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Analogical Problem Solving Technique

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Analogical Problem Solving Technique

Hello and welcome to the course Introduction to Advanced Cognitive Processes, this is the6th week and we have been talking about Problem Solving in the lectures in this week.Last lecture I talked to you about strategies of solving problems, we talked basically about2 approaches the gestalt approach and the information processing approach put forwardby Alan Newell and Herbert Simon.In today's lecture as well will just take forward this discussion about problem solvingapproaches and, will move towards a slightly different approach to the ones we have discussedalready.Now if you have ah wondered ah and, if you kind of observed the way ah you know peopleapproach solving problems in real lives, one of the useful ways is ah to you know to ahapproach a new problem ah to start thinking about a particular solution ah towards a problem.Is to ah you know ah sit back and ah recall some of the similar ah situations that youhave encountered and, ah some of the similar problems that you have come across in thepast and, then to try and apply solutions which you have used earlier ah to these newproblems and what might happen is that your earlier experiences might help you solve thesenew problems, which you know not really encountered earlier.This technique has been referred to as analogical problem solving.So, what you do is you use your older experiences or you use your older encounters with particularproblems, as analogies to problems that are new and the problems that are coming up ahin the current time and, this analogy this ah you know using of this earlier problem,sometimes help you ah reach effective solutions to the problems at hand.Let us take an example now there is this is the mutilated checkerboard problem and themutilated checkerboard problem is can be stated as such and, just borrowing this for ah fromGoldstein's book, ah a checkered board of 60 consists of 64 squares, these 64 squarescan be completely covered by placing 32 dominoes on the board.ah So, that each domino covers at least 2 squares, if we eliminate 2 corners of thecheckerboard as shown in the figure ah can we now cover the remaining squares with 31dominoes.Now that is basically the question now you can kind of pause the lecture here, try andsolve this problem, the answer is expected only in a form of a yes or a no.So, you just you know do whatever calculation you have to and give me an answer in termsof yes or no, you can pause it and start once you have a solution in mind.Let us move to a different problem let me let me give you a different problem now, andthe different problem is the Russian marriage problem which is adopted from hayes ah in1978, again I am just borrowing this from Goldstein as well, the Russian marriage problemah goes like this, in a small Russian village there were 32 bachelors and 32 unmarried women,ah through ah tireless efforts the village matchmakers succeeded in arranging 32 highlysatisfactory marriages.Everybody was proud and happy and the marriages were going on fine as well.And what happens one night, one drunken night, two bachelors, in a test of strength, stuffedeach other with particular sharp weapons and died.Now the idea is there are 62 people here, the question is can the matchmaker throughsome quick arrangements some shuffling come up with 31 heterosexual marriages amongstthe 62 survivors, you know 62 divided by 2 is 31.Now just think of this problem emphasis is on ah heterosexual marriages 31 heterosexualmarriages between 62 individuals, but remember there are 32 unmarried women and only 30 bachelors2 of them have died.If you kind of spend a minute thinking about this, you will immediately ah be able to tellthat, you know the answer the solution to this problem is no, it cannot really be done,now think back from here to the mutilated checkerboard problem.If you think back at the checkerboard problem, after you have read the Russian marriage problem,you will realize very quickly that a domino cannot cover 2 species and hence the 31 youknow ah basically 31 dominoes ah cannot be able to cover the entire thing, you will stillneed the same number of dominos.So, this is ah just an example of how one kind of problem might be able to help yousolve another problem, which has a rather similar structure.We will talk about how this works in the rest of the lecture today.This process of ah you know using features from one kind of problems to different problems,is referred to as analogical transfer.So, the starting point for much of this research on analogical problem solving, has been todetermine how well people can transfer their experiences of solving, one kind of problemsto solving another similar problem.This is analogical transfer.Now to investigate people are often presented with a story called the source problem and,that shares similarities with the target problem.So, the idea is similarly you can just see the earlier example, the Russian ah marriageah you know example could be the source problem while the checkerboard problem could be thetarget problem, or even the other way round does not really matter, but one of the problemsah because it is very similar to the other problem, will help the participant ah canhelp the participant in solving these problems.Let us take a different example now ah this one is referred to as Dunckers radiation problemI am just going to read, this one out to it and then you can pause the lecture take acouple of minutes and, reason how do you want to solve this problem.So, let me just read this out again borrowed from Goldstein's book.Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach,it is impossible to operate on this patient, but unless the tumor is destroyed the patientis going to die.There is a kind of a ray that can be used to destroy the tumor and, if the ray reachesthe tumor at a sufficiently high intensity the tumor will be destroyed, unfortunatelythere is a side effect of this, as well at this intensity which is needed to destroythe tumor the healthy tissue that the ray passes through also will be destroyed.At lower insane intensities the ray is harmless to healthy tissue, but then the tumor willnot be destroyed it will not really affect the tumor either.So, the question is what type of a procedure might be used to destroy this tumor and atthe same time avoid destroying the healthy tissue.this problem was used by Gick and Holyoak in 1980s, again it is it is an adaptationof the original dunkers problem, this is the radiation problem.Now you have to you can pause it give 2 minutes think of how you will solve it.So, when Duncker 9 in 1945 presented this problem to the participants most of them couldnot really come up with a solution, Gick and Holyoak did this in 1980 and they also foundthat only 10 percent of their participants ah could actually arrive at the correct solution.So, what happen is that Gick and Holyoak in 1980, they proclaimed that you know this isa very difficult problem and so, then what they did was they asked their participantsto read and memorize the fortress story.So, let us show you the fortress story and, the fortress story goes like this who canbe a little bit patient the fortress story is there a small country was ruled ah froma strong for a small country was ruled from a strong fortress by a dictator, the fortresswas situated in the middle of the country, surrounded by farms and villages many roadsled to the fortress and throughout the countryside.A rebel general vowed to capture the fortress, the general knew that an attack by his entirearmy would be sufficient to capture the fortress.He gathered in his army at the head of one of the roads ready to launch a full statea full scale direct attack; however, the general then realizes that the dictator had plantedlandmines on each of the roads the mines were.So, ah set such that ah they were small that small bodies of men could pass through themunharmed, ah safely since the dictator needed to move his troops and workers to and fromthe fortress; however, any large force any large number of men moving ah over these roadswould detonate the minds.Not only would this blow up the road, but it will also destroy many neighboring villagesit.Therefore, seemed impossible to capture the fortress now; however, what happens is thegeneral devises a simple plan, he divides his army into small groups and dispatcheseach group to the head of a different road, when all were ready he gives he gives a signalto each group and each group marches down a different route.Now each group continues down to it and down the road to the fortress.So, that the entire army arrives together at the fortress and at the same time and,then they can capture the fortress.So, the general captures the fortress and overthrows the dictator, this is the fortressproblem.Now unless if you have not really you know noticed it yet this is rather similar to thetumor problem so, after reading this story what happens is that the participants wereasked to start working ah on the radiation problem, this was ah source problem in somesense and, then the target problem was again given as the radiation problem, 30 percentof those people who had read and memorized the story, could solve the problem now ina few minutes; however, 70 percent of these participants could still not solve it.So, what was done is that Gick and Holyoak explicitly asked these participants to thinkabout the story they had learned and, ah you know ah and use the whatever they had ah gainedfrom that story in solving this problem.Now the success rate doubles and goes up to about 75 percent.So, what is happening it you basically you know the solution the radiation eh ah radiationproblem is that you have to you know, ah push this ah these rays from different directionsat ah smaller intensities, but all of them are reaching at the tumor at the same timeand, then they will be able to destroy the tumor much as the different armies, ah reachingat the same time when the fortress could help capture the fortress well.This is ah this is a very interesting thing you know that ah people learn and, the resultskind of ah took Gick and Holyoak ah to a set of conclusions, ah they concluded that analogicalproblem solving in basically includes 3 major steps.The first and the most important also the most difficult step is noticing that thereis an analogous relationship, if you can figure out the relationship between the current problemand, you know the problem that you aware of and the new problem at hand.Then you can start thinking of the analogy analogy Gick and Holyoak considered this themost difficult of all all the three steps to achieve and, a number of experiments havebeen done on this and they have shown that most effective source stories are that sharemost of their features with the target stories because, making this connection ah gettingthis notice is then much more easier.So, the first task is that you realize that you notice that there is an analogous relationshipbetween what you already know and, what the new problem at hand is.The next step is mapping the correspondence between the source story and the target storyfor example, ah the people who are reading these problems have to realize that you knowthe army a members the troops are basically similar to the race and, the roads are basicallysimilar to you know different sources and, as the army reaches from different roads atthe same time, the race could ah reach from different sources at the same time and destroythe tumor, or capture the fortress.So, this mapping is very important and applying this mapping ah basically is the third step.So, applying this mapping to generate a parallel solution to the target problem that is the3rd an another very important step.This application of ah or this application of the mapping and, this generation of a parallelsolution would basically involve generalizing from the small group of soldiers, ah to raiseapproaching from the you know the tumor from different directions.So, if these three steps are ah followed is these three tips are abided by that is whereanalogical problem solving, or analogous problem solving will succeed.Now having determined that analogies can help with problem solving, ah but obviously sometimeshints are required to help participants notice these map, notice there is a relationshipah and notice ah you know the presence of a source problem in their experience, Gickand Holyoake proceeded to look for factors that help facilitate this noticing and mapping,you know ah that help ah making this connections.So, one of the factors was referred to as surface features.The surface features is basically the specific elements that make up the two problems, suchas the rays and the tumor and the rays and those those kind of things, the surface featuresof the source problem and the target problem can sometimes be very different.To test this idea ah that making surface features more similar might help the