn
C	Two round turns

[edit] Bight

Any curved section, slack part, or loop between the ends of a rope, string, or yarn

Bitter end[link]

More a ropeworker's term than a knot term, it refers to the end of a rope that is tied off, hence the expression "hanging on to the bitter end".^{[citation needed]} A bitt is a metal block with a crosspin used for tying lines to, found on piers. In fact the bitter end is the end of the anchor "cable" that connects to the anchor bitts in the cable locker under the forecastle or poop using the bitter pin. (British nautical usage). Other uses may be borrowed from this derivation.

Loop[link]

A full circle formed by passing the working end over itself

Elbow[link]

Two crossing points created by an extra twist in a loop

Standing end[link]

The standing end is the longer end of the rope not involved in the knot, often shown as unfinished. It is often (but not always) the end of the rope under load after the knot is complete. For example, when a clove hitch ties a boat to a pier, the end going to the boat is the standing end.

Standing part[link]

Section of line between knot and the standing end (seen above)

[edit] Turn

A turn or single turn is a single pass behind or through an object.

A round turn is the complete encirclement of an object; requires two passes.

Two round turns circles the object twice; requires three passes.

Working end[link]

The active end of a line used in making the knot. May also be called the 'running end', 'live end', or 'tag end'.

Working part[link]

Section of line between knot and the working end

Categories[link]

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Further information: List of knot terminology

The list of knots is extensive, but common properties allow for a useful system of categorization. For example, loop knots share the attribute of having some kind of an anchor point constructed on the standing end (such as a loop or overhand knot) into which the working end is easily hitched to using a round turn. An example of this is the bowline. Constricting knots often rely on friction to cinch down tight on loose bundles; an example is the Miller's knot. Knots may belong to more than one category.

Bend 

A knot uniting two lines (for knots joining two ends of the same line, see binding knots or loops). List of bends.

Binding 

A knot that restricts object(s) by making multiple winds. List of binding knots.

Coil 

Knots used to tie up lines for storage. Another handy coil is here.

Decorative knot 

A complex knot exhibiting repeating patterns often constructed around and enhancing an object. List of decorative knots.

Hitch 

A knot tied to a post, cable, ring, or spar. List of hitch knots.

Lashing 

A knot used to hold (usually) poles together. List of lashing knots.

Loop 

A knot used to create a closed circle in a line. List of loop knots.

Plait (or braid)

A number of lines interwoven in a simple regular pattern. List of plait knots.

Slip (or running) 

A knot tied with a hitch around one of its parts. In contrast, a loop is closed with a bend. While a slip knot can be closed, a loop remains the same size. List of slip knots.

Slipped 

Some knots may be finished by passing a bight rather than the end, for ease of untying. The common shoelace knot is an example, being a reef knot with both ends slipped.

Seizing 

A knot used to hold two lines or two parts of the same line together. List of seizing knots.

Sennit 

A number of lines interwoven in a complex pattern. See also Chain sinnet.

Splice 

A knot formed by interweaving strands of rope rather than whole lines. More time-consuming but usually stronger than simple knots. List of splices.

Stopper 

A knot tied to hold a line through a hole.

Trick 

A knot that is used as part of a magic trick, a joke, or a puzzle. List of trick knots.

Whipping 

A binding knot used to prevent another line from fraying.

Basic useful knots[link]

• Alpine butterfly knot for a secure loop in the middle of a rope when the ends aren't free
• Bowline for tying a loop in the end of a rope, as around one's waist or to secure a ring or grommet. The knot is also used as an anchor knot and is used in many knot systems that are used in mountainous terrain such as a highline or hauling system.
• Constrictor knot for making bundles or cinching the neck of a sack
• Figure-of-eight knot as a stopper
• Monkey's fist used to haul a heavier rope
• Prusik for ascending a rope
• Sheet bend for joining the ends of two ropes, which need not be the same diameter
• Double sheet bend for tying the ends of two dissimilarly sized ropes together
• Spanish bowline Used to hoist crewmen aloft or suspend them over the side
• Square knot, a binding knot for joining the ends of a piece of cordage wrapped around an object or objects
• Versatackle hoist heavy loads and tighten rigging
• Water knot for tying a knot in flat material such as nylon webbing

Hitches[link]

• Buntline hitch for tying a rope to a pole
• Diamond hitch for packing trail animals
• Midshipman's Hitch (also known as a Taut-line Hitch, below)
• Rolling hitch for securing a rope to a pole, or one rope to the middle of another
• Taut-line hitch for forming an adjustable loop that keeps its size under tension
• Timber hitch for securing or hauling long narrow loads
• Trucker's hitch for clinching down a load

Knot theory[link]

A trefoil knot is a mathematical version of an overhand knot.

Knot theory is a branch of topology. It deals with the mathematical analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a knot is a figure consisting of a single loop, abstracted from any physical rope or line, with any number of crossing or "knotted" elements. As such, it has no proper ends, and cannot be undone or untied. Various mathematical techniques are used to classify and distinguish knots. For instance, the Alexander polynomial can be used to distinguish the trefoil knot from the figure-eight knot and the unknot (a simple loop).^{[citation needed]}

See also[link]

• Chinese knotting
• List of decorative knots
• List of knots
• List of knot terminology
• Knot (mathematics)
• Quipu
• Round turn and two half-hitches

References[link]

Footnotes[link]

Notations[link]

• Clifford W. Ashley. The Ashley Book of Knots. Doubleday, New York. ISBN 0-385-04025-3
• Geoffrey Budworth (1999). The Ultimate Encyclopedia of Knots & Ropework. Annes Publishing Limited. ISBN 1-55267-986-1
• John Cassidy (1985). The Klutz Book of Knots. Klutz Press, Palo Alto, California. ISBN 0-932592-10-4
• Cyrus L. Day. Knots & Splices. International Marine/McGraw-Hill Companies. ISBN 0-87742-252-4
• Raoul Graumont. Handbook of Knots. Cornell Maritime Press/Tidewater Publishers. ISBN 0-87033-030-6
• R.S. Lee. All The Knots You Need. Algrove Publishing. ISBN 0-921335-47-4
• Allen Padgett and Bruce Smith. On Rope. National Speleological Society. ISBN 0-9615093-2-5
• Des Pawson (2001). Pocket Guide to Knots & Splices. Produced for Propsero Books by RPC Publishing Ltd., London. ISBN 1-55267-218-2
• Brion Toss. The Complete Rigger's Apprentice. International Marine/McGraw-Hill Companies. ISBN 0-07-064840-9
• J.C. Turner and P. van de Griend (ed.) (1996). History and Science of Knots. World Scientific. ISBN 981-02-2469-9

External links[link]

Wikibooks has a book on the topic of Simplified list of knots

Wikimedia Commons has media related to: Knots

• Knots at the Open Directory Project
• The short film Knots, Bends And Hitches (1973) is available for free download at the Internet Archive [more]
• Over 350 Knot Videos - videos are demonstrating animated knots tying