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115-397: 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 a problem and creating a solution: the more widespread and inconvenient the problem,

230-411: A gestalt approach to the analysis of sound perception. Figure-ground organization is a form of perceptual organization, which interprets perceptual elements in terms of their shapes and relative locations in the layout of surfaces in the 3-D world. Figure-ground organization structures the perceptual field into a figure (standing out at the front of the perceptual field) and a background (receding behind

345-513: A high contention indicates sequential processing that could be parallelized, while having a high coherency suggests excessive dependencies among processes, prompting you to minimize interactions. Also, with help of USL, you can, in advance, calculate the maximum effective capacity of your system: scaling up your system beyond that point is a waste. High performance computing has two common notions of scalability: Gestalt psychology Gestalt psychology , gestaltism , or configurationism

460-439: 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

575-493: 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

690-641: A new computer to a distributed software application. An example might involve scaling out from one web server to three. High-performance computing applications, such as seismic analysis and biotechnology , scale workloads horizontally to support tasks that once would have required expensive supercomputers . Other workloads, such as large social networks, exceed the capacity of the largest supercomputer and can only be handled by scalable systems. Exploiting this scalability requires software for efficient resource management and maintenance. Scaling vertically (up/down) means adding resources to (or removing resources from)

805-659: A paper in Psychological Bulletin . It contains criticisms of then-current explanations of a number of problems of perception, and the alternatives offered by the Gestalt school. Koffka moved to the United States in 1924, eventually settling at Smith College in 1927. In 1935, Koffka published his Principles of Gestalt Psychology . This textbook laid out the Gestalt vision of the scientific enterprise as

920-410: 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

1035-594: 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

1150-493: A psychoanalyst and before she began developing Gestalt therapy together with Fritz Perls. The extent to which Gestalt psychology influenced Gestalt therapy is disputed. On one hand, Laura Perls preferred not to use the term "Gestalt" to name the emerging new therapy, because she thought that the Gestalt psychologists would object to it; on the other hand, Fritz and Laura Perls clearly adopted some of Goldstein's work. Mary Henle noted in her presidential address to Division 24 at

1265-424: A series of experiments, Wertheimer discovered that a person observing a pair of alternating bars of light can, under the right conditions, experience the illusion of movement between one location and the other. He noted that this was a perception of motion absent any moving object. That is, it was pure phenomenal motion. He dubbed it phi ("phenomenal") motion . Wertheimer's publication of these results in 1912 marks

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1380-453: A single node, typically involving the addition of CPUs, memory or storage to a single computer. Benefits to scale-up include avoiding increases management complexity, more sophisticated programming to allocate tasks among resources and handle issues such as throughput, latency, synchronization across nodes. Moreover some applications do not scale horizontally . Network function virtualization defines these terms differently: scaling out/in

1495-425: A single shape, in C a complete three-dimensional shape is seen, where in actuality no such thing is drawn. Reification can be explained by progress in the study of illusory contours , which are treated by the visual system as "real" contours. Multistability (or multistable perception ) is the tendency of ambiguous perceptual experiences to pop back and forth between two or more alternative interpretations. This

1610-406: A single unified dynamic mechanism. Reification is the constructive or generative aspect of perception, by which the experienced object of perception contains more explicit spatial information than the sensory stimulus on which it is based. For instance, a triangle is perceived in picture A , though no triangle is there. In pictures B and D the eye recognizes disparate shapes as "belonging" to

1725-408: A single warehouse for sorting, the system would not be as scalable, because one warehouse can handle only a limited number of packages. In computing, scalability is a characteristic of computers, networks, algorithms , networking protocols , programs and applications. An example is a search engine , which must support increasing numbers of users, and the number of topics it indexes . Webscale

1840-423: A starting point and not be solely focused on sensory qualities. A related principle is that of the biotic experiment, which establishes the need to conduct real experiments that sharply contrasted with and opposed classic laboratory experiments. This signified experimenting in natural situations, developed in real conditions, in which it would be possible to reproduce, with higher fidelity , what would be habitual for

