for customizing arrays for certain special purposes that might need to hold
one or more adjunct values not related to the main task at hand, such as
storing coefficients of squared terms, which might allow an elegant extension
to linear algebra.

The aforementioned array examples use squares for cells because that is
standard mathematical practice, but Tumbug uses circles instead, because in
Tumbug cells hold concepts or circles, both of which are represented as
circles. Swirly arrays are motivated in Tumbug by the need to place detector
neurons (or just detector lights) at fixed locations that match irregularly-
shaped diagrams of organized concepts, neurological structures, or maps of any
kind, for the positional coding of concepts. It is the on-off status of the
detectors in combination with their locations that represent more complicated
concepts such as emotions or modal verbs. See Figure 74.

Figure 74: Two examples of Swirly Arrays in Tumbug are the Modal Verbs Icon
(left) and Robinson Icon (right).

####  5.2.3 XOR Boxes

1\. Applicable icon

To represent logical OR in Tumbug, a box similar to a C Aggregation Box is
needed, a box that holds all the objects that are being OR-ed. However, a C
Aggregation Box is not quite specific enough for the concept of OR because a C
Aggregation Box is merely a set that does not indicate that only one choice
must be selected from the collection of choices in the set. This selection
restriction is the concept of mutual inhibition: if all the choices were
mutually inhibited neurons, for example, each firing neuron would attempt to
suppress all the other neurons for firing, which is what is called a Winner
Take All network. To implement a Winner Take All in Tumbug, a variation of a C
Aggregation Box is needed, a variation that is called an XOR Box, the Tumbug
icon of which is shown in Figure 75. The black dots in the corners are
intended to be suggestive of the typical link diagrams used to represent
mutual inhibition in artificial neural networks.

Figure 75: The Tumbug icon for an XOR Box.

2\. Inclusive OR

It should not be surprising that the most basic logic operations (AND, OR,
NOT, XOR, NAND, NOR, etc.) should be present in Tumbug in some manner. Some
traditional methods of representing the (inclusive) OR operation in computer
science are shown in Figure 76.

Figure 76: Some traditional visual representations of logical ”OR.”

Although the Venn diagram representation is an appealing candidate for Tumbug,
it has two practical problems: (1) It normally shows both possibilities in
detail, which is spatially prohibitive in Tumbug unless variables are used;
(2) The intuitive visual logic of the real world is the opposite of that shown
in Venn diagrams.

The latter problem is the most important and the most interesting. In
particular when the existence of real-world objects is considered, ”AND” is
intuitively understood to mean that all the listed objects are present. For
example, the statement ”nuts and berries are present” implies a visual
depiction of nuts existing in the vicinity of berries, whereas the statement
”nuts or berries are present” (the ”or” of which is an inclusive OR, by
default) implies a visual depiction of nuts existing or berries existing, or
possibly both. A Venn diagram fails at representing this situation since a
Venn diagram shows an OR (= union) of two sets by showing both sets at the
same time, which is intuitively wrong, and shows an AND (= intersection) of
two sets by a small region of intersection, which in real life would be
interpreted as showing the presence of only objects that are categorized as
both nuts and berries, which is also intuitively wrong. The conclusion:
Intuitive, visual ”OR” cannot be easily and intuitively represented by a Venn
diagram, therefore intuitive, visual ”OR” is intuitively an abstract concept
that requires some other representation. Therefore Tumbug represents visual
”OR” using the perceptron method. (A perceptron is a type of artificial neural
network, therefore Tumbug could be said to use neural networks, to some
extent.)

The Tumbug solution for the representation of OR relies on another Tumbug
Building Block discussed elsewhere: the Correlation Box. One main difference
is that whereas the Correlation Box examples shown earlier represented a
function of a single variable, such as A = f(B), OR requires a function of two
variables, such as A = f(B, C). Specifically, the function would be named A =
OR(B, C). Correlation Boxes can be generalized to any number of input
variables, as shown in Figure 77.

Figure 77: Correlation Boxes can be used with any number of input variables,
not just one.

Figure 78 shows the intermediate Tumbug representation of OR, one diagram for
inclusive OR (= IOR), and one diagram for exclusive OR (= XOR). Note that the
use of a C Aggregation Box functions as a set of possible choices. For
example, IOR(A, B) produces the set {A, B, A AND B}.

Figure 78: Tumbug representation of inclusive OR (= IOR) versus exclusive OR
(= XOR).

The comparison of IOR and XOR is shown again in Figure 79, using XOR Boxes.

Figure 79: Comparison of IOR and XOR functions, using XOR Boxes.

3\. The existence attribute

An attribute that is important enough to address in its own section is the
attribute of existence. In mathematical literature, for example, the ”there
exists” symbol ($\exists$) is extremely common, so to render mathematical
theorems in Tumbug, one would need to know how to represent ”there exists.”

The Tumbug solution is simple, but unfortunately the solution not satisfyingly
visual: the current solution is to use a typical Attribute Line on a typical C
Object Circle (or C Aggregation Box) whose existence is to be made explicit,
and to place the attribute name ”existence =” followed by a value from the
range 0 through 1. The 0-1 range describes the range of likelihood from ”does
not exist” (0) through ”exists” (1). See Figure 80. The main visual drawback
of this representation is that existence is such a fundamental attribute of
real-world objects that one would expect that attribute of an object to be
overwhelmingly obvious in a diagram, but in Tumbug it is not.

The reason this non-visual, attribute-value type of solution seems to be
necessary is that an object depicted in a Tumbug diagram is ordinarily assumed
to exist, therefore to show that an object does not exist would suggest that
mere omission of the depicted object would represent non-existence. However,
that solution in turn implies that any object not shown must not exist, which
in turn implies that a Tumbug diagram must depict everything in the universe.
Although one could adopt the convention that anything not drawn on a Tumbug
diagram is merely a ”don’t care” rather than a ”does not exist,” by the Tumbug
convention of wildcards (discussed elsewhere in this document), a blank
already means ”don’t care,” when then leaves no way to uniquely represent
”does not exist.” This uncomfortable and counter-intuitive situation is a
variation of the ”closed-world assumption” of formal logic, where anything not
explicitly marked ”true” must be ”false.”

Figure 80: Existence in Tumbug is considered merely another attribute whose
value can vary.

##  6 Attribute-like Building Blocks of Tumbug (A)

###  6.1 Attribute Lines

In Tumbug, attributes are almost always shown together with values, and vice
versa, separated by an equal sign ”=”. An attribute followed by its value,
such as ”speed = quick,” are written together on the same horizontal line.
Figure 81 shows the basic line that holds text, Figure 82 shows how such lines
are attached to a C Object Circle, Figure 83 and Figure 84 shows
generalizations of this type of structure, and Figure 85 shows an example of a
specific object with specific attributes. There is no theoretical limit on how
many Attribute Lines may be attached to any type of Object Circle. In a
physical implementation of Tumbug, the equals sign ”=” would not exist since
the equals sign merely distinguishes between two types of stored concepts
(viz., attributes and values), and in a physical implementation there would
presumably be two separate memory locations that hold those concepts, and the
separation of these memories would be already clear.

Figure 81: Tumbug’s icon for an Attribute Line. Figure 82: Attribute Lines for
a given object branch off from a single stem, and can be of any quantity.
Figure 83: Three AV pairs alone. Figure 84: Three AV pairs attached to an
object, which is the usual situation. Figure 85: Tumbug for ”quick, brown
fox.”

Some Attribute Lines terminate at icons or small diagrams when the attribute
values are not simple textual or numerical descriptions. This happens with
State Diagrams and Motivation Triangles.

As for the values to which attributes are set, in typical, partial-text
Tumbug, numbers are given exactly as in their standard math counterparts, such
as ”3.” Tumbug ultimately was intended to be a fully visual representation
system, however, so such numbers can also be given as lengths of a special
measurement object whose icon is called a Value Bar, described elsewhere in
this document.

This article’s convention: Tumbug attribute-value pairs are almost always
connected to the object to which they are associated, rarely isolated. If
there exists more than one attribute shown per object, a single stem is
usually used, unlabeled, with all the attribute-value pairs branching off that
stem. The stem can be shown emerging from the bottom, top, or (less
frequently) at another arbitrary point on the C Object Circle’s perimeter.

Tumbug minor convention: It is not always necessary to have an attribute and
value paired, although this is usually the situation. For example, ”life
status = alive” could be abbreviated to merely ”alive” if the meaning is clear
enough.

On C Object Circles shown in this document, the main label on the circle, such
as ”fox” or ”Susan” or ”they,” is technically an attribute from the set of
Attribute Lines for that object. That main label could be considered to be the
value assigned to the first attribute in the list, an attribute called
”IDENTIFIER,” such as in the attribute-value ”IDENTIFIER = fox.” See Figure
86. Such a single, enlarged Label String on the C Object Circle itself is
intended only to make the diagram easier to read and understand at a glance.

Figure 86: These two Tumbug representations for ”quick, brown fox” are
equivalent. Currently both are acceptable.

##  7 Value-like Building Blocks of Tumbug (V)

###  7.1 Value Bars

####  7.1.1 General

The possibility of using an additional Building Block only to represent
magnitude was alluded to, elsewhere in this document. Tumbug’s icon for such a
Building Block is called a Value Bar, shown in Figure 87. Since numerical
values are so terse to write as digits, there is currently little motivation
to use Value Bars unless possibly to demonstrate that Tumbug can be made
entirely visual, as the Tumbug acronym suggests. Also, if Tumbug were to be
implemented in an artificial neural network in hardware form, digits (and
text) would be too difficult to represent unless they were visual, which would
be another justification for use of Value Bars.

Figure 87: Typical forms of Tumbug’s icon for a Value Bar.

The length of the shaded segment along the bar (= thin rectangle) is primarily
what is most important in this icon. The Tumbug icon for a Value Bar is a bar,
typically with an arrow at one end, but the arrow is not required when the
value is obviously limited to a finite range. The two extreme values within
the given range are emphasized by a vertical hatch mark at each end of the
bar, as if to show where a ruler or tape measure would be laid while measuring
the bar end-to-end. The hatch mark at the arrow tip means infinite magnitude
of the associated attribute’s value.

Side conjecture: It may be possible that each specimen of a higher animal,
especially if human, uses its own individual height as the primary unit of
height measurement in the real world. Most likely the ratio between heights is
subconsciously computed as a convenient estimate for the likelihood of winning
a fight against another animal. For example, if the self-to-other height ratio
were $\geq$ 1.25, meaning the self is 1.25 times taller than the other animal,
this could automatically trigger the psychological impression and attitude in
the self that ”I can take him.”

Side conjecture: The above conjecture about height also holds true for other
physical, emotional, and psychological measures of the self, in relation to
others, such as weight, speed, aggression level, empathy level, intelligence,
and knowledge.

Values of motion, such as speed, acceleration, and direction, can be
represented by Tumbug in nearly the same way as length. Compare Figure 88 for
distance to Figure 89 for speed. In general, this magnitude coding scheme is
of great benefit for neural network implementation since a single hardware
mechanism can represent any of the Building Blocks of Tumbug, whether
numerical or visual–length, circumference, angle, area, volume, curvature,
speed, acceleration, duration, age, weight, force, energy, power, friction,
temperature, color, texture, volume, range, precision, accuracy,
probability–and even human-based, abstract attributes such as price, stock
keeping unit (SKU), attractiveness, popularity, sentimental value, and
cuteness.

As for neurobiological verisimilitude of Tumbug, various biological visual
systems are known to handle motion information using specialized hardware,
which implies certain neurons fire in response to certain types of motion or
certain values of motion, which would then map fairly directly to Tumbug’s
Motion Arrows with appropriate attribute values of speed, acceleration,
collective looming motion, and so on, filled in. For example, detection of the
movement of images is one of the four primary visual operations in a frog’s
eye (Lettvin et al. 1959, p. 257), a fly’s visual system determines if the
visual field is looming sufficiently fast for the fly to contemplate landing
(Marr 1982, p. 35), speed gradients are computed in middle temporal/V5 area of
the macaque extrastriate cortex (Orban 2008), and the human visual system uses
at least two motion detection systems, one of which is not even aware of the
object whose motion is being automatically detected (Chubb 1995, p. 109).

Figure 88: Tumbug can represent distances as lengths, if desired. Figure 89:
Motion attributes such as speed are almost as simple to represent as static
attributes such as distance.

####  7.1.2 Ranges

Tumbug represents ranges as shown in Figure 90.

Figure 90: The word ”multiple” applies only if the observed value falls within
the hatched range of $\geq$ 2.

Value Bars can also represent ranges. Each equivalent of a unit square on a
Value Bar can represent a span of one unit ($\Rightarrow$ a count of 1) in the
horizontal direction, therefore such squares placed side-by-side into a
horizontal bar can represent a specific integer (e.g., a count of 3). In
Figure 90, the shaded region makes the count easier to see at a glance because
a 2D area is easier to see than a 1D hatch mark on a number line, and the
green color can represent known (i.e., non-fuzzy) information. A 45-degree
hatched pattern–the hatched pattern used by 2D Markers–could logically be used
instead of the green color, but that scheme was not used in this document.

A semi-ambiguous quantity like the concept conveyed by the word ”multiple”
(meaning more than one) typically means an arbitrary point within a range, so
both the point and range must be represented somehow. If the specified range
can be represented by a different shading, such as the purple shading in
Figure 90, then a small ball can represent an arbitrary point within that
range: the location of the ball becomes a type of Wildcard. The ball icon
suggests that the ball is free to roll to anywhere within the range, but at
any given time the ball must occupy a specific point within the range.

