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87-537: [REDACTED] Look up difficulty in Wiktionary, the free dictionary. Difficulty or Difficult may refer to: A problem Degree of difficulty , in sport and gaming Counter-majoritarian difficulty , in legal theory Difficult, Tennessee , a community in the United States "Difficult" (song) , by Uffie Hill Difficulty, a fictional place in

174-462: A type–token distinction , a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball'). Abstraction in its secondary use is a material process , discussed in the themes below . Thinking in abstractions is considered by anthropologists , archaeologists , and sociologists to be one of the key traits in modern human behaviour , which is believed to have developed between 50,000 and 100,000 years ago. Its development

261-509: A book of modern scientific philosophy written in the late Jacobean era of England to encourage modern thinkers to collect specific facts before making any generalizations. Bacon used and promoted induction as an abstraction tool; it complemented but was distinct from the ancient deductive -thinking approach that had dominated the intellectual world since the times of Greek philosophers like Thales , Anaximander , and Aristotle . Thales ( c.  624 –546 BCE) believed that everything in

348-743: A concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals . It has also recently become popular in formal logic under predicate abstraction . Another philosophical tool for the discussion of abstraction is thought space. John Locke defined abstraction in An Essay Concerning Human Understanding : 'So words are used to stand as outward marks of our internal ideas, which are taken from particular things; but if every particular idea that we take in had its own special name, there would be no end to names. To prevent this,

435-453: A detective or philosopher/scientist/engineer might seek to learn about something, at progressively deeper levels of detail, to solve a crime or a puzzle. In philosophical terminology , abstraction is the thought process wherein ideas are distanced from objects . But an idea can be symbolized . Typically, abstraction is used in the arts as a synonym for abstract art in general. Strictly speaking, it refers to art unconcerned with

522-565: A framework (categorical concepts related to computing problems) from specific instances which implement details. This means that the program code can be written so that code does not have to depend on the specific details of supporting applications, operating system software, or hardware, but on a categorical concept of the solution. A solution to the problem can then be integrated into the system framework with minimal additional work. This allows programmers to take advantage of another programmer's work, while requiring only an abstract understanding of

609-472: A general name that is applicable to any existing thing that fits that abstract idea.' (2.11.9) Carl Jung 's definition of abstraction broadened its scope beyond the thinking process to include exactly four mutually exclusive, different complementary psychological functions: sensation, intuition, feeling, and thinking. Together they form a structural totality of the differentiating abstraction process. Abstraction operates in one of these functions when it excludes

696-440: A hypothesis in the form of a rule that could have been used to create that triplet of numbers. When testing their hypotheses, participants tended to only create additional triplets of numbers that would confirm their hypotheses, and tended not to create triplets that would negate or disprove their hypotheses. Mental set is the inclination to re-use a previously successful solution, rather than search for new and better solutions. It

783-496: A hypothesis with empirical data (asking "how much?"). The objective of abduction is to determine which hypothesis or proposition to test, not which one to adopt or assert. In the Peircean logical system, the logic of abduction and deduction contribute to our conceptual understanding of a phenomenon, while the logic of induction adds quantitative details (empirical substantiation) to our conceptual knowledge. Forensic engineering

870-448: A material process. Alfred Sohn-Rethel (1899–1990) asked: "Can there be abstraction other than by thought?" He used the example of commodity abstraction to show that abstraction occurs in practice as people create systems of abstract exchange that extend beyond the immediate physicality of the object and yet have real and immediate consequences. This work was extended through the 'Constitutive Abstraction' approach of writers associated with

957-496: A particular place and time. However, in the secondary sense of the term 'abstraction', this physical object can carry materially abstracting processes. For example, record-keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers. According to Schmandt-Besserat 1981 , these clay containers contained tokens,

