# Heuristics for Solving Technical Problems - Theory, Derivation, Application

| On 16, Jan 2005

Abstract
Heuristics used by engineers and scientists in solving design-type problems are the non-algorithmic, empirical tricks, tools, and techniques learned academically and from experience. They do not solve problems. Instead they give pause to look at problems in different ways for new insights. An axiomatic basis consisting of six assumptions, inferred from the physical world of interacting objects, is used for a first-time derivation of heuristics. The derivation leads to a surprising number of heuristics.

As the axioms are couched in generic terms, independent of a particular fieldâ€™s argot, the resulting heuristics are also generic. Hence, a particular derived heuristic can be adapted to a specific field by wording it appropriately. This allows personalization of derived heuristics. Conversely, it provides a unified system for cataloging personal heuristics in a generic classification.

These derived heuristics and their underlying strategies constitute a new problem-solving methodology. The resulting methodology presents problem solvers an attribute-centered methodology in contrast to conventional objectcentered methodologies.

Heuristics for Solving Technical Problems

in Three Parts
This discourse is in three parts. It is a somewhat theoretical discussion aimed at problem solvers experienced in, or just interested in, the use of heuristics for structured-type problem solving. This includes experience such as gained using TRIZ, USIT, SIT, and/or ASIT. Please read Part I if you are unfamiliar with this type of problem solving. The derivation of heuristics in Part II is directed toward discovering new heuristics and using them to embody new focus for structured, problem-solving methodology. They are designed to provide new perspectives to problems and thus serve as tools for innovative inspiration. Their application is demonstrated in Part III.

Part I: Use of Heuristics in Problem Solving
Part I covers a background of heuristics, describes examples, demonstrates their use in solving technical problems, and explains how selected heuristics are used in the second part to derive new heuristics. Those familiar with heuristics in problem solving and with structured, problem-solving methodologies may wish to skip Part I.

Part II: Derivation of Heuristics
Part II is devoted to the derivation of heuristics at an abstract level. An attribute-centered approach to problem definition is described in a graphic model. Three solution strategies are found and given graphic models. Their application is demonstrated.

Part III: Demonstration of Derived Heuristics
Part III demonstrates the application of heuristics derived in Part II to a problem of invention. While it uses USIT heuristics for problem definition and analysis, it uses the newly derived heuristics for problem solution.

Introduction
Heuristics imbue all areas of problem solving, both technical and non-technical problems. We will look first at what they are and give a few examples of some rather common heuristics. We will see how they are used, who uses them, and point out that they have been amassed empirically from the lore of problem solving. This brings up the derivation of heuristics for solving technical problems â€“ the main topic of this writing. The method to be used for deriving heuristics will be discussed and demonstrated before engaging in their derivation. Uses of the derived heuristics will be demonstrated. It will be seen that the derived heuristics are abstract. An interesting implication of this fact is that they may be applicable to non-technical problems. However, this implication is not proven here.

Heuristics in Mathematics
Twelve classical heuristics used in mathematics provide a familiar introduction to heuristics (1):
1. Search for a pattern.
2. Draw a figure.
3. Formulate an equivalent problem.
4. Modify the problem.
5. Choose effective notation.
6. Exploit symmetry.
7. Divide into cases.
8. Work backwards.
10. Check for parity.
11. Consider extreme case.
12. Generalize.
These are not derived heuristics. They have been developed over years of trial-anderror solving of mathematical problems along with insightful introspection. Evidence of these heuristics will be seen in this writing. However, the heuristics derived here are motivated by non-mathematical, engineering design-type problems.

Definition of heuristics and intuition
Heuristics are the non-algorithmic tools, techniques, and tricks that are used in problem solving. However, unlike algorithms, they do not solve problems. Instead they give pause to look at problems in different ways to find new insights. Problem solvers use heuristics to â€œseedâ€ their subconscious during the search for new concepts. Many of the heuristics commonly used do not have names and may not be recognized as heuristics. They are recalled as simple rules; i.e., phrases indicating a possible thought process. Consequently, problem solvers often are unaware how dependent they are on the use of heuristics.

Probably the main reason for professional problem solversâ€™ lack of realization that they use heuristics is their dominant reliance on intuition. It may also reflect a lack of momentary introspection to analyze the actual mental process of problem solving being used. Intuition uses heuristics so practiced and ingrained in oneâ€™s subconscious that they come into action instantaneously without conscious summons.

Examples of some heuristics and suggested generic names for them are shown in Table (1). Those who know and use these heuristics probably recognize them as being similar to the quoted phrases. Names, or even references to being heuristics, are rare.