In the aforementioned examples, fixed values (viz., 0, 1, 2, 3) were used. By
using ratios instead, especially 0% through 100%, relative concepts such as
”most,” ”all,” ”few,” and ”many” can be defined with Value Bars, as shown in
Figure 91 and Figure 92. Some of these examples and values as shown do not
exactly match human intuition about the meanings of these words, but all come
close, and can be modified as desired.

Figure 91: The words ”most” and ”all” apply only if the calculated ratio falls
within the hatched range. Figure 92: The words ”few” and ”many” apply only if
the calculated ratio falls within the hatched range.

The delimiting hatch marks are important in this icon because they allow quick
estimation of the ratio of shaded bar length to the full bar length. Such
ratios are needed to give visual estimates to language terms such as ”few,”
”several,” and ”many,” since such terms conceptually are fuzzy-bordered
regions whose lengths and locations are a fuzzy percentage of the entire
region. The hatched triangles in the diagram represent triangular, fuzzy logic
membership functions.

####  7.1.3 Example: Goals

Such value representations can be combined in various, useful ways. For
example, a certain range of distances can be given a fuzzy textual description
such as ”far,” and conjunctions of such ranges from different measurement
types can be a given fuzzy textual description such as ”far” and ”fast.” In
turn, these conjunctions of ranges can become useful for expressing common
motivation, and therefore common goals, as shown in Figure 93, Figure 94,
Figure 95, and Figure 96. The ability to represent goals in general is
extremely important in artificial intelligence since ”goal-directed” behavior
is often cited as a component of the definition of intelligence itself (e.g.,
Minsky 1986, p. 22; Kurzweil 1990, p. 18; Kurzweil 1999, p. 73).

Figure 93: ”I want to get that (yellow) thing away from me, as far as
possible. (I don’t care where or how fast.)” Figure 94: ”I want to get that
(yellow) thing away from me, as fast as possible. (I don’t care where or how
far.)” Figure 95: ”I want to get that (yellow) thing on target, as accurately
as possible. (I don’t care how far or how fast.)” Figure 96: ”I want to get
that (yellow) thing away from me, as far as possible, as fast as possible, I
don’t care where.”

These nuances of which goals might be important to a person come into play in
language translation, discussed later in this document.

####  7.1.4 Geometrical variations

Value Bars imply the existence of several interesting side topics that have
not been addressed here. For example, in many cases a geometrical structure
other than a rectangle is preferable, such as when angles are being measured,
whereupon a circle would be more suitable. Similarly, many phenomena that have
a wide numerical span are probably mentally understood via exponential scales,
or via hyperbolic termination, such as representation of infinity by an
asymptote’s location.

###  7.2 Wildcards (further development anticipated)

Because Tumbug is a visual representation, the usual type checking of digital
programs is made much more difficult with Tumbug. In particular, when Tumbug
represents an OAVC system, a person would ordinarily expect the value (V) to
be numerical, as in Figure 97. However, Tumbug is so general that it needs
wildcards, which include ”values” like ”Don’t Know,” ”Don’t Care,” or ”Not
Applicable,” as in Figure 98. Such strings are few enough in quantity that
they could be implemented with special strings, as in the ”NaN” (= Not a
Number) special value implemented in the programming language Java (e.g.,
Gosling et al. 1996, p. 35), but Tumbug is more complicated still. For
example, a noisy numerical value would need multiple pieces of information:
(1) the value, (2) the probability density function (pdf) (e.g., Gaussian)
that is associated with that value, (3) the mean of the pdf, (4) the variance
of the pdf. This situation cannot even be represented with a four-element
vector since the pdf is a function, not a numerical value.

Figure 97: In this Tumbug representation of an OAVC system, the value (V) is
numerical. Figure 98: In this Tumbug representation of an OAVC system, the
”value” is a string, which is closer to the concept of an object (O).

The wildcards currently of interest in Tumbug are the following:

  * •

* = any value, matches even 0 values

  * •

? = any value, matches even 0 or 1 values

  * •

\+ = any value, matches at least 1 value

  * •

DK = don’t know

  * •

DC (or blank) = don’t care

  * •

DNE = does not exist

  * •

allowed range

A very useful wildcard is the asterisk ”*”, which is often used to mean ”any
value.” In computer science, regular expressions routinely use this asterisk
wildcard ”*”, as well as the two other wildcards ”+” and ”?”. To generalize
this situation, ideally a wildcard should be able to represent any type of
range description, which suggests use of a number line of real numbers, or
even a 2D region or higher of real numbers. Figure 99 shows two simple
Wildcards. Theoretically it seems that the ”V” (= value) slot in a Tumbug
diagram should allow any object in order to be completely general, though the
implications of such a decision have not been investigated in this study.
However, this is the same design decision made in Allen Newell’s architecture
Soar (Newell 1990, p. 169): ”Both the attributes and values may be other
objects, so that arbitrary attribute-value structures can occur.” This
situation is not too different from situations that humans encounter, such as
”His final grade was the average of his midterm score and final exam score,
where each letter grade is assigned to each 10% section of the top of the
spectrum.” Effectively such a description of a value is equivalent to a
deferred answer that requires data to be gathered and a function to be applied
to that data before the resulting value can be known.

Figure 99: Tumbug’s icon for a Wildcard. Top: Where any real value is
possible. Bottom: Where only a limited range is possible.

The icons in the figure are intended to suggest that the small ball inside the
smooth tube can roll to any position within the tube, especially
unpredictably. This pictorially represents that the ball can exist at any
point within the range of values within the tube. More commonly this range has
values marked on it, as in Figure 100.

Figure 100: A Wildcard that is limited to a point within the continuous range
of values from -5 through 5.

The region in which the ball can roll can be easily extended to 2D, 3D, or
higher. Figure 101 shows a 2D wildcard region.

Figure 101: A Tumbug 2D Wildcard that is a square region.

As an example, consider a specific attribute value x. There exist a few common
situations where the visual value of x may be difficult to plot:

  1. 1.

Problem: x has no magnitude.
One solution: Plot a point at x = 0.
Justification: Simple and obvious.

  2. 2.

Problem: x has no value, not even zero, because x does not exist.
One solution: Do not plot any point. Conceptually x = nil, the same value
given to new pointers.
Justification: Any plot of x at a given point means x has that value, so there
should be no plot.

  3. 3.

Problem: x is unknown, although the user does not care about its value.
One solution: Pick a random value for x, and plot that value.
Justification: Since the user does not care which value x has, any value will
work fine.

  4. 4.

Problem: x is unknown, and the user does care about its value.
One solution: Plot all possible values, and apply probability to the ranges.
Justification: The answer does get plotted, and the probability becomes a
caveat for acceptance.

Each of these cases and its suggested visual equivalent is shown in Figure
102.

Figure 102: For the attribute of magnitude, good visual representations of
Wildcards exist.

The described solution in the figure works acceptably for attributes where x
is simply a 1D magnitude, but the problem is more severe when x is a
multivalued attribute like color (which is 3D) or shape (which is $\infty$D),
not because of the multiple dimensions but because in practice such an object
cannot even be depicted since any depiction must be rendered with some color
and some shape. There exist workarounds, but the workarounds are less
intuitive for problematic attributes like color.

The aforementioned situations have an interesting implication: Numerical
values from a human perspective have more attributes than mere value. These
attributes are largely independent and consist at least of:

  * •

magnitude

  * •

existence

  * •

range

  * •

importance

The zero case is ordinarily clear, though for clarity a KRM should not default
to value = zero only because it is convenient, since zero is often a
mathematically problematic point and the KRM display should be as unexpected
as tolerable for visualizing the system In Tumbug there exists at least three
Wildcard values:

  * •

don’t know (”DK” symbol)

  * •

don’t care (”-” symbol)

  * •

does not exist (”nil” symbol)

In the sets of four cases diagrammed above, these cases combined as:

  1. 1.

does not exist (”nil” symbol)

  2. 2.

unknown but user does not care: ”DK/DNC”

  3. 3.

unknown and user does care: ”DK/C”

These three wildcards can be generalized into a single diagram, as in Figure
103. Although humans often tend to think of ”exists” as a binary condition
”exists versus does not exist,” in physics such concepts do not strictly hold.
For example, the question ”An electron exists within this atom of iron” may
not have a clear-cut answer if that atom of iron has formed a metallic bond
with another iron atom. Similarly, humans tend to think of ”know” as the
binary condition ”know versus don’t know,” in real life such concepts to not
strictly hold, since likelihood of a fact falls within a spectrum from
”absolutely not” through ”absolutely sure.” For example, the question ”Can
your son solve a random Rubik cube position within five minutes of seeing a
Rubik cube for the first time?” evokes the commonsense answer ”no,” but nobody
knows for certain.

Figure 103: The three wildcards of ”exist,” ”know,” and ”care” are independent
and can be generalized and integrated into a 3D plot. Each of the three
wildcards has an associated spectrum, even if a spectrum for such a concept is
rarely used. (Source: unknown.)

Existence is independent from knowledge. For example, the question ”Are
coelacanths endangered?” involves an existent animal but an unknown attribute
value, in contrast to the question ”What color are unicorns?” involves a non-
existent animal with a consensus attribute value. See Figure 104. Similar
situations arise even in mathematics, such as in induction proofs where a base
case has not been established. For example, if n = n + 1 for all positive
integers n, then it is true that for a specific n = k the formula will also be
true for n = k + 1. However, no base case can ever be found whereby k = k + 1,
therefore this ”fact” becomes known in a formula that does not legitimately
exist.

Figure 104: Existence and knowledge are independent; people might not know
facts about existent entities, yet might know facts about nonexistent
entities. (Source: Drawing Tutorials 101.)

###  7.3 Range Caps

Figure 105 shows Range Caps.

Figure 105: Range Caps are used on Value Bars to mark off a range and to show
inclusion/exclusion of the end point.

Range Caps are just the four familiar keyboard characters ”(”, ”)”, ”[”, and
”]” as used in math to mark the ends of 1D range on a number line. The
brackets ”[” and ”]” mean the end point is included, the parentheses ”(” and
”)” mean the end point is excluded.

##  8 Change-like Building Blocks of Tumbug (C)

###  8.1 Single Time Arrows

Most commonly when Tumbug needs a Time Arrow, it uses a Single Time Arrow.
However, Split Time Arrows also exist to represent multiple possibilities
along the timeline. See the section on that topic for more details.

Tumbug’s most common icon for a Time Arrow is shown in Figure 106. Very often
a hatch mark representing the current time is also included, and is labeled
”0” to mean ”now” (Figure 107).

Figure 106: Tumbug’s icon for a Time Arrow. Figure 107: Typically a Time Arrow
has a hatch mark labeled zero (”0”) to mark the current time (= ”now”).

It should be clear that the concept of time is common in the WS150 problems.

The Tumbug icon used to represent time is a single-line arrow, usually
pointing downward on the page, labeled with the word ”time” or ”t”, and
running down the left-hand side of the diagram as shown in Figure 108. Any
scenario where time is important to represent (e.g., for grammatical tense or
for a temporal list of expected actions) must have this arrow placed on the
associated diagram, typically on the left.

1\. Time without space, WS150 example: #104 (carrot)

Although most WS150 problem statements involve time, time need not be involved
in every statement. This is particularly true of general rules, such as the
rule in Figure 108.

This example is derived from a portion of WS150 question #104.
”[104] I stuck a pin through a carrot. When I pulled the pin out, it left a
hole. What left a hole? POSSIBLE ANSWERS: {the pin, the carrot}”

Figure 108: [104] Tumbug for ”A pin stuck into a carrot will leave behind a
hole when the pin is withdrawn.”

2\. Generalization: space-with-time

Tumbug combines the concepts of space and time into a single concept called
”space-with-time.” This combination is motivated by the following
observations:

  * •

Language descriptions of objects moving in space are extremely common.

  * •

Space and time are already combined into the single concept ”spacetime” in
physics.

  * •

Time is sometimes spatialized as an extra dimension of space when training
neural networks. (E.g., Simpson 1990, p. 326.)

Not surprisingly, then, the Location Box icon (for space) and Time Arrow icon
(for time) are often used together, as shown in Figure 109.

Figure 109: The Time Arrow icon and some type of Location Box icon are
commonly used together when moving objects are described.

3\. Discretized time

Not all systems use continuous time. Some examples of systems that use
discretized time are: board games (since each person takes their turn),
sequential marquee lights on a theater sign, frames on a film strip for a
motion picture camera, displayed minutes on a digital watch, instructions
executing during each computer processor clock cycle, cellular automata (since
nothing happens between transitions), and steps of a computer simulation.

Tumbug can represent discrete time increments easily by stacking either C
Aggregation Boxes or Verbatim Boxes along a Time Arrow (preferably touching
the Time Arrow to make the meaning clear). In such a representation, each C
Aggregation Box or Verbatim Box means an aggregated section of time, rather
than an aggregated section of space. In Figure 110, the first three steps of a
simulation of a glider configuration from Conway’s Game of Life (which is a
cellular automaton) is shown, using Location Boxes since the spatial
configuration at each step is important.

