This meant that physicists, such as peter guthrie tait, tried to create a table of the elements corresponding to a classi. Magnetic nanoknots evoke lord kelvins vortex theory of atoms. In the 19th century, lord kelvin made the inspired guess that elements are knots in the ether. A knot invariant is a mapping from a knot or a picture of a knot to an output via a set of rules. In 1997, faddeev and niemi suggested that knots might exist as stable soliton solution in a simple three dimensional classical field theory. During the 1860s, the scientific world was divided into two groups. Hydrogen would be one kind of knot, oxygen a different kind of knot. In the 1860s, lord kelvin s theory that atoms were knots in the aether led to peter guthrie taits creation of the first knot tables for complete classification. Peter guthrie tait scottish mathematician and physicist. Lord kelvin, in an attempt to reconcile several competing. In the latter part of the 20th century there was a renewed interest in knot theory. The ideas used in this chapter can be found in most introductory books or courses on. After watching one of these experiments, william thomson, later lord kelvin, concluded that.
Aug 15, 2019 in the 1860s, lord kelvin s theory that atoms were knots in the aether led to peter guthrie taits creation of the first knot tables for complete classification. Scottish physics and knot theorys odd origins introduction. The efforts of thomson and tait gave rise to knot theory, today. A mathematicians knot is the same as the one you might tie in a piece of string, but with the ends of the string. The basic question one asks in knot theory is, given two knots how to know if they are the same knot or not. Hydrogen would be one kind of knot, oxygen a different kind of knot and so forth throughout the.
Lord kelvin kinetic theory of the dissipation of energy. Now we know that periodic table looks di erent, but knots are still important for. In mathematical terminology we say that a knot1 is an embedding of s1 a circle in r3 that does not intersect itself. Although these do have a signi cant in uence on elementary knot theory, via unknotting number. He became lord kelvin, or more precisely, baron kelvin of largs, 26 years later. Three dimensions of knot coloring university of south. More than a century ago, lord kelvin propounded his celebrated \vortex atom theory, which asserted that atoms are made of vortex knots in the aether 1. A brief survey of the vast field of knot theory is given in this final report named knot theory. While knot theory is now considered a branch of topology, it originated not in mathematics but in chemistry. However topologists continued to study the knot theory as an area of pure mathematics. Hyperbolic geometry on the figureeight knot complement alexander j. Devising the absolute temperature scale, now called the kelvin scale formulating the second law of thermodynamics. In 1867 lord kelvin 1 proposed that atoms, which at the time were considered as elementary particles, are knotted vortex tubes in ether.
A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Knot theory this chapter looks at some of the fundamental building blocks of knot theory. Illustrations of knots and links, including a trefoil knot, top left, in an 1869 paper by lord kelvin on his knotted vortex theory of. At the university of glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to. Reidemeister and alexander around about 1930 were able to make signi cant progress in knot theory. What properties of knots lead lord kelvin to hypothesize that. In the late 1800s lord kelvin suggested that atoms might represent knots in the ether, with di erent elements corresponding to di erent types of knots. Even though this concept did not stand the test of time, the investigations of kelvin and tait led to a new branch of mathematics knot theory. The kelvin necktie knot is named after lord kelvin william thomson, 18241907 a mathematical physicist who contributed to the theory of knots in relation to atomic structure. He is best known for the mathematical physics textbook treatise on natural philosophy, which he cowrote with kelvin, and his early investigations into knot theory.
Lord kelvin and tait, inspired by experiments of helmholtz, theorized that atoms were knotted tubes of aether, distinguished by their. Later, listing stated that the figure eight knot and its mirror image are equivalent, or amphichiral. Chemical elements would thus correspond to knots and links. Knot theory was rst proposed as the awed vortex model of atoms by lord kelvin, but was later proved to be incorrect. This is all a realization of this dream of understanding fluids in terms of the knots and links of the streamlines, said randy kamien, a professor of physics and astronomy at the university of pennsylvania. This forms a continuous loop which cannot be undone by manipulation. Kinetic theory of the dissipation of energy by sir william thomson lord kelvin nature, april 9, 1874, pp. The history of knot theory and physics has a deep roots. Ams short course lecture notes introductory survey. Khovanov homology and torus knots uc davis mathematics. Lord kelvin s theory of the atom stated that chemical properties of elements were related to knotting that occurs between atoms, implying that insights into chemistry would be gained with an understanding of knots. The origins of modern knot theory, however, stem from a suggestion by the scottish mathematicianphysicist william thomson lord kelvin in 1869 that atoms might consist of knotted vortex tubes of the ether, with different elements corresponding to different knots. Ive often heard that lord kelvin was one of the first people to study knot theory, as he hypothesized that atoms were knots in the ether. Once this idea was shown to be false, knot theory remained as a beautiful mathematical theory in its own right.
