Function Analyses Produce

Thought Generating Paths to Solution Concepts


Ed Sickafus, PhD


Identification and analysis of functions, as defined in unified structured inventive thinking (USIT)[1], is a valuable approach to discovering solution concepts for invention and routine problem solving. When their verbal and graphic representations[2] are applied to specific problem situations they bring immediate focus to unusual perspectives, i.e., new thought paths. Three examples are discussed, a clinical rash-identification problem, an automotive accidental-acceleration problem, and an ad-placement marketing problem.


Transduce (a transitive verb) means to convert energy from one form to another. It is a generic definition of functions. This idea is extrapolated into structured problem solving by interpreting energy to include information. Thus, the infinitive to transduce becomes to convert information from one form to another, which is what transducers do. Hence, information becomes an object characterized by its active attributes. Two information objects may interact at a metaphoric, through an attribute of each, to maintain or alter an attribute of an information object. The following object-attribute-function diagram illustrates the graphic representation of a function.


Figure 1.  Two objects (subscripts 1 and 2) interact, through an attribute of each, at a metaphoric point of contact, to modify or maintain the attribute of an object (a third object or an input object(s)). The interaction is shown as inputs to a function.


For example, consider the functional interaction of objects in three problem situations listed in Table 1:


Table 1. OAF table for three problem situations.

Interaction of two information objects, through their attributes, to sustain or modify an attribute of a third information object, per Fig. 1.














to infer malady








to adjust








to capture




Interactions shown in Table 1 represent the following functions:

a)      A doctor, while examining the skin of a patient, notes a disturbing coloration. Upon examining photographs of skin conditions, the doctor is able to infer that this patient has a rash in need of treatment.

b)      An operator of a vehicle depresses the accelerator pedal to increase the vehicle’s speed. Pedal position is noted in the on-board computer and associated with a particular datum in a ‘look-up’ table and the appropriate fuel injector on-time is adjusted.

c)      A salesman judiciously positions the location of a sign in a super market so as to capture the interest of a customer.


Likely, readers will see these three situations in different ways with different verbalizations and prefer their personal choices of objects, attributes, and functions. Therein lies the pregnant potential of metaphoric analysis by individuals and by teams. Metaphors break the barrier of strict technical thinking when searching pre-engineering solution concepts. Metaphors are a right-brain preference, as opposed to strict technical analysis, a left-brain preference.


Fundamental to the USIT procedure of verbalizing and diagramming functions is to uncover new perspectives, and therefore thought paths, of a problem situation. Thought paths are exactly the actual verbalizations and visualizations occurring as one mentally tests and rationalizes potential object-object interactions and their associated functions. Since the procedure is based on metaphors there is, with one exception, little that is inviolable about one’s selection of objects, their active attributes, and functions. The only limitations are those guided by the verbal and graphic definitions of objects their attributes and the functions they support (e.g. see demonstrations in Table 1 and Figs. 2 & 4). Each problem solver brings his or her personal experience and training to a given problem. Plausibility of every decision in verbalization and visualization of a problem is based on personal background.


There are many ways one can pursue thought paths in the verbal and visual heuristics of problem expression. Particularly conducive for invention and routine problems are the transductional aspects of a function. Notes I made on my thoughts paths for the three examples follow.


In Table 1.a, transduction involves mental comparison of skin color and photograph color to infer a malady of skin. A mental image of skin and its color, as well as photograph and its color, are information objects. They are inputs for the function to infer. The doctor does transduction mentally as visual comparison is made with a patient’s skin and a photograph. Suppose an invention is desired that would improve diagnostic accuracy of a doctor’s clinical examination, one that retains the closed-world procedure of comparing image of skin with a photographic image.


One idea that comes to mind is to assume that the database of photographs of skin maladies is sufficiently dense, i.e., exceeding the doctor’s visual acuity (e.g., wavelength resolution in the visible band of color). Two transduction concepts seem feasible: 1) replace the doctor’s eye with an optical sensor that has greater wavelength resolution; and 2) replace the doctor’s mental comparison procedure with digitized electronic image comparison. Assuming increased spatial resolution and wavelength sensitivity, examination of a rash could be reduced to examining a single tiny skin eruption. The eruption could be further analyzed for spatial distribution of color and wavelength distribution (e.g., using radial distribution of color and Fourier transformation of wavelength intensities).


The last two paragraphs illustrate how a verbal analysis of functions (words in a table and their mental discussion) enables thought paths for solution concepts. Now consider visual analysis of functions in the form of mentally discussing words in a graphic.


In Table 1.b, transduction involves electronic comparison of accelerator-pedal position information from a displacement transducer and tabulated pedal-positions vs. injector-pulse-width modulation in an on-board computer’s memory of modern vehicles. Suppose, for safety purposes, that it is desired to avoid vehicle acceleration when pressure is also applied to the brake pedal, either with the same foot, another foot, or an accidental object. This brings a new information object and function into the picture; brake pedal position and its comparison with accelerator-pedal position.