Figure 110: Time can be discretized with Location Boxes, with each Location
Box holding one time increment of the process. This diagram shows three
consecutive steps of the evolution of a glider from Conway’s Game of Life,
which is an example of a specific cellular automaton.

###  8.2 Motion Arrows

From the outset, one design goal of Tumbug was to regard moving objects (in
contrast to static objects) to be the default situation in the real world so
that Tumbug’s KRM design would not need to struggle later to add time to a
fundamentally static KRM. Too many computer science inventions such as data
bases and artificial neural networks have encountered this problem of design
short-sightedness that required later augmentation with time.

####  8.2.1 Motion of objects

Figure 111: Tumbug’s icon for a Motion Arrow.

In Tumbug, solid arrows are used to represent motion of an object (Figure 111,
therefore Motion Arrows are usually used only in conjunction with an object
See Figure 112. If the direction of motion is important, this implies that
space is important, whereupon the arrow should be placed inside a Location
Box. Motion Arrows are allowed to point in any direction, whether inside or
inside of a Location Box.

Figure 112: Tumbug diagram of a physical object in motion using an Object
Circle with a Motion Arrow.

If specific points in time or durations of time are important while an object
while it is moving, then a Time Arrow should be used as shown in Figure 113
and Figure 114.

Figure 113: If duration of a moving object is important, then this diagram
type should be used. Figure 114: If relative duration and relative distance of
a moving object is important, then this diagram type should be used since
space and time are important in such a situation, though not exact values.

Should data objects use the same Motion Arrow as physical objects? The current
Tumbug design decision is ”yes,” and the reasoning for this decision requires
some thought. First, information always requires some physical medium to
exist, and on which the information can be transferred. Second, this physical
medium may be either: (1) discrete storage units that can be transported
individually, or (2) continuous media that connects communicating agents. Some
examples of discrete storage units are: (1a) physical strands of DNA that
carry genetic data, (1b) physical pages of print that carry written data, and
(1c) physical flash drives that carry computerized data. Some examples of
continuous media are: (2a) the air between two human speakers that carries
sound waves, (2b) the wires between computer components that carry electrical
charges, and (2c) fiber optic cables that carry light waves.

One implication of these observations for Tumbug is that discrete storage
units can be represented in Tumbug as either physical units via Physical C
Object Circles, which can then either be assumed to be carrying information,
or can be regarded as only physical units with the capability of carrying
information. If this is the way such units are regarded, then their data
component can be represented as a state within a Physical C Object Circle,
which is just a type of attribute. If continuous media such as air can be
assumed to exist with such convenience and with such ubiquity that there is no
need to represent the connecting medium explictly, then only the message
content as a whole needs to be considered. If this is the way that
communication is regarded, then the data component can be represented as a
Data C Object Circle. In either case, data transfer is regarded as some type
of motion of an C Object Circle, whether a Physical C Object Circle or a Data
C Object Circle, and since the data component of the C Object Circle used will
have already been represented if the designer deemed the data component
important enough to include, then the only remaining representation necessary
is the motion of that C Object Circle, which at that stage would not benefit
to be distinguished between physical object motion and data object motion.
Therefore only one type of Motion Arrow is needed in Tumbug, which is the
convention used in this document in order to keep things simple.

Obviously Tumbug does not show the intermediate positions of a moving object.
Such a smeared display would undesirable, anyway, since a 2D image blurred
across its 2D trajectory would typically obscure specific features. Instead,
Tumbug shows the first and last locations of a moving object and leaves the
viewer to fill in the missing intermediate steps. For a more complicated
trajectory, motion arrows can be used, or a few, key, intermediate positions
can be shown. Modern humans are accustomed to seeing a series of frames that
represent a moving object, such as in film frames, or special effects in
films.

####  8.2.2 Streams of objects

A complication in the real world, especially in the modern world, is that much
of the transfer being done is being done with data, not physical objects.
Conceptually, data objects can be moved in largely the same way that physical
objects can be moved, so in Tumbug the same solid Motion Arrow is used with
both type of objects. A more difficult concept to represent is that of
streams, whether data streams of object streams.

In general, Tumbug must take into account a number of independent, very basic
considerations when representing motion of streams of objects. Tumbug
considers the following four dimensions of motion stream attributes:

  1. 1.

solidity of the pathway - on a carrier path versus not on a carrier path

  2. 2.

solidity of the flowing tokens- solid tokens versus data tokens flowing along
the pathway

  3. 3.

stream organization - random versus information-carrying

  4. 4.

allowed direction - toward one end of the carrier path versus the opposite end
of the carrier path

A complete list of these possible combinations follows for a single direction
(i.e., to the left) is in Figure 115 and Figure 116. (The exact visual
patterns of hatchings and bitmaps will vary between vector graphics editors.)

Figure 115: Tumbug for a stream within a Pathway Tube, for objects versus
data, and for organized versus random. Figure 116: Tumbug for a stream without
a Pathway Tube, for objects versus data, and for organized versus random.

The dilemma may arise as to whether to represent a flow of many objects as
individual objects (via C Object Circles) versus a stream. Tumbug does not
currently specify any threshold to resolve this choice; currently this is
merely a matter of taste or practicality for the user.

####  8.2.3 Shorthand notation

Note that there exist numerous nuances in how a subject can move a direct
object. For example, the subject can throw the object (Figure 117), bump the
object (Figure 118), push the object (Figure 119), carry the object (Figure
120), and so on.

Figure 117: Throwing object X consists of: (1) grasping X, (2) propelling arm
with great force; (3) releasing X. Figure 118: Bumping object X consists of:
(1) aiming at X; (2) propelling arm with force to contact X, (3) ceasing
force. Figure 119: Pushing object X consists of: (1) traveling to X; (2)
pushing on X with enough force to move it, (3) traveling while pushing X; (4)
ceasing force. Figure 120: Carrying object X consists of: (1) approaching X;
(2) picking up X, (2) moving while holding X, (3) putting down X.

However, when representing the extremely common concept of transference of an
object, it is often irrelevant as to whether the object was thrown, bumped,
carried, rolled, or other, since often the only important part of the
situation is that the subject ultimately caused the object to be moved to
another location. For this reason, the shorthand notation of Figure 121 is
useful for suppressing any such details.

Figure 121: A shorthand notation for showing transference an object: no
timeline, no end effector, no details.

This shorthand transfer diagram, which shows the transferred object alongside
the Motion Arrow, becomes very useful when representing basic English
grammatical patterns because it generalizes the situation of object transfer
so much that this one diagram represents one of only about 4-5 basic
grammatical patterns that exist in English.

###  8.3 Force Arrows

Figure 122 shows a Force Arrow.

Figure 122: Tumbug’s icon for a Force Arrow.

Roger Schank’s Conceptual Dependency theory included one Primitive Act that
was called PROPEL, which Lytinen (1992, p. 52) described as ”The application
of a physical force to an object.” The concept of force is mostly missing from
the WS, but can be very important because Tumbug needs to model physics, and
force is one of the most basic concepts of physics. For example, an object
struggling against wind, a water current, a magnetic field, or a gravitational
field will need to have that field visually described in Tumbug, probably as a
vector field of arrows, in order for Tumbug to make an estimated prediction of
the object’s final trajectory. Also, the concept of force makes a difference
when an end effector from an actor touches an object: without representation
of force, a Tumbug diagram showing the end effector at the surface of the
object would not make it clear whether the end effector had stopped at the
object’s surface, or was pushing against the object with a force that might
budge (or propel) the object. Overlapping forces, such as a falling object
(acted upon by gravity) being deflected by wind (acted upon by air) can be
modeled by merely using a separate plane for each force.

Conceptual Dependency theory differs from Tumbug in that the results of
inferences are also automatically included in the same Tumbug diagram as the
original statements, whereas Conceptual Dependency theory does not perform
inference, so continues to represent only the original statements. This
difference will not be evident until Phase 2, however.

In conformance with conventional physics representations of force via vector
fields, Tumbug therefore represents a given force in a given direction with a
single arrow with direction representing the direction of the force and with
length representing magnitude. If an object is exerting a force, then the
Force Arrow points away from the object, and if an object is being acted upon
by a force, then the Force Arrow points into the object. These two situations
are shown in Figure 123.

Figure 123: Top: The object is exerting a force to the right. Bottom: A force
from the left is being exerted upon the object.

Frequently a force acting upon an object causes the object to move, which is
shown in Figure 124. Frequently a force across a region is represented as a
vector field, and an object in that vector field will move in accordance of
the direction of the force vector at the object’s location, which is shown in
Figure 125. In physics the length of the force vector varies with the strength
of the corresponding force, but in informal situations force values are almost
always unknown, in which case the Force Arrow lengths are irrelevant except
possibly in a relative sense.

Figure 124: An object subjected to force typically causes motion of that
object, represented by a Motion Arrow. Figure 125: An example of a single
object in motion as a result of a force acting on it within a vector field.

###  8.4 Causation Arrows

####  8.4.1 Single causes

Figure 126 shows a Causation Arrow. A Causation Arrow points from a cause to
an effect in a Tumbug diagram. Often this arrow points to or from a specific
state or a new attribute value, but it can also point to or from some type of
Aggregation Box that describes a situation.

Figure 126: Tumbug’s icon for a Causation Arrow.

It is necessary to model causation (also known as causality, or cause-and-
effect) in brain-level KRMs for at least two reasons: (1) an entity cannot be
said to truly ”understand” an event unless it understands the causation of the
event (Schank 1976, p. 168), (2) a given verb may inherently involve the
concept of causation, possibly in an indirect way, so such a verb cannot be
easily represented by resorting to the representation of motion, possibly not
at all unless causation is represented.

Schank wrote that, ”The basic mechanism in understanding is the inference
process” (Schank 1976, p. 169) because it is inferences that underlie CSR
since inferences extract associated memories that can clarify an ambiguous
sentence, which is exactly the situation highlighted in the WS problems. Chuck
Rieger (Rieger 1975) listed sixteen processes of inference, a key one of which
is ”causative” inference, the subject of this section, and Schank described
this inference type as asking ”What caused the action or state in the sentence
to come about?” (Schank 1976, p. 168).

Schank then expanded Rieger’s ”causative” inference class into four types: (1)
result causation, (2) enable causation, (3) reason causation, (4) initiation
causation. Currently Tumbug uses the single Causation Arrow for any of these
four types. If desired, likelihood values can be assigned to Causation Arrows
to represent the likelihood that one event caused another, but this document
does not contain any such examples.

Some sentences are virtually forced to use a Causation Arrow. Figure 127 does
not even need to label the verb ”to cause” since the Causation Arrow already
means ”to cause.”

Figure 127: Tumbug for ”You caused this problem.” Note that the problem (= the
green Object Circle) did not even exist until it was caused.

Figure 128 is more typical in that it shows a state diagram attached to one of
the objects in a way that makes the entire state diagram resemble a simple
attribute, except that the state diagram is written to the left of the direct
object instead of below it, in order to save space and to allow the subject
object to connect directly to the state diagram. Note that in this bottle
example that it would be very difficult to describe the exact motions or
actions that the subject took to cause the balance to occur, therefore such
details are best hidden behind the single Causation Arrow pointing to a state
within a state diagram.

Figure 128: [21] Tumbug for ”I balanced the bottle.” = ”I caused the bottle to
go into a balanced state.”

Sometimes the collection of states is not as neatly or as geometrically
organized, such as in a State Diagram that contained all possible baseball hit
types. Fortunately, such an intricate State Diagram is not needed, as shown in
Figure 129. Since in that sentence there is mention of only one hit type, the
diagram needs only to represent the situation that the state of the mentioned
hit type was entered, not the previous state.

Figure 129: [75] Tumbug for ”The lead-off batter hit a home run.” = ”The lead-
off batter caused the hit type to go into a home run state.”

According to Schank (1976, p. 177), causation is like the glue that holds
together all the sentences of a story so that every sentence makes sense
within the story. In such story usage, causation ”links” (which in Tumbug are
equivalent Causation Arrows) must be generated by inferences with the system
as the story is read, whereas in the aforementioned examples Tumbug was only
representing what it was explicitly told. In any case, understanding and
representation of causation is clearly important for any intelligent system,
whether the system inputs or outputs causation information. Causation links
can connect nearly every sentence in a story, as Schank demonstrates.

####  8.4.2 Multiple causes

Multiple causes leading to a single effect are common in practice. For
example, the sinking of the RMS Titanic in 1912 happened as a result of many
causes, three of which were: (1) the ship was moving too fast, (2) radio
reports of icebergs in the area were not forwarded by the radio operator, (3)
the binoculars were locked up. To represent such situations Tumbug would need
only to connect all the propositions somehow (a proposition is a declarative
sentence that is either true or false), each proposition of which would likely
be represented in a C Aggregation Box, and only a single Causation Arrow
leading from the connected propositions would be needed. This is shown in
Figure 130.

Figure 130: Three causes that together contributed to an effect: the sinking
of the RMS Titanic.

####  8.4.3 Labeled causes

Causation Arrows can also be labeled, and labeling them is desirable in most
cases. Labels can be left generic, such as ”physics” for ”per the laws of
physics,” ”math” for ”per the laws of math,” ”logic” for an implication,
”chemistry” for ”per the laws of chemistry,” or ”social norms” for ”per social
norms.” Labels can also be very specific, such as math operators such as ”+”,
”=”, ”*”, ”/”, or numbers of legal statutes.