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1044-551: A particular property (e.g., good ). Questions about the properties of things are then propositions about predicates, which propositions remain to be evaluated by the investigator. In the graph 1 below , the graphical relationships like the arrows joining boxes and ellipses might denote predicates. Abstractions sometimes have ambiguous referents . For example, " happiness " can mean experiencing various positive emotions, but can also refer to life satisfaction and subjective well-being . Likewise, " architecture " refers not only to

1131-502: A problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution. There are many specialized problem-solving techniques and methods in fields such as science , engineering , business , medicine , mathematics , computer science , philosophy , and social organization . The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences . Also widely researched are

1218-413: A process known as transfer . Problem-solving strategies are steps to overcoming the obstacles to achieving a goal. The iteration of such strategies over the course of solving a problem is the "problem-solving cycle". Common steps in this cycle include recognizing the problem, defining it, developing a strategy to fix it, organizing knowledge and resources available, monitoring progress, and evaluating

1305-594: A product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems. In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, abduction generates new ideas or hypotheses (asking "how?"); deduction evaluates and refines hypotheses based on other plausible premises (asking "why?"); and induction justifies

1392-441: A single piece of abstract data; based on similarities in the constituent data, for example, many different physical cats map to the abstraction "CAT". This conceptual scheme emphasizes the inherent equality of both constituent and abstract data, thus avoiding problems arising from the distinction between "abstract" and " concrete ". In this sense the process of abstraction entails the identification of similarities between objects, and

1479-442: A type of mental set known as functional fixedness (see the following section). Rigidly clinging to a mental set is called fixation , which can deepen to an obsession or preoccupation with attempted strategies that are repeatedly unsuccessful. In the late 1990s, researcher Jennifer Wiley found that professional expertise in a field can create a mental set, perhaps leading to fixation. Groupthink , in which each individual takes on

1566-435: Is a process where general rules and concepts are derived from the use and classifying of specific examples, literal ( real or concrete ) signifiers, first principles , or other methods. "An abstraction" is the outcome of this process — a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a group , field , or category . Conceptual abstractions may be made by filtering

1653-400: Is a reliance on habit. It was first articulated by Abraham S. Luchins in the 1940s with his well-known water jug experiments. Participants were asked to fill one jug with a specific amount of water by using other jugs with different maximum capacities. After Luchins gave a set of jug problems that could all be solved by a single technique, he then introduced a problem that could be solved by

1740-554: Is an elementary methodological tool in several disciplines of social science. These disciplines have definite and different concepts of "man" that highlight those aspects of man and his behaviour by idealization that are relevant for the given human science . For example, homo sociologicus is the man as sociology abstracts and idealizes it, depicting man as a social being. Moreover, we could talk about homo cyber sapiens (the man who can extend his biologically determined intelligence thanks to new technologies), or homo creativus (who

1827-412: Is an important technique of failure analysis that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures. Reverse engineering attempts to discover the original problem-solving logic used in developing a product by disassembling the product and developing a plausible pathway to creating and assembling its parts. In military science , problem solving

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1914-573: Is an unintentional tendency to collect and use data which favors preconceived notions. Such notions may be incidental rather than motivated by important personal beliefs: the desire to be right may be sufficient motivation. Scientific and technical professionals also experience confirmation bias. One online experiment, for example, suggested that professionals within the field of psychological research are likely to view scientific studies that agree with their preconceived notions more favorably than clashing studies. According to Raymond Nickerson, one can see

2001-554: Is dependent upon personal motivational and contextual components. One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia. In conceptualization, human problem solving consists of two related processes: problem orientation, and

2088-439: Is different from Wikidata All article disambiguation pages All disambiguation pages Problem solving Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing

2175-508: Is likely to have been closely connected with the development of human language , which (whether spoken or written) appears to both involve and facilitate abstract thinking. Abstraction involves induction of ideas or the synthesis of particular facts into one general theory about something. It is the opposite of specification , which is the analysis or breaking-down of a general idea or abstraction into concrete facts. Abstraction can be illustrated by Francis Bacon 's Novum Organum (1620),

