Knot theory Knottiness Cat’s cradle Gordian Knot Commentary

Alexandre-Théophile Vandermonde, Peter Guthrie Tait mathematics

Knot theory

• A cord may be wound around itself
• and after its two ends are fused together
• it will stay tied.
• The question arose as to how
• closed loops like this
• were to be related or distinguished.
• To Vandermonde, a knot
• was like the path of a knight in chess
• as it covers the board without repeating.
• To Lord Kelvin, an atom
• was a knot of aether tied to itself,
• which is both interesting and wrong.
• And this got Peter Guthrie Tait
• to classify all possible knots,
• at least up to ten crossings.

Knottiness

• The minimum number of crossings
• is a particular knot’s knottiness—counted
• after undoing any nugatory crossings.

Cat’s cradle

• Let me show you how to make
• a manger for feeding cows
• from a loop of string.
• Thread it through
• the fingers of your two hands
• and let me take the string from you.

Gordian Knot

• To untangle a mess of yarn,
• it is not permissible to cut it.
• However, one reason
• problems remain unsolved
• and poems remain unwritten
• is a desire to obey the rules.