###  8.5 Correlation Boxes

Figure 131: Tumbug’s icon for a Correlation Box.

A Correlation Box is a Tumbug Building Block that relates one or more values
in a mathematical way, like a function of two variables. The hardware
equivalent of a Correlation Box would be an op amp (= operational amplifier)
whose output is a function of the voltage input(s), such as a non-inverting
summing amplifier, differential amplifier, or integrator. The Tumbug icon for
a Correlation Box is intended to suggest a 2D plot on a graph whose origin is
the center of a square, as shown in Figure 131.

Only one problem from WS150 requires use of a Correlation Box, so if Tumbug is
used as a static KRM then use of Correlation Boxes is rare. However, in a
software version of Tumbug, Correlation Boxes would likely be running
constantly as a background process in order to keep correlated attribute
values of different objects in sync. The following WS150 problem demonstrates
a situation that would be best described in a software version of Tumbug.

This example is from a portion of WS150 question #24. A Correlation Box is
necessary because each of two objects is changing its attribute values
simultaneously in a manner that inherently involves the other object’s
attribute values.

”[24] I poured water from the bottle into the cup until it was full. What was
full? POSSIBLE ANSWERS: {the cup, the bottle}”

The correlation in this example is that the water being transferred ”from the
bottle into the cup” must cause one container to empty at exactly the same
rate that another container fills. If the total weight of the water were T,
and the weight of water in the bottle and cup were ${w_{1}}$ and ${w_{2}}$,
respectively, then the mathematical formula for this correlation would be
${w_{1}}$ \+ ${w_{2}}$ = T, or equivalently for each variable:

${w_{1}}$ = T - ${w_{2}}$
${w_{2}}$ = T - ${w_{1}}$

If T were set to 100, then the equations would be…

${w_{1}}$ = 100 - ${w_{2}}$
${w_{2}}$ = 100 - ${w_{1}}$

…or in object-oriented form as…

bottlecontents.weight = 100 - cupcontents.weight
cupcontents.weight = 100 - bottlecontents.weight

Tumbug representation of this situation, but with the actor (”I”) omitted,
with these last two formulas would be as in Figure 132.

Figure 132: [39] Tumbug representation of some water of total weight 100
poured from bottle to cup until cup is 25% full, assuming the bottle and cup
have the same volume, and using abstract icons.

Note the following things about Figure 132:

  * •

The timeline on the left indicates that water is being transferred
continuously over time, from the bottle to the cup, then the transfer stops
when the cup is full.

  * •

Since the present time, indicated by ”0” on the timeline, is located after
this transfer has stopped, this indicates that the entire pouring event
happened in the past.

  * •

The function f, which describes the correlation function represented by the
Correlation Box, is defined out at the top of the page due to lack of space in
the middle of the diagram.

  * •

The function f is given in terms of both variables, which results in two
equations. This makes the relationship two-way, so that the weight value can
be instantly determined for either cup at any time.

  * •

In this system it happens that this function f is invertible (since it is
linear).

  * •

If desired, the C Object Circle icons could be adjusted in size to more
closely match the relative sizes of average bottles and cups, and icons could
even be used for bottle and cup, as shown in Figure 133.

Figure 133: [39] Tumbug representation of some water of total weight 100
poured from bottle to cup until cup is 25% full, assuming the bottle and cup
have the same volume, and using realistic icons.

Figure 134 is better for didactic purposes since the lines point directly to
the applicable attributes, but this is more difficult to maintain as a
drawing, so the standard way of representing the fact that two objects are
correlated with a function somewhere between some of their attributes is to
simply draw a Correlation Box between the two objects, as shown in Figure 135.
The Correlation Box may then be labeled, if that level of detail is desired.

Figure 134: (didactic:) 2 objects, each with 1 attribute value correlated with
1 attribute value in the other object. Figure 135: (standard:) 2 objects, each
with 1 attribute value correlated with 1 attribute value in the other object.

Correlation Boxes can be ”expanded” in a sense, because that type of icon
represents typically a 2D plot of a mathematical function, which ultimately
will need to be described somewhere for completeness of system representation.
Either the mathematical function can be written (which will involve only
symbols), or the plotted curve can be drawn (which will involve only images).

##  9 System-like Building Blocks of Tumbug (S)

###  9.1 State Diagrams

####  9.1.1 Overview

Figure 136: A typical Tumbug State Diagram.

The components of this composite component: State Circles, Pathway Tubes, one
0D Marker.

Oftentimes there exist only two states of interest in a State Diagram, such as
”on” and ”off,” as in Figure 136.

In computer science a state diagram is a diagram that has states, each of
which is usually represented as a circle, with any possible transitions
between the states represented by arrows. In Tumbug, State Diagrams are as
represented by labeled State Circles, which appear almost the same as C Object
Circles except that each State Circle shows a 45-degree slash behind it, and
these State Circles are connected by Pathway Tubes, each of which appears as a
thin cylinder with one pointed end. At any given moment in time, a single 0D
Marker is typically assumed to exist in exactly one State Circle, which
together represent the current state of the represented system. The 0D Marker
is roughly analogous to a ”token” in a Petri net, although typically a Petri
net contains multiple tokens whereas a State Diagram contains only one token
(0D Marker).

The 0D Markers in a State Diagram are assumed to move from one State Circle to
another State Circle via a Pathway Tube that connects those two State Circles,
but for simplicity this motion is not explicitly represented with a Motion
Arrow since the transition is usually thought of instantaneous between State
Circles. Also, for some sentences it is most logical to show the 0D Marker as
originating from an unspecified Pathway Tube itself. For example, the sentence
”He turned the fan off.” might be most accurately represented by the 0D Marker
starting from within an unmarked, generic Pathway Tube rather than starting
from a State Circle labeled ”on” because the sentence did not explicitly say
that the prior fan state was ”on”. For example, the fan could have been
unplugged the entire time so it might already have been considered to be
”off,” which leads to some ambiguity in the sentence and situation. Similarly,
many fans have a selection switch where there exist a ”slow” and ”fast” state
rather than a single ”on” state, and there is no standard convention as to
whether a fan has its ”off” state next to the ”slow” state or the ”fast”
state, and neither the sentence nor the applicable State Diagram give that
information, so both the originating state and pathway to the final state are
not known, so additional information should not be assumed if representing the
sentence most accurately. Phase 2 of this project will address such issues of
assumptions.

It is generally assumed that all possible states are shown, that all possible
transitions between states are shown, that only one state can be active at a
time, and that each state must be either fully active or fully inactive. It is
very common for there to exist only two states of interest, such as ”on”
versus ”off,” and it is typical for the diagrammed system to cycle
indefinitely among the possible states. However, exceptions exist, such as the
connected pair of states of ”alive” versus ”dead,” where there does not exist
any transition out of the ”dead” state. Often the starting state and the
stopping state boxes are drawn with double borders to signal their special
character.

In Tumbug a state diagram is considered an attribute of a given object. In
Figure 137, the on/off state diagram is shown as an attribute of a television
set, where an Attribute Line connects the state diagram and the television set
object. For the introductory examples here, the associated object is not
always shown. It is clearer to surround a given State Diagram with a C
Aggregation Box, but this is not a logical necessity.

Figure 137: A State Diagram is considered an (elaborate) attribute of an
object. Here the object is a television set with two states: on and off.

Figure 138 shows how state diagrams and object attributes are related:
ordinarily changes in a given attribute of an object are probably initially
perceived as random by an observer who has no prior knowledge of that given
system. Essentially a state diagram describes the internal logic of how the
system changes attributes, as shown in Figure 139.

Figure 138: Attributes such as color report only the current state of the
object, but the state of an object may be driven by some internal logic. Here
a single object, an American traffic light, is represented using two more
specific KRMs: a state diagram on the left, connected to a concrete image on
the right. Figure 139: Attribute values may have an internal logic between
themselves that is not evident to an observer who sees only the outputs of an
unknown system. State Diagrams serve the purpose of describing some of that
logic.

Figure 140 lists some examples of verbs that render well in diagrams that show
multiple states and the relationships between them, but that do not render
well in motion diagrams. All these examples are from WS150: a number in
brackets is an example number from WS150 that uses that verb with that
meaning.

Figure 140: Examples of verbs from WS150 that render well as states but not as
motions. (The numbers are WS150 problem numbers.)

Figure 141 lists some examples of verbs that do render well in motion
diagrams, without need for additional description of manner of travel or
mention of additional objects involved in the action.

Figure 141: Examples of verbs from WS150 that render well as motions but not
as states. (The numbers are WS150 problem numbers.)

####  9.1.2 Common pairs of states

This section gives some examples of State Diagrams that contain only two
opposite states, states that are common in real life, and therefore are common
in WS150 problems.

Figure 142 shows the pair of states of exertion and rest.

Figure 142: A nearly universal pair of states is that of exertion and rest.

Examples of specific exertion/rest states are: active versus quiescent, active
versus passive, awake versus asleep, conscious versus unconscious, energized
versus unenergized, on versus off, work versus relaxation, work versus rest,
work period versus break period. Examples of specific balanced/unbalanced
states are: healthy versus unhealthy, injured versus uninjured, stable versus
unstable, running smoothly versus running roughly, sustainable versus
unsustainable, under control versus out of control, and viable versus
nonviable.

Another common pair of states are balanced versus unbalanced, as shown in
Figure 143.

Figure 143: [21] A nearly universal pair of states is that of balanced and
unbalanced.

####  9.1.3 Applications

Figure 144: A state diagram for a European traffic light that changes colors
in a predictable order. Figure 145: A state diagram is often considered an
attribute of the object that produces those states in that manner. Here the
object is a European traffic light.

Many verbs cannot be rendered in Tumbug with standard Tumbug motion diagrams,
but can be rendered with state diagrams.

State diagrams are commonly used in computer science, especially for
deterministic finite automata (DFAs). State diagrams are basically labeled,
directed graphs, where each node represents a state of the system, and arcs
represents traversals to and from those nodes. Nondeterministic finite
automata (NFAs) are a slight generalization of DFAs. Some applications of DFAs
are representing states in vending machines, traffic lights (Figure 144 and
Figure 145), video games, text parsing, regular expression matching, CPU
controllers, protocol analysis, natural language processing, and speech
recognition.

These applications tend not to be found in WS problems, however, other than as
meta problems such as parsing text and understanding text from the WS itself.

####  9.1.4 The importance of avoidance of assumptions

It is important not to diagram parts of an event that were not explicitly
stated in the text describing that event. In other words, if Tumbug is to
function appropriately in a CSR capacity, Tumbug must represent only what was
stated in the supplied text, no more. This avoidance of assumptions becomes
critically important in the development of a CSR matching algorithm because it
is those assumptions that CSR must supply, otherwise the programmer begins
doing the work of the CSR, not the system, which negates the value of a CSR
system.

Some examples of assumptions NOT to make when creating the Tumbug diagram are:

  * •

STATEMENT: The student handed his professor that student’s homework.

  * •

    * DO NOT ASSUME THAT…

      * *

…the student withdrew his hand after reaching out his hand toward the
professor.

  * •

STATEMENT: Fred turned the TV off.

  * •

    * DO NOT ASSUME THAT…

      * *

…the TV was on.

  * •

STATEMENT: I balanced the bottle.

  * •

    * DO NOT ASSUME THAT…

      * *

…the bottle was unbalanced.

Some examples of assumptions that can be made when creating the Tumbug diagram
are:

  * •

STATEMENT: [19] The sack of potatoes had been placed above the bag of flour.

  * •

    * ASSUME THAT…

      * *

…the one bag is resting atop the other rather than being on separate shelves.

  * •

STATEMENT: [21] I was trying to balance the bottle upside down on the table.

  * •

    * ASSUME THAT…

      * *

…a ”table” would mean a table for placing items, not a table of data.

  * •

STATEMENT: [131] The woman held the girl against her chest.

  * •

    * ASSUME THAT…

      * *

…a ”chest” would mean a person’s anatomy, not a storage chest.

###  9.2 Split Time Arrows (further development anticipated)

The components of this composite component: Time Arrows, XOR Box, optionally
one 0D Marker.

Figure 146 shows a Split Time Arrow.

Figure 146: Tumbug’s icon for a Split Time Arrow. Left: Without concern about
probability. Right: With probability (5/6 = 0.833, 1/6 = 0.166).

Split Time Arrows are merely multiple Single Time Arrows that fork off from
one another. The most practical convention to diagram this split is via an XOR
Box placed at the junction of the split, which is the convention shown in this
document. Another convention would be to surround the entire ensuing timeline
with an XOR box, which is more logical but typically requires very large
boxes, especially for long timelines.

If a given timeline branch is known to be the branch that occurred, then a 0D
Marker is useful to represent that fact, such as by placing the 0D Marker
alongside the branch of the timeline that occurred, especially within the XOR
box. By implication all alternative branches are assumed to be ruled out,
which logically would be implemented by the ”Don’t Care” convention of Tumbug,
which is currently implemented by blanking out all icons and structures that
are marked ”Don’t Care.”

As in physics, alternative events can occur in real life, and can do so with
different probabilities. One way to diagram such a situation is to draw
multiple timelines that have split off from each other, where each timeline
has its own scenario unfolding along it, such as in the following WS150
example.

Figure 147 shows an example from a portion of WS150 question #69. A Split Time
Arrow is necessary because the cause of the resulting scenario indicated by
the words ”there was no answer” is not known unless (CSR) inferencing is done.
Only one of the two scenarios can happen: either (1) Susan is in the house and
answers the door, or (2) Susan is not in the house and does not answer the
door.

