HUMAN PROBLEM SOLVING:THE STATE OF THE THEORY IN 1970 1

HERBERT A. SIMON AND ALLEN NEWELL 2

Carnegie-Mellon University

WHEN the magician pulls the rabbitfrom the hat, the spectator can respondeither with mystification or with curios-

ity. He can enjoy the surprise and the wonder ofthe unexplained (and perhaps inexplicable), or hecan search for an explanation.

Suppose curiosity is his main response—that headopts a scientist's attitude toward the mystery.What questions should a scientific theory of magicanswer? First, it should predict the performanceof a magician handling specified tasks—producing arabbit from a hat, say. It should explain how theproduction takes place, what processes are used,and what mechanisms perform those processes. Itshould predict the incidental phenomena that ac-company the magic—the magician's patter and hispretty assistant—and the relation of these to themystification process. It should show how changesin the attendant conditions—both changes "inside"the members of the audience and changes in thefeat of magic—alter the magician's behavior. Itshould explain how specific and general magician'sskills are learned, and what the magician "has"when he has learned them.

1 The research reported here was supported in part byUnited States Public Health Service Research Grant MH-07722, from the National Institute of Mental Health.

2 Since the Distinguished Scientific Contribution Awardcitation last year recognized that the work for which itwas awarded was done by a team, rather than an individual,Dr. Simon thinks it appropriate that Allen Newell, withwhom he has been in full partnership from the very begin-ning of the effort, should be enlisted into coauthorship ofthis report on it. Both authors would like to acknowledgetheir debts to the many others who have been membersof the team during the past decade and a half, but es-pecially to J. C. Shaw and Lee W. Gregg. This article isbased on the final chapter of the authors' forthcoming book,Human Problem Solving (Englewoocl Cliffs, N. J.: Pren-tice-Hall, in press).

Requests for reprints should be sent to the authors,Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213.

THEORY OF PROBLEM SOLVING—1958

Now I have been quoting—with a few word sub-stitutions—from a paper published in the Psycho-logical Review in 1958 (Newell, Shaw, & Simon,1958). In that paper, titled "Elements of a Theoryof Human Problem Solving," our research group re-ported on the results of its first two years of activ-ity in programming a digital computer to performproblem-solving tasks that are difficult for humans.Problem solving was regarded by many, at thattime, as a mystical, almost magical, human activity—as though the preservation of human dignity de-pended on man's remaining inscrutable to himself,on the magic-making processes remaining unex-plained.

In the course of writing the "Elements" paper,we searched the literature of problem solving for astatement of what it would mean to explain humanproblem solving, of how we would recognize anexplanation if we found one. Failing to discover astatement that satisfied us, we manufactured oneof our own—essentially the paragraph I para-phrased earlier. Let me quote it again, with theproper words restored, so that it will refer to themagic of human thinking and problem solving, in-stead of stage magic.

What questions should a theory of problem solvinganswer? First, it should predict the performance of aproblem solver handling specified tasks. It should explainhow human problem solving takes place: what processesare used, and what mechanisms perform these processes.It should predict the incidental phenomena that accom-pany problem solving, and the relation of these to theproblem-solving process. . . . It should show how changesin the attendant conditions—both changes "inside" theproblem solver and changes in the task confronting him—alter problem-solving behavior. It should explain howspecific and general problem-solving skills are learned, andwhat it is that the problem solver "has" when he haslearned them [p. 151].

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146 AMERICAN PSYCHOLOGIST

A Strategy

This view of explanation places its central em-phasis on process—on how particular human be-haviors come about, on the mechanisms that enablethem. We can sketch out the strategy of a re-search program for achieving such an explanation, astrategy that the actual events have been followingpretty closely, at least through the first eight steps:

1. Discover and define a set of processes that wouldenable a system capable of storing and manipulating pat-terns to perform complex nonnumerical tasks, like those ahuman performs when he is thinking.

2. Construct an information-processing language, and asystem for interpreting that language in terms of ele-mentary operations, that will enable programs to be writ-ten in terms of the information processes that have beendefined, and will permit those programs to be run on acomputer.

3. Discover and define a program, written in thelanguage of information processes, that is capable of solvingsome class of problems that humans find difficult. Usewhatever evidence is available to incorporate in the pro-gram processes that resemble those used by humans. (Donot admit processes, like very rapid arithmetic, that humansare known to be incapable of.)

4. If the first three steps are successful, obtain data,as detailed as possible, on human behavior in solving thesame problems as those tackled by the program. Searchfor the similarities and differences between the behavior ofprogram and human subject. Modify the program toachieve a better approximation to the human behavior.

5. Investigate a continually broadening range of humanproblem-solving and thinking tasks, repeating the first foursteps for each of them. Use the same set of elementaryinformation processes in all of the simulation programs, andtry to borrow from the subroutines and program organiza-tion of previous programs in designing each new one.

6. After human behavior in several tasks has been ap-proximated to a reasonable degree, construct more generalsimulation programs that can attack a whole range oftasks--winnow out the "general intelligence" componentsof the performances, and use them to build this more gen-eral program.

7. Examine the components of the simulation programsfor their relation to the more elementary human perform-ances that are commonly studied in the psychologicallaboratory: rote learning, elementary concept attainment,immediate recall, and so on. Draw inferences from simu-lations to elementary performances, and vice versa, so asto use .standard experimental data to test and improve theproblem-solving theories.

8. Search for new tasks (e.g., perceptual and languagetasks) that might provide additional arenas for testing thetheories and drawing out their implications.

9. Begin to search for the neurophysiological counter-parts of the elementary information processes that arepostulated in the theories. Use neurophysiological evidence

to improve the problem-solving theories, and inferencesfrom the problem-solving theories as clues for the neuro-physiological investigations.

10. Draw implications from the theories for the improve-ment of human performance—for example, the improvementof learning and decision making. Develop and test pro-grams of application.11. Review progress to date, and lay out a strategy for

the next period ahead.

Of course, life's programs are not as linear as thisstrategy, in the simplified form in which we havepresented it. A good strategy would have to con-tain many checkpoints for evaluation of progress,many feedback loops, many branches, many itera-tions. Step 1 of the strategy, for example, was amajor concern of our research group (and otherinvestigators as well) in 1955-56, but new ideas,refinements, and improvements have continued toappear up to the present time. Step 7 representeda minor part of our activity as early as 1956, be-came much more important in 1958-61, and hasremained active since.

Nor do strategies spring full-grown from the browof Zeus. Fifteen years' hindsight makes it easy towrite down the strategy in neat form. If anyonehad attempted to describe it prospectively in 1955,his version would have been much cruder and prob-ably would lack some of the last six steps.

The Logic Theorist

The "Elements" paper of 1958 reported a suc-cessful initial pass through the first three steps inthe strategy. A set of basic information processesfor manipulating nonnumerical symbols and symbolstructures had been devised (Newell & Simon,1956). A class of information-processing or list-processing languages had been designed and im-plemented, incorporating the basic informationprocesses, permitting programs to be written interms of them, and enabling these programs to berun on computers (Newell & Shaw, 1957). Aprogram, The Logic Theorist (LT), had been writ-ten in one of these languages, and had been shown,by running it on a computer, to be capable of solv-ing problems that are difficult for humans (Newell,Shaw, & Simon, 1957).