Heuristics seed the subconscious
Technologists have learned to solve problems, a creative cognition process, without an understanding of how the brain does it. An idea arises from the subconscious while examining the details of a problem. It is clarified, defined, and subjected to an appropriate algorithm for verification, and further improved in generating a viable solution. Multiple algorithms may be used in the engineering-scaling process to eventually validate the original concept. Thus, technical problem solving is itself a two-part mental problem: finding an idea and finding an algorithm. Finding an algorithm succeeds from years of training in mathematics, and the conscious selection and application of its algorithms. Finding an idea is less tractable because it relies on the subconscious to recall past experience and offer ideas for conscious reasoning â€“ a process lacking understanding or algorithms for its logical manipulation.

How to induce the subconscious to offer ideas is one of the more interesting problems technologists have solved without the use of algorithms. It is done using heuristics. They seed the subconscious to spark ideas. We all use heuristics, sometimes automatically, and often without recognizing the act.

The simple, reliable process of repeated seeding, by stepping through the alphabet to recall a personâ€™s name, is a well-known heuristic. A mnemonic for remembering pi to a large number of digits is another kind of heuristic. â€œHow I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard.â€ (The number of letters in each word yields pi to 24 significant figures: 3.14159 26535 89793 23846 264 (I)) That sound intensity decreases inversely as the square of the distance from its source is an example of a rule-of-thumb heuristic. â€œThink outside (or inside) of the boxâ€, is one of the slogan-like heuristics suggested for creative thinking. Koen discusses the importance and ubiquity of heuristics in all manner of applications. (2) His thesis is that heuristics constitute the engineering method.

In this discussion, I divide the technical problem-solving process into two parts:
concept generation and engineering-type scaling. I treat the two parts as independent activities in structured, problem solving. Heuristics are used in both activities. Our focus is on the derivation of heuristics for concept generation.

The use of heuristics in problem solving
Heuristics (and intuition) play a dominant role in the creative thinking involved in problem solving. (II) They are so widely used and relied upon that for decades heuristics have been searched, collected, named, categorized, computerized, and taught in problem solving classes. Yet, they are not nearly as generally accepted, as are algorithms in the scaling phase of problem solving. This, I think, is due in part to a misunderstanding leading to unrealistic expectations of heuristics, or how it may be regarded that they are used.

Heuristics are often referred to as techniques for finding conceptual solutions, and inventive ones at that. Hence, they may be incorrectly thought of as algorithms for formulated production of ideas from the (intractable) subconscious. This is a self-contradictory idea. Nonetheless, heuristics are gaining recognition, as methodologies that explicitly use them are becoming known. Structured, problem-solving methodologies make heavy use of heuristics. These methodologies are marketed both in the form of training classes teaching a methodology and in the form of expertise of professionals who apply their methodology to solve clientâ€™s problems. Some engineering schools teach them in senior design classes. Informally, they are taught throughout our academic experiences â€“ an elementary school example teaches how to multiply by 9â€™s on your fingers.

Unstructured brainstorming
Organization of problem-solving tools into a logical structure that guides a thorough process toward solution concepts is not common lore of technologists. Most technologists are so practiced at problem solving that they have their own intuitive steps, which may vary with each problem situation. Initial mental approach to a problem often is instantaneous reaction to offer an intuitive solution. It is quick. This type of reaction is commonly referred to as â€œbrainstormingâ€. (3) We all do it. It works, to a degree, and we are good at it.

Knee-jerk-type brainstorming, such as this, is performed without organization, analysis, or conscious use of heuristics. It is productive although an unstructured and unguided, intuitive process. After this initial mental activity subsides consideration may be given to a more organized process. Or, a common occurrence, the problem solver may delay any organized effort and decide to let the problem incubate a while (a heuristic) and have another brainstorming session later. By then, a heuristic may have been remembered to try. This unorganized process attests the reliance we have on the capabilities of our intuitions. It also suggests an opportunity for a structured methodology based on a self-consistent set of derived heuristics.

Background
Structured problem-solving methodologies The methodology called unified structured inventive thinking (USIT) (4,5) is used in this discussion. It is an offshoot of systematic inventive thinking (SIT, now known as advanced systematic inventive thinking [ASIT (6)] ). SIT is an offshoot of the theory of solving inventive problems (TRIZ) originating in Russia in 1947. (7) TRIZ followers have been active in the continued search of the patent literature to glean new examples of inventive ideas and heuristics. These methodologies all are devoted to the use of heuristics. Ball has published an excellent collection of heuristics for use in TRIZ, although not named as such. (8)

Origin of heuristics
Historically, heuristics have been discovered in personal experience, taught in problem-solving classes, and gleaned from the literature. They may be viewed as being anecdotal. They have not achieved the status or acceptance of algorithms, which often are backed by generations of research. Heuristics have not been derived in a logical procedure analogous to the derivation of algorithms. And no algorithms exist for that purpose. Nonetheless heuristics continue to be used by technologists. They are effective.