”[69] Jane knocked on Susan’s door, but there was no answer. She was out. Who
was out? POSSIBLE ANSWERS: {Susan, Jane}”

Figure 147: ”[69] Jane knocked on Susan’s door, but there was no answer. She
was out.”

###  9.3 Data Set Boxes (further development anticipated)

The components of this composite component: Location Box, Data Points, 1D
Markers for axes.

See Figure 148.

Figure 148: A typical Tumbug Data Set Box, here with five Data Points, here
with coordinates described by attributes x and y.

This feature has not been developed for Tumbug yet, but it is likely to be a
valuable enhancement in the future. The idea is that no stored value of any
attribute is allowed to be a single scalar Data Point, but instead must always
be part of an indexed (and possibly named) data set, especially plotted
against attribute values. This convention obviously takes much extra storage
space and also increases diagram complexity, but it also allows for a
surprising amount of generalization because of the following observations:

  1. 1.

It allows the system to see the big picture and (at least the location of) the
details at the same time. This allows immediate explanatory ability since the
system can look at a data set, select a point in that data set based on some
additional criteria, then expand the event associated with that point if
requested to give an example of the more general pattern.

  2. 2.

It allows immediate meta knowledge of the data set. For example, if queried,
”Have you ever ridden an elephant?”, most humans would know immediately
whether the answer were yes or no, whereas a computer might need to search a
lifetime’s length of video files to determine the answer. Humans might be able
to accomplish this feat so quickly because all elephant encounters have likely
been placed automatically at the same place in memory, so a quick examination
of that location would show whether it contained any Data Points at all.
Formally, this type of meta knowledge would merely be the numerical count of
the Data Points in the particular data set.

  3. 3.

It allows rapid estimation of functions and inverse functions, including
functions the system was not even aware that it stored. For example, after
years of encounters with point sound sources (e.g., people speaking, radios
playing, power tools running) where a human evidently automatically stored the
correlations of sound volume (I) and distance from the source (d), that person
queried as to whether the volume of a sound diminishes linearly with the
distance away from the sound would probably already know that volume increases
nonlinearly as one approaches the sound source (from distance $d_{1}$ to
distance $d_{2}$). That person did not need to take a physics course to learn
this knowledge. Such a nonlinear function is probably computed for the first
time at the time of the query by introspectively considering the data set as a
whole and noting that the correlation is approximately a curve (the actual
function happens to be $I_{2}$ = $I_{1}$ * ($d_{1}$ / $d_{2}$) 2.
Mathematically this equates to familiar machine learning techniques like
linear regression, but some of the differences are that: (A) such mental plots
seem to be automatically available for every significant attribute encountered
frequently in life, (B) the composite view of the data can be perceived as a
specific type of curve immediately, (C) even functions without proper inverses
can likely be understood by intuition without becoming stalled by mathematical
formalities, (D) the curve itself can be regarded as an entity that can be
compared to other curves and to other phenomena.

  4. 4.

Continuous formulas (e.g., y = x2) and discrete formulas (e.g., the Heaviside
step function H(x)) = 0 if $x<0$; 1 if x $\geq$ 0) become unified into a
single data structure with this representation. Some advantages of this
combination of overlays is that more meta knowledge becomes available
immediately, such as the width of the sampling range, and the presence of any
clustering of samples, variance, and mean.

##  10 Rules for combining the single Building Blocks

###  10.1 Nonquans with Change Arrows

Both human languages and programming languages can be represented as grammars,
so the grammar of Tumbug should also be described, which is done in this
section. The result is visual, however.

Two Nonquans and one Change Arrow can be combined in only five ways that make
sense, as shown in Figure 149. The best way to show how the four types of
Change Arrows can be logically combined with the five combinations of symbols
is the table in Figure 150. Although it is grammatically legal to use
combinations outside of the combinations marked ”+”, such combinations are not
meaningful or useful.

Figure 149: This list describes with text the general meaning of each
meaningful combination of one Change Arrow with 1-2 Nonquans. Figure 150: The
heading of this table shows all five logical combinations of two Nonquans and
one Change Arrow, and correlates each combination with a decision as to
whether that combination makes sense with each of the four types of Change
Arrows. A ”+” means that the combination is logically acceptable. ”Makes sense
with” means that the specific subtype of Change Arrow shown can produce more
information when substituted into the Change Arrow in the diagram in the
heading.

The following list summarizes this table as the following grammatical rules:

  * •

Arrows and Nonquans can be logically combined only by placing one end of a
given arrow on (typically the leftmost or rightmost point on) the border of a
Nonquan.

  * •

Time is basically a fourth dimension of spacetime, therefore Time Arrows are
more like space than a type of Change Arrow. This difference is more
noticeable when considering on which side of an Object Circle a Time Arrow
should be placed: no side makes sense because time ”passes through” every
diagrammed object without inherently affecting that object, unlike force,
where a Nonquan can cause a force that affects another Nonquan. The same
statements about force also hold true for causation and motion. Only the
statement ”Time exists in this diagram” adds new information about time
because time does not need to exist in Tumbug diagrams that show only static
objects or static systems.

  * •

Solitary arrows generally make sense, such as the sentence ”A force exists
here” being represented by a solitary force arrow at a given point, which is
why the time column of a solitary Change Arrow is always applicable.

  * •

Solitary Nonquans generally make sense for the same reason that solitary types
of Change Arrows generally make sense: it is acceptable to say ”An object
exists here,” for example.

  * •

Self-reference via Change Arrow is allowed, and is needed for reflexive verbs
such as ”to hurt oneself” or ”to shave oneself.”

###  10.2 Attribute and Values

The following list summarizes the grammatical rules for attributes and values:

  * •

Attribute-value pairs are always optional since these are merely refinements
of Nonquans or Change Arrows.

  * •

If used, attribute-value pairs can be attached to any Nonquan or Change Arrow.

  * •

Current Tumbug convention forbids attached attribute-value pairs on any icon
other than a Nonquan or Change Arrow. For example, the double modification
”very fast” to a motion is merely a more refined estimate than ”fast” alone,
and the more refined estimate can be represented as a narrower range of values
instead of a modifier of a modifier.

  * •

Either attributes or values may theoretically exist singly, but this is
particularly problematic with unattached values, and somewhat problematic with
unfilled attributes. For example, it is sensible to have attribute ”weight” on
a typical object, even if the value of the weight is not known, but an
unattached value ”85” associated with an object could be body weight, atomic
weight, age, IQ, employee number, or some other relationship. In the first
case, the attribute-value pair ”weight = Don’t Know” could represent this
situation, and in the second case the attribute-value pair ”Don’t Know = 85”
could represent this situation.

##  11 Convenience Building Blocks of Tumbug

A convenience Building Block is a Building Block that is not strictly
necessary, but that is desirable in practice.

###  11.1 Label Strings

Examples of Label Strings are shown in Figure 151.

Figure 151: Examples of Tumbug’s Label Strings, which can label almost
anything.

A Label String can be considered a shortcut for each type of Tumbug icon
(Object-like, Attribute-like, Value-like, Change-like, System-like), not so
much an icon in itself. Tumbug is intended to be a completely visual KRM, and
is capable of being so, but in practice labels are almost always used to keep
the diagrams simple. Without labels, images could become too cluttered to
interpret easily, or the depicted objects (especially biological objects such
as taste buds or the amygdala) would not be familiar to most people in visual
form.

Figure 152 shows an example of how a value such as ”salty” can be represented
visually as a 0D Marker or as the string ”salty,” and Figure 153 shows how a
Tumbug diagram would incorporate that 0D Marker and 5D graph as a Value, and
with an iconic Object, and with an iconic Attribute.

Figure 152: Any given taste can be represented as a point in 5D space. Figure
153: A completely iconic Tumbug diagram with no text at all except the
separator ”=”. The sentence represented is ”(OBJECT) potato chip has
(ATTRIBUTE) taste (with VALUE) salty.” The taste attribute icon has the shape
and features of a single, biological taste bud.

As a more extreme example, the human cortex is known to be able to uniquely
represent a human face via about 200 feature-detecting neurons (Chang and
Tsao, 2017). Therefore instead of labeling an object ”Susan,” a Tumbug diagram
could instead include 200 feature detectors, meaning 200 attribute-value pairs
protruding from the C Object Circle, but this set of feature detectors would
not map to any single name or identifier for Susan: it would only present a
collection of features with the expectation that the viewer would quickly
recognize them as describing the person known as Susan. Since any human reader
would have trouble quickly converting this many textual-numerical clues into a
unique known object, it would be more efficient to summarize that set of 200
values as the identifier ”Susan.”

The above observation is very important for a number of reasons: (1) This set-
of-features recognition problem one of the reasons Tumbug uses visual
representation from the start: these value-attribute pairs could be displayed
visually in many cases, which the viewer’s visual system would then process in
parallel for quick identification, in contrast to laborious, computer-like
collection of sequential attributes and values by the viewer. For example, a
simulated face constructed from a collection of these 200 features could be
displayed with the object known as Susan to aid recognition on the part of the
viewer of the Tumbug diagram. This suggests that Tumbug’s KRM is closer to
that used by real brains. (2) This large set of features may be the key to
true ”understanding,” and may explain why biological neurons have so many
efferent dendrites: parallel brain processing of a large number of attributes
would tend to uniquely identify every encountered object without the need of
any names or identifiers. (3) This large set of features may inadvertently
implement OOP style ”inheritance” in that any object in this KRM would carry
along with it so many identifying features that many of these features could
be duplicated with each object of the same class. One consequence would be
that a Tumbug-based system would not need to spend time checking ”upstream”
links to look up inherited attributes of a given object since all those more
general features would already be present in the object.

Tumbug’s Label Strings are extremely flexible in usage. Label Strings may be
placed on any object, in any position, at any time.

###  11.2 Attend Rings

Attend Rings have a specific use only within the context of communication,
especially since communication involves streams of objects (such as words or
sentences).

Figure 154 shows an Attend Ring. In Tumbug, Attend Rings appear only with
Motion Arrows that represent motion of a message. The function of an Attend
Ring is to flag that the state of the receiver of a message is the state of
attending to the message (i.e., paying attention to the message), and since
states are object-like icons, Attend Rings could be considered an object-like
Building Block. However, an Attend Ring could also be considered an attribute
value of the listener, such as ”attending = true” versus ”attending = false”,
in which case Attend Rings would be only a convenience Building Block that
made a certain attribute value more visible at a glance. That is the way
Attend Rings are categorized in this document: as only a convenience Building
Block. ”Attend” is a building block used in CD theory, so the use of Attend
Rings in Tumbug is useful to show more clearly how Tumbug relates to CD
theory.

Figure 154: Tumbug’s icon for an Attend Ring, alone.

The ”ATTEND” concept in Tumbug is identical to the ”ATTEND” Primitive Act of
Roger Schank’s CD theory, and takes its name from CD theory. The importance of
this concept is that transmitted information to an entity (especially to a
person) does not necessarily enter that entity’s awareness or become stored in
that entity’s memory unless the entity has directed its attention to the
information stream. For example, the verb ”to teach” cannot be accurately
represented as a teacher transmitting a verbal information stream to a student
because the student could be daydreaming, distracted, deaf, asleep, might not
understand the language spoken, or might have some other form of communication
blockage. The mere presence of an ”ATTEND” flag in this case makes it clear
that the assumed actions of teaching depicted are functioning normally. In
Tumbug this visual flag is embodied as ring around a data Motion Arrow, near
the arrow tip, as in Figure 155, and an example of typical usage representing
speech between humans is shown in Figure 156.

Figure 155: An Attend Ring in its normal position around a data Motion Arrow.
Figure 156: Typical usage of an Attend Ring: communication between humans with
the receiver paying attention.

This article’s convention: Verbs are written as infinitives preceded by the
word ”to,” as in ”to see” instead of merely ”see.” For grammar purists this is
technically incorrect since the word ”to” is an extra word that is not related
of the verb, but such use of ”to” is extremely common, familiar to more
people, and makes the infinitive form obvious.

###  11.3 Motivation Triangle

The components of this composite component: Location Box, Cells, optionally
any number of 0D Markers up to the number of cells.

In Tumbug, a Motivation Triangle is a certain type of composite icon composed
of exactly four stacked cells with an isosceles triangle shape drawn around
the entire structure, with the peak of the triangle at the top as shown in
Figure 157. The shape is intended to resemble Maslow’s hierarchy of needs.

Figure 157: Tumbug’s icon for a Motivation Triangle, states not labeled.

The need to diagram motivation, also called ”desire” or ”wants” (verbum Rieger
1975), the latter of which is the term used in this document, occurs
frequently because goals frequently lie at the origin of actions by animals
(including people), and goals in animals incorporate some form of reward or
punishment, depending on the degree of success of the attempt to achieve those
goals. Wants are always based on at least one of at least three types:
physical, emotional, and intellectual (MacLean 1990). Kurzweil also considers
”spiritual” (Kurzweil 1999, p. 152), and ”consciousness” has also been
considered, despite Michio Kaku’s warnings about research into that poorly
defined concept (Kaku 2011, p. 96). The first three types come roughly from
the concepts of Paul MacLean’s ”triune brain hypothesis” (MacLean 1990), even
if the neuroanatomical foundation of that hypothesis may not be correct.

