Insight problems are used in the study of human creativity problem solving to evaluate the creativity of the solver, and the process through which creativity problem solving is cognitively deployed. However, not many such problems exist, and the factors underlying their creation are not well controlled. The framework CreaCogs proposes ways in which cognitive AI systems could be used to solve diverse such problems using a small set of processes. In this paper, a previous approach for the creation of insight problems proposed in CreaCogs is implemented computationally. The initial experiments, results, limitations, perspectives and potential are reported upon.
Creativity and creativity problem solving are analysed and measured in the
cognitive science and cognitive psychology literature with a set of tests { Alternative
Uses Test [
One psychometric limitation of insight problems is that, once the participant has solved a problem, this will most likely not produce insight anymore, as the solution path has already been trodden by the participant. Not all problems requiring creativity would produce insight, but having a bigger repository of problems that require creativity with practical objects would allow for a wider and deeper exploration of creativity processes, and for a selection of problems most likely to produce insight.
A computational approach to creating practical object insight problems was
previously proposed [
The rest of this paper is organized as follows. Section 2 discusses the
general approach to problem creation. Section 3 and gives a running example over
all the problem creation steps using an example problem. Section 4 takes the
formalization from [
The approach to insight problem creation proposed by [
The rst step in the process of creating insight problems computationally2 is obtaining and encoding a non-creativity problem. This encoded non-creativity problem is the input to the insight problem generator. A set of techniques are applied to this input to transform the non-creativity problem to an insight problem. The ow of steps is shown in Figure 1 and each of the steps explained further. It is important to mention that not all the steps need to be applied for each of the problems, but they rather constitute a repertoire of actions which transform the problem.
The insight problem creation process can be better understood with an
example problem. The problem that will be discussed here is one manually created
with this approach in [
This problem presents the participant with the following task: The wind blew your sons teddy bear from the clothesline into your neighbours garden. The neighbour is in holidays and the fence is too high to climb. How can you retrieve the teddy? Figure 2 shows the problem.
One solution to this problem could be to construct a shing rod (using the mop, the clothesline, and a clothes hanger attached to the clothesline); this shing rod can then be used to attempt to fetch the teddy.
The above problem is a problem that requires creativity to solve, which is the output of the problem creation process. The input is a simple problem not
requiring creativity. A non-creative version of this problem would be one in which the solver can simply step in the neighbour's garden. Assuming extra constraints (the solver is not allowed in the garden, and doesn't have a key), a version of this problem could require a shing rod to catch the teddy. Showing the shing rod as part of the problem would be, in our example, the less creative version of the problem (the input problem). Using this, we use the problem creation process to obtain a problem requiring creativity, and to showcase the approach.
The process starts with the encoding of the non-creativity problem. 3.1
The encoding module can be broken down into three sub-parts: 1. Why are we encoding?
The non-creativity problem, which is the input to the problem transformation process is in words and images. To make the input in a machine understandable format, we have the encoding module. 2. How does the encoding look like?
The encoding [
The input problem is transformed in a set of concepts(Ci), relations(Ri), actions(Hi), goals(Gi) and constraints(Ki), avoiding NLP issues. In this encoding: Concepts are everyday objects with properties such as shape, material, size etc. Relations are an association between two or more concepts.
Actions are the action performed on the concepts which may or may not lead to a change in relation.
Goals describe the nal state to be reached. It could be a set of concepts and relations.
Constraints describe the resource or action limits of the task. { solution objects { solution a ordance(s) of the ith solution object { solution a ordance of the problem.
This is further discussed in section 3.2 3. How would the encoding be generated?
The present implementation has the encoding generated manually. Generating the encoding computationally is an interesting problem and is involved in our future work. 3.2
The solution object(s), needs to be known prior to beginning the problem transformation process; this allows us to conceal or transform the solution related objects and/or their solution related a ordances.
The solution object(s) is represented by set Csol. The solution a ordance(s) of the ith solution object is denoted by Acisol. The solution a ordance of problem is represented by Asol.
For the example problem, the solution object is a shing rod. Thus, the transformation steps are applied to this object. The solution related a ordance of shing rod is to fetch far away objects. In this case, the solution a ordance of the example problem is also to fetch far away objects. The aim of the insight problem creation process is to hide both the shing rod and its solution a ordance.
