Dr

(you may click the number of the subfile to be viewed, or scroll down)

This file contains the following subfiles:

12 - quantifying angular relations among axes
12.25 - details of other relationships between axes
12.28 - operator mediated relations - again
12.29 - initial levels of discourse, ranking of axes, and ranking of words
12.5 - distances in MS
13 - representation of clouds in real memory

(subfile 12: angular relations among axes)

Common vector arithmetic suggests that axes that are completely unrelated ( say, “color” and “manufacturability” ) exist at right angles to each other, while those which are related ( say, “color” and “redness”) would exist at lesser angles. Just as momentum along the x axis need not effect that along the (orthogonal) y axis, a change in the “color” value in a definition implies no change in the value for “manufacturability”, and vice versa. A completely different situation exists with regard to “red” and “color”, however: a change in the “color” information in a definition could very easily imply a change in the value for “red” - thus these two axes do not enjoy the independence of axes at right angles, and computation involving them is analogous to that performed in simple physics problems in which motions are decomposed into orthogonal components.

Even everyday calculations (like distance) are inconvenient and moderately disgusting in a space with non-orthogonal axes, but it is not particularly complicated. Some examples are presented in the appendices.

(subfile 12.25: other relationships between axes)

    = Measures of similarity

There are various ways for axes to be more or less "similar".

    1) Comparisons can be made between the elements of their definitions or between the pattern of angles formed with other axes - these two types of comparisons deal with the axis' location in MS.

    2) Another type of relation has to do with common axis-definition elements or MS regions: what are the details of elements common to two axes, or what regions in MS are surrounded in common?

    3) Finally, comparisons can be made by enumerating the uses of an axis - those objects in which it appears - and then comparing the groups of objects obtained.

= Distances between axis-words

Part of an axis' definition uses the word data-structure, and consequently the axis definitions exist as points in MS. This curious circularity is shallower than might at first appear, because different parts of an axis’ definition are present in different bodies of information. An axis exists because of the items it defines, and as an item itself (defined in the same way as are the items it is used for), and as a geometrical object in MS. There is thus an MS distance between the axis-definition-word-objects, and this distance expresses a relation separate from the angular one. For instance, the "color" and "mass" axes are orthogonal, since one can easily imagine objects of any mass having any color. But "color" and "originality" are also orthogonal, and they have a relationship much more distant than "color" and "mass", both of which are simple properties of physical objects. This more distant relationship is reflected in the distance between the word-objects that define the axes. But the line from the origin in MS through the point that defines the axis-word-object is itself yet another axis. Ideally it would be the same as the axis itself, but that would require that MS be somehow “real” when in fact it is just a way to structure completely circular definitions inside a computer.

     = Various frequencies

Certain axes appear most frequently as origins of pointers (e.g., "greenness" almost always points at a physical-object axis). Therefore we can form a single group: all of the axes that ever serve as destinations of these pointers. This group can be characterized or compared with groups serving other axes; these groups are like parts-of-speech, since the presence of these pointers indicates some sort of similarity in function among the grouped words.

Different axes are destinations of pointers different numbers of times - this simplest mode of comparison is frequency of occurrence. Frequency of juxtaposition is somewhat more complicated. Axes do not necessarily appear in any particular order in objects' definitions; this is another way of saying that adjacency in axis lists is not relevant to anything. (It is useful to know if a pair of axes never appear together in a word-object - see below.) Fortunately the 'frequency of occurrence together' is just the inverse of the incompatibility matrix calculated elsewhere (subfile 41).

    = Operator-mediated associations

This type of relation cannot be explained without resort to several as-yet-undefined types of objects. Please read subfile #12.28 after getting through chapter 9.


= Tuple-associations

These relations arise naturally from the Purr-Puss way of thinking, and are extremely simple and efficient both to store and retrieve. (see subfile 62.4 and p. 27)

        1) Start with object A.

        2) Through any function, discover that A is associated with B or with some "tuple" BC, BCD, etc.
(The simplest such function is adjacency, but the program can use any of its ways of getting from A to B)

        3) Form the sum or concatenation of A and the associated tuple; that is, make them into one object.

        4) Measure the consistency of associations with this sum. That is, execute the program's various association-memory-retrieval methods, seeing what associations exist with the summed object, and examine the result.