LT was, first and foremost, a demonstration ofsufficiency. The program's ability to discoverproofs for theorems in logic showed that, with nomore capabilities than it possessed—capabilities forreading, writing, storing, erasing, and comparing

HUMAN PROBLEM SOLVING 147

patterns-—a system could perform tasks that, inhumans, require thinking. To anyone with a tastefor parsimony, it suggested (but, of course, did notprove) that only these capabilities, and no others,should be postulated to account for the magic ofhuman thinking. Thus, the "Elements" paper pro-posed that "an explanation of an observed behaviorof the organism is provided by a program of primi-tive information processes that generates this be-havior [p. 151]," and exhibited LT as an exampleof such an explanation.

The sufficiency proof, the demonstration of prob-lem-solving capability at the human level, is only afirst step toward constructing an information-pro-cessing theory of human thinking. It only tellsus that in certain stimulus situations the correct(that is to say, the human) gross behavior can beproduced. But this kind of blind S-R relationbetween program and behavior does not explain theprocess that brings it about. We do not say thatwe understand the magic because we can predictthat a rabbit will emerge from the hat when themagician reaches into it. We want to know how itwas done-—how the rabbit got there. Programslike LT are explanations of human problem-solvingbehavior only to the extent that the processes theyuse to discover solutions are the same as the humanprocesses.

LT's claim to explain process as well as resultrested on slender evidence, which was summed upin the "Elements" paper as follows:

First, . . . (LT) is in fact capable of finding proofs fortheorems—hence incorporates a system of processes that issufficient for a problem-solving mechanism. Second, itsability to solve a particular problem depends on the se-quence in which problems are presented to it in much thesame way that a human subject's behavior depends onthis sequence. Third, its behavior exhibits both preparatoryand directional set. Fourth, it exhibits insight both in thesense of vicarious trial and error leading to "sudden" prob-lem solution, and in the sense of employing heuristics tokeep the total amount of trial and error within reasonablebounds. Fifth, it employs simple concepts to classify theexpressions with which it deals. Sixth, its program exhibitsa complex organized hierarchy of problems and subprob-Icms [p. 162].

There were important differences between LT'sprocesses and those used by human subjects to solvesimilar problems. Nevertheless, in one fundamentalrespect that has guided all the simulations that havefollowed LT, the program did indeed capture thecentral process in human problem solving: LT used

heuristic methods to carry out highly selectivesearches, hence to cut down enormous problemspaces to sizes that a slow, serial processor couldhandle. Selectivity of search, not speed, was takenas the key organizing principle, and essentially nouse was made of the computer's ultrarapid arith-metic capabilities in the simulation program. Heu-ristic methods that make this selectivity possiblehave turned out to be the central magic in all hu-man problem solving that has been studied to date.

Thus, in the domain of symbolic logic in whichLT worked, obtaining by brute force the proofs itdiscovered by selective search would have meantexamining enormous numbers of possibilities—10raised to an exponent of hundreds or thousands.LT typically searched trees of SO or so branches inconstructing the more difficult proofs that it found.

Mentalism and Magic

LT demonstrated that selective search employingheuristics permitted a slow serial information-proc-essing system to solve problems that are difficultfor humans. The demonstration defined the termsof the next stages of inquiry: to discover the heuris-tic processes actually used by humans to solve suchproblems, and to verify the discovery empirically.

We will not discuss here the methodological issuesraised by the discovery and certification tasks, apartfrom one preliminary comment. An explanation ofthe processes involved in human thinking requiresreference to things going on inside the head. Amer-ican behaviorism has been properly skeptical of"mentalism"—of attempts to explain thinking byvague references to vague entities and processeshidden beyond reach of observation within theskull. Magic is explained only if the terms of ex-planation are less mysterious than the feats ofmagic themselves. It is no explanation of therabbit's appearing from the hat to say that it"materialized."

Information-processing explanations refer fre-quently to processes that go on inside the head—inthe mind, if you like—and to specific propertiesof human memory: its speed and capacity, its or-ganization. These references are not intended tobe in the least vague. What distinguishes the in-formation-processing theories of thinking and prob-lem solving described here from earlier discussionof mind is that terms like "memory" and "symbolstructure" are now pinned down and defined in

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sufficient detail to embody their referents in pre-cisely stated programs and data structures.

An internal representation, or "mental image,"of a chess board, for example, is not a metaphoricalpicture of the external object, but a symbol struc-ture with definite properties on which well-definedprocesses can operate to retrieve specified kinds ofinformation (Baylor & Simon, 1966; Simon &Barenfelcl, 1969).

The programmability of the theories is the guar-antor of their opcrationality, an iron-clad insuranceagainst admitting magical entities into the head.A computer program containing magical instruc-tions does not run, but it is asserted of these infor-mation-processing theories of thinking that they canbe programmed and will run. They may be em-pirically correct theories about the nature of humanthought processes or empirically invalid theories;they are not magical theories.

Unfortunately, the guarantee provided by pro-grammability creates a communication problem.Information-processing languages are a, barrier tothe communication of the theories as formidable asthe barrier of mathematics in the physical sciences.The theories become fully accessible only to thosewho, lay mastering the languages, climb over thebarrier. Any attempt to communicate in naturallanguage must perforce be inexact.

There is the further clanger that, in talking aboutthese theories in ordinary language, the listener maybe seduced into attaching to terms their traditionalmeanings. ]f the theory speaks of "search," hemay posit a little homunculus inside the head to dothe searching; if it speaks of "heuristics" or "rulesof thumb," he may introduce the same homunculusto remember and apply them. Then, of course, hewill be interpreting the theory magically, and willobject that it is no theory.

The only solution to this problem is the hardsolution. Psychology is now taking the roadtaken earlier by other sciences: it is introducing es-sential formalisms to describe and explain itsphenomena. Natural language formulations of thephenomena of human thinking did not yield ex-planations of what was going on; formulations ininformation-processing languages appear to beyielding such explanations. And the pain and costof acquiring the new tools must be far less thanthe pain and cost of trying to master difficultproblems with inadequate tools.

Our account today will be framed in ordinarylanguage. But we must warn you that it is a trans-lation from information-processing languages which,like most translations, has probably lost a good dealof the subtlety of the original. In particular, wewarn you against attaching magical meanings toterms that refer to entirely concrete and opera-tional phenomena taking place in fully defined andoperative information-processing systems. The ac-count will also be Pittsburgh-centric. It will refermainly to work of the Carnegie-RAND group, al-though information-processing psychology enlistsan ever-growing band of research psychologists,many of whom arc important contributors of evi-dence to the theory presented here.