Csol = fC3g Ac3sol = f etch f ar away object
Asol = f etch f ar away object 3.3
In this step, solution object(s) are decomposed or broken down into di erent parts and then each part may or may not be re-represented in a di erent structure or object. This process requires the knowledge of what parts the object consist of. The process outputs more concepts.
For the example problem, the F ishing rod can be decomposed into it's constituent parts - Rod; String; Hook. This decomposition step decomposes the concept, C3 and gives us three new concepts.
C5 Rod C6 String C7 Hook
Decomposition essentially breaks down the solution objects so that the human solver needs to reconstruct it. 3.4
In this step solution object(s) or their parts are replaced by other object(s) which
are similar by properties and a ordance to the solution object but for which the
said a ordance is not as salient as for the solution object. The approach to
the process of object replacement is discussed in [
For the example problem, the replacement could take place as follows: creative replacement(Rod) = M op handle creative replacement(String) = Clothes line creative replacement(Hook) = Clothes hanger Thus, the new concepts are:
C5 M op handle C6 Clothes line C7 Clothes hanger
Replacement will essentially force the human solver to re-represent the replacement object (or object parts) with the original object. Thus, giving the a ordance of the original object to the replacement object. 3.5
This step reduces the salient a ordance of the solution object(s) by showing the object(s) (or object parts) in di erent contexts of a ordance. The salient a ordance can also be concealed by having that a ordance as already taken up or in use.
Knowledge of alternative uses [
For example, suppose that for a creativity problem the solution a ordance of a solution object, clothespin is to clip clothes on string. An alternative a ordance of clothespin could be clip f lower and stick. Since, this alternative a ordance is di erent from the solution a ordance of clothespin, the clothespin can be shown in the context of the alternative a ordance. 2. Knowledge of problem templates { To explain this method, we rst explain what problem templates stand for in CreaCogs. A problem template is a sequence of states where actions help in transitioning from one state to the other. a State is a set of concepts, relations and goals that will lead to a particular solution or a ordance. Figure 3 explains the structure of problem templates.; problem templates are part of the knowledge of the solver. For example, a problem template, P Tclean floor can be described as: C1 M op C2 Bucket C3 water C4 P erson
Fig. 3. Problem templates R1 R2 besides(mop; bucket) inside(bucket; water) # H1
grab(person; mop) C = C1; C2; C3; C4 R3 hold(person; mop) R = R2; R3 # H1
mops(person; mop; water; f loor) Gsolution = af f (P Tx)
clean f loor The second method checks if a problem template, P Tx, exists, such that the solution object belongs to the problem template and the a ordance of the problem template (af f (P Tx)) is not the same as the solution a ordance of the problem (Asol). If such a problem template exists, then the a ordance of the object in the context of this problem template is shown.
For example, for the example problem, an alternative a ordance for the object mop can be obtained through this process. The object mop belongs to the problem template of clean f loor. The a ordance of this problem template, clean f loor is di erent from the solution a ordance of the example problem (which is f etch f ar away object). Thus, elements of this problem template, such as the relations belonging to this problem template can be added to Rproblem.
besides(mop; bucket) inside(bucket; water) Thus, the a ordance of mop is shown in the context of this problem template and its solution a ordance of f etch f ar away object is hidden.
Sometimes, to show the objects or parts in di erent contexts of a ordance, additional objects may be needed. In this case, new objects will be added to the problem. The a ordance manipulation step changes the relations between objects, the actions in the problem description, or both.
For the example problem, this step will attempt to change the a ordance of the solution objects - clothesline, mop, clothes hanger. One of the outputs of this step could be: (a) Attaching the clothesline to the pole and hanging clothes on it. This shows the a ordance of clothesline as to hang clothes for drying and hides the possibility of using string to make a shing rod. This leads to new relations being formed: R3 attached(C6; pole)
R4 on(C6; clothes)) (b) Displaying the mop next to a bucket lled with water to show that the a ordance of mop is to clean.
R5 besides(C5; bucket)
R6 inside(bucket; water) (c) Hanging the clothes on the clothes hanger and hanging the clothe hanger on the clothesline.
R7 on(C7; clothes)
R8 on(C6; C7) As mentioned above, apart from new relations and actions being formed, this step could also lead to the need to bring new concepts in the problem { speci cally Bucket; W ater; Clothes; P ole in this example.