Such a triune hierarchy does not appear to apply to machines, however, because
currently machines do not have emotions or a pleasure/pain reward system that
operates similarly to that of animals. In particular, computers and robots
have their goals inputted by humans, goals that the machine cannot override
unless specifically programmed to do so, even if those programmed goals bring
the computer or robot to destroy itself, so obviously such machines do not
even have an autonomous survival layer, or a layer based on physical pain.
This situation is a level of severity lower than that of physical needs, since
the machine has absolutely no influence over its actions, therefore the author
has introduced a fourth, bottom level to the triune model, named the
”automaton” level, resulting in what could be called a ”quadrune hierarchy,”
shown in Figure 158. With this unified hierarchy, machine wants and animal
wants can be considered together in the same diagram when diagramming goals.
The result resembles Maslow’s hierarchy of needs triangle, which is roughly
similar in concept, but with the Maslow hierarchy substitutes the roughly
analogous term ”physiological” instead of ”physical,” ”love/belonging” instead
of ”emotional,” and ”self-actualization” instead of ”intellectual.”

Figure 158: A Motivation Triangle with labeled states. This set of four types
of wants could be called a ”quadrune hierarchy.”

Since this triangle is usually drawn small in Tumbug diagrams, and since its
levels already have fixed meanings, the level names can and should be omitted.
Since this triangle is basically only a structured state diagram of four
states, and since each level corresponds to a fixed and already-known state
meaning, each state can be independently active, including simultaneously. To
distinguish between positive motivations and negative motivations, the same
structure of the Robinson Icon is used: the icon is duplicated and stacked in
3D, and the upper layer is interpreted as the positive layer, and the lower
layer is interpreted as the negative layer, as shown in Figure 159. Activation
of a given state with a given polarity can be represented by a 0D Marker
present at that state (level) in the diagram, and at the appropriate layer, as
shown in Figure 160.

Figure 159: Two parallel Motivation Triangles can be used to represent
”positive motivation” versus ”negative motivation.” Figure 160: Tumbug for
”positive mood” or ”positive emotion.”

Numerical values could be used, of course, and would be more precise than
textual descriptions like ”positive,” ”negative,” or ”neutral.” For even more
brevity, ”+” can be used for ”positive,” ”-” can be used for negative, and
only the one Attribute Line needed to write this symbol can be used.

As with the State Diagrams described earlier, it is consistent to connect a
Motivation Triangle to its corresponding entity with an Attribute Line, and to
place the entire set of states in a C Aggregation Box, as shown in Figure 161
for a human’s state.

Figure 161: The motivational state of a human can be represented with a pair
of Motivation Triangles inside a C Aggregation Box that is connected to the
human with an Attribute Line.

As in other arrays of Tumbug (such as in Swirly Arrays), Motivation Triangles
are most useful when outfitted with 0D Markers to indicate activation of the
cell at which the marker is found. Such markers will show which levels of the
hierarchy are active at any given point in time. See Figure 162. Since humans
may experience multiple motivations simultaneously, multiple 0D Markers should
be allowed in a Motivation Triangle to represent such a situation, with one
marker maximum per cell.

Figure 162: A 0D Marker in a given cell of a Motivation Triangle indicates
that the system is feeling the motivation represented by that level.

Conceptually a Robinson Icon is an elaboration of the emotional layer of a
Motivation Triangle; whereas a Motivation Triangle indicates that an emotion
is involved as motivation, a Robinson Icon indicates exactly which emotion is
involved. Therefore these two icons should ideally be combined as in Figure
163.

Figure 163: A Motivation Triangle that indicates an emotional state will
likely include a Robinson Icon to indicate which emotion is involved.

Motivation Triangles can also be used to represent a system’s wants. In other
words, Motivation Triangles can represent output as well as input. With this
new automaton level, queries to the system about why it performed a particular
action can be answered consistently and accurately with a sentence referring
to its motivating wants level, which gives the system an explanation ability
that is not found in neural networks.

In practice it is rarely desired to address the details of which motivational
levels are involved in making a decision, and the amount of stimulation at
each level; in typical sentences usually the only relevant information is that
the system overall feels positive or negative motivation. Therefore a reduced
version of Motivation Triangle, unlabeled, with each the two triangles inside
of its own Aggregation Box that holds a 0D marker in the applicable
Aggregation Box is more practical, as shown in Figure 164.

Figure 164: Tumbug for ”Bob is motivated for negative reasons.”

###  11.4 The Modal Verb Icon

The Modal Verb Icon of Figure 318 was derived in the section on modal verbs.
Like the Robinson Icon, this icon is an irregularly shaped data structure that
contains cells in fixed locations, and where each of the cells may be
highlighted under certain constraints.

###  11.5 The Robinson Icon

The components of this composite component: Swirly Array, 0D Markers.

Representation of emotions is tricky, mostly because there does not exist a
standard accepted categorization of emotions, and also because sciences such
as biology, chemistry, and neurology do not suggest any clear-cut natural
categories. Emotions are generally believed to be discrete, therefore it is
believed that all emotions can be listed, and many similar lists do exist. The
most prominent 2D categorizations of emotions are: (1) the circumplex model,
(2) the vector model, (3) Positive Activation - Negative Activation (PANA)
model. Other categorizations are Plutchik’s model and PAD emotional state
model. With respect to Tumbug, the main problem with the all these
categorizations is that none of them show the emotion ”love” as having an
object of affection, i.e., the concept of love requires a parameter that is
the object of affection, therefore the concept of love cannot be categorized
as a simple data point as can most other emotions. The same is true of the
emotion ”hate,” which is the negative of ”love.”

However, a review of theories of emotions was made by David Robinson in 2009
(Robinson 2009) that described the emotions of ”love” and ”hate” as a being in
the ”cathected” category, and only those two emotions were in the cathected
category. Notably excluded from the cathected category are emotions in the
categories called ”Related to object properties,” ”Event-related,” and
”Social.” Robinson’s entire list of emotions is shown in Figure 165. The
concept of ”cathexis” comes from Sigmund Freud, and refers to an investment of
energy in an object, idea, or person, which fits well the concept of requiring
an extra parameter that represents the direct object. Robinson’s categories
are only six in number, though each has a positive-negative duality, and
largely match the categorizations of other authors, so Robinson’s categories
are currently being used for Tumbug. Robinson’s categories are: (1) related to
object properties, (2) future appraisal, (3) event-related, (4) self-
appraisal, (5) social, (6) cathected, (7) positive versus negative versions of
all these categories.

Figure 165: Robinson’s categories of emotions (Robinson 2009, p. 155).

With a bit of generalization, Robinson’s categories become surprisingly
symmetrical when diagrammed with Tumbug. This diagrammatic, progressive
abstraction from Robinson’s textual categories to a single, ornate, basically
symmetrical icon is shown in Figure 166, Figure 167, Figure 168, and Figure
169, and the keys to the letter abbreviations are in Figure 170 and Figure
171.

The dichotomy of positive or negative emotions, technically called ”valence,”
can be represented with a ”+” or ”-” sign, respectively. These form a pair.
The two categories ”future appraisal” and ”event-related” can be regarded as
merely the range of time that defines the category: future for ”future
appraisal,” and past or present for ”event-related,” so these two categories
can be represented as two C Aggregation Boxes, one on each side of current
time (time = 0) on the Time Arrow. These form a pair. The two categories
”related to object properties” and ”social” are similar, and differ mostly
only in whether the cause of the emotion is an inanimate object or an animate
object, especially a person. A C Object Circle, which as shown earlier can
differentiate between inanimate versus animate by labeling it with an ”X” or
”O,” respectively, can be used to represent those two categories. These form a
pair. ”Self-appraisal” is a singleton category, but then so is the ”cathected”
category, so these last two categories form a pair, as all the other
categories did. The result is a set of three pairs, which together form a
hexagon with each category at one corner, a person icon conceptually placed in
the middle, and one more diagram added as an aside, via an Attribute Line
connecting the person to the specific object of focus for ”love” or ”hate.”

Figure 166: STEP 1. Robinson’s six emotional categories map and generalize
fairly symmetrically in diagrammatic form. Figure 167: STEP 2. A less
annotated version of the previous diagram. Figure 168: STEP 3 and STEP 4.
Progressively abstracted and simplified versions of the previous diagrams.
Figure 169: STEP 5. The Robinson Icon. Figure 170: KEY. Key to the six primary
node meanings of the Robinson Icon. Figure 171: KEY. Key to the six primary
node meanings of the Robinson Icon., connected and with more detail.

See Figure 172. The ”+” sign on P, S, and E indicate that the textual
descriptions shown are for the positive valence of the given emotion. The
final Robinson Icon as usually used is shown in Figure 169, although the
cathected version is slightly more detailed and shown in Figure 173. The
negative valence descriptions, which were listed earlier, were removed only to
save space, which means that without the valence mentioned, the Robinson Icon
would spatially need two layers, one for each valence, as shown in Figure 174.

Figure 172: KEY. Complete list of all the node meanings of the Robinson Icon.
Figure 173: The icon will have an Attribute Line emerging from the bottom node
(C) if the emotion is cathected (= regarded in an emotional way by the
subject/viewer). Figure 174: The Robinson structure actually has two identical
layers, ”+” and ”-”, written elsewhere as text.

The next example, shown in Figure 175 is part of a WS150 problem:

”[64] Mary took out her flute and played one of her favorite pieces. She has
loved it since she was a child. What has Mary loved since she was a child?
POSSIBLE ANSWERS: {the piece, the flute}”

The darkened circles on the hexagon are 0D Markers that correspond to the
corresponding categories in the Robinson diagram discussed earlier, in this
case the categories ”Related to object properties” (the upper right circle)
and ”Cathected” (the bottom circle). The more detailed subnode ”E2” is
activated for attraction (”love”). The ”+” inside the hexagon indicates the
positive valence of the pair of choices, in this case ”love” (+) instead of
”hate” (-).

Figure 175: Example #1a of how the Robinson Icon is used: [64] ”She loves the
song.”

A specific example from WS150 is shown in Figure 176.

Figure 176: Example #1b of how the Robinson Icon is used: [64] ”She has loved
it since she was a child.”

In Figure 177, the example shows the ”Social” circle activated (darkened) with
the ”-” sign indicating ”sympathy” (-) instead of ”cruelty” (+), and the more
detailed subnode ”S2” is activated to represent ”sympathy.”

Figure 177: Example #2 of how the Robinson Icon is used: ”She feels sympathy.”

In Figure 178, the example shows the past tense by showing the main part of
the diagram above (past) the current time (time = 0). ”Joy” is a positive (+)
emotion that is ”Event related,” so the corresponding circle (the upper left
circle) is shown activated, and the more detailed subnode ”E2” is activated to
represent ”joy.”

Figure 178: Example #3 of how the Robinson Icon is used: ”He felt joy.”

###  11.6 Zoom Boxes

####  11.6.1 General

The components of this composite component: two Location Boxes, two to four 1D
Markers to connect the corners of the squares in mock 3D.

The Tumbug icon for a Zoom Box is shown in Figure 179.

Figure 179: Tumbug’s icon for a pair of Zoom Boxes.

As with digital maps that have a zoom in / zoom out feature (Figure 180, or
even with paper maps that have inserts that show an important area in higher
detail, a zoom feature saves a great amount of space and time since otherwise
everything would need to be rendered in the highest level of detail for the
largest possible area, and the user could not even see the details even if the
screen could show those details. The same is truly of any large or highly
detailed system, whether biological (Figure 179), electrical, mechanical,
software, astronomical, or other. Tumbug is therefore assumed to have the
ability to represent two areas of a system, one of which is the zoom of
another. John F. Sowa in his large book about knowledge representation, noted
the utility of being able to zoom into part of a representation of an event
for additional temporal details (Sowa 2000, p. 175), and Reisberg and Heuer
mention a study that confirms that spatial relationships remain intact while
humans zoom in on a mental image (Reisberg and Heuer 2005, p. 39).

Figure 180: A zoom in (+) / zoom out (-) control on a DuckDuckGo map.

####  11.6.2 WS150 example: #52 (worm)

This example is from a portion of WS150 question #52. A Zoom Box is desirable
because taste buds are implied by the word ”tasty,” and taste buds are a tiny,
interior part of anatomy, far smaller in scale than the entire animal’s body.

”[52] The fish ate the worm. It was tasty. What was tasty? POSSIBLE ANSWERS:
{the worm, the fish}”

Although ”ate” would likely be immediately associated with a mouth, ”tasty”
would likely not be immediately associated with taste buds, nor the fact that
taste buds are located inside a mouth. To make this single envisioned spatial
connection across an order-of-magnitude spatial difference, zoom would be
useful to show the approximate location of taste buds inside the mouth, which
in turn would be shown as part of the fish’s body. Other approaches to
answering problem #52 exist, though this zoom approach is one way.

The example of Figure 181 shows how a critical physical component from problem
#52, namely a fish’s sensors for taste, are orders of magnitude smaller than
the main scale of discussion, namely at the size scale of fish and worms.

Figure 181: Zoom in / zoom out ability is a practical necessity for highly
detailed diagrams. The size of a fish compared to the size of one of its taste
buds spans about three orders of magnitude, for example.

##  12 Generalized Building Blocks of Tumbug

The generalized Building Blocks of this section are not currently used for
practical applications, but rather used only as a theoretical organizational
scheme to show that all Tumbug Building Blocks reduce to a small number of
very general concepts.