Functional logic of this system is illustrated in the OAF diagram in Fig. 2. Safety state has been included as an information object having three values of its condition as metrics (they are ratios of brake and accelerator pedal positions being >, =, or <). This simple diagram emphasizes the roles and interconnection of two functions. Note that it is technology free.



Figure 2. Safety state has been introduced as an information object whose attribute condition can have values for brake-pedal vs. accelerator-pedal positions (e.g., position ratios greater, equal, and less than).  This safety-state attribute then interacts with the table data to determine pulse-width for the fuel injector.


In this example words are assembled in a graphic that emphasizes connectivity. It is especially effective in more complex problem descriptions.


The coupling of brake and accelerator pedals in Fig. 2, and the desired safety state, suggests (to me) one solution concept having brake-pedal position inversely coupled to accelerator-pedal position. This is illustrated in conventional mechanical technology in Fig. 3.



Fgure 3. a) Brake and accelerator pedals are in their neutral up-positions. b) Accelerator pedal is depressed and slides freely through a connecting bar as long as the brake pedal remains in its neutral position. c) When the brake pedal is depressed, the otherwise freely sliding connecting bar becomes clamped to the brake pedal shaft causing the accelerator pedal to be lifted as the brake pedal lowers, thus overriding acceleration. (Position sensors and the clamping mechanism are not shown.)


This discussion of Fig. 3 illustrates how a mechanical, yet, generic solution concept can be generated graphically. Several problems were discovered in the process of drawing the concept but where left unresolved. These include a mechanism to capture the brake pedal shaft at the appropriate time, how to release it, potential use of a fulcrum, and (not discussed in the figure caption) a potential assist force to return the accelerator pedal using a spring. The spring could be kept inactive with a clamp that would be released when the brake shaft is captured – another problem. Of course, these problems are further opportunities for useful discovery using structured problem solving.


A power of the metaphoric solution concept is its ability to open thought paths to introduce other technologies. For example, the unfinished mechanical solution (as illustrated in Fig. 3) could be embodied in several technologies: it could be completely mechanical, it could be an internally coupled electromechanical system using electronic sensors and actuators and a digital or analog processor, it could be a remote electronic control system coupled with optic fibers connecting electronic and mechanical transducers, logic components could be made from fluidics, and so on. 


Information as an object opens the way to discuss many kinds of transduction. Every field of problem solving can have its own array of transduction examples for many specialized objects. Several examples from physics are discussed in Ref. 2 (pp. 457 – 463). [3]  Sensors and actuators are two kinds of physical transducers.


In Table 1.c. transduction involves coupling of sign location and customer focus in order to capture customer interest. In this example, two of the objects are the same customer, albeit different parts of the same brain being involved. An OAF diagram for this situation is shown in Fig. 4. Sign is an information object. However, I chose its location as an active attribute to be considered. Specific content of the sign is made up of a variety of attributes and they too offer thought paths. I chose sign location in order to illustrate how versions of an OAF diagram give focus when you adhere to the scope of each version.



Figure 4.  The information object’s attribute location is coupled to customer’s attribute focus in order to capture the customer’s attribute interest.


Imagine for a moment the possible attributes of sign location; e.g., eye-to-eye, surrounding, underneath, overhead, behind, out of sight, out of hearing, touching, within sniffing range, within tasting range, variable, imaginary, and others (?). At least twelve thought paths came to mind quickly. I’ll leave it to the reader’s imagination to find solution concepts for each of the twelve metrics of the attribute location. In doing this, imagine, for example, how to transduce a particular attribute, say ‘variable’, into customer interest.[ I have one: an ad banner being pulled by a toy airplane flying around the customer’s head. I got another from touching; an ad suddenly appears on a customer’s clothing. I quit. You try it.]


Verbal tables and graphic diagrams have been demonstrated for finding thought paths in function analysis of problem situations. Functions have been treated as transducers. Information has been used as objects. Together these devices enable metaphoric analyses of real world problem situations that generate new thought paths. The methodology is the same when used to solve routine problems as it is when used for invention.




[1] I first encountered this idea in unpublished notes of R. Horowitz’s class in structured inventive thinking; 1985.

[2] See Unified Structured Inventive Thinking – How to Invent;

[3] While writing this paragraph I glanced down at the keyboard and noted the variety of simple symbols, non-alphanumeric types, that can serve as attributes of information objects and/or as metrics of their attributes: ~, !, @, #, $, %, ^, &, *, (, ), -, _, +, =, {, [, }, ], |, \, :, ;, “, ‘, <, ,, >, ., and ?.