Category: Knots

Timber hitch
Names	Timber hitch, Fig.8 Timber Hitch, Bowyer’s Knot, Lumberman’s Knot, Countryman’s Knot
Category	Hitch
Related	Killick hitch
Releasing	Non-jamming
ABoK	#1668,#195, #479, #1665, #2161
Instructions

The timber hitch is a knot used to attach a single length of rope to a cylindrical object. Secure while tension is maintained, it is easily untied even after heavy loading.^[1][2][3]

The timber hitch is a very old knot. It is first known to have been mentioned in a nautical source c. 1625^[4] and illustrated in 1762.^[1]

As the name suggests, this knot is often used by lumbermen and arborists for attaching ropes or chains to tree trunks, branches, and logs.^[3][5] For stability when towing or lowering long items, the addition of a half-hitch in front of the timber hitch creates a timber hitch and a half hitch,^[6] or known as a killick hitch^[2] when at sea.^[7] A killick is “a small anchor or weight for mooring a boat, sometimes consisting of a stone secured by pieces of wood”.^[8] This can also prevent the timber hitch from rolling.^[3] The timber hitch is one of the few knots that can easily be tied in a chain, leading to its use in applications where ropes lack the necessary strength and would break under the same amount of tension.

The Timber Hitch is very convenient for hoisting boards and timbers, as it cannot jam and may be instantly loosened. If timber is to be hoisted on end the Timber Hitch is made with the end of the rope below the center of the timber and then a Half Hitch is added in the standing part at the upper end of the timber.

This knot is also known as the Bowyer’s Knot, as it is used to attach the lower end of the bowstring to the bottom limb on an English longbow.^[9]

The hitch is also one of the methods used to connect ukulele^[10] and classical guitar^[11][12] strings to the bridge of the instruments.

• 
  Timber hitch on a tree trunk.
• 
  Timber hitches on the bridge of a classical guitar

To make the knot, pass the rope completely around the object. Pass the running end around the standing part, then through the loop just formed. Make three or more turns (or twists) around the working part. Pull on the standing part to tighten around the object.

A common error in tying can be avoided by assuring that the turns are made in the working part around itself.^[13] When making the hitch in laid rope, the turns should be made with the lay of the rope, that is, in the same direction as the twist of the rope.^[1][2]

• 
  Timber hitch step by step. Three turns are shown.
• 
  Tying technique for stringed instruments

Although The Ashley Book of Knots states that “three tucks or turns are ample”,^[1] this work was written prior to the wide use of synthetic fiber cordage. Later sources suggest five or more turns may be required for full security in modern synthetic ropes.^[3][14]

The Timber Hitches list almost immediately in “CHAPTER 21: HITCHES TO SPAR AND RAIL (RIGHT-ANGLE PULL)”, only preceded there by 3 Half Hitch base forms. The context begins with typical Half Hitch#1662 as worst security/nip warnings warning with Skull/Crossbones, but a base structure to build on. Then shows the most security at top nip/opposing the linear load pull position as a safer Half Hitch form#1663 awarding Anchor icon if constant pull. Then introduces Timber Hitch #1665 concept from extension of worst nip Half Hitch tail#1662 . #1666 then shows Fig.8 concept as upgrade to Half Hitch#1662 and shows the nip position pushed to halfway between normal and top nip Half Hitch. Also adds a geometric consideration of:”particularly if the encompassed object is small.” of even higher nip. #1668 then shows the Fig.8 Timber Hitch with nip more to side and not bottom as improvement.^[1]

Next trick is in #1669 Fig.8 Hitch with Round Turn. Where the Round Turn is around the Standing Part and Fig.8 portion actually pictured as fig.8 Timber Hitch and so adds that the “Round Turn on the Standing Part adds materially to the strength of the knot.”^[1]

Next chapter is “CHAPTER 22: HITCHES TO MASTS, RIGGING, AND CABLE (LENGTHWISE PULL) To withstand a lengthwise pull without slipping is about the most that can be asked of a hitch. Great care must be exercised in tying the following series of knots, and the impossible must not be expected” that starts off with a Timber Hitch preceded by ‘lengthwise’ Half Hitch form to convert Timber from “RIGHT-ANGLE PULL” to “LENGTHWISE PULL” usage in the back to back chapters.^[1]