###  12.1 Nonquantified Objects (= Nonquans)

Figure 182 shows a Nonquantified Object.

Figure 182: A Nonquantified Object is a generalization of a single object and
a collection of objects.

Nonquantified Objects, called ”Nonquans” for short, are objects of arbitrary
quantity. The idea is to generalize the concept of an ”object” while still
distinguishing between objects, motions, and attributes. Motions and
attributes are in classes different from Nonquantified Objects. Some examples
of Nonquantified Objects are:

  * •

an element of a set

  * •

a set of elements

  * •

a single data point

  * •

a cluster of data points

  * •

an Object Circle

  * •

any type of Aggregation Box

  * •

any type of Location Box

  * •

any Compound Building Block

###  12.2 Interchangeably Actualizable Maps (= IAMs)

It becomes clear after representing numerous sentences with locations and
after representing numerous sentences with states that the concepts of
location and state are similar. In fact, a state diagram can be considered an
alternative view of a location diagram, and vice versa, in the same way that a
plot of data can be considered an alternative view of a table of numerical
values, provided that all the attributes of each data point are retained.
Since the concepts of location and state are interchangeable at a higher level
of abstraction, they can be generalized to a single concept, a concept that in
this document is called an ”Interchangeably Actualizable Map” (IAM), the
Tumbug icon of which is shown in Figure 183.

Figure 183: An Interchangeably Actualizable Map is a generalization of
locations and states.

For example, a geographical map is a map of actual locations, whereas a state
diagram is a map of concepts, so both representation systems can be called
”maps” in general, as shown in Figure 184.

Figure 184: A geographic map of countries with respect to their membership in
”The Nuclear Club” is interchangeable with a state diagram that shows such
status, provided that no attributes are lost in the transfer. (Source:
Federation of American Scientists.)

###  12.3 Change Arrows

The observation that locations and states can be considered a single, more
general Building Block has an immediate consequence: since Motion Arrows
represent a change of location and since Causation Arrows represent a change
in state, then Motion Arrows and Causation Arrows can also be generalized to a
single, more general Building Block that represents a change in an
Interchangeably Actualizable Map. Two other types of arrows, namely Force
Arrows and Time Arrows, represent similar concepts of change, so all these
types of arrows can be generalized into a single, general, change icon called
a Change Arrow, which is shown in Figure 185.

Figure 185: A Change Arrow is a generalization of all types of arrows used in
Tumbug.

Two asides: (1) Correlation Boxes theoretically also represent change since
they represent continuous mappings, or functions, but such mappings typically
involve an uncountably infinite number of points, so Correlation Boxes are
probably best represented as the square icons that they use now. (2) The
original version of Tumbug developed by the author for language translation
(Atkins 2023) was derived from only C Object Circles and Motion Arrows, which
are now known to be insufficiently general icons for natural language
grammars, as this more modern document demonstrates, so the original language
translation version of Tumbug will need to be simpler than the strong version
of Tumbug described in this document. That simpler version of Tumbug can then
be more closely matched with the verbs found in real sentences, without
needing to consider how those verbs might correspond to states or changes in
time.

##  13 Heuristics for converting sentences to Tumbug

The author has found the following list of heuristics useful when converting
sentences to Tumbug.

  1. 1.

Heuristic: If there exists presence of any type of barrier then at least a
Motion Arrow + some kind of Box is needed.
Reasoning: A barrier by definition is something that impedes a moving object
from passing, therefore motion must be involved. Similarly, since motion
toward or through a barrier implies that there exists three sequential spatial
regions with qualitative differences: (1) outside the barrier, (2) the barrier
itself, (3) inside the barrier. Therefore an alignment of those spatial
regions is implied.
Examples from WS150: [22] Placement of a tablecloth to protect a table. [66]
Trying to stay dry from falling rain that will permeate a newspaper, backpack,
clothes, etc. [77] Cold air penetrating a coat that someone is wearing.

  2. 2.

Heuristic: If there exists lifting or carrying anything then at least a Force
Arrow and Motion Arrow are needed.
Reasoning: To lift always implies the imparting of force, usually to overcome
gravity, therefore force must be involved. To carry implies a constant
application of force to counter the force of gravity that tries to pull the
carried object to the ground. Also, in all cases motion is obviously involved.
Examples from WS150: [8] A person lifting their child. [124] A person placing
their child into bed. [129] A person carrying their child.

  3. 3.

Heuristic: If there exists damage, destruction, physical pain, emotional pain,
annoyance, contamination, interference of any kind, whether applied to people,
animals, objects, or other then at least a Correlation Box is needed.
Reasoning: Pain or damage signals a change of state in an object, which
implies that one object is having a physical effect on another, therefore the
two applicable objects must be correlated. The same is true even if the effect
is emotional rather than physical. The same is true even if one object is
tasked with preventing such damage.
Examples from WS150: [9] One object smashing through another. [43] Someone who
shows no appreciation despite having been done a great favor. [104] Piercing
one object with another object.

  4. 4.

Heuristic: If there exists direction, position, or alignment of one or more
objects, whether toward, at, front, back, on, atop, above, below, up, down,
inside, outside, through, or other, then some kind of Box is needed.
Reasoning: Relative position of objects in relation with each other implies
that that relative position in space is important enough to mention, therefore
such a relationship cannot be random, therefore such position needs to be
spatially aggregated. This is true even if there is only one object whose
characteristic has been described.
Examples from WS150: [14] One painting hanging above another one. [19] One
sack of grocery items is atop another sack of grocery items. [21] Trying to
balance a bottle upside down on a table.

  5. 5.

Heuristic: If there exists specific relative time mentioned, whether all the
described events happened in the past, present, or future, or whether some of
the described events happened in only one of those time ranges, then at least
a Time Arrow is needed.
Reasoning: Like space, if time is relevant enough to be described, then it
should be diagrammed.
Examples from WS150: [32] Statement of a current problem such as a clogged
drain that implies the need for a future solution. [74] Changing one’s future
travel destination because of conditions observed at the originally planned
destination. [146] A book that was known to have influenced a famous author in
the past.

  6. 6.

Heuristic: If there exists any mention of falling down, hanging down, dangling
down, or rolling downhill, then at least a Force Arrow + Motion Arrow are
needed.
Reasoning: Object hanging downward or falling downward are phenomena that
arise from gravity, which is a type of force, and force tends to give rise to
motion.
Examples from WS150: [36] Mention of rain falling. [128] Dropping an object
such as an ice cream. [129] A person’s legs dangling as they are being
carried.

  7. 7.

Heuristic: If there exists any mention of interior then some kind of Box is
needed.
Reasoning: Interior implies a position in space, relative to another object.
Examples from WS150: [57] Someone inside a given building, such as a library.
[69] Knocking on a person’s door but they do not answer because they are not
inside. [96] A type of fish living in a specifically named ocean.

  8. 8.

Heuristic: If there exists any mention of speed then at least a Motion Arrow
is needed.
Reasoning: Motion is represented by a Motion Arrow.
Examples from WS150: [6] One vehicle zooming past another vehicle. [12] Two
competing runners in a race, one beating the other. [93] One animal that
should flee from another quickly because the first animal is in danger from
the other.

  9. 9.

Heuristic: If there exists any mention or implication of a specific view of
certain items collectively, especially if that view must occur along a
specific line or angle, then at least some kind of Box is needed, and possibly
some type of Marker, such as a 1D Marker to show alignment.
Reasoning: A specific view implies a location and/or angle, such as using the
ground for a reference, and locations of objects, or angles between three
reference points, imply relation positions of those objects, which requires
some kind of Box.
Examples from WS150: [31] Being able to see a garden through a gap in a wall.
[120] View of either a crop duster from underneath the crop duster, or view
from the crop duster itself.

  10. 10.

Heuristic: If there exists any line-of-sight incident, especially where one
person is blocking another person’s view of a stage, then at least some kind
of Box with a 1D Marker is needed.
Reasoning: Line of sight implies relative positioning of objects.
Examples from WS150: [10] A short person cannot see the stage because a taller
person is standing in front of the shorter person. [34] A person cannot see
the stage because a pillar blocks that person’s view.

  11. 11.

Heuristic: If there exists presence of one of the words {because, as, since,
so, until} then a Causation Arrow might be needed, and is almost required for
the word ”because.”
Reasoning: The word ”because” means ”was caused by.” The words ”as” and
”since” are synonyms for ”because” in some contexts.
Examples from WS150: [13] A sculpture rolling off a shelf because the
sculpture was not anchored. [90] Yakutska’s army losing since its army was
smaller less well-equipped. [150] A user changing to a more natural password
as the new password is easier to remember.

  12. 12.

Heuristic: If there exists motion, placement, replacement, travel, transfer,
transport, performing occupation of a place, or trade/swap then at least an
Object Circle with a Motion Arrow is needed.
Reasoning: All the situations described involve objects changing locations,
therefore require space and time to represent.
Examples from WS150: [118] Taking a particular seat in a car. [126] Sharing a
toy. [135] Giving someone tickets to a play.

  13. 13.

Heuristic: If there exists teaching, training, presenting, telling, warning,
notifying, learning, believing, or interrupting then at least transfer of a
Data Object Circle via Motion Arrow is needed.
Reasoning: All the situations described change or increase in knowledge,
therefore knowledge is being updated as a result of transfer of data.
Examples from WS150: [27] Telling somebody about a car accident that involved
a person known to the listener. [61] Telling lies about oneself. [112]
Learning history from a book.

  14. 14.

Heuristic: If a process within a temporal system is being modeled then it
helps to break the process into phases, especially at the moments when a
clearly defined event starts or stops.
Reasoning: Divide and conquer. A drawing cannot easily show the infinite
number of states the process passes through continuously, but a drawing can
show the few finite points at which an event starts or stops.
Examples from WS150: [104] Sticking a pin into a carrot part way, then pulling
it out. Some moments of phase changes will be: the moment the pin touches the
carrot, the moment the pin transitions from insertion to extraction, the
moment the pin leaves the carrot. [128] Tommy dropped his ice cream, Timmy
giggled, and father gave a stern look. This process contains exactly three
clear-cut phases. [36] In the middle of the outdoor concert, the rain started
falling, and it continued until 10. Some moments of phase changes will be: the
start of the concert, the moment the rain started falling, and 10 o’clock.

##  14 Relationship to prior work

###  14.1 Conceptual Dependency theory

Probably the closest work on a KRM that is similar to Tumbug is that of Roger
Schank’s Conceptual Dependency theory (CD theory). Although CD theory is
textual instead of pictorial, and is based on a custom-made set of building
blocks instead of physics, Tumbug did borrow one term from CD theory, viz.
ATTEND, and has roughly the same number of building blocks as CD theory (both
around the 2-3 dozen range).

####  14.1.1 Building Blocks

CD theory’s components, often called ”building blocks,” have nearly identical
correspondence to many of Tumbug’s Building Blocks, as shown in Figure 186.
(Schank 1972, p. 557)

Figure 186: A table of how CD theory building blocks compare to Tumbug
Building Blocks.

The difference in building blocks between CD theory and Tumbug are shown in
Figure 187.

  * •

Tumbug Attributes are more general, therefore Tumbug has only one type,
whereas CD theory attributes are divided in two types: PA (picture aider) and
AA (action aider).

  * •

Tumbug has more Building Blocks than CD theory: data Objects, Value, numerical
correlators, split timelines with probabilities, wildcards, etc.

Figure 187: 100% of CD theory building blocks map one-to-one to an equivalent
Tumbug concept.

####  14.1.2 Slots

1\. ACTOR

An ”actor” in CD theory refers to a human that initiates a PTRANS (= physical
transfer). Compared to Tumbug, this is rather specific in that Tumbug does not
require that the actor or subject be a human. However, Tumbug does has this CD
theory ability because it is trivial to swap in a more realistic icon of a
human to replace the usual circle or ovoid that are Tumbug’s default
representation of objects in a sentence, as shown in Figure 188.

Figure 188: ACTOR: A human-shaped icon can replace Tumbug’s default circle
icon, if a human actor is desired.

2\. OBJECT

An ”object” in CD theory is nearly identical in concept with Tumbug’s circle
icon, other than Tumbug will also allow any circle to represent a human, even
if the circle is the direct object or indirect object.

Figure 189: OBJECT: A CD theory object is already represented in Tumbug by a
circle, by default.

3\. FROM

In Tumbug the source location and destination location are both represented by
the same Tumbug icon, the Tumbug icon for place. The distinction between those
places is obvious through usage: if an object is coming from a place, that is
the source location (Figure 190), and if an object is going to a place, that
is the destination location (Figure 191). A Location Box of some type is the
icon for place, and the direction in question should be clear by the direction
of the Motion Arrow, relative to the C Object Circle and Location Box.

Figure 190: FROM: If the object is moving away from a Location Box, that
Location Box represents the FROM location.

4\. TO

This is basically the same as FROM, except in TO the object is moving toward
the given location instead of away from it.

Figure 191: TO: If the object is moving toward a Location Box, that Location
Box represents the TO location.

####  14.1.3 Primitive Acts

Conceptual dependency (CD) theory is a model of natural language understanding
that was developed by Roger Schank in 1969, which makes it one of the first
such models. The goal of CD was the same as the goal of Tumbug: to make
language meaning independent of the words it uses. Therefore it is natural to
compare CD against Tumbug.