Cognitive psychologists have recognized that heuristics play a significant role in creative cognition during problem solving. In the last decade or so, they have begun serious study of creative cognition, an area neglected in the past because of unscientific connotations and uncertainty regarding how to conduct definitive experiments. (9) As these barriers have been overcome, research is contributing to a better understanding of the creative processes in problem solving. Their research emphasizes the â€œcreativeâ€ part of creative cognition. Here interest is more on the side of â€œcognitionâ€. Heuristics will be used to obtain as many solution concepts as possible whether or not they are creative. This is an important issue for adoption of a structured problem-solving methodology in industry â€“ multiple concepts lead to alternative solutions.

A simple model of cognition
I use a simple, naive model of the creative cognition process employed in problem solving. (III) It is intentionally superficial in order to grasp a few essentials of the process without the detail. The simple model: When in need of an idea, the mind can consciously seed the subconscious. Subsequently, recall and association of past experience may occur resulting in a trial concept for conscious testing. Recall is a critical component of the model. Recall means to make a subconscious association of past experience with a conscious concept. There is no magic involved. Past experience must already exist otherwise recall is meaningless. Our mental store of experience builds from every imaginable conscious interaction with the physical world. Solving technical problems depends heavily on training, practice, knowledge, and on-going curiosity to build a functional base of experience.

It is assumed further that the lag time between a thought, involving observation, recall, association, and modification, is very brief. Thus, it becomes instantly available for recall in the next mental iteration of trial-and-error seeding. The consequence of this assumption is that memory is refreshed dynamically during problem solving â€“ experience is constantly updated.

An interesting aspect of recall, for problem-solving concepts, is the age of the information being recalled from memory â€“ milliseconds to decades. Another interesting aspect is the nature of what is needed in recall. It is not facts, or data and specifications, but ambiguous associations with the simplest of artifacts (man-made objects) to the most complex high-tech device, from the simplest living organism to the most complex biological system, from subatomic particle interactions to cosmological phenomena. And most interesting is the trickery of recall using ambiguous stimuli from our senses.

Perspectives and biases in problem solving Although problems arise from misbehaving functions, their understanding begins with the source objects. Engineering design refers to the formalized conceptualization of artifacts. Conventional, engineering-type problem solving can be characterized, in its analytical phase, as developing levels of abstraction of objects. At the initial level, the problem solver may have â€œin handâ€ a malfunctioning component â€“ an object, either simple or complex. There may also be available photographs, a working prototype having most of the current features, a non-functional scale model, and blue prints; all serving as various metaphors of the original object. Ensuing discussions will generate simple pictorial sketches readily recognized as the subject. As the objects become more familiar, in the problem solving process, sketches become less detailed, even crude. Occasionally a simple labeled box will represent the original object.

Thus, object expression can gradually lose definition but the object is still in oneâ€™s mind: real object ? photograph ? prototype ? model ? blueprints ? sketches ? labeled box and, even as abstract as an unlabeled box (discussed later). Similar abstraction occurs in verbal and written reports. The device initially is referred to by its full name. This will quickly be simplified to one or two words, then to an acronym, and then to a nickname, or even a comical name. The point is that our technical training, used for description and analysis in problem solving, is object oriented at all levels of abstraction.

The second most important feature in technical problem solving is a function. When an object is understood, understanding of its function follows. Functions are the purposes for the existence of objects. Considerable care is taken to understand functions; this can lead to extensive mathematical abstraction. Third in importance in features of technical problems are the attributes of the objects. These are usually summarized in lists of materials and in design specifications of the objects. They may be accepted as conditions of solutions and, as such, serve as filters to cull solution concepts. Minimal abstraction, if any, is involved for attributes.

The point of this somewhat simplified view is that objects are the center of focus in conventional problem analysis and solution. Furthermore, the abstractions of objects used in discussion and analysis often retain graphic semblances to the original object. These create a biased perspective of the problem. Such bias is a limited view that can dissuade a problem solver from broader investigation.

It is the objective of structured problem-solving methodology to draw the problem solver away from such a (subconsciously) biased perspective and suggest ways of finding new perspectives. Of course, these will have their own biases; but they have not yet been exploited for new insights. An obvious opportunity for a new perspective is an attribute-centered system of analysis and solution. The heuristics derived in Part II will be seen to take advantage of this opportunity.

Object-oriented bias is desirable in the scaling phase of problem solving. In the idea-generation phase one needs as much freedom of association with past experience as can be evoked in the subconscious for unusual recall. An excellent heuristic for this purpose is the use of â€œambiguityâ€. One form of ambiguity is known as â€œgenerification of object namesâ€ (Table 1, No. 8). That is, referring to objects not by their commercial names but by generic names that reflect their functions. For example, a mechanical screw might be named a clamp, a fastener, a marker, an adjuster, a pivot, a support, a pump, a balance weight, a point of reference, a hole filler, or a propeller, according to its main use in a given problem.

