(subfile 6.5: musical and positional information)

A musical event (one of those objects represented by the ‘word’ data-structure in this program) is inevitably very much simpler than a linguistic word, often involving no more axes than “pitch” and “rhythmic symbol”. In conversation, physical locations for locomotion are seldom expressed  as coordinates on a map (we are prone to saying things like “I would like to sit in the comfy chair” rather than things like “I would like to sit down 4.3 meters from the North wall”) but they are always simpler than definitions of English words. For some applications, a Cartesian grid is used, but for such worlds as the now ubiquitous A.I. “blocks world”, designations such as “next to” are more useful. It is of fundamental importance to these applications that the reader be ready to consider “next-to-ness” to be equivalent in complexity to “near-ness”, which is Cartesian distance: that is, an inexact, conversational description can provide a value on an axis (in this case, the “am I next to?” axis) just as readily as can a distance on a rectangular grid.

(subfile #6.75: properties of axes)

The axis properties currently in use are group, persistence, role, value style, mass, angles, compatibilities, single associated words such as question words and comparison words, and scalar constants such as level.

These properties are variously stored as
     1) files listing values for every pair of axes (angles between axes and compatibility among them)
     2)  information in axis-word-objects, or
     3) as elements of the axis' definition (properties held in a file, separate from the word-objects).

Each axis can to some extent be defined by others; such definitions look exactly like definitions of words, and consequently, can be interpreted as themselves having a location in the word-space. These axis-word-objects are not complete definitions (unless you subscribe to the idea that all human knowledge is a matter of circular definitions).

group - Axes are assigned to a single group (currently there are 28) for the convenience of the human programmer; this is useful even though many axes end up being used in a variety of ways. Examples are "physical, social, or abstract properties" or "data-structure housekeeping" or "axis-defining axes". An example of group-to-group crossover would be the physical property "large" can have a useful interpretation in areas not relating to physical size. It may prove useful eventually to provide each axis with a list of values representing how often, or how well, that axis is used as a member of the group.

persistence - Some data is temporary, some permanent. Temporary-ness arises primarily from context-activation of axis subsets (see "context-controlled axis activation", p.5) and from the need for older data to decay out of the Big Buffer (p.25), both which see.

role - Some axes do not participate in the location of objects in MS. This includes the substantial number of "housekeeping" axes that organize information in word-objects, such as ID numbers or english word forms.

value style - the values associated with axes may represent
    1) scalar values from 0 to 100 ( for concepts such as speed, redness, pitch, etc.),
    2) ID numbers of other objects, or
    3) short strings (for lists of objects in a group, such as the arithmetic operators 'add', subtract', etc).

An example of type three is the axis that holds the value style for an axis. The values that axis can assume currently include the three listed here, abbreviated in short strings indexed as values 1,2, and 3.

mass - Certain MS calculations have a parameter conceptually similar to physical mass or to the particle physicist's quantity "cross-section". For example, a piece of apple can have a variety of sizes, shapes, ages, etc., but always remains a physical object (that is, for instance, visible, palpable, etc.). There is a need for a quantity that records the flexibility of values along each axis that an object may assume (in this case, the  piece of apple would be said to have values along "physical object" axes that are given a high mass - meaning they are hard to change - and a shape-axis mass that is very low - meaning that the shape of the piece is easily changed or is seldom relevant.)

anglefiles - Each axis is associated with a file of values representing the angles between it and all other axes. This type of relationship is limited to the question: does a change in the value on one axis necessitate a change in the value of the other?

compatibility files - Comparable to the anglefiles are sets of values that define the compatibility of pairs of axes. For instance, something that has the property "density" will rarely have a value on the axis that records the extent to which something is intentional or accidental. There is a statistical way to extract this information from conversation – it need not be entered by the programmer.

levels - Each axis, upon its initial entry into the database, is given a value corresponding to the programmer's subjective impression of the "age" at which the program should first be allowed to use the axis (hence this axis' name is "piaget".) For example, "color" might be quite early while "topological dimension" would be quite late. This allows the axes themselves to contribute to the structure of the total learning process, starting with simple concepts and gradually adding complexity.

A second type of level has a value for each axis that is proportional to the number of other axes necessary to define the target axis. For example, "physical size" is a simple - nearly monaxial - idea, while "disorder" is so complex as to require concepts from thermodynamics.

All axes are also provided with three other objects:

A question-word is that word or phrase that by default allows for a linguistic query about that axis' value. For example, a "wealth" axis might have the question word "how-rich".

A comparison-word is similar but is used to characterize verbally the relation among values along the axis; this is for words like "bigger" with the "size" axis.

verb/procedure - One important aspect of many things we call a 'property' is the association of such ideas with specific modes of change - ideas often communicated by verb forms. Thus "size" is associated with "growth" or "shrinkage" and "taste" with "sweetening" or "smoking". Since everything this algorithm ever does exists as a word-object made of axes, it is natural to use the verbs associated with axis definitions as fundamental or primitive behaviors (see "Great Wall o' Daemons").

(subfile #9: How complex are definitions, complexity of coordinates)

Since the axes used in defining words relate to different words in different ways, it might appear that the individual coordinates are themselves somewhat more complex than familiar 3-d spatial ones. This is a detail of the definition of the space, however, since the axis “red” can be replaced by several axes whose definitions are “red as a property”, “red as a frequency”, “red as an aesthetic value”, etc.