A classic example of this is the development of knot theory. Torus knots and links from eikonal equations and knot. Inspired by lord kelvins vortex theory of the atom 59, the scottish physicist p. For about 20 years his theory was taken seriously, and motivated an extensive study of knots. Included are reprints of the work of lord kelvin sir william thomson on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in. Knot theory project gutenberg selfpublishing ebooks. Although this idea turned out to be completely wrong, it ushered in modern knot theory, which today is used in various areas of. Peter guthrie tait frse 28 april 1831 4 july 1901 was a scottish mathematical physicist and early pioneer in thermodynamics.
Knots and applications series on knots and everything. Knot theory has since become a central subject in topology and began to undertake important roles in diverse elds of sciences. In 1858, he invented the mirror galvanometer knot theory s odd origins the modern study of knots grew out an attempt by three 19thcentury scottish physicists to apply knot theory to fundamental questions about the universe daniel s. His work on knot theory contributed to the eventual formation of topology as a mathematical discipline. Tait set out to systematically enumerate knots based on their crossing number. Knot theory as we know it today started in 1867, when the physicist william thomson, now known as lord kelvin, came up with his vortex theory, according to which atoms could be explained as knots in the ether background of the universe.
We have also avoided 4dimensional questions, such as the sliceribbon conjecture problem 1. In this chapter, we briefly explain some elementary foundations of knot theory. This theory of the ether was thoroughly debunked by. The work of thomson knot theory was attracting the attention of physicists as well as mathematicians. Neither can taits dubious efforts to defend christianity with an.
Although the subject matter of knot theory is familiar to everyone and its problems are easily stated, arising not only in many branches of mathematics but also in such diverse. This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Lord kelvin william thomson was an eminent physicist with a wide range of interests and enthusiasms. Maxwells theory of solid angle and the construction of. To demonstrate how knot invariants work, we will use the example of the kau man invariant2. The first steps toward a mathematical theory of knots were taken about 1800 by the german mathematician carl friedrich gauss. Vandermonde which included the topological properties of knots. Two knots are regarded as the same if one can be smoothly deformed into the other. Nov 10, 2011 in the 19th century, lord kelvin made the inspired guess that elements are knots in the ether. The periodic motion of flexible knots, and the connection.
Like the simple knot, the kelvin starts with the tie lying inside out resulting in an inverted tail. In the 1860s, lord kelvins theory that atoms were knots in the aether led to peter guthrie taits creation. Lord kelvins theory of the atom stated that chemical properties of elements were. During the later 1800s, when lord kelvin and his physicist cronies were speculating on the nature of the universe, they hypothesized that perhaps atoms corresponded to knots in the ether, the mysterious. The theory of kelvin was later replaced by other theories about the nature of our basic matter and the theory of knots was put on the shelf. As each branch resembles, both geometrically and electrically, lord kelvins rc model of the transatlantic telegraph cable, the mathematical study of dendritic branches has come to be called cable theory. James clerk maxwell, william thompson lord kelvin and peter tait. The rules must be cooked up in such a way that two topologically equivalent knots give the same output. Sir william thomson, 1st baron kelvin, om, gcvo, pc, prs, frse 26 june 1824 17 december 1907 was an irishscottish of ulster scots heritage mathematical physicist and engineer who was born in belfast in 1824.
Relaxing our axioms, as virtual knot theory demands, mightjustbringthatdaycloser. The study of mathematical theory of knots as now referred to as knot theory can be traced back to the 19th century when the german mathematician, carl friedrich gauss created a method for tabulation of knots. The histories of the two subjects were clearly intertwined. A very brief summary of the history of knot theory 1880s. A reidemeister move is an operation that can be performed on the diagram of a knot whithout altering the corresponding knot. Tait, in 1885, published a table of knots with up to ten crossings, and what came to be known as the tait conjectures. Guthrie tait were responsible for modern knot theory. Knot theory was started in the 1860s by peter guthrie tait, a scottish mathematician, who endeavored to make a list of topologically distinct knots in response to a request by william thompson later lord kelvin. A conjecture by lord kelvin that atoms were knots in the aether led to a renewed interest in the studies of knots.
A knot is a circle smoothly embedded in 3dimensional euclidean space or its compacti cation, the 3sphere. Lord kelvin biography science hall of fame national. As each branch resembles, both geometrically and electrically, lord kelvin s rc model of the transatlantic telegraph cable, the mathematical study of dendritic branches has come to be called cable theory. Tait published the first in a series of papers addressing the enumeration of knots. Knots have been used for basic purposes such as recording information, fastening and tying objects together, for thousands of years. William thomson lord kelvin 1824 1907 team webpage report by tom woolman, terri nicholson, marco allain history of geology go521 spring semester, 20 there cannot be a greater mistake than that of looking superciliously upon the practical applications of science. A brief history of knot theory while knot theory is now considered a branch of topology, it originated not in mathematics but in chemistry. The electrical analogy to kelvin however only holds in the subthreshold, in fact passive, regime. Knots, electrostatic knots, minimum energy knots, vortices, gauge theory. The origin of modern knot theory should be associated with four physicists. Three dimensions of knot coloring university of south alabama. Lord kelvin conjectured that atoms might actually be. This theory inspired the celebrated scottish physicist peter tait to undertake an extensive study and tabulation of knots in collaboration with c. Some fundamental theorems of involved in knot theory include one involving reidemeister moves transforming knots into unknots and knot.