• List of knots
• Killick hitch

• https://knots.neocities.org/timberhitch

In folklore, fairy-locks (or elflocks) are the result of fairies tangling and knotting the hairs of sleeping children and the manes of beasts as the fairies play in and out of their hair at night.^[1]

The concept is first attested in English in Shakespeare’s Romeo and Juliet in Mercutio’s speech of the many exploits of Queen Mab, where he seems to imply the locks are only unlucky if combed out:

“She is the fairies’ midwife, and she comes

In shape no bigger than an agate stone…….

That plaits the manes of horses in the night

And bakes the elflocks in foul sluttish hairs,

Which once untangled, much misfortune bodes.”

Therefore, the appellation of elf lock or fairy lock could be attributed to any various tangles and knots of unknown origins appearing in the manes of beasts or hair of sleeping children.

It can also refer to tangles of elflocks or fairy-locks in human hair. In King Lear, when Edgar impersonates a madman, “elf all my hair in knots.”^[2] (Lear, ii. 3.) What Edgar has done, simply put, is made a mess of his hair.

See also Jane Eyre, Ch. XIX; Jane’s description of Rochester disguised as a gypsy: “… elf-locks bristled out from beneath a white band …”

German counterparts of the “elf-lock” are Alpzopf, Drutenzopf, Wichtelzopf, Weichelzopf, Mahrenlocke, Elfklatte, etc. (where alp, drude, mare, and wight are given as the beings responsible). Grimm, who compiled the list, also remarked on the similarity to Frau Holle, who entangled people’s hair and herself had matted hair.^[3] The use of the word elf seems to have declined steadily in English, becoming a rural dialect term, before being revived by translations of fairy tales in the nineteenth century and fantasy fiction in the twentieth.

Fairy-locks are ascribed in French traditions to the lutin.^[4]

In Poland and nearby countries, witches and evil spirits were often blamed for Polish plait. This can be, however, a serious medical condition or an intentional hairstyle.

In the mathematical theory of knots, the Thurston–Bennequin number, or Bennequin number, is an invariant associated with a Legendrian knot in a three dimensional contact manifold. It is named after William Thurston and Daniel Bennequin. The Thurston-Bennequin number measures the “twisting of the contact structure around the knot”.^[1] Together with the rotation number, they are often referred as the “classical” invariants of Legendrian knots.

The Thurston-Bennequin number of a Legendrian knot ${\displaystyle K}$ is usually denoted by ${\displaystyle \mathrm {tb} (K)}$. The maximal Thurston–Bennequin number, ${\displaystyle {\overline {\mathrm {tb} }}(K)}$, over all Legendrian representatives of a knot in ${\displaystyle \mathbb {R} ^{3}}$ is a topological knot invariant.^[2]

Let ${\displaystyle K}$ be a null-homologous oriented Legendrian knot in a co-oriented three-dimensional contact manifold ${\displaystyle (M^{3},\xi )}$ and fix a Seifert surface ${\displaystyle \Sigma }$ to ${\displaystyle K}$, that is an embedded connected, compact, orientable surface with boundary ${\displaystyle \partial \Sigma =K}$. The Thurston-Bennequin number of ${\displaystyle K}$ relative to ${\displaystyle \Sigma }$ is the defined as the signed intersection number of the contact plane field ${\displaystyle \xi }$ with ${\displaystyle \Sigma }$.^[3]

Let ${\displaystyle K’}$ be a small push-off of ${\displaystyle K}$ obtained by pushing along a vector field ${\displaystyle v}$ transverse to ${\displaystyle \xi }$. The Thurston-Bennequin number can also be defined as ${\displaystyle \mathrm {lk} (K,K’)}$, where ${\displaystyle \mathrm {lk} }$ denotes the linking number.^[3]