Each generic object name becomes a seed to spark the subconscious. At this juncture, minds diverge through individual-dependent backgrounds of experience. The generification of an objectâ€™s commercial name according to its application will produce rather similar results among different problem solvers, but the subsequent sparks of imagination can vary in surprising ways. As an example, consider one of the above generifications of a mechanical screw; say, a â€œfastenerâ€. In quick succession (without filtering), these ideas came to my mind: a gate latch, a staple, a railway spike, a Cleco button, a safety pin, a straight pin, a tack, a ratchet, Velcro, a belt buckle, a mechanical detent, a cog, a knot, a welded joint, a bottle cap, a shoe string, a skewer, a shoe stuck in mud, a rivet, a friction joint, a differential thermal-expansion joint, and â€¦ (I quit when the rate of ideas slowed). Note that some of the â€œsparksâ€ produced sequences in which one idea gave rise to the next. Hence, a particular idea may appear to be disconnected from the original one. The purpose of this demonstration is to show that some resulting associations may seem logical to the reader and others may not. All were logical to me for specific reasons. Such variability among individuals should be borne in mind when judging whether a proffered solution concept follows logically from a specific heuristic.

A major benefit of the use of ambiguity to invoke broad associations is to suppress the rigor of engineering-type analysis. Presumably, when a problem solver has reached the point of applying a structured problem-solving methodology, rigorous engineering-type thinking has been already exploited and useful ideas captured. The strategy now is to shift to an unconventional approach that is not whimsical and retains phenomenological validity.

Abstraction of heuristics
The heuristic to â€œsimplifyâ€ a problem, without identifying what to simplify, sounds very abstract. But it is only applied when the problem solver has begun to formulate verbal and graphic metaphors and complexity has been recognized. Most often the complexity relates to the number of objects, repeated patterns, or extraneous information. Once complexity is recognized, simplification may come to mind intuitively or as a practiced discipline of problem solving. At this point, when complexity has been recognized, the problem solver has physical world images to deal with.

â€œReverse the order of functionsâ€ and â€œreverse the order of objectsâ€ are less abstract heuristics because they are worded to make their point of application specific and mentally visible. â€œReverse orderâ€, would be a more abstract level of thinking. In any case, the problem solver usually will mentally translate a heuristic to the specific situation at hand, making object and function associations relevant to the physical world. At this point the heuristic assumes the bias associated with the physical world objects in its new wording and images. This facilitates execution of a heuristic. At the same time, it may reduce its potential scope. In the derivation of heuristics it will be seen that they can be executed at an abstract level that widens their scope.

Because no algorithms exist for deriving heuristics it will be necessary to call on heuristics to assist the process. Heuristics selected for this task must be reasonably well known and accepted, or at least tolerated while postponing judgment in order to see the outcome. Procedural steps will include creation of a well-defined problem, use of assumptions composing a set of axioms, and logical deduction of heuristics (while applying known heuristics throughout the process).

Note that the eighteen heuristics listed in Table (1) are all abstract, meaning that a specific physical-world object, attribute, or function is never mentioned. Such abstraction poses no mental problem in applying the heuristics to physical-world problems because the necessary associations are obvious. In fact, their history usually involved reduction or generalization of similarities seen among multiple real-world problems. However, their application to an abstract problem might be troublesome on first encounter.

A well-defined problem will be established following the guidelines of USIT. (4, 5) One requirement for a well-defined problem is a single unwanted effect. (4, 5) Since the to-be-derived heuristics will be used to produce solutions to technical problems, the unwanted effect will be the existence of a technical problem, although an undefined one.

It is also required that an unwanted effect be defined in terms of objects, attributes, and functions. Furthermore, it is recommended to introduce ambiguity through generification of objectsâ€™ names. In this case â€“ the derivation of heuristics â€“ the problem is abstract and ambiguous from the beginning because no physical-world components are referenced whose names would be generified. To complete the well-defined problem, verbal and graphic statements of the problem are constructed.

Notice that a well-defined problem requires a single-unwanted effect. It might occur to define the lack of derived heuristics as the unwanted effect, since the target is to obtain derived heuristics. This would imply that the solution to the abstract unwanted effect, lack of derived heuristics, is derived abstractheuristics, which smells of a trap in circular reasoning.

Mathematical algorithms are not derived from mathematical algorithms. Instead a class of problems is characterized by a set of axioms designed to permit their translation into a generic (abstract) equation, such as a quadratic polynomial, for example. A general solution of the equation is deduced, which becomes an algorithm for solving future quadratic equations. In other words, a generic problem is solved of the class needing an algorithm. A general algorithm is deduced from its solution.

An analogous procedure can be applied here. We define a generic problem of the type needing heuristics and from its solution deduce the target heuristics. Hence, we will create an unwanted effect as a generic problem composed of objects, attributes, and functions, find its solutions and deduce â€œderivedâ€ heuristics from the results.

The method for derivation of abstract heuristics We will first analyze a physical-world problem using known heuristics in order to observe how the application of heuristics can work on a â€œrealâ€ problem. Next, we will apply heuristics to the same problem cast in abstract form; i.e., divested of its specific physical-world identities. This will enable comparison of the application of heuristics to real and to abstract problems. As the application of heuristics unfolds, note the phase of problem solving where each heuristic is introduced: problem definition, analysis, and solution. Note also the nature of each heuristic, the ideas it evokes, and how they differ between two minds (yours and mine).