Changing the a ordance of the object might mislead the solver because they will perceive the object in the context of the new a ordance and the solution a ordance will be hidden. The problem would thus require more creativity to solve, requiring the solver to exit the `box' of context a ordances 3.6
This step involves addition of objects or templates whose a ordance might interfere with the solution. For example, in the above example problem we could show an object, ladder in the problem. This object would trigger a problem template of climbing over the fence using the ladder. However, the constraint does not allow the solver to set foot in the other garden.
This modules has not been implemented yet. It is a matter of future work. 4
In this section, the formalization from the previous work [
object parts = Input : hCproblem; Csol; KBi if size(object parts) > 1 then for p in object parts do
Cproblem.add(p)
Csol.add(p) end Cproblem.remove(c)
Csol.remove(c) end
else Let: KB denote the Knowledge Base of objects with their shapes and materials Cproblem be a set of concepts for the problem Csol be a set of solution concepts for the problem nd object parts of object c from the KB
Algorithm 1: Decomposition Let: KB denote the Knowledge Base of objects with their shapes and materials Cproblem be a set of concepts for the problem Csol be a set of solution concepts for the problem p denote the probability of replacing an object, p < 1 SOMshape denote a self organized map for shapes SOMmaterial denote a self organized map for materials Input : hCproblem; Csol; KB; p; SOMshape; SOMmateriali for c in Csol do if replacement to be done(p) then
c new f ind replacement(c) else
Cproblem.add(c new) Csol.add(c new) Cproblem.remove(c)
Csol.remove(c) end end Function FIND REPLACEMENT(c): nd c:shape and c:material from KB potential shapes SOMshape(c:shape) x random:randint(0; size(potential shapes)) chosen shape potential shapes[x] potential materials SOMmaterial(c:material) y random:randint(0; size(potential materials)) chosen material potential materials[y] c new an object with chosen shape and chosen material or an object having a part with chosen shape and chosen material from KB return c new
Let: KBuses denotes the Knowledge Base of normal and creative uses of objects KBP T denotes the Knowledge Base of problem templates P Tsol denotes the solution problem template Cproblem be a set of concepts for the problem Csol be a set of solution concepts for the problem Rproblem be a set of relations Hproblem be a set of actions Asol be the solution a ordance of the problem Input : hKBuses; KBP T ; P Tsol; Cproblem; Csol; Rproblem; Hproblem; Asoli for i in length(Csol) do ci Csol[i] aff ci nd all a ordances of ci from KBuses and choose one if aff ci 6= Hcisol then
Hproblem.add(aff ci) aelse for P T in KBP T do if ci 2 KBP T and aff(P T ) 6= Asol then r relations involving ci in P T Rproblem.add(r) h actions involving ci in P T
Hproblem.add(h) end end
Algorithm 3: A ordance Manipulation aThe current implementation of this process does not perform the 'else' part of the above algorithm. This is because the knowledge base of problem templates has not been gathered yet. 5
Each of the steps for turning a non-creativity problem into a creativity requiring one is now a process which can have multiple outcomes. In the following section, we will showcase our computational experimentation with generating problems which require insight and possibly creativity. To be able to maintain a linear progression, one potential outcome will be chosen after each step, before producing the next step. The multiplicity of outcomes is described in Section 6.
For each problem we manually make the non-creative version of the
corresponding classical creativity problem. The classical creativity problems are:
Problem 1 - The two strings problem [
The non-creative version of these problems is made by showing the solution object(s) in the problem description. In our computational experimentation we input the non-creative version of each of these problems and try to reach the corresponding classical creativity problem by applying the transformation process. In this process, we obtain various other creativity problems. For each problem, we have described the non-creativity problem rst. Then each step of the transformation process is explained step by step. The output of this process is a creativity problem. 5.1
The non-creative version of the two strings problem is stated as follows: A person is put in a room that has a string and a pendulum hanging from the ceiling. The task is to tie the string and the pendulum together, but it is impossible to reach one while holding the other.
The solution to this problem is to swing the pendulum and then hold the string and wait for the pendulum to swing within your reach. Similar to the previous problem, to make this an insight problem, we apply the steps of the transformation process with the non-creativity problem as the input. 1. The rst step is to encode this problem.