participants,Holyoak and Koh in 1987, they created a problem that had similar surface features to the radiationproblem.The light bulb ah problem was is a very similar problem to the you know a radiation problemand, this goes like this in a physics lab at a major university a very expensive lightbulb, ah they use a very expensive light bulb which would emit precisely controlled qualitiesof light and, they it was being used in a lot of experiments, one morning Ruth the researchassistant comes into the lab and finds a light bulb no longer works.She notices that the filament inside the bulb had broken into 2 parts.This the surrounding glass bulb was completely sealed.So, there was no way to open it Ruth knew that the light bulb could be repaired, ifa brief high intensity laser beam could be used to fuse the 2 parts of the filament together;however, a high intensity laser beam would also break the surrounding fragile glass,surrounding the filament, at lower intensities the laser would not break the glass, but thenit will not fuse the filament together as well.Now the question is what type of procedure might be used to fuse the filament and thelayer filament with the laser at the same time avoiding breaking the glass.Again if you just ah spend a minute reading that understanding that this is very similarto the radiation problem and, when participants were giving this one group of participantswere taught about the radiation problem and it is solution in a psychology class and,another group of participants were not really aware of the radiation problem.So, what they found was that 81 percent of the participants, who knew about the radiationproblem could very quickly solve this ah light bulb problem, but only ten percent peopleof the control group could solve this problem.So, what is happening here Holyoak and koh hypothesize that this excellent analogicaltransfer is occurring because, there is a high similarity of surface features betweenthe two problems, you know radiation problem and the rays in the radiation problem andlasers in the light bulb problem.Now so, you know surface features similarity is very important, another kind of similarityshould be ah was investigated and this was the similarity between structural features.Now structural features are the ah underlying principles ah behind a particular solutionthat govern a particular solution.So, what they did was the radiation problem and the light bulb problems structural featuresare also similar, you know the weak laser beams are used to avoid breaking the glassand, the weak rays are used to avoid damaging the healthy tissue.So, these are aspects of the solution that are similar.So, Holyoak and Koh kept the surface features constant by now using a light bulb problem,as the source problem and the radiation problem as the target problem and, what they did wasthey tried to vary the structural features by presenting 2 different ah versions of thelight bulb problem, both versions began the story about the broken filament and the informationthat the filament could be fused using the high intensity laser beam beam was given,but the problem that needed to be solved in order to fix the filament was different inthe 2 versions.So, I will just read you out the 2 versions the first version is the fragile glass version,it is essentially same as the original version.The second version is called the insufficient intensity version; it had a different structuralfeature I will just read that out to you.So, the first version is exactly same so, Ruth placed several lasers in a circle acrossthe light bulb around the light bulb and, administered low intensity laser beams fromseveral directions all at once the beams all converged on the filament, when their combinedeffort was enough to fuse it because, each spot on the surrounding glass received a lowintensity beam the glass was also not broken.Now let us move to the next version of the problem today the problem, is laser generatesonly low intensity means that were not strong enough to fuse the filament.A much more intense laser beam is now needed again, there is a same thing.The Ruth solution now, is Ruths Ruth places several lasers in a circle around a lightbulb and, administered low intensity laser beams from several directions all at.Once the beams all converge on the filament where their combined effort was enough tofuse it, now the solution is is slightly you know different here, the glass aspect is notthere.Only 33 percent of the participants who read the solution to the second version, wherenow able to solve the radiation problem, those aspects of the solution have been taken awayyou know the healthy tissue thing has been taken away.The conclusion from comparing the results from the 2 versions of the light bulb problem,is that analogical transfer is also far better when the structural features of the sourceand target problems are very similar to each other.So, both kinds of similarities is basically ah are going to help ah ensure the analogicaltransfer.Now again as I was talking earlier, you know analogy people use analogy all the time peopleuse analogous problem solving all the time.There are many real world examples of analogical problem solving, they referred to as the analogicalparadox, ah as referred to by Dunbar in 2001, he saw that participants in psychologicalah experiments tended to focus on surface features in analogy problems, there is peoplein real life ah they frequently use you know much deeper and much more structural features,how the solution is ah attained say, when Dunbar colleagues ah they were videotapingah the conversations of molecular biologists and immunologist, during their lab meetingsthey found that the researchers use analogies from 3 to up from 3 to up to 15 times in justa one hour lab meeting.So, people are kind of making these very deep connections almost very frequently.For example, and the things could be like for example, if E coli works like this maybeyour gene is also doing the same thing.Similarly when Christensen and Schunn ah they recorded meetings of design engineers whoare creating new plastic products for medical applications, they found that these engineersalso proposed an analogy, almost about every five minutes.So, they are also making all of these connections.So, you can see that analogies play a very important role both in solving scientificproblems and designing new products.This is all from me about analogical problem solving, you will talk about a new aspectof problem solving in the next lecture.Thank you .