Application of heuristics to a physical-world
problem
Problem-definition phase
The problem:
â€œHand held binoculars produce blurring of images resulting from motion of the binoculars caused by breathing.â€ This problem statement has specific objects identified including, binoculars, image, and hand. Other objects are implied including light, the components of binoculars, lungs, the components connecting hand to retina, and retina (the image-encoding object).
Several known heuristics were applied in constructing this problem statement:
1) include objects, attributes, and functions (the function to form an image is implied);
2) include a single unwanted effect (blurring of image);
3) include root cause (motion of lens relative to eye caused by lung expansion and contraction), and
4) identify object-object interactions (e.g., hand holding binoculars, light forming an image on the retina, lung moving chest, shoulder moving arm, etc.). Another heuristic is
5) include a simple sketch (an example is shown in Fig. 1).

Figure 1. Simple sketch of hand-held binoculars showing light passing through a lens and forming an image on the retina of an eye. Eye is treated as a single compound object. The binoculars are shown connected to the source of motion, the lungs, through lens frame, hand, arm, shoulder, and chest.

A heuristic that applies to both verbal and graphic statements is

6) to simplify.
In this case, we see in the sketch that all of the physiological components from
shoulder to hand, plus the lens frame, perform the same function, namely to
support. A simplification of the sketch would be to combine these into one
object (see Fig. 2). Another heuristic is to

7) name objects for their functions rather than use their common or their manufactured names. In this case the unified element in Fig. (2) is named support.

Figure 2. Simplification of Fig. (1) that combines components from shoulder to lens as a single object, the support.

Further simplification comes to light on examining the simpler sketch in Fig. (2). Since lung is the source of motion, and the motion moves lens relative to eye, other objects can be eliminated, as illustrated in Fig. (3), without loss of the problem â€“ the unwanted effect. Note that eye includes its lens and its retina, which together form an image. They are combined into one object, eye, since neither is seen as root cause. This follows the heuristic to 8) eliminate unnecessary objects (and further simplification).

Figure 3. Simplification of Fig. (2) by eliminating unnecessary objects without loss of the unwanted effect.

Although not defined explicitly in the figure, this sketch has components that are graphic metaphors for smaller components. The mind readily deals with them once they have been defined. And it does not forget them.

Problem analysis phase
A problem is ready to be analyzed once it is reasonably simplified both verbally and graphically. A first tool for this purpose is to construct an object-function diagram to identify the beneficial functions of each object. A heuristic advises one

9) construct a hierarchical diagram of objects linked by their single most important functions (IV).

The object-function diagram is illustrated in Fig. (4). (V)

As shown in Fig. (4), eye, light, and image have been combined as an imageforming system that is inaccessible to the problem solver. (VI) Lens is beneficial to this combined system in that it collects and focuses the incoming light.

Support is beneficial to lens, being designed to align lens and eye. This construction reveals that lung, which is a vibrator, has no beneficial function to any of the objects.

Figure 4. Object-function diagram illustrating the beneficial relationship of object-object
interactions in a hierarchical relationship. Vibrator, the lung, has no beneficial function
to any of the objects and is set to the side in the diagram.

The sketch should be examined for further simplification opportunities using ideas learned from the first analysis before moving to the next analytical tool. It is evident that the binocular lens focuses light for the purposes of forming an image. However, we see now that focused light has nothing to do with blurring of image. Both a focused and an unfocused image can be blurred by motion. The critical factor is the alignment of the axes of the two optical elements, lens and image forming system, â€œeyeâ€. This axis is emphasized in Fig. (5).

Figure 5. Simplified version of Fig. 3 in which the optical axes of lens and â€œeyeâ€ are aligned. The two supports have been further qualified to distinguish them.

The next phase of problem analysis requires
10) examining interactions between pairs of objects, and

11) identifying one attribute from each object and a function they support. Another heuristic for problem definition is to

12) identify plausible root causes of the unwanted effect. This is done using a

13) plausible root causes diagram
shown in Fig. (6) as a proforma diagram. Each double-layer row has a cause related to the effect in the row above it. Each cause is treated as an effect for the double row below it. The hierarchical diagram terminates on active attributes. The diagram is annotated for the blurring of image problem in Fig. (7). Note in the figure that â€˜coupling to supportâ€ refers to â€œdegreeâ€ or â€œstrengthâ€ of coupling.

After active attributes of objects are identified the next step in analysis is to
14) determine attribute trends; i.e.,
15) determine whether increasing or decreasing their intensities causes an increase or decrease in the unwanted effect.
16) Construct qualitative-change graphs (VII) for this purpose, as illustrated in Fig. (8). The objects light and â€œeyeâ€ are not included in Fig. (8) since their attributes can be considered fixed. Vibration amplitude has three components: along-axis, off-axis, and tilt. Alongaxis vibration is immaterial, whereas both off-axis and tilt components are detrimental in the same sense and have been combined in Fig. (8).