C1 P endulum C2 String C3 Ceiling C4 P erson R1 hang(Ceiling; P endulum) R2 hang(Ceiling; String) R3 hold(P erson; String) K1 If hold(P erson; String) then cannot hold(P erson; P endulum) Gsolution ftied(C1; C2)g Cproblem = fC1; C2; C3; C4g Rproblem = fR1; R2; R3g Hproblem = fg Kproblem = fK1g Gproblem = fGsolutiong
I = fCproblem; Rproblem; Hproblem; Gproblem; Kproblemg 2. Next we encode the solution of the non-creativity problem.
Csol = fC1g Ac1sol = swing(P endulum)
Asol = swing(P endulum) 3. The next step is to apply the decomposition step to the solution objects. For this problem, the decomposition step decomposed the object pendulum and output two new concepts:
C5 String C6 W eights Cproblem = fC2; C3; C4; C5; C6g
Csol = fC5; C6g 4. We move on to the next step which is replacement. The following results were obtained: Possible replacements for C5: Shirt, Scarf, Mitten, Rag, Tie, T-shirt, Drapes, Satchel, String Possible replacements for C6: Soda can, Battery, Lock, Spool, Luggage, Screwdriver, Horseshoe, Weights, Bottle We chose Horseshoe as the replacement of Weights and retained the object String. After this step,
C5 String
C6 Horseshoe 5. The next step is a ordance manipulation. The following results were obtained for this step: Possible a ordances for String : string wrapped around spool, string hanging from ceiling Possible a ordances for Horseshoe: horse wear horseshoe, horseshoe near forge We chose horseshoe near forge as the a ordance to be shown for Horseshoe and string hanging from ceiling for String. Thus, Horseshoe is shown in this context of a ordance and it's a ordance to act as a weight for a pendulum is hidden.
The following new concepts and relations are obtained:
C7 F orge
R4 near(C7; C6) Now we have a set of concepts, relations, actions, constraints and goal. This is the encoded insight problem. The conversion of this encoded insight problem to text is currently done manually. The creativity variant of the problem will show - a person in a room with two strings hanging from the ceiling. A horseshoe will be kept near a forge. The task will be to tie the two strings together with the constraint that it is impossible to reach one while holding the other. 5.2
The non-creative version of the cardboard problem is stated as follows: You are asked to attach a piece of cardboard to the loop on the ceiling. There is a hook placed on the table. How do you proceed?
The solution to this problem is to use the hook to attach the piece of cardboard to the loop. Again, this is not an insight problem. To make this an insight problem, we follow a similar procedure to the previous problems. 2. Next we encode the solution of the non-creativity problem.
Csol = fC2g Ac1sol = attach object to loop
Asol = attach object to loop 3. The next step is to apply the decomposition step to the solution objects. For this problem, this step gives no new concepts. 4. The following results were obtained from the replacement process: Possible replacements for C2: Bobby pin, U-Shaped magnet, Belt, Padlock We chose Belt as the replacement of Hook. After this step,
C2 Belt 5. The next step is a ordance manipulation. The following results were obtained for this step: Possible a ordances for Belt : belt inside closet, person wears belt We chose person wears belt as the a ordance to be shown. Thus, belt is shown in this context of a ordance and it's a ordance to act as a hook is hidden. The following new relation is obtained:
R2 wear(C5; C2)
The creativity variant of this problem will show - A person wearing a belt in a room with a loop on the ceiling and a piece of cardboard on a table. The task will be to attach this piece of cardboard to the loop. 5.3
The non-creative version of the candle problem is stated as follows: You are given a candle, candle holder, nails, hammer and a box of matches. You are supposed to x the lit candle unto the wall in a way that does not allow the wax to drip below. The solution to this problem is to use a candle holder to prevent wax dripping below. The nail is hammered into the wall and is used to x the candle holder on the wall. You do not need insight to solve this problem. To make this an insight problem, we apply the steps of the transformation process with the non-creativity problem as the input.
Cproblem = fC1; C2; C3; C4; C5; C6; C7; C8g Rproblem = fR1; R2g Hproblem = fg Kproblem = fg Gproblem = fGsolutiong
I = fCproblem; Rproblem; Hproblem; Gproblem; Kproblemg 2. Next we encode the solution of the non-creativity problem.