2262-433: Is linked to the concept of "end-states", the conditions or situations which are the aims of the strategy. Ability to solve problems is important at any military rank , but is essential at the command and control level. It results from deep qualitative and quantitative understanding of possible scenarios. Effectiveness in this context is an evaluation of results: to what extent the end states were accomplished. Planning

2349-460: Is not necessarily common. Mathematical word problems often include irrelevant qualitative or numerical information as an extra challenge. The disruption caused by the above cognitive biases can depend on how the information is represented: visually, verbally, or mathematically. A classic example is the Buddhist monk problem: A Buddhist monk begins at dawn one day walking up a mountain, reaches

2436-469: Is now constitutively and materially more abstract than at the time when princes ruled as the embodiment of extended power'. The way that physical objects, like rocks and trees, have being differs from the way that properties of abstract concepts or relations have being, for example the way the concrete , particular , individuals pictured in picture 1 exist differs from the way the concepts illustrated in graph 1 exist. That difference accounts for

2523-407: Is one of the most common forms of cognitive bias in daily life. As an example, imagine a man wants to kill a bug in his house, but the only thing at hand is a can of air freshener. He may start searching for something to kill the bug instead of squashing it with the can, thinking only of its main function of deodorizing. Tim German and Clark Barrett describe this barrier: "subjects become 'fixed' on

2610-426: Is simply creative). Abstraction (combined with Weberian idealization ) plays a crucial role in economics - hence abstractions such as "the market" and the generalized concept of " business ". Breaking away from directly experienced reality was a common trend in 19th-century sciences (especially physics ), and this was the effort which fundamentally determined the way economics tried (and still tries) to approach

2697-471: Is that highly abstract concepts are more difficult to learn, and might require a degree of mathematical maturity and experience before they can be assimilated. In music, the term abstraction can be used to describe improvisatory approaches to interpretation, and may sometimes indicate abandonment of tonality . Atonal music has no key signature, and is characterized by the exploration of internal numeric relationships. A recent meta-analysis suggests that

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2784-438: Is the dot problem: nine dots arranged in a three-by-three grid pattern must be connected by drawing four straight line segments, without lifting pen from paper or backtracking along a line. The subject typically assumes the pen must stay within the outer square of dots, but the solution requires lines continuing beyond this frame, and researchers have found a 0% solution rate within a brief allotted time. This problem has produced

2871-563: Is the process of determining how to effect those end states. Some models of problem solving involve identifying a goal and then a sequence of subgoals towards achieving this goal. Andersson, who introduced the ACT-R model of cognition, modelled this collection of goals and subgoals as a goal stack in which the mind contains a stack of goals and subgoals to be completed, and a single task being carried out at any time. Knowledge of how to solve one problem can be applied to another problem, in

2958-439: Is the ultimate and common feature of all bodies. Neoclassical economists created the indefinitely abstract notion of homo economicus by following the same procedure. Economists abstract from all individual and personal qualities in order to get to those characteristics that embody the essence of economic activity. Eventually, it is the substance of the economic man that they try to grasp. Any characteristic beyond it only disturbs

3045-489: Is the work of Allen Newell and Herbert A. Simon . Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks. These simple problems, such as the Tower of Hanoi , admitted optimal solutions that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit

3132-470: Is to find and fix errors in computer programs: debugging . Formal logic concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution. The use of computers to prove mathematical theorems using formal logic emerged as

3219-949: The advice taker , to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by Cordell Green in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning. The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution , which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking. When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further failures . Such techniques can also be applied to

3306-465: The agent and CAT:Elsie depicts an example of an is-a relationship, as does the arrow between the location and the MAT . The arrows between the gerund / present participle SITTING and the nouns agent and location express the diagram 's basic relationship; "agent is SITTING on location" ; Elsie is an instance of CAT . Although the description sitting-on (graph 1) is more abstract than

3393-408: The commodity abstraction recognizes a parallel process. The state (polity) as both concept and material practice exemplifies the two sides of this process of abstraction. Conceptually, 'the current concept of the state is an abstraction from the much more concrete early-modern use as the standing or status of the prince, his visible estates'. At the same time, materially, the 'practice of statehood