From the identified attributes, Fig. (7), and attribute trends, Fig. (8), it is evident that the two supports behave identically. This suggests that they can be combined in the sketch as one object and further simplify the sketch.

Figure 9. Simplification of Fig. (5) by combining supports into one object. Vibrator now moves support relative to â€œeyeâ€. (Vibrator and support could have been reversed.)

Problem-solution phase

We move now from problem analysis to the application of solution techniques, which are also heuristics. The process actually begins with completion of the QC-diagrams. Solution concepts may be found using these graphs by

17) considering a worsening trend as working against us and finding ways to make it work for us. Solution concepts may also be found from the graphs by
18) considering the implications of making a particular attribute trend have a zero slope (VIII), i.e., â€¦
19) eliminate an attribute. Elimination of an attribute means to make an active attribute inactive by discontinuing its use.

Solution techniques
Make an unwanted effect work for us (#17). [S1] Construct the lens and support as a spring-and-damper assembly mounted within an outer enclosure that is handheld. The inner lens will then lag the motion of the outer enclosure and dampen its motion. Reduce an attributeâ€™s characteristic slope to zero, Fig. (8) and heuristic (#18).

The characteristic of vibration amplitude of vibrator could be reduced to zero by [S2] holding oneâ€™s breath. This is a known solution that works for short periods.

The degree of coupling of vibrator to support can be given zero slope by [S3] adding a new support between head and lens to bypass the vibrating support. A particular embodiment of this concept could be binoculars mounted to a head frame, which eliminates need of handholding.

Eliminate an attribute. (#19) Lens alignment with â€˜eyeâ€™ can be eliminated by [S4] combining lens and â€œeyeâ€. This suggests a contact lens that would move with the â€œeyeâ€ and whose curvature could be altered electronically â€“ such as a â€œfluid lensâ€. (10)

Uniqueness
20) identify unique features of a system and examine them for solution concepts.

Note that the lens has rotational and three translational degrees of freedom with respect to the path of light: translation includes horizontal and vertical plus longitudinal motions. The latter, longitudinal, has little effect on blurring (but a large effect on focusing). Both transverse motions affect blurring adversely but do not affect focus.

[S5] This uniqueness suggests stabilizing the lens in at least two directions. Stabilization can be accomplished using a built-in, battery-operated gyroscope mounted to an optical element, such as, an internal lens, prism, or mirror. This is a known solution that is available in commercial products.

Multiplication of objects

21) Multiplication of objects allows one to introduce copies of existing objects and employ them differently. [S6] Multiplication of supports brings to mind two, hinged supports containing a vibration dampener between them. An example is illustrated in Fig. (10). Vibrations are transmitted through the arm to the lower leg of the hinged support. The damper connecting the two legs attenuates vibration transmitted to the upper leg of the support. A second damper could be used to attenuate vibration in an orthogonal direction. Hinges provide mechanical connectivity. This function could be incorporated in the dampers. (IX)

Figure 10. A hinged support containing a damper on one leg and the lens attached to the other leg is held by hand to align the lens and â€œeyeâ€.

Division of objects
22) Division of objects allows use of the parts differently.[S7] Division of lens into quadrants, with each quadrant being coated with a transparent, light-sensitive material, or coated on its rim (or bezel), would enable detection of lens motion in two transverse directions by differentialmeasurement of light intensities on opposing pairs of quadrants. This information could be fed back to transducers coupled to an internal optical element (lens, prism, or mirror) to be moved in direction and amplitude so as to cancel motion that would cause blurring.

Distribution of functions
23) Distribution of functions suggests moving functions to different objects. [S8] Could, for example, â€œsupportâ€™s function to alignâ€ be moved to â€œeyeâ€ (Fig. 4)? For â€œeyeâ€ and light to perform alignment suggests recording sequences of digital images, then comparing and correcting successive pairs of images, and playing back the motion-corrected image on a viewing screen on the binoculars.

Transduction
Transduction suggests
24) considering the addition of attribute-function-attribute links to construct a solution concept.
To visualize the process first
25) construct a block-type diagram of interacting objects, a pair of their attributes, and the unwanted effect they support, with its affected attribute (as shown in Fig. 11).

Figure 11. Amplitued of vibration of vibrator and stiffness of support interact to support the unwanted effect of â€œlensâ€ motion affecting â€œlensâ€ position.
26) using the affected attribute (deflection) as an input attribute to another function that would affect some other attribute of an object in a useful way.
27) Multiple A-F-A links are allowed. An example is illustrated in Fig. (12). [S9] An A-F-A link of [internal friction of support] â€“toâ€“ [dampen motion] â€“toâ€“ [deflection of support] has been added to the system of Fig. (11).