The Euclidean case

We consider the case where ${\displaystyle (M,\xi )=(\mathbb {R} ^{3},\xi _{\mathrm {std} })}$ is the standard contact structure on ${\displaystyle \mathbb {R} ^{3}}$. If we denote ${\displaystyle (x,y,z)}$ the coordinates in ${\displaystyle \mathbb {R} ^{3}}$, the contact structure ${\displaystyle \xi _{\mathrm {std} }}$ is the kernel of the one-form ${\displaystyle dz-ydx}$. The applications ${\displaystyle \Pi \colon \mathbb {R} ^{3}\to \mathbb {R} ^{2},(x,y,z)\mapsto (x,z)}$ and ${\displaystyle \pi _{L}\colon \mathbb {R} ^{3}\to \mathbb {R} ^{2},(x,y,z)\mapsto (x,y)}$ denote respectively the front projection and the Lagrangian projection. The Thurston-Bennequin number can be computed easily from its front and Lagrangian projections.

Lagrangian projection description

The Thurston-Bennequin number of a Legendrian knot ${\displaystyle K\subset \mathbb {R} ^{3}}$ is the writhe of its Lagrangian projection ${\displaystyle \pi _{L}(K)}$.

Front projection description

For a Legendrian knot ${\displaystyle K\subset \mathbb {R} ^{3}}$, its front projection ${\displaystyle \Pi (K)\subset \mathbb {R} ^{2}}$ is called its front diagram. The front diagram of a Legendrian knot does not have vertical tangencies, however cusps can appear. Generically, the front diagram of a knot as no tangency point, no triple intersection and standard cusp singularities. In this case the Thurston-Bennequin number is

${\displaystyle \mathrm {tb} (K)={\textrm {writhe}}(\Pi (K))-{\dfrac {1}{2}}{\big (}\#{\text{number of cusps}}{\big )},}$

where ${\displaystyle {\textrm {writhe}}(\Pi (K))}$ denotes the writhe of the front diagram.^[1]

The invariant can also be computed using a grid diagram corresponding to a particular Legendrian representative of a knot.^[4][5] In this setting, the number can be computed as the writhe of the diagram minus the number of ‘northwest’ corners.

By smoothing the ‘northeast’ and ‘southwest’ corners and rotating the diagram and switching all crossings, one can convert a grid diagram into the associated Legendrian knot.

In his thesis ^[1], Daniel Bennequin proved an inequality involving the Thurston-Bennequin number. He proved that for all Legendrian knot ${\displaystyle K}$ in the standard contact ${\displaystyle \mathbb {R} ^{3}}$ the following inequality is true:

${\displaystyle \mathrm {tb} (K)+\vert {\textrm {rot}}(K)\vert \leq -\chi (\Sigma ),}$

where ${\displaystyle \chi (\Sigma )}$ denotes the Euler characteristic of a Seifert surface ${\displaystyle \Sigma }$ of ${\displaystyle K}$ and ${\displaystyle {\textrm {rot}}(K)}$ denotes the rotation number of ${\displaystyle K}$.

In particular, the maximal Thurston-Bennequin number gives a lower bound on the genus of a topological knot.

• “Thurston–Bennequin number“, The Knot Atlas.
• Lee Rudolph (1997). “The slice genus and the Thurston–Bennequin invariant of a knot”. Proceedings of the American Mathematical Society. 125: 3049–3050. doi:10.1090/S0002-9939-97-04258-5. MR 1443854.

Eskimo Bowline
Names	Eskimo Bowline, Sitka Loop, Anti-bowline, Cossack knot
Category	Loop
Origin	Ancient
Related	Kalmyk loop, Bowline, Cowboy bowline, Sheet bend
Releasing	Non-jamming
Typical use	Placing a loop in the end of a rope

The Eskimo bowline, Cossack knot (Russian: Казачий узел), reverse bowline, or ‘anti-bowline’ is in a class of knots known as ‘eye knots’ or ‘loop knots’. The eye is formed in the end of the rope to permit attachments/connections. It is quite common in Russia and is often used instead of the bowline (ABoK #1010). In the simple bowline, the collar component forms around the ‘standing part’. In contrast, the collar component of an Eskimo bowline forms around the outgoing eye-leg.