THEORY OF PROBLEM SOLVING—1970

The dozen years since the publication of the"Elements" paper has seen a steady growth of ac-tivity in information-processing psychology—bothin the area of problem solving and in such areas aslearning, concept formation, short-term memoryphenomena, perception, and language behavior.Firm contact has been made with more traditionalapproaches, and information-processing psychologyhas joined (or been joined by) the mainstream ofscientific inquiry in experimental psychology today.8

Instead of tracing history here, we should like togive a brief account of the product of the history, ofthe theory of human problem solving that hasemerged from the research.

The theory makes reference to an information-processing system, the problem solver, confrontedby a task. The task is defined objectively (orfrom the viewpoint of an experimenter, if you pre-fer) in terms of a task environment. It is definedby the problem solver, for purposes of attacking it,in terms of a problem space. The shape of thetheory can be captured by four propositions(Newell & Simon, in press, Ch. 14):

1. A few, and only a few, gross characteristics ofthe human information-processing system are in-variant over task and problem solver.

2. These characteristics are sufficient to deter-mine that a task environment is represented (in theinformation-processing system) as a problem space,

3 The authors have undertaken a brief history of thesedevelopments in an Addendum to their book, Human Prob-lem Solving (Newell & Simon, in press).

HUMAN PROBLEM SOLVING 149

and that problem solving takes place in a problemspace.

3. The structure of the task environment deter-mines the possible structures of the problem space.

4. The structure of the problem space determinesthe possible programs that can be used for problemsolving.

These are the bones of the theory. In the nextpages, we will undertake to clothe them in someflesh.

Characteristics of the Information-ProcessingSystem

When human beings are observed working onwell-structured problems that are difficult but notunsolvable for them, their behaviors reveal certainbroad characteristics of the underlying neurophysio-logical system that supports the problem-solvingprocesses; but at the same time, the behaviors con-ceal almost all of the detail of that system.

The basic characteristics of the human informa-tion-processing system that shape its problem-solv-ing efforts are easily stated: The system operatesessentially serially, one-process-at-a-time, not inparallel fashion. Its elementary processes taketens or hundreds of milliseconds. The inputs andoutputs of these processes are held in a small short-term memory with a capacity of only a few symbols.The system has access to an essentially infinite long-term memory, but the time required to store asymbol in that memory is of the order of seconds ortens of seconds.

These properties-—serial processing, small short-term memory, infinite long-term memory with fastretrieval but slow storage—impose strong con-straints on the ways in which the system can seeksolutions to problems in larger problem spaces. Asystem not sharing these properties—a parallel sys-tem, say, or one capable of storing symbols in long-term memory in milliseconds instead of seconds—might seek problem solutions in quite different waysfrom the system we are considering.

The evidence that the human system has theproperties we have listed comes partly from prob-lem-solving behavior itself. No problem-solvingbehavior has been observed in the laboratory thatseems interpretable in terms of simultaneous rapidsearch of disjoint parts of the solver's problemspace. On the contrary, the solver always appearsto search sequentially, adding small successive ac-

cretions to his store of information about the prob-lem and its solution.*

Additional evidence for the basic properties ofthe system as well as data for estimating the systemparameters come from simpler laboratory tasks.The evidence for the 5 or 10 seconds required tostore a symbol in long-term memory comes mainlyfrom rote memory experiments; for the seven-sym-bol capacity of short-term memory, from immediaterecall experiments; for the 200 milliseconds neededto transfer symbols into and out of short-termmemory, from experiments requiring searches downlists or simple arithmetic computations.5

These things we do learn about the information-processing system that supports human thinking—but it is significant that we learn little more, thatthe system might be almost anything as long as itmeets these few structural and parametral specifica-tions. The detail is elusive because the system isadaptive. For a system to be adaptive means thatit is capable of grappling with whatever task en-vironment confronts it. Hence, to the extent asystem is adaptive, its behavior is determined bythe demands of that task environment rather thanby its own internal characteristics. Only when theenvironment stresses its capacities along some di-mension—presses its performance to the limit—dowe discover what those capabilities and limits are,and are we able to measure some of their param-eters (Simon, 1969, Ch. 1 and 2).

Structure of Task Environments

If the study of human behavior in problem sit-uations reveals only a little about the structure ofthe information-processing system, it reveals a greatdeal about the structure of task environments.

4 Claims that human distractability and perceptual capa-bility imply extensive parallel processing have been refutedby describing or designing serial information-processingsystems that are distractable and possess such perceptualcapabilities. (We are not speaking of the initial "sensory"stages of visual or auditory encoding, which certainly in-volve parallel processing, but of the subsequent stages,usually called perceptual.) For further discussion of thisissue, see Simon (1967) and Simon and Barenfeld (1969).Without elaborating here, we also assert that incrementalgrowth of knowledge in the problem space is not incom-patible with experiences of sudden "insight." For fur-ther discussion of this point, see Newell, Shaw, and Simon(1962) and Simon (1966).

5 Some of this evidence is reviewed in Newell and Simon(in press, Ch. 14).

150 AMERICAN PSYCHOLOGIST

Consider the cryptarithmetic problem

DONALD+GERALD

ROBERT

which has been studied on both shores of the At-lantic, in England by Bart.lett (1958), and in theUnited States in our own laboratory (Newell, 1967;Newell & Simon, in press, Part II). The problemis to substitute numbers for the letters in the threenames in such a way as to produce a correct arith-metic sum. As the problem is usually posed, thehint is given that D = 5. If we look at the proto-cols of subjects who solve the problem, we find thatthey all substitute numbers for the letters in ap-proximately the same sequence. First, they setT = 0, then E - 9 and R = 7, then A = 4 andL = 8, then G = 1, then N = 6 and B = 3, and,finally, 0 = 2.

To explain this regularity in the sequence ofassignments, we must look first at the structure ofthe task itself. A cryptarithmetic problem maybe tackled by trying out various tentative assign-ments of numbers to letters, rejecting them andtrying others if they lead to contradictions. Inthe DONALD + GERALD problem, hundreds ofthousands of combinations would have to be triedto find a solution in this way. (There are 9! =362,880 ways of assigning nine digits to nineletters.) A serial processor able to make and testfive assignments per minute would require a monthto solve the problem; many humans do it in 10minutes or less.

But the task structure admits a heuristic thatinvolves processing first those columns that are mostconstrained. If two digits in a single column arealready known, the third can be found by applyingthe ordinary rule of arithmetic. Hence, from D= 5, we obtain the right-most column: 5 + 5 = T,hence T = 0, with a carry of 1 to the next column.Each time a new assignment is made in this way,the information can be carried into other columnswhere the same letter appears, and then the most-constrained column of those remaining can be se-lected for processing. For the DONALD + GER-ALD problem (but not, of course, for all crypt-arithmetic problems), it turns out that the correctassignments for T, E, R, A, L, and G can all befound in this way without any trial-and-errorsearch whatsoever, leaving only N, B, and 0 forthe possible permutations of 6, 3, and 2.