1955-558: A subject. The Gestaltists were the first to document and demonstrate empirically many facts about perception—including facts about the perception of movement , the perception of contour , perceptual constancy , and perceptual illusions . Wertheimer's discovery of the phi phenomenon is one example of such a contribution. The key principles of gestalt systems are emergence , reification , multistability and invariance. These principles are not necessarily separable modules to model individually, but they could be different aspects of

2070-598: A textbook on visual perception states that, "The physiological theory of the gestaltists has fallen by the wayside, leaving us with a set of descriptive principles, but without a model of perceptual processing. Indeed, some of their 'laws' of perceptual organisation today sound vague and inadequate. What is meant by a 'good' or 'simple' shape, for example?" One historian of psychology, David J. Murray, has argued that Gestalt psychologists first discovered many principles later championed by cognitive psychology, including schemas and prototypes . Another psychologist has argued that

2185-440: 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

2300-471: A whole. Science, he said, is not the simple accumulation of facts. What makes research scientific is the incorporation of facts into a theoretical structure. The goal of the Gestaltists was to integrate the facts of inanimate nature, life, and mind into a single scientific structure. This meant that science would have to accommodate not only what Koffka called the quantitative facts of physical science but

2415-405: Is not Gestalt psychology." One form of psychotherapy that, unlike Gestalt therapy, is actually consistently based on Gestalt psychology is Gestalt theoretical psychotherapy . The Gestalt psychologists practiced a set of theoretical and methodological principles that attempted to redefine the approach to psychological research. This is in contrast to investigations developed at the beginning of

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2530-462: Is a school of psychology and a theory of perception that emphasises the processing of entire patterns and configurations, and not merely individual components. It emerged in the early twentieth century in Austria and Germany as a rejection of basic principles of Wilhelm Wundt 's and Edward Titchener 's elementalist and structuralist psychology . Gestalt psychology is often associated with

2645-427: Is a computer architectural approach that brings the capabilities of large-scale cloud computing companies into enterprise data centers. In distributed systems , there are several definitions according to the authors, some considering the concepts of scalability a sub-part of elasticity , others as being distinct. According to Marc Brooker: "a system is scalable in the range where marginal cost of additional workload

2760-413: Is a form of perceptual organization. Perceptual grouping is the process that determines how organisms perceive some parts of their perceptual fields as being more related than others, using such information for object detection . The Gestaltists were the first psychologists to systematically study perceptual grouping. According to Gestalt psychologists, the fundamental principle of perceptual grouping

2875-399: 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

2990-667: Is a vital consideration for businesses aiming to meet customer expectations, remain competitive, and achieve sustainable growth. Factors influencing scalability include the flexibility of the production process, the adaptability of the workforce, and the integration of advanced technologies. By implementing scalable solutions, companies can optimize resource utilization, reduce costs, and streamline their operations. Scalability in industrial engineering and manufacturing enables businesses to respond to fluctuating market conditions, capitalize on emerging opportunities, and thrive in an ever-evolving global landscape. The Incident Command System (ICS)

3105-411: 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

3220-571: 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

3335-434: Is called closure. The law of closure states that individuals perceive objects such as shapes, letters, pictures, etc., as being whole when they are not complete. Specifically, when parts of a whole picture are missing, our perception fills in the visual gap. Research shows that the reason the mind completes a regular figure that is not perceived through sensation is to increase the regularity of surrounding stimuli. For example,

3450-551: 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

3565-429: 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

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3680-633: Is nearly constant." Serverless technologies fit this definition but you need to consider total cost of ownership not just the infra cost. In mathematics, scalability mostly refers to closure under scalar multiplication . In industrial engineering and manufacturing, scalability refers to the capacity of a process, system, or organization to handle a growing workload, adapt to increasing demands, and maintain operational efficiency. A scalable system can effectively manage increased production volumes, new product lines, or expanding markets without compromising quality or performance. In this context, scalability

3795-459: 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

3910-531: Is often advised to focus system design on hardware scalability rather than on capacity. It is typically cheaper to add a new node to a system in order to achieve improved performance than to partake in performance tuning to improve the capacity that each node can handle. But this approach can have diminishing returns (as discussed in performance engineering ). For example: suppose 70% of a program can be sped up if parallelized and run on multiple CPUs instead of one. If α {\displaystyle \alpha }

