Number

The factor glyphs begin with zero and one, a circle and a vertical line. These are special cases as these numbers do not take part in factorization. Two is a straight horizontal line. Three is a curve. Four is the first factored number, made of two times two, two straight lines joined. Five is a spiral. Six is the curve of three joined to the straight line of two. Seven and all subsequent primes are formed by taking the glyph of the previous number, shifting the final line to a diagonal, and making a cross mark. When there are multiple such cross marks they are joined in an arc, primarily for aesthetics.

The relationships between the numbers are readily apparent because these glyphs are constructed procedurally from the factorization. This aids in intuitive association.

The sequence glyphs are used to order things which occur in a sequence but which are not necessarily comparable in a sense of magnitude. This second set of symbols is particularly useful when numbering paths, which will have one number given by its emanation order and a second number given by its sequence in the fool’s journey.

The form of the sequence glyphs is formed first by the same initial forms as the factor glyphs. Starting at five the pattern emerges of dot, line, arc indicating the base glyph plus one, two or three. Twelve is formed as a merging of glyphs for eight and four. Twenty is formed from sixteen and four. Twenty-four is formed from sixteen and eight. Twenty-eight is formed from sixteen, eight, and four.

In addition to the glyph sets each number is also given a pronunciation. Like the glyphs these pronunciations allow for a fresh encounter with the idea of number. The pronunciations are based on the spoken sounds in English ordered systematically by a number of rules to bring out the relationships between the numbers. The rules themselves are not important other than that they build phonetic associations to help us intuitively identify relationships.

The pronunciations are paired in a cycle where the initial and final sounds of each are paired. Zero and sixteen are their own opposite. For the mathematically inclined, you might note that this pairing follows a two’s complement of five-digit binary representation of each number. In normal binary notation this matches each number one to fifteen with its negative.

Consonant sounds are arranged in voiced and unvoiced pairs such as the sounds of “d” and “t”. These are then paired with primes such that the unvoiced consonant is the initial sound of the prime, and the voiced consonant is is assigned as the initial sound of the preceding composite number. The ordering of the vowels and remaining consonants is the result of aesthetic choice following much experimentation.

Pronunciation is given in both English pronunciation (enPR) and International Phonetic Alphabet (IPA). An exception is the dotted “ṙ”, which is used for the trilled “r” such as in Spanish. The modified enPR notation will be used in naming throughout this work. Note that enPR uses italic “𝑡ℎ” for the voiced sound as in “they” while “th” is unvoiced as in “with”.

In various ways these pronunciations will be mixed and mutated to give systematic names to each path and sphere.