Not only does this heuristic of processing themost-constrained columns first almost eliminate theneed for search, but it also reduces the demands onthe short-term memory of the problem solver. Allthe information he has acquired up to any givenpoint can be represented on a single external dis-play, simply by replacing each letter by the digitassigned to it as soon as the assignment is made.Since the assignments are definite, not tentative,no provision need be made by an error-free process-ing system for correcting wrong assignments, norfor keeping track of assignments that were triedpreviously and failed. The human information-processing system is subject to error, however, hencerequires back-up capabilities not predictable fromthe demands of the task environment.

Hence, from our knowledge of properties of thistask environment, we can predict that an error-free serial information-processing system using theheuristic we have described could solve the DON-ALD + GERALD problem rather rapidly, andwithout using much short-term memory along theway. But if it solved the problem by this method,it would have to make the assignments in the par-ticular order we have indicated.

The empirical fact that human solvers do makethe assignments in roughly this same order providesus with one important piece of evidence (we canobtain many others by analyzing their thinking-aloud protocols and eye movements) that they areoperating as serial systems with limited short-termmemories. But the empirical data show that thereare few task-independent invariants of the humanprocessor beyond the basic structural features wehave mentioned. Since the problem solver's be-havior is adaptive, we learn from his protocol theshape of the task environment of DONALD +GERALD—the logical interdependencies that holdamong the several parts of that problem. We alsolearn from the protocol the structure of the prob-lem space that the subject uses to represent thetask environment, and the program he uses to searchthe problem space. Though the problem spaceand program are not task-invariant, they constitutethe adaptive interface between the invariant fea-tures of the processor and the shape of the environ-ment, and can be understood by considering thefunctional requirements that such an interface mustsatisfy.

HUMAN PROBLEM SOLVING 151

Problem Spaces

Subjects faced with problem-solving tasks repre-sent the problem environment in internal memoryas a space of possible situations to be searched inorder to find that situation which corresponds to thesolution. We must distinguish, therefore, betweenthe task environment—the omniscient observer'sway of describing the actual problem "out there"—and the problem space—the way a particular sub-ject represents the task in order to work on it.

Each node in a problem space may be thought ofas a possible state of knowledge to which the prob-lem solver may attain. A state of knowledge issimply what the problem solver knows about theproblem at a particular moment of time—knowsin the sense that the information is available to himand can be retrieved in a fraction of a second.After the first step of the DONALD + GERALDproblem, for example, the subject knows not onlythat D = S, but also that T = 0 and that the carryinto the second column from the right is 1. Theproblem solver's search for a solution is an odysseythrough the problem space, from one knowledgestate to another, until his current knowledge stateincludes the problem solution—that is, until heknows the answer.

Problem spaces, even those associated with rela-tively "simple" task environments, are enormous.Since there are 9! =362,880 possible assignmentsof nine digits to nine letters, we may consider thebasic DONALD + GERALD space to be 9! insize, which is also the size of the space of tic-tac-toe. The sizes of problem spaces for games likechess or checkers are measured by very largepowers of ten—10120, perhaps, in the case of chess.The spaces associated with the problem called "life"are, of course, immensely larger.

For a serial information-processing system, how-ever, the exact size of a problem space is not im-portant, provided the space is very large. A serialprocessor can visit only a modest number of knowl-edge states (approximately 10 per minute, thethinking-aloud data indicate) in its search for aproblem solution. If the problem space has even afew thousand states, it might as well be infinite—only highly selective search will solve problems in it.

Many of you have tried to solve the Tower ofHanoi problem. (This is very different from theproblem of Hanoi in your morning newspaper,but fortunately much less complex.) There are

three spindles, on one of which is a pyramid ofwooden discs. The discs are to be moved, one byone, from this spindle, and all placed, in the end,on one of the other spindles, with the constraintthat a disc may never be placed on another thatis smaller than it is. If there are four discs, theproblem space comprised of possible arrangementsof discs on spindles contains only 3* = 81 nodes,yet the problem is nontrivial for human adults.The five-disc problem, though it admits only 243arrangements, is very difficult for most people; andthe problems with more than five discs almost un-solvable—until the right heuristic is discovered!

Problems like this one—where the basic problemspace is not immense—tell us how little trial-and-error search the human problem solver is capableof, or is willing to endure. Problems with immensespaces inform us that the amount of search re-quired to find solutions, making use of availablestructure, bears little or no relation to the size ofthe entire space. To a major extent, the power ofheuristics resides in their capability for examiningsmall, promising regions of the entire space andsimply ignoring the rest. We need not be con-cerned with how large the haystack is, if we canidentify a small part of it in which we are quitesure to find a needle.

Thus, to understand the behavior of a serialproblem solver, we must turn to the structure ofproblem spaces and see just how information is im-bedded in such spaces that can be extracted byheuristic processes and used to guide search to aproblem solution.

Sources of Information in Problem Spaces

Problem spaces differ not only in size—a differ-ence we have seen to be usually irrelevant to prob-lem difficulty—but also in the kinds of structurethey possess. Structure is simply the antithesisof randomness, providing redundancy that can beused to predict the properties of parts of the spacenot yet visited from the properties of those alreadysearched. This predictability becomes the basis forsearching selectively rather than randomly.

The security of combination safes rests on theproposition that there is no way, short of exhaus-tive search, to find any particular point in a fullyrandom space. (Of course, skilled safecrackersknow that complete randomness is not alwaysachieved in the construction of real-world safes,but that is another matter.)

152 AMKKICAN PSYCHOLOGIST

Nonrandomness is information, and informationcan he exploited to search a problem space in prom-ising directions and to avoid the less promising. Alittle information goes a long way to keep withinbounds the amount of search required, on average,to find solutions.

Hill climbing. The simplest example of informa-tion that can be used to solve problems withoutexhaustive search is the progress test—the test thatshows that one is "getting warmer." In climbinga (not too precipitous) hill, a good heuristic rule isalways to go upward. If a particular spot is higher,reaching it probably represents progress toward thetop. The time it takes to reach the top will de-pend on the height of the hill and its steepness,but not on its circumference or area—not on thesize of the total problem space.

Types oj information. There is no great mysteryin the nature of the information that is availablein many typical problem spaces; and we now knowpretty well how humans extract that informationand use it to search selectively. For example, inthe DONALD + GERALD problem, we saw howinformation was obtained by arithmetic and al-gebraic operations. Now, abstracting from par-ticular examples, can we characterize the structureof problem spaces in more general terms?

Each knowledge state is a node in the problemspace. Having reached a particular node, the prob-lem solver can choose an operator from among aset of operators available to him, and can apply itto reach a new node. Alternatively, the problemsolver can abandon the node he has just reached,select another node from among those previouslyvisited, and proceed from that node. Thus, he mustmake two kinds of choices: choice of a node fromwhich to proceed, and choice of an operator toapply at that node.

We can think of information as consisting of oneor more evaluations (not necessarily numerical, ofcourse) that can be assigned to a node or an op-erator. One kind of evaluation may rank nodeswith respect to their promise as starting points forfurther search. Another kind of evaluation mayrank the operators at a particular node with respectto their promise as means for continuing fromthat node. The problem-solving studies have dis-closed examples of both kinds of evaluations: fornode and operator selection, respectively.