This completes the demonstration of heuristics used in problem solving following the USIT methodology. Heuristics used in this demonstration problem are summarized in Table (2). Although nine solution concepts were found (S1 â€“ S9) this was not a thorough execution of the methodology. More phenomenology could have been discussed, more heuristics applied, and more solution concepts found. However, it is sufficient to illustrate a variety of heuristics and to show where they play a role and how they work. In all cases they work as seeds to spark ideas.

Table 2 Summary of heuristics used in the blurring of image problem.

Abstract heuristics â€“ no physical-world references

You probably noted apparent redundancies in some heuristics being named as well as listed again in an explanatory form or even repeated in different words. Such is the method of using heuristics. Since they are seeds to spark mental action, they have no unique proforma of expression that is guaranteed to work for all problem solvers. Or even to work for the same problem solver on different occasions. For this reason, heuristics tend to take on personalized wording to the liking of an individual. They also take on the argot of particular fields of use.

Of particular interest is that none of the heuristics in Table (1) cites a specific, physical-world object, attribute, or function; consequently all of the heuristics are abstract. When heuristics are applied to a specific problem, the problem solver gives objects, attributes, and functions identities belonging to the problem. This observation implies that heuristics should be transportable to various fields. In fact, they should be transportable to any field in which problems can be couched in terms of objects, attributes, and functions. That begs the question of appropriate definitions for objects, attributes, and functions in non-technical areas.

Specific physical-world objects became immediately obvious as heuristics were introduced in the process of defining, analyzing, and solving the demonstration problem. Then came identification of functions (object-object interactions), and finally, perhaps with more effort, came the identification of object attributes (heuristics were used to identify these). In fact, without these direct associations between the abstract words, object, attribute, and function, and physical-world examples of the problem, some readers would find the heuristics too abstract to understand. On the other hand, once it is understood how abstract heuristics work, i.e., how they spark the thought process, it is proposed that they can be used to solve abstract problems. This is the process used in the derivation of heuristics in Part II. To see how this might work, I will cast the demonstration problem in abstract form, determine which heuristics can be applied, and apply them to solve the abstract problem.

There is a working level of logic that ties together object, attribute, and function allowing their definitions and realistic associations in the physical world. It is that functions affect attributes by changing or maintaining their degree of intensity. Objects are the carriers of attributes and are characterized by their active attributes. Pairs of active attributes interact to support functions. This circle of logic, while stated in the abstract, is readily satisfied in the physical world.

Application of heuristics to an abstract problem
Problem definition phase

The original physical-world problem statement:

â€œHand held binoculars produce blurring of images resulting from motion of the binoculars caused by breathing.â€

This problem statement is to be elevated to an abstract form. When cast into abstract form, by stripping the statement of specific, physical- world references, the problem can be written as follows.

â€œAn object interacts with another object causing an unwanted effect in a third attribute as a result of a causal attribute of an object.â€

This statement incorporates heuristics (1 â€“ 4) in Table (2). A simple sketch is an additional need for a well-defined problem. This is done readily for realworld objects, but how is it to be done for abstract objects? Solution heuristic, 25) â€œConstruct a block-type diagram of interacting objects, a pair of their attributes, and the unwanted effect they support, with its affected attribute.â€

in Table (2), is useful for this purpose and is substituted for #5, as shown in Fig. (13). Although the components are all abstract, their general relationships to one another are clearly illustrated.

Figure 13. Problem statement and simple sketch (block diagram) for an abstract problem using heuristics (#1 – #5, #27) of Table (2) as indicated. Wavy lines indicate the zone of interaction of input attributes A1 and A2.

The abstract verbal statement and abstract block diagram constitute an abstract problem definition not associated with a particular field, or even a particular problem. The diagram in Fig. (13) is a graphic heuristic, H1. (H(x) identifies new heuristics by subscript number.)

Problem analysis phase
The only analytical heuristic in Table (2) that can be used without specific information about objects and attributes is heuristic (#5), â€œa simple sketchâ€, which has been cast in the abstract in Fig. (13) using heuristic (#27). Thus we move on to the solution phase.

Problem solution phase
Solution-phase heuristics (#17, 18, 20, and 23) in Table (2) require specific details about objects and attributes. Hence, they cannot be used for the abstract problem. Heuristics (#19, 21 â€“ 22, and 24 â€“ 27) can be used. These are illustrated in the following figures.

Three attributes are available to select for elimination (A1, A2, and Am, the affected attribute). These constitute three new heuristics (H2 â€“ H4 for removing
A1 â€“ Am respectively.) (X)
H2) Eliminate active attribute A1 of object O1 by moving, removing, or reshaping O1.
H3) Eliminate active attribute A2 of object O2 by moving, removing, or reshaping O2.
H4) Eliminate the affected attribute Am of object O3 by moving, removing, or reshaping O3.
The consequences of eliminating an attribute are to render its associated object useless, for supporting the unwanted effect, thus eliminating the unwanted effect (if the object has only one attribute supporting the unwanted effect). One choice of eliminating an attribute is shown in Fig. (14).