If the sum points to just a few objects (that is, if there are only a few associations), and points to them a lot (that is, many conversational instances of the association are remembered), then the relation between A and the B-tuple is stronger. ("Points to" in this sentence uses exactly the same flexible set of possible functions as in step 2.)

For example, suppose that in conversation, the phrases "to go to school" and "to go to Mars" have appeared. The first phrase will have happened much more often, and will therefore have more links. In the absence of a context-activation of "outer-space" or "exaggeration" this fact would enhance the likelihood of using, in everyday thought, the first phrase over the second. This is no surprise: school is a place lots of us go, and Mars isn't. Going to Mars should only come up if very specific, special contexts are present.

= Compatibility

Certain axes are mutually incompatible, and these pairs are stored in exactly the same way as the inter-axis angles. This incompatibility can be found by a crawler (see subfile 11.75) as soon as all word definitions have been entered; therefore, this part of the data-base does not depend on conversation for its formation.

This type of relation can also be expanded to –tuples, but we find ourselves then in the exponential growth situation. This makes the parallel-processed crawler of the utmost importance, and, since the process requires no input, it could proceed continuously on a separate machine.

    = Partnership

Whenever a daemon or a pointer uses more than one axis as arguments, the pairs present are stored with "partner" bombs between them. These are bi-directional bombs, so that the appearance of either axis in a splash of data will bring up an association-link to the other.

These links help provide the side-contexts so essential in conversation. For example, a discussion of "current" will often involve involve a discussion of "voltage". Consequently the program needs to have the "voltage" frame handier, during a "current" discussion, than it would be during a "color" discussion. Such readily available numerical rankings of relevance are essential to keep a conversation flexibly on track, while allowing related concepts to float nearby. Cf. Minsky's argument that the reason humans appear to be able to recall so much in a blinding instant is that they already have relevant default contexts available - we don't so much "remember a lot of stuff real fast" as we "efficiently and unconsciously predict what's going to be involved", the moment a subject is introduced.

= Operator-mediated associations

This type of relation cannot be explained without resort to several as-yet-undefined types of objects. Please read subfile #12.28 after getting through chapter 9.

Subfile # 12.28 = Operator-mediated associations - again

Since all the objects in this program exist in MS and have the same data-structure, all of the operations available to one level are available to the others. The idea of "bombs" discussed elsewhere is usable by single axes, as well as by words. For example, suppose that the program hears a number of sentences of the form "<plural noun> are <adjective>". It is always desirable to know that the structures available to the program are capable of extracting useful information from such collections (information that is not explicitly asserted), and this example suggests a route via which operator bombs could participate. For the purposes of this example, all that's necessary is to know that an "operator bomb" is a pointer associated with an operator such as "must precede" or "is a member of".

We wish to demonstrate that a useful relationship between two axes can be derived from conversation alone (that is, without direct teaching of the relationship), and that such a derivation can be brought about using operator-mediated associations. I will work towards one of the objects corresponding to the template above, namely "physical objects are colored". "To the extent that something is a physical object" is one axis, and "color" is another, while the mediating operator is "has the property of".

The following steps must be plausible for this relationship to be establish-able from conversation:
    1) "are" must be found to signify "is a property of"
    2) an example of "plural noun" must point at, and select, the concept   "physical objects"
    3) an example of "adjective"    must point at, and select, the concept   "color"

First,

- all nouns will be associated with a large number of i.p.o. ("is a property of") bombs
    (that is, most nouns have a number of properties, stored as i.p.o. bombs)

These bombs would already be available, directly from these words, via an associative mechanism "vibration". (Why this is a useful image is not important for this example.)

- all adjectives are also associated with many such bombs (this is true because an adjective is fundamentally an object that forms the 'subject' for the phrase "is a property of")

The vibrational association of both a noun and an adjective to the same i.p.o. bomb constitutes a third kind of association, convenient to think of as a "resonance". As it happens (it's tautological!) an object formed by combining all such resonant pairs yields the template for a generalized i.p.o. bomb. (Combination in this sense is simply using an exclusive-or operation on the sets of axes in the words in a pair.) Thus from conversational associations with nouns and adjectives there is a direct route to the bomb i.p.o. operator.

The i.p.o. pointer will unquestionably exist somewhere in the definition of "to be", but this verb has so many meanings it will be essential to have some way to decide which one is involved. This resonance-output-template would add weight to the choice we need for this example.