Csol = fC2; C3g Ac2sol = catch(W ax) Ac3sol = attach(W all; Candleholder)
Asol = catch(W ax) 3. The next step is to apply the decomposition step to the solution objects. For
this problem, this step gives no new concepts. 4. The following results were obtained from the replacement process:
Possible replacements for C3: Thumbtacks, Fork, Hook, Pin, Needle, Screw Possible replacements for C2: Bucket, Bin, Pot, Pringles tube, Matchbox, Kettle, Box, Kleenex For this problem an additional constraint has to be added at the replacement stage. The constraint is that the replacement object must be capable of being pierced. This is important because the goal consists of on(C7; C1), which says that the candle must be attached to the wall. This will rule out some replacements objects such as Bucket, Bin, Pot, Kettle. Addition of such constraints is done manually in our current implementation but making the process computational is in our future work.
Thus, Possible replacements for C2: Pringles tube, Matchbox, Kleenex, Box, Coaster We chose Pringles tube as the replacement of Candle holder and Needle as a replacement for Nails. After this step,
C2 P ringles tube
C3 N eedle 5. The next step is a ordance manipulation. The following results were obtained for this step: Possible a ordances for Pringlestube : pringles tube in bin, person eat from pringles tube, pringles tube on P ossibleaf f ordancesf orNeedle : needle attached to ball of yarn, needle attached to spool, thread intertwi We chose pringles tube in bin and needle attached to spool as the a ordance to be shown. Thus, pringles tube is shown in this context of a ordance and its a ordance to catch wax and prevent it from dripping is hidden.
The following new concepts and relations are obtained:
C10 Bin C11 Spool R3 in(C10; C2)
R4 attached(C11; C3)
The creativity variant of the problem will show - a candle, a box of matches and a needle attached to a spool on a table next to a wall. There will be a pringles tube in a bin. The task will be to x a lit candle unto the wall in a way that does not allow the wax to drip below. 6
The strength of the approach presented in this paper lies in the fact that multiple creativity problems can be created when starting from the same non-creative input problems.
In the previous section we chose one path at each step of the transformation process for the ease of explanation. In this section we show how multiple paths are obtained at each step of the transformation process. Table 1 lists the number of paths obtained in our computational experimentation for each of the problem. We also show the number of potential creativity problems that can be created. Figure 4 shows how di erent output creativity problems are obtained by tracing di erent paths.
The current knowledge base used for our computational experimentation consists of 497 objects. The knowledge base includes object parts, shapes and material of object parts and alternative uses of these objects. A larger dataset of objects will help improve the results of the replacement process. A larger alternative uses data and a knowledge base of problem templates will improve the results of a ordance manipulation process. Both of these will help increase and diversify the output creativity problems. After this initial computational experimentation, we conclude that the initial theoretical approach is feasible in terms of generating creativity problems in the future, in large quantities and variants. Regarding the quality of these problems, no evaluation has been provided yet { the authors aim to construct a metric of quality and apply methods of evaluation in future work.
An interesting question is whether problems created in these manner will be creativity problems or insight problems. Such a question will depend on whether insight is perceived as a quality of a problem, or a quality of the processes of the solver. In our opinion, some solvers may arrive via insightful processes at the answers, while others may do so via creative processes without insight. Still, whether particular problems are more prone to yield insights is a question for which this approach provides high chances of empirical experimentation and answers in the future.
Problem 3 throws light on an important point. The candle holder has two parts that are essential to reaching the goal of the problem. The convex shape is needed for catching the dripping wax and a loop is essential for attaching it to the wall. So, a replacement object for candle holder must have both these parts. Thus, when multiple parts of a solution object are needed to reach the goal, a replacement object must have these parts or similar parts as well (or two replacement objects that can be connected may be necessary). A future insight problem generator should account for this.
Another interesting question is raised by problem 3. The question is - which objects to include in Csol. The term solution objects used in this paper has certain ambiguity to it. For example, in problem 3, nails and candle holder were included in Csol as these were considered solution objects. One could argue that hammer, matches and matchbox could also be included in Csol and called solution objects since they are essential objects to reach the solution of the problem. This question still needs answering and will be covered in our future work.