When we examine how evaluations are made—-

what information they draw on—we again dis-cover several varieties. An evaluation may dependonly on properties of a single node. Thus, intheorem-proving tasks, subjects frequently declineto proceed from their current node because "theexpression is too complicated to work with." Thisis a judgment that the node is not a promising one.Similarly, we find frequent statements in the proto-cols to the effect that "it looks like Rule 7 wouldapply here."

In most problem spaces, the choice of an efficientnext step cannot be made by absolute evaluation ofthe sorts just illustrated, but instead is a functionof the problem that is being solved. In theoremproving, for example, what to do next depends onwhat theorem is to be proved. Hence, an im-portant technique for extracting information to beused in evaluators (of either kind) is to comparethe current node with characteristics of the desiredstate of affairs and to extract differences from thecomparison. These differences serve as evaluatorsof the node (progress tests) and as criteria forselecting an operator (operator relevant to thedifferences). Reaching a node that differs less fromthe goal state than nodes visited previously isprogress; and selecting an operator that is relevantto a particular difference between current node andgoal is a technique for (possibly) reducing thatdifference.

The particular heuristic search system that findsdifferences between current and desired situations,finds an operator relevant to each difference, andapplies the operator to reduce the difference isusually called means-ends analysis. Its commonoccurrence in human problem-solving behavior hasbeen observed and discussed frequently sinceDuncker (1945). Our own data analyses revealmeans-ends analysis to be a prominent form ofheuristic organization in some tasks—proving the-orems, for example. The procedure is captured inthe General Problem Solver (GPS) program whichhas now been described several times in the psycho-logical literature.8 The GPS find-and-reduce-differ-ence heuristic played the central role in our theoryof problem solving for a decade beginning with its

0 Brief descriptions of GPS can be found in Hilgard andBower (1966) and Hilgard and Atkinson (1.967). Foran extensive analysis of GPS, see Ernst and Newell (1969).The relation of GPS to human behavior is discussed inNewell and Simon (in press, Ch. 9).

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discovery in 1957, but more extensive data froma wider range of tasks have now shown it to be aspecial case of the more general information-extract-ing processes we are describing here.

Search strategies. Information obtained by find-ing differences between already-attained nodes andthe goal can be used for both kinds of choices theproblem solver must make—the choice of node toproceed from, and the choice of operator to apply.Examining how this information can be used toorganize search has led to an explanation of animportant phenomenon observed by de Groot (1965)in his studies of choice in chess. De Groot foundthat the tree of move sequences explored by playersdid not originate as a bushy growth, but was gen-erated, instead, as a bundle of spindly explorations,each of them very little branched. After eachbranch had been explored to a position that couldbe evaluated, the player returned to the base posi-tion to pick up a new branch for exploration. DCGroot dubbed this particular kind of exploration,which was universal among the chessplayers hestudied, "progressive deepening."

The progressive deepening strategy is not im-posed on the player by the structure of the chesstask environment. Indeed, one can show that adifferent organization would permit more efficientsearch. This alternative method is called the scan-and-search strategy, and works somewhat as fol-lows: Search proceeds by alternation of two phases:(a) in the first phase, the node that is most promis-ing (by some evaluation) is selected for continua-tion; (b) in the second phase, a few continuationsare pursued from that node a short distance for-ward, and the new nodes thus generated are evalu-ated and placed on a list for Phase 1. The scan-search organization avoids stereotypy. If searchhas been pursued in a particular direction becauseit has gone well, the direction is reviewed re-peatedly against other possibilities, in case itspromise begins to wane.

A powerful computer program for finding check-mating combinations, called MATER, constructedwith the help of the scan-search strategy, appearsa good deal more efficient than the progressivedeepening strategy (Baylor & Simon, 1966).Nevertheless, in chess and the other task environ-ments we have studied, humans do not use thescan-search procedure to organize their efforts. Inthose problems where information about the cur-

rent node is preserved in an external memory, theytend to proceed almost always from the currentknowledge state, and back up to an earlier node onlywhen they find themselves in serious trouble (Ne-well & Simon, in press, Ch. 12 and 13). In taskenvironments where the information about the cur-rent node is not preserved externally (e.g., thechessboard under rules of touch-move), and espe-cially if actions are not reversible, humans tend topreserve information (externally or internally)about a base node to which they return when evalu-ation rejects the current node. This is essentiallythe progressive deepening strategy.

We can see now that the progressive deepeningstrategy is a response to limits of short-term mem-ory, hence provides additional evidence for thevalidity of our description of the human informa-tion-processing system. When we write a problem-solving program without concern for human limita-tions, we can allow it as much memory of nodeson the search tree as necessary—hence we can usea scan-search strategy. To the human problemsolver, with his limited short-term memory, thisstrategy is simply not available. To use it, hewould have to consume large amounts of time stor-ing in his long-term memory information about thenodes he had visited.

That, in sum, is what human heuristic search ina problem space amounts to. A serial informationprocessor with limited short-term memory uses theinformation extractable from the structure of thespace to evaluate the nodes it reaches and the op-erators that might be applied at those nodes. Mostoften, the evaluation involves finding differences be-tween characteristics of the current node and thoseof the desired node (the goal). The evaluationsare used to select a node and an operator for thenext step of the search. Operators are usually ap-plied to the current node, but if progress is notbeing made, the solver may return to a prior nodethat has been retained in memory—the limits ofthe choice of prior node being set mostly by short-term memory limits. These properties have beenshown to account for most of the human problem-solving behaviors that have been observed in thethree task environments that have been studied in-tensively: chess playing, discovering proofs in logic,and cryptarithmctic; and programs have beenwritten to implement problem-solving systems withthese same properties.

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Alternative Problem Spaces

Critics of the problem-solving theory we havesketched above complain that it explains too little.It has been tested in detail against behavior inonly three task environments—and these all in-volving highly structured symbolic tasks.7 Moreserious, it explains behavior only after the problemspace has been postulated—it does not show howthe problem solver constructs his problem space ina given task environment. How, when he is facedwith a cryptarithmetic problem, does he enter aproblem space in which the nodes are defined asdifferent possible assignments of letters to numbers?How does he become aware of the relevance ofarithmetic operations for solving the problem?What suggests the "most-constrained-column-first"heuristic to him?

Although we have been careful to distinguishbetween the task environment and the problemspace, we have not emphasized how radical can bethe differences among alternative problem spacesfor representing the same problem. Consider thefollowing example: An elimination tournament, with109 entries, has been organized by the local tennisclub. Players are paired, the losers eliminated, andthe survivors re-paired until a single player emergesvictorious. How should the pairings be arrangedto minimize the total number of individual matchesthat will have to be played? An obvious representa-tion is the space of all possible "trees" of match-ings of 109 players—an entirely infeasible spaceto search. Consider an alternative space in whicheach node is a possible sequence of matches con-stituting the tournament. This is, again, an enor-mous space, but there is a very simple way to solvethe problem without searching it. Take an arbitrarysequence in the space, and note the number ofsurviving players after each match. Since thetournament begins with 109 players, and since eachmatch eliminates one player, there must be exactly108 matches to eliminate all but one player—nomatter which sequence we have chosen. Hence,the minimum number of matches is 108, and anytree we select will contain exactly this number.