3480-407: The human brain suggests that the left and right hemispheres differ in their handling of abstraction. For example, one meta-analysis reviewing human brain lesions has shown a left hemisphere bias during tool usage. Abstraction in philosophy is the process (or, to some, the alleged process) in concept formation of recognizing some set of common features in individuals , and on that basis forming

3567-409: The information content of a concept or an observable phenomenon , selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, excluding but not eliminating the other phenomenal and cognitive characteristics of that particular ball. In

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3654-409: The ontological usefulness of the word "abstract". The word applies to properties and relations to mark the fact that, if they exist, they do not exist in space or time, but that instances of them can exist, potentially in many different places and times. A physical object (a possible referent of a concept or word) is considered concrete (not abstract) if it is a particular individual that occupies

3741-496: The 1678 Christian allegory The Pilgrim's Progress Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Difficulty . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Difficulty&oldid=1259221024 " Category : Disambiguation pages Hidden categories: Short description

3828-841: The Journal Arena . Two books that have taken this theme of the abstraction of social relations as an organizing process in human history are Nation Formation: Towards a Theory of Abstract Community (1996) and an associated volume published in 2006, Globalism, Nationalism, Tribalism: Bringing Theory Back In . These books argue that a nation is an abstract community bringing together strangers who will never meet as such; thus constituting materially real and substantial, but abstracted and mediated relations. The books suggest that contemporary processes of globalization and mediatization have contributed to materially abstracting relations between people, with major consequences for how humans live their lives . One can readily argue that abstraction

3915-518: The Sun is the center of the Solar System ; Kepler (1571–1630) compressed thousands of measurements into one expression to finally conclude that Mars moves in an elliptical orbit about the Sun; Galileo (1564–1642) repeated one hundred specific experiments into the law of falling bodies. An abstraction can be seen as a compression process, mapping multiple different pieces of constituent data to

4002-412: The abstract requires an intuitive or common experience between the communicator and the communication recipient. This is true for all verbal/abstract communication. For example, many different things can be red . Likewise, many things sit on surfaces (as in picture 1 , to the right). The property of redness and the relation sitting-on are therefore abstractions of those objects. Specifically,

4089-800: The characteristic cognitive processes by which more complex "real world" problems are solved. An outstanding problem-solving technique found by this research is the principle of decomposition . Much of computer science and artificial intelligence involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs . Steps for designing such systems include problem determination, heuristics , root cause analysis , de-duplication , analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, queuing systems , and simulation. A large, perennial obstacle

4176-427: The color red . That definition, however, suffers from the difficulty of deciding which things are real (i.e. which things exist in reality). For example, it is difficult to agree to whether concepts like God , the number three , and goodness are real, abstract, or both. An approach to resolving such difficulty is to use predicates as a general term for whether things are variously real, abstract, concrete, or of

4263-561: The concept "cat" or the concept "telephone". Although the concepts "cat" and "telephone" are abstractions , they are not abstract in the sense of the objects in graph 1 below . We might look at other graphs, in a progression from cat to mammal to animal , and see that animal is more abstract than mammal ; but on the other hand mammal is a harder idea to express, certainly in relation to marsupial or monotreme . Perhaps confusingly, some philosophies refer to tropes (instances of properties) as abstract particulars —e.g.,

4350-414: The conceptual diagram graph 1 identifies only three boxes, two ellipses, and four arrows (and their five labels), whereas the picture 1 shows much more pictorial detail, with the scores of implied relationships as implicit in the picture rather than with the nine explicit details in the graph. Graph 1 details some explicit relationships between the objects of the diagram. For example, the arrow between

4437-626: The consequences of confirmation bias in real-life situations, which range in severity from inefficient government policies to genocide. Nickerson argued that those who killed people accused of witchcraft demonstrated confirmation bias with motivation. Researcher Michael Allen found evidence for confirmation bias with motivation in school children who worked to manipulate their science experiments to produce favorable results. However, confirmation bias does not necessarily require motivation. In 1960, Peter Cathcart Wason conducted an experiment in which participants first viewed three numbers and then created