4025-407: 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

4140-542: Is only peripherally linked to Gestalt psychology. Max Wertheimer , Kurt Koffka , and Wolfgang Köhler founded Gestalt psychology in the early 20th century. The dominant view in psychology at the time was structuralism , exemplified by the work of Hermann von Helmholtz , Wilhelm Wundt , and Edward B. Titchener . Structuralism was rooted firmly in British empiricism and was based on three closely interrelated theories: Together, these three theories give rise to

4255-597: Is seen, for example, in the Necker cube and Rubin's Figure/Vase illusion . Other examples include the three-legged blivet , artist M. C. Escher 's artwork, and the appearance of flashing marquee lights moving first one direction and then suddenly the other. Invariance is the property of perception whereby simple geometrical objects are recognized independent of rotation, translation, and scale, as well as several other variations such as elastic deformations, different lighting, and different component features. For example,

4370-465: Is solving a problem deliberately based on previous experience and knowledge. Reproductive thinking proceeds algorithmically —a problem solver reproduces a series of steps from memory, knowing that they will lead to a solution—or by trial and error . Karl Duncker , another Gestalt psychologist who studied problem solving, coined the term functional fixedness for describing the difficulties in both visual perception and problem solving that arise from

4485-433: Is something else than the sum of its parts, because summing is a meaningless procedure, whereas the whole-part relationship is meaningful." The principle of psychophysical isomorphism hypothesizes that there is a correlation between conscious experience and cerebral activity. Based on the principles, phenomenon experimental analysis was derived, which asserts that any psychological research should take phenomena as

4600-738: Is suitable when availability and responsiveness are rated higher than consistency, which is true for many web file-hosting services or web caches ( if you want the latest version, wait some seconds for it to propagate ). For all classical transaction-oriented applications, this design should be avoided. Many open-source and even commercial scale-out storage clusters, especially those built on top of standard PC hardware and networks, provide eventual consistency only, such as some NoSQL databases like CouchDB and others mentioned above. Write operations invalidate other copies, but often don't wait for their acknowledgements. Read operations typically don't check every redundant copy prior to answering, potentially missing

4715-693: Is the ability to scale by adding/removing resource instances (e.g., virtual machine), whereas scaling up/down is the ability to scale by changing allocated resources (e.g., memory/CPU/storage capacity). Scalability for databases requires that the database system be able to perform additional work given greater hardware resources, such as additional servers, processors, memory and storage. Workloads have continued to grow and demands on databases have followed suit. Algorithmic innovations include row-level locking and table and index partitioning. Architectural innovations include shared-nothing and shared-everything architectures for managing multi-server configurations. In

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4830-437: 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

4945-413: Is the fraction of a calculation that is sequential, and 1 − α {\displaystyle 1-\alpha } is the fraction that can be parallelized, the maximum speedup that can be achieved by using P processors is given according to Amdahl's Law : Substituting the value for this example, using 4 processors gives Doubling the computing power to 8 processors gives Doubling

5060-428: Is the law of Prägnanz, also known as the law of good Gestalt. Prägnanz is a German word that directly translates to "pithiness" and implies salience, conciseness, and orderliness. The law of Prägnanz says that people tend to experience things as regular, orderly, symmetrical, and simple. Gestalt psychologists attempted to discover refinements of the law of Prägnanz , which involved writing down laws that predict

5175-559: 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

5290-469: Is the property of a system to handle a growing amount of work. One definition for software systems specifies that this may be done by adding resources to the system. In an economic context, a scalable business model implies that a company can increase sales given increased resources. For example, a package delivery system is scalable because more packages can be delivered by adding more delivery vehicles. However, if all packages had to first pass through

5405-486: 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

5520-470: 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

5635-658: Is used by emergency response agencies in the United States. ICS can scale resource coordination from a single-engine roadside brushfire to an interstate wildfire. The first resource on scene establishes command, with authority to order resources and delegate responsibility (managing five to seven officers, who will again delegate to up to seven, and on as the incident grows). As an incident expands, more senior officers assume command. Scalability can be measured over multiple dimensions, such as: Resources fall into two broad categories: horizontal and vertical. Scaling horizontally (out/in) means adding or removing nodes, such as adding