While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined together so that it cannot be undone, the simplest knot being a ring or unknot. Although knots have a long history in celtic and islamic art, sailing etc. The physicist sir william thomson also known as lord. The rst mathematical study of knots was done by alexander t. Rather it is to try to understand the beliefs and bold expectations that motivated thomson and tait. I assume that he had some compelling evidence for this fact. In topology, knot theory is the study of mathematical knots. Topological quantum field theories a meeting ground for.
Although kelvin s theory was eventually rejected along with ether, knot theory continued to develop as a purely mathematical theory for about 100 years. Alexander introduced algebraic methods into the theory, and the rst book about knots, knotentheorie was published by k. Indeed lord kelvin would have wanted to develop a new theory of gasses, theory of elastic solids and liquids based on the dynamics of these vortex atoms a programme he did not complete nor was considered by 5. Knot theory is the embedding of one topological space into another topological space. This idea led peter guthrie tait to prepare meticulous and quite beautiful tables of knots. Lord kelvin william thomson, 18241907 claimed that atoms knots made of ether. Thomson lord kelvin released his paper on vortex atoms. One of the first times knot theory appeared as a subject of scientific study was in 1860. It was believed that a substance called ether filled all of space. By the early 1900s, kelvin s theory had been proven wrong. The results obtained at the time by tait 2 remain a classic contribution to mathematical knot theory 3. The first chapter introduces the path which led to the study of the mathematical theory of knots and a brief history of the subject with the relevance of research in it. Hydrogen would be one kind of knot, oxygen a different kind of knotand so forth throughout the periodic table of elements. The perko pair listed as different knots since 19th century, found to be the same by perko in 1974.
The early, significant stimulus in knot theory would arrive later with sir william thomson lord kelvin and his. Hyperbolic geometry on the figureeight knot complement. It started by lord kelvin, in 1867, when he conjectured that atoms were knotted vortex tubes of ether. Knot theory was attracting the attention of physicists as well as mathematicians.
The most prominent of these was english physicist, sir william thomson lord kelvin 18241907. Listed as different knots since 19th century, found to be. Origins of knot theory in 1867, lord kelvin conjectured that atoms were knotted tubes of ether and the variety of knots were thought to mirror the variety of chemical elements. Tricolorability of knots massachusetts institute of. So students were able to see the point of the course. Working to install telegraph cables under the atlantic. On vortex atoms by lord kelvin sir william thomson proceedings of the royal society of edinburgh, vol. What properties of knots did lord kelvin consider similar to atomic properties. The mathematical theory of knots emerged from the smoky ruins of lord kelvin s \vortex atom theory, a hopelessly optimistic theory of matter of the nineteenth century in which atoms appeared as microscopic vortices of. Gauss applied the mathematical concept of knots for his work in electro dynamics.
Knot theory was a respectable if not very dynamic branch of topology until the discovery of the jones polynomial 1984 and its connections with physics speci cally, quantum eld theory, via the work of witten. Finally, we discuss computational implementation of the formulae derived, with c code provided, and give illustrations for how the. Scottish physics and knot theorys odd origins university of south. Gutierrez mat 598 final report arizona state university, fall 2012 1 introduction and history the exact relationship between knot theory and noneuclidean geometry was a puzzle that survived more than 100 years. One publication, journal of knot theory and its rami. Some of the material will be used later in this report, while some is included simply to give an idea of di erent techniques used in knot theory. Lord kelvin and peter guthrie tait were responsible for modern knot theory. Near the end of the nineteenth century, lord kelvin suggested.
In 1858, he invented the mirror galvanometer knot theorys odd origins the modern study of knots grew out an attempt by three 19thcentury scottish physicists to apply knot theory to fundamental questions about the universe daniel s. Knot theory may seem to stand alone as a eld of study, but it has strong. Knot theory and its applications occidental college. Silver, dan 2006, knot theorys odd origins pdf, american scientist, 94 2, pp. By 1970, knot theory had become a welldeveloped area of topology 7. Unfortunately, the same cant be said of thomson and taits theory of atoms as knots in the ether, which never really got off the ground. The advantage i found in teaching knot theory, as against say homology theory, was that the basic problems could be stated at the beginning, and some methods were given, relating as said above to other nice mathematics, for some measure of solution. What properties of knots lead lord kelvin to hypothesize. In 1867 lord kelvin then known as william thomson witnessed a demonstration of a machine that could produce smoke rings. Inspired by helmholtzs work on vortex motion, thomson theorised that matter was composed of vortex atoms or 3dimensional knotted tubes of ether 25, p. Jun 23, 2017 magnetic nanoknots evoke lord kelvin s vortex theory of atoms. During the later 1800s, when lord kelvin and his physicist. Atoms could thus be classi ed by theknotsthat they resembled, with di erent. Maxwells theory of solid angle and the construction of knotted fields.
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