Figure (14) illustrates one of three new graphic heuristics for solving an abstract problem, H2. They have been derived from a known heuristic; (#19) â€œeliminate an attributeâ€. The three graphics represent solutions of the original abstract problem (Fig. 13). Thus, the abstract problem has been solved.

To apply these three solution heuristics to a physical-world problem, first construct the block diagram inserting the specific objects, attributes, and unwanted effect of the problem. If its components have the same relative relationships as shown in the abstract problem of Fig. (13) then Fig. (14) represents a solution. The problem solver, at this stage, studies the physicalworld block diagram just created and considers the consequences of eliminating object-1. If the heuristic has the desired effect the problem solver will discover solution concepts involving removal of attribute-1. The process is repeated for removal of the other two attributes, one at a time.

The identification of pairs of interacting attributes is a tool of USIT designed to simplify problem analysis. There can be multiple pairs of attributes supporting

the same function. There may also be multiple functions at the same point of object-object contact. The closed-world diagram heuristic is used to identify the most important function. Others can be ignored (and should be) during analysis of the most important one.

Heuristic #21: Multiplication of objects With three potential objects to choose from (O1, O2, and O3), multiplication of objects brings three more graphic heuristics (H5 â€“ H7). Multiplication of an object refers to using a copy of it in a different way (XI) by activating a new attribute to support a useful function when joined with an existing attribute (see Fig. 15).

Figure 15. Object multiplication introduces a copy of an existing object (O1 â€“ O3) having a new active attribute, A4, which combined with an existing attribute (A1, A2, or Am) supports a function that is useful as a solution to the problem through its affected attribute.

Figure (15) is a graphic heuristic (H5); it illustrates the starting point â€“ multiplication of an object, O1. The next step in this example of multiplication is to consider which attributes the new attribute (A4) will interact with (A1, A2, or Am). The interaction of A4 with A1 is illustrated in Fig. (16) where the function, the interaction supports, modifies the original attribute, Am, so as to counteract its unwanted effect. In this manner twelve graphic multiplication heuristics are created; see Table (3) (heuristics H5 â€“ H16).

Figure 16. Attribute A4 of multiplication object O1 is allowed to interact with attribute A1 to support a function that affects the original unwanted-effect attribute, Am, in a manner to nullify or make useful the unwanted effect.

Heuristics, H5 â€“ H7, can be subsequently combined with any one of the three attributes to form a total of nine new graphic heuristics (H8 â€“ H16). (XII) Figure 17. Attribute A4 of multiplication object O1 is allowed to interact with attribute A2 to support a function that affects the original unwanted effect attribute, Am, in a manner to nullify or make useful the unwanted effect.

Figure 18. Attribute A4 of multiplication object O1 is allowed to interact with attribute Am to support a function that affects the original unwanted effect attribute, Am, in a manner to nullify or make useful the unwanted effect.

Figures (17) and (18) illustrate multiplication of object O1 followed by interaction of attribute A1 with A2 (Fig. 17) and Am (Fig. 18).

Heuristic #22: Division of objects
Division of an object allows using its parts differently by activating new attributes in the parts. This is particularly useful for compound objects where finding different functions for components may be useful. Division of O1 is illustrated in Fig. (19).

Figure 19. Object division introduces a part of an existing object (O1 â€“ O3) having a new active attribute, A4, which combined with an existing attribute (A1, A2, or Am) supports a function useful as a solution to the problem through its affected attribute.

Again, three new heuristics arise, one for each object to be divided (H17 â€“ H19).The second step, selecting which of the original attributes to interact with,produces nine more heuristics (H20 â€“ H28). One is illustrated in Fig. 20.

Figure 20. Attribute A4 of division object O1 is allowed to interact with attribute A1 to support a function that affects the original unwanted-effect attribute, Am, in a manner to nullify or make useful the unwanted effect.

Heuristic #29: Add attribute â€“ function â€“ attribute links Attribute-function-attribute (A-F-A) links connect the affected attribute in an unwanted effect to support a useful function. This is illustrated in Fig. (21).
Adding an A-F-A link allows introduction of a new object and an active attribute from the new object (H29). Multiple links can be used (#26 of Table 2).

Figure 21. An A-F-A link has been introduced to the problem diagram through a new object, O4, and its active attribute, A4, to support a new function through interaction of A4 with Am.

The newly found graphic heuristics for solving an abstract problem are summarized in Table (3).

Abstract heuristics for abstract problems
The solutions of the image-blurring problem, a physical-world problem, were accomplished using twenty-seven known heuristics. All of the solution heuristics used are abstract in that they have no specific objects or attributes
mentioned in their wordings. The image-blurring problem was then stripped of specific object, attribute, and function references to convert it to and equivalent abstract form. Thirteen of the original heuristics were used to formulate abstract solutions. In the process, twenty-nine new graphic-type solution heuristics were