5750-573: Is what forms patterns for individuals, the halo effect being classified as a cognitive bias which occurs during impression formation. The halo effect can also be altered by physical characteristics, social status and many other characteristics. As well, the halo effect can have real repercussions on the individual's perception of reality, either negatively or positively, meaning to construct negative or positive images about other individuals or situations, something that could lead to self-fulfilling prophesies , stereotyping, or even discrimination. Some of

5865-946: 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

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5980-487: The "structure" of a problem, over and above the associative and incremental manner of learning that Ivan Pavlov and Edward Lee Thorndike had demonstrated with dogs and cats, respectively. In 1921, Koffka published a Gestalt-oriented text on developmental psychology, Growth of the Mind . With the help of American psychologist Robert Ogden , Koffka introduced the Gestalt point of view to an American audience in 1922 by way of

6095-406: The 20th century, based on traditional scientific methodology, which divided the object of study into a set of elements that could be analyzed separately with the objective of reducing the complexity of this object. The principle of totality asserts that conscious experience must be considered globally by taking into account all the physical and mental aspects of the individual simultaneously, because

6210-473: The Analysis of Sensations, 1886), in formulating their very similar concepts of gestalt and figural moment , respectively. By 1914, the first published references to Gestalt theory could be found in a footnote of Gabriele von Wartensleben 's application of Gestalt theory to personality. She was a student at Frankfurt Academy for Social Sciences, who interacted deeply with Wertheimer and Köhler. Through

6325-467: The Gestalt movement were forced out of Germany to the United States by 1935. Köhler published another book, Dynamics in Psychology , in 1940 but thereafter the Gestalt movement suffered a series of setbacks. Koffka died in 1941 and Wertheimer in 1943. Wertheimer's long-awaited book on mathematical problem-solving, Productive Thinking, was published posthumously in 1945, but Köhler was left to guide

6440-541: The Gestalt psychologists made a lasting contribution by showing how the study of illusions can help scientists understand essential aspects of how the visual system normally functions, not merely how it breaks down. The gestalt laws are used in several visual design fields, such as user interface design and cartography . The laws of similarity and proximity can, for example, be used as guides for placing radio buttons . They may also be used in designing computers and software for more intuitive human use. Examples include

6555-635: The Gestaltists in Germany marks the beginning of the scientific study of problem solving. Later this experimental work continued through the 1960s and early 1970s with research conducted on relatively simple laboratory tasks of problem solving. Max Wertheimer distinguished two kinds of thinking: productive thinking and reproductive thinking. Productive thinking is solving a problem based on insight—a quick, creative, unplanned response to situations and environmental interaction. Reproductive thinking

6670-524: The adage, "The whole is greater than the sum of its parts". In Gestalt theory, information is perceived as wholes rather than disparate parts which are then processed summatively. As used in Gestalt psychology, the German word Gestalt ( / ɡ ə ˈ ʃ t æ l t , - ˈ ʃ t ɑː l t / gə- SHTA(H)LT , German: [ɡəˈʃtalt] ; meaning "form" ) is interpreted as "pattern" or "configuration". It differs from Gestalt therapy , which

6785-411: The beginning of Gestalt psychology. In comparison to von Ehrenfels and others who had used the term "gestalt" earlier in various ways, Wertheimer's unique contribution was to insist that the "gestalt" is perceptually primary. The gestalt defines the parts from which it is composed, rather than being a secondary quality that emerges from those parts. Wertheimer took the more radical position that one hears

6900-406: The central criticisms of Gestaltism are based on the preference Gestaltists are deemed to have for theory over data, and a lack of quantitative research supporting Gestalt ideas. This is not necessarily a fair criticism as highlighted by a recent collection of quantitative research on Gestalt perception. Researchers continue to test hypotheses about the mechanisms underlying Gestalt principles such as

7015-798: 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

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7130-465: The collection of circles in groups. Specifically, we perceive that there is a group of 36 circles on the left side of the image and three groups of 12 circles on the right side of the image. This law is often used in advertising logos to emphasize which aspects of events are associated. The law of similarity states that elements within an assortment of objects are perceptually grouped together if they are similar to each other. This similarity can occur in