On the first of arctic explorer John Ross’ expeditions (1818) the Inuit (Eskimos) presented him a sled that contained several of these knots, showing that it is a genuine Inuit knot.^[1]
The knot is not mentioned in The Ashley Book of Knots but in its Russian equivalent, the book “Морские узлы”
^[2]
(Marine Knots) by Lev Skryagin (1930–2000). The knot is referred to in the Russian book as the Cossack knot, and its slipped version is known as the Kalmyk loop.

The Eskimo bowline is about as strong as and even more secure than the bowline,^[4][1] especially in synthetic lines.

Under cross load (ring loading, transverse loading profile), i.e. when the loop is pulled apart, the shown common Eskimo loop effectively mimics an ends-opposite (and inferior) left-hand sheet bend and thus can slip like the bowline; the less common Eskimo loop variant with the A–C loop (see bowline family diagram) would give a proper same-side sheet bend, thus being much stronger under cross load. Similarly, when the eye of a simple bowline is subject to a transverse loading profile, it mimics the inferior version of the Lapp bend, and so can slip and untie; the wrongly demeaned left-handed or cowboy bowline becomes the proper Lapp bend, and should hold..

All of the maneuvers to tie this knot are generally in the opposite (or ‘anti’ direction) relative to the bowline. After forming the ‘nipping loop’ with C & D (which can be formed as ‘S’ or ‘Z’ chirality) the working end is fed through that loop from the same side A as the outgoing eye leg C. This is opposite (or ‘anti’) direction relative to the simple (ABOK #1010) Bowline (A–D on opposite sides).

The so called ‘Eskimo’ Bowline has also been known as Boas Bowline and Cossack knot – all of these names referring to the same structure. The Kalmyk loop^[5][6] can be made ‘TIB’ (Tiable In the Bight); however, it will not be ‘EEL’ (Either End Loadable).

• Kalmyk loop

• Скрягин Л. Н. (Lev Skryagin): Морские узлы (Marine Knots) as PDF
• Little Campfires (2020-08-01). “How to Tie a Bowline Knot (Plus Variations): Eskimo Bowline”. YouTube.

Three-twist knot
Common name	Figure-of-nine knot
Arf invariant	0
Braid length	6
Braid no.	3
Bridge no.	2
Crosscap no.	2
Crossing no.	5
Genus	1
Hyperbolic volume	2.82812
Stick no.	8
Unknotting no.	1
Conway notation	[32]
A–B notation	52
Dowker notation	4, 8, 10, 2, 6
Last / Next	51 / 61
Other
alternating, hyperbolic, prime, reversible, twist

In knot theory, the three-twist knot is the twist knot with three-half twists. It is listed as the 5₂ knot^[1] in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the cinquefoil knot.

The three-twist knot is a prime knot, and it is invertible but not amphichiral. Its Alexander polynomial is

${\displaystyle \Delta (t)=2t-3+2t^{-1},\,}$

since ${\displaystyle {\begin{pmatrix}1&-1\\0&2\end{pmatrix}}}$ is a possible Seifert matrix, or because of its Conway polynomial, which is

${\displaystyle \nabla (z)=2z^{2}+1,\,}$

and its Jones polynomial is

${\displaystyle V(q)=q^{-1}-q^{-2}+2q^{-3}-q^{-4}+q^{-5}-q^{-6}.\,}$^[2]

Because the Alexander polynomial is not monic, the three-twist knot is not fibered.

The three-twist knot is a hyperbolic knot, with its complement having a volume of approximately 2.82812.

If the fibre of the knot in the initial image of this page were cut at the bottom right of the image, and the ends were pulled apart, it would result in a single-stranded figure-of-nine knot (not the figure-of-nine loop).