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4524-457: The correct use of a tool. Unnecessary constraints are arbitrary boundaries imposed unconsciously on the task at hand, which foreclose a productive avenue of solution. The solver may become fixated on only one type of solution, as if it were an inevitable requirement of the problem. Typically, this combines with mental set—clinging to a previously successful method. Visual problems can also produce mentally invented constraints. A famous example

4611-622: The design function of the objects, and problem solving suffers relative to control conditions in which the object's function is not demonstrated." Their research found that young children's limited knowledge of an object's intended function reduces this barrier Research has also discovered functional fixedness in educational contexts, as an obstacle to understanding: "functional fixedness may be found in learning concepts as well as in solving chemistry problems." There are several hypotheses in regards to how functional fixedness relates to problem solving. It may waste time, delaying or entirely preventing

4698-456: The design of safe, functional buildings, but also to elements of creation and innovation which aim at elegant solutions to construction problems, to the use of space, and to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building. Abstraction uses a strategy of simplification, wherein formerly concrete details are left ambiguous, vague, or undefined; thus effective communication about things in

4785-481: The difficulty. Similar strategies can often improve problem solving on tests. People who are engaged in problem solving tend to overlook subtractive changes, even those that are critical elements of efficient solutions. This tendency to solve by first, only, or mostly creating or adding elements, rather than by subtracting elements or processes is shown to intensify with higher cognitive loads such as information overload . Abstract thinking Abstraction

4872-452: The economic aspects of social life. It is abstraction we meet in the case of both Newton's physics and the neoclassical theory, since the goal was to grasp the unchangeable and timeless essence of phenomena. For example, Newton created the concept of the material point by following the abstraction method so that he abstracted from the dimension and shape of any perceptible object, preserving only inertial and translational motion. Material point

4959-423: The effectiveness of the solution. Once a solution is achieved, another problem usually arises, and the cycle starts again. Insight is the sudden a ha! solution to a problem, the birth of a new idea to simplify a complex situation. Solutions found through insight are often more incisive than those from step-by-step analysis. A quick solution process requires insight to select productive moves at different stages of

5046-424: The expression " think outside the box ". Such problems are typically solved via a sudden insight which leaps over the mental barriers, often after long toil against them. This can be difficult depending on how the subject has structured the problem in their mind, how they draw on past experiences, and how well they juggle this information in their working memory. In the example, envisioning the dots connected outside

5133-604: The field of automated theorem proving in the 1950s. It included the use of heuristic methods designed to simulate human problem solving, as in the Logic Theory Machine , developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the resolution principle developed by John Alan Robinson . In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science. In 1958, John McCarthy proposed

5220-421: The framing square requires visualizing an unconventional arrangement, which is a strain on working memory. Irrelevant information is a specification or data presented in a problem that is unrelated to the solution. If the solver assumes that all information presented needs to be used, this often derails the problem solving process, making relatively simple problems much harder. For example: "Fifteen percent of

5307-642: The graphic image of a cat sitting on a mat (picture 1), the delineation of abstract things from concrete things is somewhat ambiguous; this ambiguity or vagueness is characteristic of abstraction. Thus something as simple as a newspaper might be specified to six levels, as in Douglas Hofstadter 's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979): An abstraction can thus encapsulate each of these levels of detail with no loss of generality . But perhaps

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5394-405: The human problem-solving processes using methods such as introspection , behaviorism , simulation , computer modeling , and experiment . Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods. Problem solving has been defined as a higher-order cognitive process and intellectual function that requires

5481-579: The implementation of another's work, apart from the problem that it solves. Abstractions and levels of abstraction play an important role in the theory of general semantics originated by Alfred Korzybski . Anatol Rapoport wrote "Abstracting is a mechanism by which an infinite variety of experiences can be mapped on short noises (words)." Francis Fukuyama defines history as "a deliberate attempt of abstraction in which we separate out important from unimportant events". Researchers in linguistics frequently apply abstraction so as to allow an analysis of