7245-433: The concept of Gestalt to philosophy and psychology in 1890, before the advent of Gestalt psychology as such. Von Ehrenfels observed that a perceptual experience, such as perceiving a melody or a shape, is more than the sum of its sensory components. He claimed that, in addition to the sensory elements of the perception, there is something additional that is an element in its own right, despite in some sense being derived from

7360-624: 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

7475-441: The context of scale-out data storage , scalability is defined as the maximum storage cluster size which guarantees full data consistency, meaning there is only ever one valid version of stored data in the whole cluster, independently from the number of redundant physical data copies. Clusters which provide "lazy" redundancy by updating copies in an asynchronous fashion are called 'eventually consistent' . This type of scale-out design

7590-453: 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

7705-456: The design and layout of a desktop's shortcuts in rows and columns. In map design, principles of Prägnanz or grouping are crucial for implying a conceptual order to the portrayed geographic features, thus facilitating the intended use of the map. The Law of Similarity is employed by selecting similar map symbols for similar kinds of features or features with similar properties; the Law of Proximity

7820-618: 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

7935-1735: 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 . Scalability Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour Social network analysis Small-world networks Centrality Motifs Graph theory Scaling Robustness Systems biology Dynamic networks Evolutionary computation Genetic algorithms Genetic programming Artificial life Machine learning Evolutionary developmental biology Artificial intelligence Evolutionary robotics Reaction–diffusion systems Partial differential equations Dissipative structures Percolation Cellular automata Spatial ecology Self-replication Conversation theory Entropy Feedback Goal-oriented Homeostasis Information theory Operationalization Second-order cybernetics Self-reference System dynamics Systems science Systems thinking Sensemaking Variety Ordinary differential equations Phase space Attractors Population dynamics Chaos Multistability Bifurcation Rational choice theory Bounded rationality Scalability

8050-556: The downward moving dots as two distinct units. The law of continuity (also known as the law of good continuation) states that elements of objects tend to be grouped together, and therefore integrated into perceptual wholes if they are aligned within an object. In cases where there is an intersection between objects, individuals tend to perceive the two objects as two single uninterrupted entities. Stimuli remain distinct even with overlap. We are less likely to group elements with sharp abrupt directional changes as being one object. For example,

8165-423: 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

8280-421: 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

8395-424: The fact that one element of a whole situation already has a (fixed) function that has to be changed in order to perceive something or find the solution to a problem. Gestalt psychology struggled to precisely define terms like Prägnanz, to make specific behavioural predictions, and to articulate testable models of underlying neural mechanisms. It was criticized as being merely descriptive. These shortcomings led, by

8510-467: The facts of two other "scientific categories": questions of order and questions of Sinn , a German word which has been variously translated as significance, value, and meaning. Without incorporating the meaning of experience and behavior, Koffka believed that science would doom itself to trivialities in its investigation of human beings. Having survived the Nazis up to the mid-1930s, all the core members of

8625-604: 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

8740-444: The figure depicting the law of continuity shows a configuration of two crossed keys. When the image is perceived, we tend to perceive the key in the background as a single uninterrupted key instead of two separate halves of a key. The law of past experience implies that under some circumstances visual stimuli are categorized according to past experience. If objects tend to be observed within close proximity, or small temporal intervals,

8855-461: The figure depicting the law of symmetry shows a configuration of square and curled brackets. When the image is perceived, we tend to observe three pairs of symmetrical brackets rather than six individual brackets. The law of common fate states that objects are perceived as lines that move along the smoothest path. Experiments using the visual sensory modality found that the movement of elements of an object produces paths that individuals perceive that

8970-461: The figure that depicts the law of closure portrays what we perceive as a circle on the left side of the image and a rectangle on the right side of the image. However, gaps are present in the shapes. If the law of closure did not exist, the image would depict an assortment of different lines with different lengths, rotations, and curvatures—but with the law of closure, we perceptually combine the lines into whole shapes. The law of symmetry states that

9085-454: The figure). Pioneering work on figure-ground organization was carried out by the Danish psychologist Edgar Rubin . The Gestalt psychologists demonstrated that people tend to perceive as figures those parts of our perceptual fields that are convex, symmetric, small, and enclosed. Gestalt psychology contributed to the scientific study of problem solving. In fact, the early experimental work of