There are many "trick" problems of this kindwhere selection of the correct problem space per-mits the problem to be solved without any search

7 The empirical findings, only some of which have beenpublished to date, are collected in Parts II, III, and IV, ofNewell and Simon (in press).

whatsoever. In the more usual case, matters arenot so extreme, but judicious selection of the prob-lem space makes available information that reducessearch by orders of magnitude in comparison withwhat is required if a less sophisticated space isused.

We cannot claim to have more than fragmentaryand conjectural answers to the questions of repre-sentation. The initial question we asked in ourresearch was: "What processes do people use tosolve problems?" The answer we have proposed is:"They carry out selective search in a problemspace that incorporates some of the structural in-formation of the task environment." Our answernow leads to the new question: "How do peoplegenerate a problem space when confronted witha new task?" Thus, our research, like all scien-tific efforts, has answered some questions at thecost of generating some new ones.

By way of parenthesis, however, we should liketo refute one argument that seems to us exag-gerated. It is sometimes alleged that search in awell-defined problem space is not problem solvingat all—that the real problem solving is over assoon as the problem space has been selected. Thisproposition is easily tested and shown false. Pick atask environment and a particular task from it. Todo the task, a person will first have to construct aproblem space, then search for a solution in thatspace. Now give him a second task from the sameenvironment. Since he can work in the problemspace he already has available, all he needs to dothis time is to search for a solution. Hence, thesecond task—if we are to accept the argument—isno problem at all. Observation of subjects' be-havior over a sequence of chess problems, crypt-arithmetic puzzles, or theorem-finding problemsshows the argument to be empirically false. Forthe subjects do not find that all the problems be-come trivial as soon as they have solved the firstone. On the contrary, the set of human behaviorswe call "problem solving" encompasses both theactivities required to construct a problem space inthe face of a new task environment, and the ac-tivities required to solve a particular problem insome problem space, new or old.

WHERE Is THE THEORY GOING?

Only the narrow seam of the present divides pastfrom future. The theory of problem solving in 1970

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—and especially the part of it that is empiricallyvalidated—is primarily a theory that describes theproblem spaces and problem-solving programs, andshows how these adapt the information-processingsystem to its task environment. At the same timethat it has answered some basic questions aboutproblem-solving processes, the research has raisednew ones: how do problem solvers generate prob-lem spaces; what is the neurological substrate forthe serial, limited-memory information processor;how can our knowledge of problem-solving processesbe used to improve human problem solving andlearning? In the remaining pages of this article,we should like to leave past and present and lookbriefly—using Milton's words-—into "the never-end-ing flight of future days."

Constructing Problem Spaces

We can use our considerable knowledge aboutthe problem spaces subjects employ to solve prob-lems in particular task environments as our taking-off place for exploring how the problem spaces comeinto being, how the subjects construct them.

Information for construction. There are at leastsix sources of information that can be used to helpconstruct a problem space in the face of a taskenvironment:

1. The task instructions themselves, which de-scribe the elements of the environment more orless completely, and which may also provide someexternal memory—say, in the form of a chessboard.

2. Previous experience with the same task or anearly identical one. (A problem space availablefrom past experience may simply be evoked bymention of the task.)

3. Previous experience with analogous tasks, orwith components of the whole task.

4. Programs stored in long-term memory thatgeneralize over a range of tasks.

5. Programs stored in long-term memory forcombining task instructions with other informationin memory to construct new problem spaces andproblem-solving programs.

6. Information accumulated while solving a prob-lem, which may suggest changing the problem space.(In particular, it may suggest moving to a moreabstract and simplified planning space.)

The experience in the laboratory with subjectsconfronting a new task, and forced, thereby, to

generate within a few minutes a problem space fortackling the task, suggests that the first source—task instructions and illustrative examples accom-panying them—plays a central role in generation ofthe problem space. The array presented with thecryptarithmetic problem, for example, suggests im-mediately the form of the knowledge state (or atleast the main part of i t ) ; namely, that it consistsof the same array modified by the substitution init of one or more digits for letters.

The second source—previous experience with thesame task—is not evident, of course, in the be-havior of naive subjects, but the third source—analogous and component tasks—plays an impor-tant role in cryptarithmetic. Again, the form ofthe external array in this task is sufficient to evokein most subjects the possible relevance of arith-metic processes and arithmetic properties (odd,even, and so on).

The fourth source—general purpose programs inlong-term memory—is a bit more elusive. But, aswe have already noted, subjects quite frequentlyuse means-ends programs in their problem-solvingendeavors, and certainly bring these programs tothe task from previous experience. We have al-ready mentioned the General Problem Solver, whichdemonstrates how this generality can be achievedby factoring the specific descriptions of individualtasks from the task-independent means-ends analy-sis processes.

The fifth and sixth sources on the list above arementioned because common sense tells us that theymust sometimes play a role in the generation ofproblem spaces. We have no direct evidence fortheir use.

What evidence we have for the various kinds ofinformation that are drawn on in constructing prob-lem spaces is derived largely from comparing theproblem spaces that subjects are observably workingin with the information they are known to haveaccess to. No one has, as yet, really observed theprocess of generation of the space—a research taskthat deserves high priority on the agenda.

Some simulation programs. Some progress hasbeen made, however, in specifying for computersseveral programs that might be regarded as candi-date theories as to how it is done by humans. Twoof these programs were constructed, by Tom Wil-liams (1965) and Donald Williams (1969), re-spectively, in the course of their doctoral research.

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A General Game Playing Program (GGPP), de-signed by Tom Williams, when given the instruc-tions for a card or board game (somewhat as theseare written in Hoyle, but with the language sim-plified and smoothed), is able, by interpreting theseinstructions, to play the game—at least legal!}' ifnot well. GGPP relies primarily on the first,fourth, and fifth sources of information from thelist above. It has stored in memory general in-formation about such objects as "cards," "hands,""boards," "moves," and is capable of combiningthis general information with information derivedfrom the specific instructions of the game.

The Aptitude Test Taker, designed by DonaldWilliams, derives its information from worked-outexamples of items on various kinds of aptitude tests(letter series, letter analogies, number series andanalogies, and so on) in order to construct its ownprograms capable of taking the corresponding tests.

These programs put us into somewhat the sameposition with respect to the generation of problemspaces that LT did with respect to problem solvingin a defined problem space: that is to say, theydemonstrate that, certain sets of information-proc-essing mechanisms are sufficient to do the job oversome range of interesting tasks. They do not provethat humans do the same job in the same way, usingessentially the same processes, or that these proc-esses would suffice for all tasks. Tt should be notedthat the programs written by the two Williamsesemploy the same kind of basic information-process-ing system that was used for earlier cognitive simu-lations. They do not call for any new magic to beput in the hat.

