If you really want to understand how a chiralkine system works, release your inner child and buy two Winkel toys supplied by The Manhattan Toy Company! These teething toys for babies embody all of the features of a chiralkine system. Babies cut their teeth on quaternion mathematics using these fantastic toys, then the adult-run educational system takes over and all of the wonderful teaching inherent in the design of these toys is lost. The whole global economy could run on Winkel toys instead of weighing scales, and would probably run a whole lot better!
Each face of the Winkel is connected to its opposite face through four coloured tubes, the ends of which can be distinguished as + and -. If one face is coded – + – + the other is coded + – + -. Each pair of faces is distinguished from the others by the order of red, yellow, green and blue turning clockwise (one side) and anticlockwise (other side). It is the same as if the order of red, yellow, green and blue is unchanging, but the signs sort. In that case instead of always having the signs in order – + – + and + – + -, opposed sides (representing relationship states) can now be coded – + – + and + – + -; – + + – and + – – +; and – – + + and + + – -.
Two Winkels can represent all of the possible relationship states for two people and a resource, one representing the buyer’s side and one representing the seller’s side. An array of Winkels can be used as a clearinghouse for exchange of goods and services that can function as a marketplace, but without using money. “Who Gets What and Why, The Hidden World of Matchmaking and Market Design” by Alvin E. Roth, Winner of the Nobel Prize for Economics, published in 2015 in the UK by William Collins, British Library catalogue ISBN 978-0-00-752076-3.
A pair of Winkels is to a ciralkine system as a pair of scales is to the financial system. The invention of chiralkine (left- and right-handed money) solves the double co-incidence of wants problem solved by money, but it does it in a new way. Everyone exchanges their offers and wants in balance, but the coloured tubes of the Winkel pairs keep everyone’s interests connected together throughout their cycles of exchange, so nobody needs to exchange anything for an imaginary store of value: nobody needs money.