Computing Spatial Metaphor

previously Copyright 2008 David Dodds

(refer to David's barchart SVG illustration, shown in a previous posting)

'The orange bar is the best year.' [Lakoff "GOOD IS UP" metaphor.]

Might alternatively have said, '1997 is the best year.'

(The (colour of the) bar whose height is 'the most UP'{ie in direction
UPward} is of the year which has the 'most GOOD') ["GOOD IS UP"].

The bar that is 'the highest' (or 'tallest') {actually "most UP"}
is 'the most GOOD' (otherwise known as 'best'), and it has the (fill)
colour of orange.

Synonyms for UP: Tall, Height(High), scalarMagnitudeTerm (such as
'great', 'large' as in tallest, highest, greatest, largest).
Therefore (in this example) the tallest bar is also the best bar.
(and also) Therefore the greatest bar is also the best bar.
(and also) Therefore the worst bar is also the smallest (or shortest) bar.
(and also) Therefore the 'worst' year 'is' (actually 'has') also the
'smallest' (or 'shortest', or 'lowest', or 'worst') bar.

Concepts good, better, best : worse, worst. They can be represented
in an ontology:
Good lessThan Better [ both pairs on positive side
Better lessThan Best [ of real number line

Worse greaterThan Worst [ both words on negative side of

real number line

Worse is closer to zero point of real number line than is Worst.

Semantically, the terms "lessThan" and "greaterThan" are defined in
the NASA JPL numeric.owl ontology, as 'numerical things',
(relationships), and so are computationally defined, rather than being
meaningless strings.

The words 'good, better, best : worse, worst' can be treated as
"honorary number values" (ie virtual numbers, where these XML IDs have
properties 'numeric' (type) and 'associated-value' (typically each a
segment (not a point) on the real number line). In set terminology
they comprise ordered sets. Here they each can have associated
value-ranges as well. When there is no co-ordinate system or other
such reference available then the computer can use the percentage
line, such as is defined going between DOWN to UP, to provide concrete
number values to compute with. (Avoiding doing analytical mathematical
processing.)

[notice in adult english there is no negative equivalent to "better"
as in 'worser') I believe it is said as "even worse" or "more worse
(than)"].

Percentage, 100 equally sized subparts, is used to specify a metric
ofdistance between (the SVG x,y location or position of) UP and DOWN.
The value 100% is AT 'UP', 0% AT 'DOWN'. 100% UP means completely in
the UPward direction, and 100% DOWN means completely in the DOWNward
direction. What this means is that the *usage* of (the number value of
or magnitude of) 100% to refer to (the location of) 'UP' is a default
*directionally-based* (ie vector) [in the direction of the maximum
value of (the axis=) 'UP'].
In the case of an SVG 'picture' with default origin location (where
origin of x=0, y=0 occurs in the upper left corner) the (default
(direction) value) 100% occurs at the location y=0 ( ! ) [ not y=max !].

Percentage allows computational use of fuzzy hedges such as 'some', 'a
little', 'a lot' 'nearly', 'almost', 'mostly', 'near', 'far', even
'no-where near', and 'sort-of near' by using ('Zadeh equations')
mathematical definitions of the strings (such as 'near') as they
relate to (math) functions of percentage. "half way", 'half empty'
'half full' are defined as being the terms meaning 50%.

More spatial metaphor, if the Y axis is 'rate', then the green bar at
the year 2000 'has' 'the lowest' rate. ( "Height"["High", "Low"] used
as synonyms for "UP", "DOWN"). If the metaphoric terms are keyed to
the Y axis, such as Y axis='rate' then the metaphoric terms might be
"Fast", "Slow" as ('rate'-keyed) synonyms for 'UP', 'DOWN'.

Here next is the actual SVG RECT (rectangle) statement which causes
the orange bar to be displayed in the barchart illustration. (There
are, of course, somewhat more SVG statements comprising the entire SVG
barchart program.) Notice that the actual code contains the attribute
named "height". Height was mentioned above (as being part of the
knowledge / "conceptual") source for creating the metaphor "GOOD IS UP".

<rect id="bar3" x="80" y="111" width="20" height="89"
style="stroke:blue; fill:orange; stroke-width:0" />

A simple XML parsing or XSLT pattern-match of that SVG Rect statement
provides the parser using analysis program information such as the bar
is orange in colour, has a height of 89 units, is 20 units wide, has
an upper left corner at SVG location (units) x=80 y=111, and that it
has a 'name' (XML ID) of bar3. Bar3, since it is an XML ID, can be
used by ontologies and other XML data structures as reference to this
item, it could be used as a stringname in a topic map for example.

The snippet from a NASA JPL ontology, next, shows that there is an
item, 'rdf:ID="hasHeight"', can be matched up with the height
component of the actual SVG visual, the orange bar named 'bar3'. What
this statement accomplishes is that the computer can discover / detect
that the semantic notion, height of bar3, is a property of type
length. (ie The ontology apprises the computer that 'height' (of bar3)
is a thing which has a length, which is represented by means of a
scalar numeric value.) Now the computer 'knows' that a bar's height is
a spatial thing which has numeric-valued length. Such things are
well-known to adults but it provides some knowledge hints ('background
knowledge') to the computer which allow it to perform a number of
extra-inferences about bars in barcharts that it could not have
without that information.

<owl:ObjectProperty rdf:ID="hasWidth">
<rdfs:range
rdf:resource="http://sweet.jpl.nasa.gov/ontology/property.owl#Length"/>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:ID="hasHeight">
<rdfs:range
rdf:resource="http://sweet.jpl.nasa.gov/ontology/property.owl#Length"/>
</owl:ObjectProperty>
</rdf:RDF>

Computationally, 'The orange bar is the best year.', can be computed,
based on the located values of various things from the (SVG XML code)
parsing, where bar3 is the orange bar and it has a height of 89, which
is closer to the location of UP than the heights of any of the other
bars. The term 'best' corresponds to the largest value term in the set
'GOOD'. From Lakoff "GOOD IS UP" metaphor.

We have seen some of the computation that a computer can perform in
order to 'detect the meaning" or "understand" certain kinds of spatial
metaphor. Other spatial metaphors can be shown to be "understood" by
performing their representative computations, in context.