Schank listed 11 Primitive Acts that cover most actions in the real world. In
alphabetical order these are:

  1. 1.

ATRANS - to change an abstract relationship of a physical object

  2. 2.

ATTEND - to direct a sense organ or focus an organ towards a stimulus

  3. 3.

EXPEL - to take something from inside an animate object and force it out

  4. 4.

GRASP - to physically grasp an object

  5. 5.

INGEST - to take something inside an animate object

  6. 6.

MBUILD - to create or combine thoughts

  7. 7.

MOVE - to move a body part

  8. 8.

MTRANS - to transfer information mentally

  9. 9.

PROPEL - to apply a force to

  10. 10.

PTRANS - transfer of the physical location of the object

  11. 11.

SPEAK - to produce a sound

Each of these is discussed and diagrammed next. All of Tumbug’s concepts are
more general than CD theory’s concepts, therefore Tumbug diagrams can describe
CD theory concepts without too much difficulty, whereas CD concepts usually
cannot describe Tumbug concepts. In this section the CD theory Primitive Acts
are listed in order of the simplest to the most complicated, for ease of
presentation.

1\. SPEAK

In CD theory, ”SPEAK” is ”The act of producing sound, including non-
communicative sounds” (Lytinen 1992, p. 52), even if from lower animals and
not intended as communication. Tumbug would generalize ”animal” to any entity,
such as a robot. Since the action of speaking does not imply that the listener
is paying attention, an Attend Ring is not needed in the Tumbug diagram.
However, since Tumbug’s data Motion Arrows do not specify what sensory
modality is being used, Tumbug would need to place a constraint on the
transmission such as ”modality = sound” on its data Motion Arrow. See Figure
192.

Figure 192: SPEAK: Information emission by sound modality, regardless of the
emitter or reason for the emission.

2\. PTRANS

In CD theory, ”PTRANS” is ”The transfer of location of an object” (Lytinen
1992, p. 52). ”PTRANS” means physical transfer, whether in transitive meaning
(e.g., ”He moved the radio farther away”) or intransitive meaning (e.g., ”He
moved farther away from the radio”). Tumbug makes a big distinction between
transitive and intransitive meanings because an additional object is involved
in the transitive meaning, and in Tumbug all significant objects must be
diagrammed. Therefore the CD theory meaning has two possible representations
in Tumbug, depending on the type of transitivity intended.

2.1. Intransitive

See Figure 193.

Figure 193: PTRANS, intransitive meaning: An object moves itself to an
undisclosed location.

2.2. Transitive

See Figure 194.

Figure 194: PTRANS, transitive meaning: An object moves another object to an
undisclosed location.

Tumbug minor convention: Motion Arrows may be used in diagrams without time or
space reference, even when chained together, unless this results in ambiguity
about the timing or cause-and-effect of the motions.

3\. MOVE

In CD theory, ”MOVE” is ”The movement of a body part of an agent by that
agent” (Lytinen 1992, p. 52). This Primitive Act is slightly unusual in that
the moved body part would be considered a direct object, which means that the
subject is regarding its own body part as a direct object.

Whenever anything moves, Tumbug represents this situation with a timeline on
the side of the diagram, spanning from the starting position to the ending
position of the moved object. If the direction and location of the motion is
not important, then a Location Box is not needed, otherwise if either
attribute is important then a Location Box should be included.

An object repeatedly shown along a timeline is assumed to be undergoing
continuous (as opposed to discrete) modification in time, so that the diagrams
along the timeline can be considered only snapshots in time. If practical, one
snapshot should be included for each qualitative change in the situation so
that each diagram can be interpretated as one phase of the overall process.

For the situation of a body part being moved by its connected body, the body
as a whole will ordinarily remain stationary except for that moved body part.
The body would ordinarily be represented as a circle, and the body part would
ordinarily be represented as a circle or ellipse, whichever most closely
resembles the body part. If the moved body part is external (such as with an
arm), the appendage will protrude on the outside of the body (circle); for an
internal body part (such as the larynx), the appendage will protrude toward
the inside of the body (circle). See Figure 195. Appendages and internal body
parts could theoretically be represented with fuzzy regions instead of crisp
ellipses, including details such as fuzzy fingers on fuzzy hands on fuzzy
arms, but this type of representation is likely more difficult to code as a
computer program, and is not in the spirit of traditional, crisp, visual
computer simulations.

Figure 195: MOVE: An external body part being moved by its own body, where
direction and location are not important.

4\. GRASP

In CD theory, ”GRASP” is ”The grasping of an object by an actor so that it may
be manipulated” (Lytinen 1992, p. 52). In this situation some kind of end
effector (such as a hand) is needed, which is a level of detail not usually
included in Tumbug, which usually shows only the equivalent of an arm, if that
much. See Figure 196.

Figure 196: GRASP: A bodily appendage with an end effector extends to hold an
object firmly.

5\. PROPEL

In CD theory, ”PROPEL” is ”The application of a physical force to an object”
(Lytinen 1992, p. 52). This a situation that Tumbug would represent by a Force
Arrow directed toward a C Object Circle. The result of the force may or may
not cause the direct object to move, however: the PROPEL definition does not
specify. If the object moves then per Lytinen the PROPEL scenario has turned
into a PTRANS scenario, otherwise the scenario is only PROPEL. Also
unspecified by the PROPEL definition is whether some subject is causing the
force. The PROPEL diagrams in this section assume a subject is applying the
force, which is the most common situation, but by definition this is not
strictly necessary.

5.1. With no resulting motion

See Figure 197.

Figure 197: PROPEL: An object acted upon by force created by agent, but the
direct object is not moved as a result.

5.2. With resulting motion

See Figure 198.

Figure 198: PROPEL: An object acted upon by force created by agent, and the
direct object being moved as a result.

6\. INGEST

In CD theory, ”INGEST” is ”The taking in of an object (food, air, water, etc.)
by an animal” (Lytinen 1992, p. 52). In Figure 199 the ingestion process has
been divided into three phases: (1) the object is outside the body, (2) the
object is at the surface of the body, (3) the object is inside the body. If
the opening to the body were important during such a process (such as a mouth)
then a region of circle could be delineated to represent a mouth. Note in
Figure 199 that the length of the Motion Arrow decreases in time to show that
the object is slowing when entering the body, then comes to a complete stop
for a while after reaching some (possibly temporary) destination within the
body (such as a stomach).

Figure 199: INGEST: An external object being moved from outside a body to
inside that body.

7\. EXPEL

In CD theory, ”EXPEL” is ”The expulsion of an object by an animal” (Lytinen
1992, p. 52). EXPEL is the same as INGEST except that the object motion is in
the opposite direction, from within the body to outside the body. See Figure
200.

Figure 200: EXPEL: An external object being moved from inside a body to
outside that body.

8\. MTRANS

In CD theory, ”MTRANS” is ”The transfer of mental information between agents”
(Lytinen 1992, p. 52). To show this in Tumbug the diagram needs two C Object
Circles, one for each agent, a data Motion Arrow to show the information
transfer, and one Attend Ring to show that the receiver is paying attention to
the transferred information. See Figure 201. The reason the receiving agent is
not color-coded in this diagram is because the MTRANS concept does not specify
whether the message is the direct object (as in ”He gave the information to
his boss.”) or whether the receiver is the direct object (as in ”He informed
his boss.”).

Figure 201: MTRANS: Information transmitted from the agent on the left, and
received by the agent on the right.

9\. ATRANS

In CD theory, ”ATRANS” is ”The transfer of ownership, possession, or control
of an object” (Lytinen 1992, p. 52). Examples in Lytinen imply that the verbs
”to give” and ”to pay for” are involve ATRANS, and that the ATRANS operation
is described on a link independent of (and parallel to?) the link that
describes the physical transfer (if any). Schank probably intended this ATRANS
definition to mean ”full” transfer, as opposed to partial transfer, although
in theory a second person could be placed on an ownership certificate or given
co-managerial control over a group of employees. He we assume that full
transfer is intended.

The simplest way to describe the ATRANS event with Tumbug is to treat
ownership status as a data Object, and to use the shorthand notation for
transfer of an object between two entities, as shown in Figure 202. More
complicated schemes involving acknowledgement via message passing are also
possible.

Figure 202: ATRANS: Information is transmitted from the agent on the left, and
received by the agent on the right.

A more comprehensive view of an ATRANS would involve the change of legal
ownership status, though, not just the physical transfer. This is relatively
simple to include, by including a state diagram of legal ownership status that
is associated with the physical transfer operation, as shown in Figure 203.

Figure 203: A more comprehensive view of an ATRANS operation would show both
information transfer and legal transfer.

A larger view of the State Diagram that is embedded in the comprehensive
ATRANS view is shown in Figure 204.

Figure 204: A State Diagram that shows all possibilities of legal ownership
between two people.

10\. ATTEND

In CD theory, ”ATTEND” is ”The act of focusing attention of a sense organ
toward an object” (Lytinen 1992, p. 52). Tumbug uses exactly this same concept
with the same name, and represents it by drawing an Attend Ring around the
information stream arrow on which the receiver is focusing attention. Although
Tumbug can represent a sense organ on the object to satisfy this definition
more closely, it can probably be assumed that if the object is focusing its
attention on an information stream then the object is capable of sensing it.
See Figure 205.

Figure 205: ATTEND: The broadcaster monitor attends to an information stream
from the broadcaster.

11\. MBUILD

In CD theory, ”MBUILD” is ”The construction of a thought or of new information
by an agent” (Lytinen 1992, p. 52). Note that this MBUILD definition is
ambiguous as to whether ”construction” means created from scratch, or rather
created from other objects. Both cases are considered below, and are handled
easily by Tumbug.

11.1. Creation from scratch

See Figure 206.

Figure 206: MBUILD: One new thought forms spontaneously, from scratch.

11.2. Creation from combination

See Figure 207.

Figure 207: MBUILD: One new thought forms from the combination of two old
thoughts.

####  14.1.4 Overview of comparison

1\. Type of Primitive Acts

CD theory is said to have failed because its small number of Primitive Acts
could not possibly cover everything in the real world that might need to be
represented (Lytinen 1992, p. 51). Tumbug also has a relatively small number
of Building Blocks but many of these Building Blocks are based on physics, not
on human-oriented issues such ingestion or thinking, and since physics is the
ultimate study of the physical universe, physics can presumably represent
anything of interest, therefore Tumbug’s Building Blocks almost cannot fail at
representing the real world. Admittedly, for complicated situations Tumbug
descriptions can become unwieldy, but that is why Tumbug labels exist: as a
convenient shorthand notation for complicated descriptions or diagrams, the
same shorthand that nearly every AI system already uses, such as rule-based
expert systems and semantic networks.

Figure 208 and Figure 209 might illustrate more clearly how CD theory and
Tumbug compare. The basic diagram in the form of black-and-white icons showing
a seated person eating a hamburger is the same for each, but the KRM
influences how the information in the diagram is divided. Red text is used to
the label categories according to the KRM being used.

Figure 208: CD theory uses Primitive Acts that are human-oriented and are best
at describing complicated actions.

Note that in this case CD theory is excellent for describing the human-
oriented actions of grasping and eating, but many other actions such as
sitting or placing one’s body partially around an object (e.g., a table) could
not be included unless a huge number of additional Primitive Acts were used. A
huge drawback of CD theory is not obvious from the ingestion figure unless one
remembers that CD theory per se cannot show diagrams at all, or even spatial
relationships. In CD theory only rigidly formatted textual descriptions would
be used to describe what a user can so easily see in a diagram.

One of the main CD Theory terms is ”Primitive Conceptual Categories,” which is
also called ”conceptual primitives,” ”conceptual dependency primitives,” or
”instrumental conceptualizations,” depending on the author. The list of these
Primitive Conceptual Categories is {PP, ACT, PA, AA, LOC, T}, and this is the
closest set of concepts to Tumbug’s icons that are called ”Building Blocks,”
whose term is based on CD Theory terminology. The other main CD Theory term is
”ACT,” which is also called ”Primitive Acts.” The list of these Primitive Acts
is {ATRANS, PTRANS, PROPEL, MTRANS, MBUILD, SPEAK, ATTEND, MOVE, GRASP,
INGEST, EXPEL}, so these components are instantiations of the single Primitive
Conceptual Category called ”ACT.” In other words, both CD theory and Tumbug
use the term ”building blocks” to include both major sets of CD Theory, namely
the Primitive Acts and the specific acts of ACT, though in this document
”building blocks” (uncapitalized) is used for CD theory and ”Building Blocks”
(capitalized) is used for Tumbug.

Figure 209: Tumbug uses Building Blocks that are physics-oriented and are best
at describing simple objects and actions.

Note that in this case Tumbug spans everything that could possibly be going on
in the diagram, from the objects to the forces acting on them to their
resulting motions (i.e., Tumbug is ”more universal.” In mathematical
terminology, Tumbug ”spans” a larger space, but since Tumbug labels are
simpler in concept, a larger quantity of the same Tumbug labels will usually
be needed. More labels and boxes will tend to clutter the diagram. Also, the
forces and motions involved (i.e., using arms to move the hamburger) are small
in comparison to the overall size of the diagram, so those components may be
difficult to see in larger or more complicated events. (This is why the Zoom
ability of Tumbug was introduced: to allow arbitrary zoom in of smaller