Thief knot
Names	Thief knot, Bag knot, Bread bag knot
Category	Binding
Origin	Ancient
Related	Reef knot, Granny knot, Grief knot
Releasing	Jamming, but not always
Caveat	spills
ABoK	#1207

The thief knot resembles the reef knot (square knot) except that the free, or bitter ends are on opposite sides. It is said that sailors would secure their belongings in a ditty bag using the thief knot, often with the ends hidden. If another sailor went through the bag, the odds were high the thief would tie the bag back using the more common reef knot, revealing the tampering, hence the name. It is difficult to tie by mistake, unlike the granny knot, unless one attempts to tie a square knot in a similar manner to a sheet bend (which is the correct way to tie a thief knot), then it is possible to tie accidentally.

The thief knot is much less secure than the already insecure reef knot. It unties itself if the lines are pulled when the same action would seize a reef knot.^[1]

The thief or bag knot is also called bread bag knot. It appears very like the reef knot, but there is one real and scarcely evident difference. It does not consist of two half knots. There is a legend that sailors tie clothesbags, and bread bags with this knot and that thieves always retie them with reef knots and so are inevitably detected. It is a pleasing story that should encourage honesty. However, if I have ever met this knot in practical use, I have neither recognized it nor paid penalty for my failure to do so.

• 
  Reef (square) knot
• 
  Thief knot
• 
  Granny knot
• 
  Grief knot
• 
  Surgeon’s knot

• List of binding knots
• List of knots

• The Reef Knot Family Archived 2013-12-03 at the Wayback Machine

Endless knot
A common form of the endless knot
Chinese name
Traditional Chinese	盤長結
Simplified Chinese	盘长结
Transcriptions Standard Mandarin Hanyu Pinyin pánzhǎng jié
Tibetan name
Tibetan	དཔལ་བེའུ།
Transcriptions Wylie dpal be’u
Mongolian name
Mongolian Cyrillic	түмэн өлзий
Japanese name
Kanji	盤長結
Transcriptions Romanization Banchōmusubi
Sanskrit name
Sanskrit	श्रीवत्स

In Hinduism, Jainism and Buddhism, the endless knot or eternal knot is a symbolic knot and one of the Eight Auspicious Symbols. It is an important cultural marker in places significantly influenced by Tibetan Buddhism such as Tibet, Mongolia, Tuva, Kalmykia, and Buryatia. It is also found in Celtic, Kazakh and Chinese symbolism.

The endless knot appears on clay tablets from the Indus Valley civilization (2500 BC)^[1] and on a historic era inscription.^[2] While associated with Dharmic religions, it also appears in Islamic art.^[3][4] It likely was introduced due to trade and other cultural contact with China, the Mongols, and Iran.^[5]

A stylized version of the endless knot is the logo of the Chinese state-owned telecommunications operator China Unicom.

The Knot Atlas is a website, an encyclopedia rather than atlas, dedicated to knot theory. It and its predecessor were created by mathematician Dror Bar-Natan, who maintains the current site with Scott Morrison. According to Schiller, the site contains, “beautiful illustrations and detailed information about knots,” as does KnotPlot.com.^[1] According to the site itself, it is a knot atlas (collection of maps), theory database, knowledge base, and “a home for some computer programs”.^[2]

• Official website
• Morrison, Scott (Aug 20, 2007). “Grepping the Knot Atlas”. Secret Blogging Seminar.

In mathematics, the Eilenberg–Mazur swindle, named after Samuel Eilenberg and Barry Mazur, is a method of proof that involves paradoxical properties of infinite sums. In geometric topology, it was introduced by Mazur^[1][2] and is often called the Mazur swindle. In algebra, it was introduced by Samuel Eilenberg and is known as the Eilenberg swindle or Eilenberg telescope (see telescoping sum).

The Eilenberg–Mazur swindle is similar to the following well known joke “proof” that 1 = 0:

1 = 1 + (−1 + 1) + (−1 + 1) + … = 1 − 1 + 1 − 1 + … = (1 − 1) + (1 − 1) + … = 0

This “proof” is not valid as a claim about real numbers because Grandi’s series 1 − 1 + 1 − 1 + … does not converge, but the analogous argument can be used in some contexts where there is some sort of “addition” defined on some objects for which infinite sums do make sense,
to show that if ${\displaystyle A+B=0}$ then ${\displaystyle A=B=0}$.

