Boolean Algebra and the Yi Jing - Technical Glossary

Boolean Algebra and the Yi Jing

6. Technical Glossary

In this section I shall offer some concise definitions of some of the technical terms used in the body of the essay. Readers who require a more involved explanation are referred to Wiitala [Wii87] for general material on Boolean algebra and partial orders, and to Davey and Priestly [D&P90] for more detailed material on lattices.

Bit -- binary digit. The smallest unit capable of conveying information. A bit always and only takes the value of either 1, or 0. In this context we take 1 as being yang and 0 as being yin. Thus, for example, a trigram is composed of three bits.
Boolean algebra. A mathematical structure that provides a formal interpretation of the logical operator denotes by the terms not, or and and. Set theory is a typical example of a Boolean algebra, as are the bit-wise operators from computer programming used in this essay.
HTML -- Hypertext Markup Language. The particular language for representing hypertext relationships in documents that has become dominant on the Internet.
Hypertext. The technique of linking documents together through active cross-references such that following a cross-reference takes you directly to the document where the reference is defined.
Lattice. A structure defined by a partial order where the points in the structure are connected by lines, and being connected by a line means that the higher element is "greater" than the lower element. The lattice will often have a top element which is greater than any other element in the set, and a corresponding bottom element which is less than any other element in the set.
Modulo arithmetic. Essentially "clock" arithmetic. Consider the face of a clock: if you add 3 to 10 you get back to 1, if you subtract 5 from 2 you get to 9. This is arithmetic modulo 12, but in principle any modulo factor could be used.
Partial order. A way of providing an order for a set of elements such that some elements may not be either greater or less than each other, hence the ordering is not total. Consider the trigrams ordered by degree of yangness. Clearly 101 has more yang than 100, but both 101 and 110 have the same amount of yang so neither is greater or less than the other.
Schemata. A term used in certain cognitive theories about the mental representation of events and situations. They are data structures for representing both generic and specific concepts about the outside world.
Total order. A way of providing an order for a set of elements such that every element is either greater than or less than any other element in the set. The natural numbers ...-3,-2,-1,0,1,2,3... are the most straightforward example of a totally ordered set.

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