Next, the plural nouns that appear in the original collection of sentences will have lots of disconnected and non-compossible characteristics, but one of the simplest cluster techniques creates objects that closely matches the template for 'physical objects' when it operates on words we think of as "nouns". (This technique would also find that some of the plural nouns match the template for nouns that are not physical objects, and would define other subgroups as well.) One subgroup of the sentences contained in the original collection could then be placed in a bin: a group in which the plural nouns represent physical objects.

Next, particular (physical) objects would often have been associated with particular colors, but there is nothing in those associations that necessarily implies that a generalized statement would be true. In fact, no such generalization can be confidently asserted as universal unless Teacher is called in. Even so, any thinking entity must make temporary postulates that cannot be immediately proven – we must merely make sure that the mechanisms for forming such guesses are as dependable as possible, and then that mechanisms exist for removing bad postulates if they turn out to be untrue.

The function of resonance is to extract from a group those elements that have acquired a common association. Thus a second subgroup of sentences could be formed, in which each is concerned with 'color'. These associations will also have their own template (such templates are always formed for all objects, and exist in the side-streams of the short-term-memory: which see). We find ourselves now in possession of templates for associations to color, and if every association is to an object that qualifies as a physical object, then the "score" of that resonance will be high. Obviously in this case the score will be 100%, implying (at least to us human observers) that this association is likely to be general.

At this we have a route to the i.p.o. operator from plural_noun_plus_adjectives, a route from adjectives to color, and a route from plural nouns to physical objects. Although none of these routes is unique (that is, none of them are the ONLY routes leading from the origin objects) these routes are either very strong or one of a small number of like paths. Either strength or being a member of a small set means even the simplest program would be able to come across the following relations without any theoretically complex heuristic.

1)        <plural noun>    are      <adjective>
                     |                                    |
                 via                               via
                     |                                    |
2)        (clustering)                   (resonance)
                     |                                    |
                 yields                           yields
                     |                                    |
3)    <physical objects>   are        colored (associated with a color)

A group of sentences has now been isolated, without using any logical complexity, that is of the form of line 3). Calculating the difference clusters of the two sides of this final path yields 1)the axis-subgroup that is (left side) common to all objects and 2) that which is (right side) common to all colors.

We have now acquired 1) the resonance-generated i.p.o.bomb appearing between the two sides of the original sentence form, 2)a physical-objects subgroup, and 3) a color subgroup. Retaining the original schema yields

        physical objects     have the property         color.

This relation between two axes is derived from knowledge about nouns in general, color relations in general, and some axis functions. The relation itself need never be stated for the program to suggest it.

(subfile #12.29: initial levels of discourse, ranking of axes, and ranking of words)

For the purposes of this project I have assumed some levels of discourse that combine an initial batch of un-things and a 2-"person" social interaction:

    - the first information that exists for an entity simply observes the presence of "some-unthing"
        (something is there, but it has no properties, because no properties are understood/defined)
    - the second level of information activity involves questions and answers about the same some-unthings.
        ( a "question" in this context would be any utterance taken to require a response by Mom)
    - the conversational level occurs when a train of thought is extended beyond this

Ranking axes (see subfile #6.75, "Levels")

Ranking words (words are ranked according to their constituent axes' rankings)

Beyond this data-style ranking, words, upon input, are denuded of all unfamiliar axes: the learner can only "hear" that which has been established or defined already. This means that the initial MS for the "baby" is tiny. It is much better to think of this initial MS as "small" rather than as "empty".

(subfile 12.5: distances)

In general, when I use the term distance, I mean the completely usual Cartesian distance in MS, in which distances are calculated from coordinates in the Pythagorean way. (Although there are differences required by the non-orthogonality of the axes, these difficulties are merely arithmėtical.) The other type of distance, in 'template-space' ( see the first discussion of templates ) appears to be less useful.

(subfile 13: representation in real memory

It is no problem, from the memory-capacity point of view, to store pointers to each text item such as “apple” at a large number of nearby points in MS. This fuzziness in individual words’ definitions relieves the system of the requirement of any specific level of precision when making its various calculations. (See “Fuzzy Data, Fuzzy Logic”, p.15) In general, in the discussion which follows, I will refer to word data-objects as points, and the reader should remember that this usage is approximate.