In geometric topology, the addition used in the swindle is usually the connected sum of knots or manifolds.

A typical application of the Mazur swindle is the proof that the sum of two non-trivial knots ${\displaystyle A}$ and ${\displaystyle B}$ is non-trivial.^[3] For knots it is possible to take infinite sums by making the knots smaller and smaller, so if ${\displaystyle A+B}$ is trivial then

${\displaystyle A=A+(B+A)+(B+A)+\cdots =(A+B)+(A+B)+\cdots =0}$

so ${\displaystyle A}$ is trivial (and ${\displaystyle B}$ by an analogous argument). The infinite sum of knots is usually a wild knot, not a tame knot. There are many geometric examples of the swindle.^[4]

Oriented ${\displaystyle n}$-manifolds have an addition operation given by connected sum, with identity the ${\displaystyle n}$-sphere. If ${\displaystyle A+B}$ is the ${\displaystyle n}$-sphere, then ${\displaystyle A+B+A+B+\cdots }$ is Euclidean space, so the Mazur swindle shows that the connected sum of ${\displaystyle A}$ and Euclidean space is again Euclidean space. Hence ${\displaystyle A}$ is the one-point compactification of Euclidean space and therefore ${\displaystyle A}$ is homeomorphic to the ${\displaystyle n}$-sphere. (This does not show in the case of smooth manifolds that ${\displaystyle A}$ is diffeomorphic to the ${\displaystyle n}$-sphere, and in some dimensions, such as ${\displaystyle 7}$, there are examples of exotic spheres ${\displaystyle A}$ with inverses that are not diffeomorphic to the standard ${\displaystyle n}$-sphere.)

In algebra the addition used in the swindle is usually the direct sum of modules over a ring.

A typical application of the Eilenberg swindle in algebra is the proof that if ${\displaystyle A}$ is a projective module over a ring ${\displaystyle R}$ then there is a free module ${\displaystyle F}$ with ${\displaystyle A\oplus F\cong F}$.^[5][6] To see this, choose a module ${\displaystyle B}$ such that ${\displaystyle A\oplus B}$ is free, which can be done as ${\displaystyle A}$ is projective, and put

${\displaystyle F=B\oplus A\oplus B\oplus A\oplus B\oplus \cdots }$

so that

${\displaystyle A\oplus F=A\oplus (B\oplus A)\oplus (B\oplus A)\oplus \cdots =(A\oplus B)\oplus (A\oplus B)\oplus \cdots \cong F.}$

For another application of the swindle, recall that finitely-generated free modules over commutative rings have a well-defined natural number as their dimension which is additive under direct sums, and are isomorphic if and only if they have the same dimension.^[7]

This is false for some noncommutative rings, and a counterexample can be constructed using the Eilenberg swindle as follows: let ${\displaystyle X}$ be an abelian group such that ${\displaystyle X\cong X\oplus X}$ (for example the direct sum of an infinite number of copies of any nonzero abelian group), and let ${\displaystyle R}$ be the ring of endomorphisms of ${\displaystyle X}$. Then the left ${\displaystyle R}$-module ${\displaystyle R}$ is isomorphic to the left ${\displaystyle R}$-module ${\displaystyle R\oplus R}$.

As a final interesting example,^[8] if ${\displaystyle A}$ and ${\displaystyle B}$ are any groups then the Eilenberg swindle can be used to construct a ring ${\displaystyle R}$ such that the group rings ${\displaystyle R[A]}$ and ${\displaystyle R[B]}$ are isomorphic rings: take ${\displaystyle R}$ to be the group ring of the restricted direct product of infinitely many copies of ${\displaystyle A\times B}$.

The proof of the Schröder-Bernstein theorem might be seen as antecedent of the Eilenberg–Mazur swindle. In fact, the ideas are quite similar. If there are injections of sets from X to Y and from Y to X, this means that formally we have X = Y + A and Y = X + B for some sets A and B, where + means disjoint union and = means there is a bijection between two sets. Expanding the former with the latter,

X = X + A + B.

