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to conceptual tools. From the Rosen modeling relation (Figure 14.6), it appears that metaphor

is a one-to-many expansion. A formal model, which is a set of scaling relationships, can be

encoded into and decoded from a material system as a metaphor. In our scheme, a single

metaphor can apply to more than one material thing or situation. Metaphor is associated with

a coded representation (Figure 14.6). It is in the one-to-many quadrant of Figure 14.7. If two

material systems can be represented by one formal model (Figure 14.6), then the two material

systems become analog models of each other. Analogies are compressions down to only what

the analogs have in common. They therefore belong in the many-to-one quadrant, diagonally

opposite to metaphor in Figure 14.7.

There are various usages to the term metaphor. Certainly some metaphors go only one

way, from representation to what is represented. The metaphor “time is money” does not

reverse to “money is time.” At the least, the reverse of time and money will not be the same

metaphor. We understand that some things called metaphor by some scholars go both ways

symmetrically, the first to another and the other back to the first. If there are two items with

links going both ways, like Aristotle’s plow and ship’s prow, in our parlance that would be an

analog compression down to structures both able to cut through fluid material (water or soil).

We wish to make the distinction between metaphor and analogy. For us, metaphor only

works in one direction of model to material object, as distinct from analogy, which is a

mutual compression down to what the two or many have in common (Figure 14.6).

The one-to-one quadrant of Figure 14.7 yields a mathematical function, where a point

on one variable plots to just one point on another. It is sometimes taken as a model that

means that one thing determines another. The many-to-many quadrant yields what

mathematicians call relations. Each variable value can map to many points on the other

variable. There is slack in a relation. When scatter diagrams between a pair of variables

produce an oval cluster of points, the width of the oval, or the thickness of the sausage, shows

the slack in the relationship. That is quantified by r

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for correlation coefficients. Function

means a specific relationship, while relation pertains to a more general condition.

[insert Figure 7]

A two-by-two lattice that spells out many-to-one and one-to-many

relationships in combination.

Figure 14.7 invites comparison between the cells. Those comparisons are entered in a new

lattice in Figure 14.8. The margins of the new lattice are “model” and “narrative.” The cells

are situated at one of four transitions in moving through the modeling process: model to

model; model to narrative; narrative to model; and narrative to narrative. The function

version of metaphor leads to a model, in that models are local and explicit, relative to

narratives. Alternatively, metaphor to relation is more open, and suggests narrative, not a

model. There is slack in a narrative as there is in a relation.

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