5568-577: The literal depiction of things from the visible world—it can, however, refer to an object or image which has been distilled from the real world, or indeed, another work of art. Artwork that reshapes the natural world for expressive purposes is called abstract; that which derives from, but does not imitate a recognizable subject is called nonobjective abstraction. In the 20th century the trend toward abstraction coincided with advances in science, technology, and changes in urban life, eventually reflecting an interest in psychoanalytic theory. Later still, abstraction

5655-812: The mental obstacles that prevent people from finding solutions; problem-solving impediments include confirmation bias , mental set , and functional fixedness . The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science . There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems. Solving problems sometimes involves dealing with pragmatics (the way that context contributes to meaning) and semantics (the interpretation of

5742-432: The mind makes particular ideas received from particular things become general; which it does by considering them as they are in the mind—mental appearances—separate from all other existences, and from the circumstances of real existence, such as time, place, and so on. This procedure is called abstraction. In it, an idea taken from a particular thing becomes a general representative of all of the same kind, and its name becomes

5829-466: The mindset of the rest of the group, can produce and exacerbate mental set. Social pressure leads to everybody thinking the same thing and reaching the same conclusions. Functional fixedness is the tendency to view an object as having only one function, and to be unable to conceive of any novel use, as in the Maier pliers experiment described above. Functional fixedness is a specific form of mental set, and

5916-471: The modulation and control of more routine or fundamental skills. Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems. Interpersonal everyday problem solving

6003-458: The monk's progress on each day. It becomes much easier when the paragraph is represented mathematically by a function: one visualizes a graph whose horizontal axis is time of day, and whose vertical axis shows the monk's position (or altitude) on the path at each time. Superimposing the two journey curves, which traverse opposite diagonals of a rectangle, one sees they must cross each other somewhere. The visual representation by graphing has resolved

6090-584: The motivational/attitudinal/affective approach to problematic situations and problem-solving skills. People's strategies cohere with their goals and stem from the process of comparing oneself with others. Among the first experimental psychologists to study problem solving were the Gestaltists in Germany , such as Karl Duncker in The Psychology of Productive Thinking (1935). Perhaps best known

6177-426: The particular redness of a particular apple is an abstract particular . This is similar to qualia and sumbebekos . Still retaining the primary meaning of ' abstrere ' or 'to draw away from', the abstraction of money, for example, works by drawing away from the particular value of things allowing completely incommensurate objects to be compared (see the section on 'Physicality' below). Karl Marx 's writing on

6264-485: The people in Topeka have unlisted telephone numbers. You select 200 names at random from the Topeka phone book. How many of these people have unlisted phone numbers?" The "obvious" answer is 15%, but in fact none of the unlisted people would be listed among the 200. This kind of " trick question " is often used in aptitude tests or cognitive evaluations. Though not inherently difficult, they require independent thinking that

6351-503: The phenomena of language at the desired level of detail. A commonly used abstraction, the phoneme , abstracts speech sounds in such a way as to neglect details that cannot serve to differentiate meaning. Other analogous kinds of abstractions (sometimes called " emic units ") considered by linguists include morphemes , graphemes , and lexemes . Abstraction also arises in the relation between syntax , semantics , and pragmatics . Pragmatics involves considerations that make reference to

6438-447: The problem). The ability to understand what the end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires abstract thinking or coming up with a creative solution. Problem solving has two major domains: mathematical problem solving and personal problem solving. Each concerns some difficulty or barrier that is encountered. Problem solving in psychology refers to

6525-491: The problem-solving cycle. Unlike Newell and Simon's formal definition of a move problem , there is no consensus definition of an insight problem . Some problem-solving strategies include: Common barriers to problem solving include mental constructs that impede an efficient search for solutions. Five of the most common identified by researchers are: confirmation bias , mental set , functional fixedness , unnecessary constraints, and irrelevant information. Confirmation bias