In this bijection, let Z consist of those elements of the left hand side that correspond to an element of X on the right hand side. This bijection then expands to the bijection

X = A + B + A + B + ⋯ + Z.

Substituting the right hand side for X in Y = B + X gives the bijection

Y = B + A + B + A + ⋯ + Z.

Switching every adjacent pair B + A yields

Y = A + B + A + B + ⋯ + Z.

Composing the bijection for X with the inverse of the bijection for Y then yields

X = Y.

This argument depended on the bijections A + B = B + A and A + (B + C) = (A + B) + C as well as the well-definedness of infinite disjoint union.

• Exposition by Terence Tao on Mazur’s swindle in topology

The Ashley Book of Knots

Cover illustration by George Giguere shows a sailor displaying a Tom fool’s knot
Author	Clifford W. Ashley
Illustrator	Clifford W. Ashley
Cover artist	George Giguere
Language	English
Subject	Knots
Genre	Reference work
Publisher	Doubleday
Publication date	1944
Publication place	United States
Pages	638
ISBN	0-385-04025-3

The Ashley Book of Knots (ABoK) is an encyclopedia of knots written and illustrated by the American sailor and artist Clifford W. Ashley. First published in 1944, it was the culmination of over 11 years of work. The book contains 3,857 numbered entries and approximately 7,000 illustrations.^[1] The entries include knot instructions, uses, and some histories, categorized by type or function. It remains one of the most important and comprehensive books on knots.

Due to its scope and wide availability, The Ashley Book of Knots has become a significant reference work in the field of knotting. The numbers Ashley assigned to each knot can be used to unambiguously identify them. This helps to identify knots despite local colloquialisms or identification changes. Citations to Ashley numbers are usually in the form: “The Constrictor Knot (ABoK #1249)”, “ABoK #1249”, or even simply “#1249” if the context of the reference is clear or already established.^[2]

Some knots have more than one Ashley number due to having multiple uses or forms. For example, the main entry for #1249 is in the chapter on binding knots but it is also listed as #176 in a chapter on occupational knot usage.

The Ashley Book of Knots was compiled and first published before the introduction of synthetic fiber ropes, during a time when natural fiber cordage – typically twisted, laid, or braided rope – was most commonly used. The commentary on some knots may fail to address their behavior when tied with modern synthetic fiber or kernmantle style ropes.

In the first edition, three entries have non-integer numbers: 794.5,  1034.5,  2585.5. 
Also, entry number 2545 contains no knot, reading only “This knot was mislaid”.^[1]

Ashley suffered a debilitating stroke the year after the book was published.^[3] He was not able to produce an erratum nor oversee a corrected edition.

In 1979, at least one knot was added, the Hunter’s bend (#1425A).^[4]

In 1991, corrections submitted by the International Guild of Knot Tyers were incorporated.^[5][6] The original list of revisions submitted to the publisher is believed to have been lost, but many had been collected from a series of articles in Knotting Matters, the Guild’s quarterly publication.^[7][8] Additional errors have been identified since the 1991 corrections.^[9]

The Ashley Book of Knots is quoted extensively in the novel The Shipping News (1993) by E. Annie Proulx, with its descriptions and illustrations of various knots providing the chapter headings. In the novel’s acknowledgements, Proulx writes that “without the inspiration of Clifford W. Ashley’s wonderful 1944 work, The Ashley Book of Knots, which I had the good fortune to find at a yard sale for a quarter, this book would have remained just a thread of an idea.”

• Clifford W. Ashley. The Ashley Book of Knots. Doubleday, New York 1944. ISBN 0-385-04025-3
• Reprint: Doubleday, New York 1963–1979, ISBN 0-571-09659-X
• Reprint with amendment of Geoffrey Budworth: The Ashley Book of Knots. With amendments of Geoffrey Budworth. Doubleday, New York 1993.

• The Ashley Book of Knots on Internet Archive.
• Thou Shalt Knot: Clifford W. Ashley. A New Bedford Whaling Museum exhibition