Planning and abstracting processes. The proc-esses for generating problem spaces are not unre-lated to some other processes about which we dohave empirical data—-planning processes. Tn sev-eral of the tasks that have been studied, and espe-cially in the logic task, subjects are often observedto be working in terms more abstract than thosethat characterize the problem space they beganwith. They neglect certain details of the expres-sions they are manipulating (e.g., the operations orconnectives), and focus on features they regard asessential.

One way of describing what they are doing is tosay that they are abstracting from the concretedetail of the initial problem space in order to con-struct a plan for a problem solution in a simpler

abstract planning space. Programs have beenwritten, in the context of GL'S, that are also cap-able of such abstracting and planning, hence arecapable of constructing a problem space differentfrom the one in which the problem solving begins.

The evidence from the thinking-aloud protocolsin the logic task suggests, however, that the humanplanning activities did not maintain as sharp aboundary between task space and abstract planningspace as the simulation program did. The humansubjects appeared able to move back and forth be-tween concrete and abstract objects without treat-ing the latter as belonging to a separate problemspace. In spite of this difference, the data onplanning behavior give us additional clues as tohow problem spaces can be generated and modified.

Production Systems

A hypothesis about the structure of a complexsystem—like a human problem-solving program—becomes more plausible if we can conceive how astep-by-step development could have brought aboutthe finished structure. Minerva sprang full-grownfrom the brow of Zeus, but we expect terrestrialsystems to evolve in a more gradual and lawfulfashion—our distrust of the magician again.

Anyone who has written and debugged a largecomputer program has probably acquired, in theprocess, a healthy skepticism that such an en-tangled, interconnected structure could have evolvedby small, self-adapting steps. Tn an evolving sys-tem, a limited, partial capability should grow al-most continuously into a more powerful capability.But most computer programs have an all-or-nonecharacter: disable one subroutine and a programwill probably do nothing useful at all.

A development of the past few years in computerlanguage construction has created an interestingpossible solution to this difficulty. We refer tothe languages known as production systems. In aproduction system, each routine has a bipartiteform, consisting of a condition and an action. Thecondition defines some test or set of tests to beperformed on the knowledge state. (E.g., "Test ifit is Black's move.") If the test is satisfied, theaction is executed; if the test is not satisfied, noaction is taken, and control is transferred to someother production. In a pure production system, theindividual productions are simply listed in someorder, and considered for execution in turn.

HUMAN PROBLEM SOLVING 157

The attraction of a production system for ourpresent concerns-—of how a complex program coulddevelop step by step—is that the individual pro-ductions are independent of each other's structures,and hence productions can be added to the systemone by one. In a new task environment, a subjectlearns to notice conditions and make discriminationsof which he was previously unaware (a chessplayerlearns to recognize an open file, a passed pawn, andso on). Each of these new discriminations can be-come the condition part of a production, whose ac-tion is relevant to that condition.

We cannot pursue this idea here beyond notingits affinity to some classical stimulus-response no-tions. We do not wish to push the analogy too far,for productions have some complexities and sub-tleties of structure that go beyond stimulus-responseideas, but we do observe that linking a conditionand action together in a new production has manysimilarities to linking a stimulus together with itsresponse. One important difference is that, in theproduction, it is the condition—that is, the tests—•and not the stimulus itself that is linked to theresponse. In this way, the production system il-luminates the problem of defining the effectivestimulus, an old bugaboo of stimulus-responsetheory.

Perception and Language

We have seen that research on problem solvinghas begun to shift from asking how searches areconducted in problem spaces, a subject on whichwe have gained a considerable understanding, toasking how problem spaces—internal representa-tions of problems—are built up in human minds.But the subject of internal representation linksproblem-solving research with two other importantareas of psychology: perception and psycholin-guistics. The further extension of this linkage (seeStep 8 in the strategy outlined in our introductorysection) appears to be one of the principal tasks forthe next decade.

Elsewhere, one of us has described briefly themain connections between problem-solving theoryand the theories of perception and psycholin-guistics (Simon, 1969, pp. 42-52). We will simplyindicate these connections even more briefly here.

Information comes to the human problem solverprincipally in the form of statements in natural lan-guage and visual displays. For information to be

exchanged between these external sources and themind, it must be encoded and decoded. The in-formation as represented externally must be trans-formed to match the representations in which it isheld inside. It is very difficult to imagine whatthese transformations might be as long as we haveaccess only to the external representations, andnot to the internal. It is a little like building aprogram to translate from English to Language X,where no one will tell us anything about LanguageX.

The research on problem solving has given ussome strong hypotheses about the nature of theinternal representations that humans use when theyare solving problems. These hypotheses define forus, therefore, the endpoint of the translation proc-ess—they tell us something about Language X. Thehypotheses should provide strong clues to the re-searcher in perception and to the psycholinguist inguiding their search for the translation process. In-deed, we believe that these cues have already beenused to good advantage in both areas, and weanticipate a great burgeoning of research alongthese lines over the coming decade.

Links to Ncurophysiology

The ninth step in the strategy set forth in ourintroduction was to seek the neurophysiologicalcounterparts of the information processes and datastructures that the theory postulates. In this re-spect, we are in the position of nineteenth-centurychemistry which postulated atoms on the basis ofobservations of chemical reactions among mole-cules, and without any direct evidence for theirexistence; or in the position of classical genetics,which postulated the gene before it could be identi-fied with any observed microscopic structures inthe cell.

Explanation in psychology will not rest indefi-nitely at the information-processing level. But theexplanations that we can provide at that level willnarrow the search of the neurophysiologist, forthey will tell him a great deal about the propertiesof the structures and processes he is seeking. Theywill put him on the lookout for memory fixationprocesses with times of the order of five seconds,for the "bottlenecks" of attention that account forthe serial nature of the processing, for memorystructures of small capacity capable of storing a

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few symbols in a matter of a couple of hundredmilliseconds.

All of this is a prospect for the future. We can-not claim to see in today's literature any firmbridges between the components of the centralnervous system as it is described by neurophysiolo-gists and the components of the information-process-ing system we have been discussing here. Butbridges there must be, and we need not pause inexpanding and improving our knowledge at the in-formation-processing level while we wait for themto be built.

The Practice of Education

The professions always live in an uneasy relationwith the basic sciences that should nourish and benourished by them. It is really only within thepresent century that medicine can be said to restsolidly on the foundation of deep knowledge in thebiological sciences, or the practice of engineeringon modern physics and chemistry. Perhaps weshould plead the recency of the dependence in thosefields in mitigation of the scandal of psychology'smeager contribution to education.

It is, of course, incorrect to say that there hasbeen no contribution. Psychology has provided tothe practice of education a constant reminder ofthe importance of reinforcement and knowledge ofresults for effective learning. And particularlyunder the influence of the Sldnnerians, these prin-ciples have seen increasingly systematic and con-scious application in a variety of educational set-tings.