6612-724: The process of associating these objects with an abstraction (which is itself an object ). Chains of abstractions can be construed , moving from neural impulses arising from sensory perception to basic abstractions such as color or shape , to experiential abstractions such as a specific cat, to semantic abstractions such as the "idea" of a CAT, to classes of objects such as "mammals" and even categories such as " object " as opposed to "action". Non-existent things in any particular place and time are often seen as abstract. By contrast, instances, or members, of such an abstract thing might exist in many different places and times. Those abstract things are then said to be multiply instantiated , in

6699-582: The process of finding solutions to problems encountered in life. Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping , in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an end goal to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis. Mental health professionals study

6786-423: The rational, logical qualities ... Abstract feeling does the same with ... its feeling-values. ... I put abstract feelings on the same level as abstract thoughts. ... Abstract sensation would be aesthetic as opposed to sensuous sensation and abstract intuition would be symbolic as opposed to fantastic intuition . (Jung, [1921] (1971): par. 678). Social theorists deal with abstraction both as an ideational and as

6873-486: The same technique, but also by a novel and simpler method. His participants tended to use the accustomed technique, oblivious of the simpler alternative. This was again demonstrated in Norman Maier 's 1931 experiment, which challenged participants to solve a problem by using a familiar tool (pliers) in an unconventional manner. Participants were often unable to view the object in a way that strayed from its typical use,

6960-411: The sense of picture 1 , picture 2 , etc., shown below . It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and "telephone" abstract ideas since despite their varying appearances, a particular cat or a particular telephone is an instance of

7047-502: The simultaneous influence of the other functions and other irrelevancies, such as emotion. Abstraction requires selective use of this structural split of abilities in the psyche. The opposite of abstraction is concretism . Abstraction is one of Jung's 57 definitions in Chapter XI of Psychological Types . There is an abstract thinking , just as there is abstract feeling , sensation and intuition . Abstract thinking singles out

7134-434: The top at sunset, meditates at the top for several days until one dawn when he begins to walk back to the foot of the mountain, which he reaches at sunset. Making no assumptions about his starting or stopping or about his pace during the trips, prove that there is a place on the path which he occupies at the same hour of the day on the two separate journeys. The problem cannot be addressed in a verbal context, trying to describe

7221-577: The total of which were the count of objects being transferred. The containers thus served as something of a bill of lading or an accounts book. In order to avoid breaking open the containers for the count, marks were placed on the outside of the containers. These physical marks, in other words, acted as material abstractions of a materially abstract process of accounting, using conceptual abstractions (numbers) to communicate its meaning. Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experiences, like

7308-408: The universe comes from one main substance, water. He deduced or specified from a general idea, "everything is water," to the specific forms of water such as ice, snow, fog, and rivers. Modern scientists used the approach of abstraction (going from particular facts collected into one general idea). Newton (1642–1727) derived the motion of the planets from Copernicus ' (1473–1543) simplification, that

7395-677: The user of the language; semantics considers expressions and what they denote (the designata ) abstracted from the language user; and syntax considers only the expressions themselves, abstracted from the designata. Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept or object, removing any dependence on real-world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. The advantages of abstraction in mathematics are: The main disadvantage of abstraction

7482-424: The verbal system has a greater engagement with abstract concepts when the perceptual system is more engaged in processing concrete concepts. This is because abstract concepts elicit greater brain activity in the inferior frontal gyrus and middle temporal gyrus compared to concrete concepts which elicit greater activity in the posterior cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus. Other research into

7569-590: Was manifest in more purely formal terms, such as color, freedom from objective context, and a reduction of form to basic geometric designs. Computer scientists use abstraction to make models that can be used and re-used without having to re-write all the program code for each new application on every different type of computer. They communicate their solutions with the computer by writing source code in some particular computer language which can be translated into machine code for different types of computers to execute. Abstraction allows program designers to separate

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