9200-415: The form of shape, colour, shading or other qualities. For example, the figure illustrating the law of similarity portrays 36 circles all equal distance apart from one another forming a square. In this depiction, 18 of the circles are shaded dark, and 18 of the circles are shaded light. We perceive the dark circles as grouped together and the light circles as grouped together, forming six horizontal lines within

9315-418: 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

9430-417: 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

9545-404: 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

9660-426: The interpretation of sensation. Wertheimer defined a few principles that explain the ways humans perceive objects based on similarity, proximity, and continuity. The law of proximity states that when an individual perceives an assortment of objects, they perceive objects that are close to each other as forming a group. For example, in the figure illustrating the law of proximity, there are 72 circles, but we perceive

9775-426: The mechanism of frogs' eyes indicate that perception of 'gestalts' (in particular gestalts in motion ) is perhaps more primitive and fundamental than 'seeing' as such: The halo effect can be explained through the application of Gestalt theories to social information processing. The constructive theories of social cognition are applied to the expectations of individuals. They have been perceived in this manner and

9890-586: The meeting of the American Psychological Association: "What Perls has done has been to take a few terms from Gestalt psychology, stretch their meaning beyond recognition, mix them with notions—often unclear and often incompatible—from the depth psychologies, existentialism, and common sense, and he has called the whole mixture gestalt therapy. His work has no substantive relation to scientific Gestalt psychology. To use his own language, Fritz Perls has done 'his thing'; whatever it is, it

10005-404: The melody first and only then may perceptually divide it up into notes. Similarly, in vision, one sees the form of the circle first, with its apprehension not mediated by a process of part-summation. Only after this primary apprehension might one notice that it is made up of lines or dots or stars. The two men who served as Wertheimer's subjects in the phi experiments were Köhler and Koffka. Köhler

10120-811: 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

10235-435: The mid-20th century, to growing dissatisfaction with Gestaltism and a subsequent decline in its impact on psychology. Despite this decline, Gestalt psychology has formed the basis of much further research into the perception of patterns and objects and of research into behaviour, thinking, problem solving and psychopathology. In the 1940s and 1950s, laboratory research in neurology and what became known as cybernetics on

10350-431: The mind perceives objects as being symmetrical and forming around a center point. It is perceptually pleasing to divide objects into an even number of symmetrical parts. Therefore, when two symmetrical elements are unconnected the mind perceptually connects them to form a coherent shape. Similarities between symmetrical objects increase the likelihood that objects are grouped to form a combined symmetrical object. For example,

10465-465: 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

10580-468: 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

10695-458: 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

10810-522: 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

10925-416: The movement without his two long-time colleagues. Gestalt psychology differs from Gestalt therapy , which is only peripherally linked to Gestalt psychology. The founders of Gestalt therapy, Fritz and Laura Perls , had worked with Kurt Goldstein , a neurologist who had applied principles of Gestalt psychology to the functioning of the organism. Laura Perls had been a Gestalt psychologist before she became

11040-482: The nature of the mind demands that each component be considered as part of a system of dynamic relationships. Thus, holism as fundamental aspect of Gestalt psychology. Moreover, the perception of the nature of a part depends upon the whole in which it is embedded. The maxim that the whole is more than the sum of its parts is not a precise description of the Gestaltist view. Rather, as Koffka writes, "The whole

11155-461: The object as an uppercase U. An example of the Gestalt movement in effect, as it is both a process and result, is a music sequence. People are able to recognise a sequence of perhaps six or seven notes, despite them being transposed into a different tuning or key. An early theory of gestalt grouping principles in music was composer-theorist James Tenney 's Meta+Hodos (1961). Auditory Scene Analysis as developed by Albert Bregman further extends

11270-457: The objects are more likely to be perceived together. For example, the English language contains 26 letters that are grouped to form words using a set of rules. If an individual reads an English word they have never seen, they use the law of past experience to interpret the letters "L" and "I" as two letters beside each other, rather than using the law of closure to combine the letters and interpret

11385-423: The objects are on. We perceive elements of objects to have trends of motion, which indicate the path that the object is on. The law of continuity implies the grouping together of objects that have the same trend of motion and are therefore on the same path. For example, if there is an array of dots and half the dots are moving upward while the other half are moving downward, we would perceive the upward moving dots and