Until recently, however, psychology has shownboth a reluctance and an inability to address itselfto the question of "what is learned." At a com-mon sense level, we know perfectly well that rotelearning docs not provide the same basis for lastingand transferable skills that is provided by "mean-ingful" learning. We have even a substantial bodyof laboratory evidence—for example, the researchby Katona (1940), now 30 years old—that showsclearly the existence and significance of such dif-ferences in kinds of learning. But we have largelybeen unable to go beyond common sense in charac-terizing what is rote and what is meaningful. Wehave been unable because we have not describedwhat is learned in these two different modes oflearning—what representation of information orprocess has been stored in memory. And we have

not described how that stored information and thosestored programs arc evoked to perform new tasks.

The theory of problem solving described heregives us a new basis for attacking the psychologyof education and the learning process. It allows usto describe in detail the information and programsthat the skilled performer possesses, and to showhow they permit him to perform successfully. Butthe greatest opportunities for bringing the theoryto bear upon the practice of education will come aswe move from a theory that explains the structureof human problem-solving programs to a theory thatexplains how these programs develop in the face oftask requirements—the kind of theory we have beendiscussing in the previous sections of this article.

It does not seem premature at the present stageof our knowledge of human problem solving toundertake large-scale development work that willseek to bring that theory to bear upon education.Some of the tasks that have been studied in thebasic research programs—proving theorems in logicand geometry, playing chess, doing cryptarithmeticproblems, solving word problems in algebra, solvingletter-series completion problems from intelligencetests—are of a level of complexity comparable tothe tasks that face students in our schools andcolleges.8

The experience of other fields of knowledgeteaches us that serious attempts at practical ap-plication of basic science invariably contribute tothe advance of the basic science as well as thearea of application. Unsuspected phenomena arediscovered that can then be carried back to thelaboratory; new questions are raised that becometopics for basic research. Both psychology andeducation stand to benefit in major ways if we makean earnest effort over the next decade to draw outthe practical lessons from our understanding ofhuman information processes.

IN CONCLUSION

We have tried to describe some of the main thingsthat are known about how the magician producesthe rabbit from the hat. We hope we have dis-pelled the illusion, but we hope also that you arenot disappointed by the relative simplicity of the

11 For the first three of these tasks, see Newell and Simon(in press); for algebra, Paige and Simon (1966); for letterscries, Simon and Kotovsky (1963) and Klahr and Wallace(1970).

HUMAN PROBLEM SOLVING 159

phenomena once explained. Those who have theinstincts and esthetic tastes of scientists presumablywill not be disappointed. There is much beautyin the superficial complexity of nature. But thereis a deeper beauty in the simplicity of underlyingprocess that accounts for the external complexity.There is beauty in the intricacy of human thinkingwhen an intelligent person is confronted with adifficult problem. But there is a deeper beauty inthe basic information processes and their organiza-tion into simple schemes of heuristic search thatmake that intricate human thinking possible. It isa sense of this latter beauty—the beauty of sim-plicity—that we have tried to convey to you.

REFERENCES

BARTLUTT, F. C. Thinking. New York: Basic Books, 1958.BAYLOR, G. W., JR., & SIMON, II. A. A chess mating com-

binations program. AFIPS Conference Proceedings, 1966Spring Joint Computer Conference, Boston, April 26-28,28, 431-447. Washington, D. C.: Spartan Books, 1966.

BE GROOT, A. Thought and choice in chess. The Hague:Mouton, 196S.

DUNCKEK, K. On problem solving. Psychological Mono-graphs, 194S, 58(5, Whole No. 270).

ERNST, G. W., & NEWELL, A. GPS: A case study in gen-erality and problem solving. New York: AcademicPress, 1969.

HILGARD, E. R., & BOWER, G. W. Theories of learning.(3rd ed.) New York: Applcton-Ccntury-Crofts, 1966.

HTLOARD, E. R., & ATKINSON, R. C. Introdiiction to psy-chology. (4th cd.) New York: Harcourt, Brace &World, 1967.

KATONA, G. Organizing and memorizing. New York:Columbia University Press, 1940.

KLAIIK, D., & WALLACE, J. G. Development of serial com-pletion strategy: Information processing analysis. BritishJournal of Psychology, 1970, 61, 243-257.

NEWELL, A. Studies in problem solving: Subject 3 on thecryptarithmetic task: DONALD + GERALD = ROBERT.Pittsburgh: Carnegie-Mellon University, 1967.

NEWELL, A., & STIAW, J. C. Programming the Logic The-ory Machine. Proceedings of the 1957 Western JointComputer Conference, February 26-28, 1057, 230-240.

NEWKLL, A., SHAW, J. C,, & SIMON, H. A. Empirical ex-plorations of the Logic Theory Machine: A case studyin heuristics. Proceedings of the 1957 Western JointComputer Conference, February 26-28, 1957, 218-230.

NEWELL, A., SHAW, J. C., & SIMON, H. A. Elements of atheory of human problem solving. Psychological Re-view, 1958, 65, 151-166.

XKWELL, A., SIIAW, J. C., & SIMON, H. A. The processesof creative thinking. In H. E. Gruber & M. Wertheimer(Eds.), Contemporary approaches to creative thinking.New York: Atherton Press, 1962.

NEWELL, A., & SIMON, H. A. The Logic Theory Machine:A complex information processing system. IRE Trans-actions on Information Theory, 1956, IT-2, 3, 61-79.

XEWELL, A., & SIMON, H. A. Human problem solving.Englewood Cliffs, N. J.: Prentice-Hall, 1971, in press.

PAIGK, J. M., & SIMON, II. A. Cognitive processes insolving algebra word problems. In B. Kleinmuntz (Ed.),Problem solving. New York: Wiley, 1966.

SIMON, H. A. Scientific discovery and the psychology ofproblem solving. In R. C. Colodny (Ed.), Mind andcosmos: Essays in contemporary science and philosophy.Pittsburgh: University of Pittsburgh Press, 1966.

SJMOK, H. A. An information-processing explanation ofsome perceptual phenomena. British Journal of Psy-chology, 1967, 58, 1-12.

SIMON, H. A. The sciences of the artificial. Cambridge:M.I.T. Tress, 1969.

SIMOX, II. A., & BARENFEI.D, M. Information-processinganalysis of perceptual processes in problem solving. Psy-chological Review, 1969, 76, 473-483.

SIMON, H. A., & KOTOVSKY, K. Human acquisition ofconcepts for sequential patterns. Psychological Review,1963, 70, 534-546.

WILLIAMS, D. S. Computer program organization inducedby problem examples. Unpublished doctoral disserta-tion, Carnegie-Mellon University, 1969.

WILLIAMS, T. G. Some studies in game playing with adigital computer. Unpublished doctoral dissertation,Carnegie Institute of Technology, 1965.

NOTE

Because of illness, Jean Piaget was not able to deliver hisDistinguished Scientific Contribution Award address thisyear.