11500-530: The objects in A in the figure are all immediately recognized as the same basic shape, which is immediately distinguishable from the forms in B . They are even recognized despite perspective and elastic deformations as in C , and when depicted using different graphic elements as in D . Computational theories of vision, such as those by David Marr , have provided alternate explanations of how perceived objects are classified. Like figure-ground organization, perceptual grouping (sometimes called perceptual segregation)

11615-575: The organization of the component sensory elements. He called it Gestalt-qualität or "form-quality." It is this Gestalt-qualität that, according to von Ehrenfels, allows a tune to be transposed to a new key, using completely different notes, while still retaining its identity. The idea of a Gestalt-qualität has roots in theories by David Hume , Johann Wolfgang von Goethe , Immanuel Kant , David Hartley , and Ernst Mach . Both von Ehrenfels and Edmund Husserl seem to have been inspired by Mach's work Beiträge zur Analyse der Empfindungen (Contributions to

11730-482: 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

11845-402: The person judging the individual is continuing to view them in this positive manner. Gestalt's theories of perception enforces that individual's tendency to perceive actions and characteristics as a whole rather than isolated parts, therefore humans are inclined to build a coherent and consistent impression of objects and behaviors in order to achieve an acceptable shape and form. The halo effect

11960-415: The preceding write operation. The large amount of metadata signal traffic would require specialized hardware and short distances to be handled with acceptable performance (i.e., act like a non-clustered storage device or database). Whenever strong data consistency is expected, look for these indicators: Indicators for eventually consistent designs (not suitable for transactional applications!) are: It

12075-518: The principle of similarity. Other important criticisms concern the lack of definition and support for the many physiological assumptions made by gestaltists and lack of theoretical coherence in modern Gestalt psychology. In some scholarly communities, such as cognitive psychology and computational neuroscience , gestalt theories of perception are criticized for being descriptive rather than explanatory in nature. For this reason, they are viewed by some as redundant or uninformative. For example,

12190-446: 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

12305-489: 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

12420-580: 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

12535-615: The processing power has only sped up the process by roughly one-fifth. If the whole problem was parallelizable, the speed would also double. Therefore, throwing in more hardware is not necessarily the optimal approach. In distributed systems , you can use Universal Scalability Law (USL) to model and to optimize scalability of your system. USL is coined by Neil J. Gunther and quantifies scalability based on parameters such as contention and coherency. Contention refers to delay due to waiting or queueing for shared resources. Coherence refers to delay for data to become consistent. For example, having

12650-487: The psychological "whole" has priority and that the "parts" are defined by the structure of the whole, rather than the other way round. Gestalt theories of perception are based on human nature being inclined to understand objects as an entire structure rather than the sum of its parts. Wertheimer had been a student of Austrian philosopher, Christian von Ehrenfels , a member of the School of Brentano . Von Ehrenfels introduced

12765-485: 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,

12880-413: The square of circles. This perception of lines is due to the law of similarity. Gestalt psychologists believed that humans tend to perceive objects as complete rather than focusing on the gaps that the object might contain. For example, a circle has good Gestalt in terms of completeness. However, we will also perceive an incomplete circle as a complete circle. That tendency to complete shapes and figures

12995-434: 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

13110-599: The view that the mind constructs all perceptions and abstract thoughts strictly from lower-level sensations, which are related solely by being associated closely in space and time. The Gestaltists took issue with the widespread atomistic view that the aim of psychology should be to break consciousness down into putative basic elements. In contrast, the Gestalt psychologists believed that breaking psychological phenomena down into smaller parts would not lead to understanding psychology. Instead, they viewed psychological phenomena as organized, structured wholes. They argued that

13225-463: Was an expert in physical acoustics, having studied under physicist Max Planck , but had taken his degree in psychology under Carl Stumpf . Koffka was also a student of Stumpf's, having studied movement phenomena and psychological aspects of rhythm. In 1917, Köhler published the results of four years of research on learning in chimpanzees. Köhler showed, contrary to the claims of most other learning theorists, that animals can learn by "sudden insight" into

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