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Integrating Mental Processes: Thinking and Problem Solving
“Recruitment of executive attention is normally associated with a subjective feeling of mental effort.”
Lionel Naccache, Stanislas Dehaene, Laurent Cohen, Marie-Odile Habert, Elodie Guichart-Gomez, Damien Galanaud, and Jean-Claude Willer, 2004
• Welldefined problems– Much studied in AI– Requires search– Domain general heuristics for solving problems
• What about illdefined problems?– No real mechanisms for dealing with these– The problem may be solved suddenly by ‘seeing’ the problem
differently – Often requires developing a suitable representation
Views of Problem solving
Problem solving as search
INITIAL STATE GOAL STATE
INITIAL STATE
GOAL STATE
?
Play the game: http://www.mazeworks.com/hanoi/
Problem Solving is a search problem
Initial state
Goalstate
Search Space
Solution
Search spaces can be large
#DISCS #STATES
3 33 = 274 34 = 815 35 = 2436 36 = 729
What if the search space is too large?
• It is not possible to enumerate the entire search space for many welldefined problems.
• We must use heuristics – Not guaranteed to work but easy to implement– Example heuristics
• Trial and error• Hill climbing• Meansend analysis
Trial and Error• Edward L. Thorndike (1874
1949) found that many animals search by trial and error
(aka random search)
• Found that cats in a “puzzle box” (see left) initially behaved impulsively and apparently random.
• After many trials in puzzle box, solution time decreases.
In order to escape the animal has to perform three different actions: press a pedal, pull on a string, and push a bar up or down
Hill Climbing
• Find some measure of the distance between your present state and the end state.– Take a step in the direction that most reduces that distance
Hill Climbing
• Might lead to suboptimal solutions: local maximum
fence
3 4 5 FOOD 5 4
1 2 30
2
3
1
1 2 1
1
Meansend analysis
• Set up a goal• Look for a difference between
current state and goal or subgoal state
• Find an operator to reduce this difference. One operator is the setting of a new subgoal
• Apply operator• Repeat until final goal is
achieved
Setting subgoals in meansend analysis
• Painting your house (GOAL 1)• Apply paint (SUBGOAL 2)• Need paint and brush (SUBGOAL 3)• Go to hardware store (SUBGOAL 4)
• Went to hardware store (SUBGOAL 4)• Got paint and brush (SUBGOAL 3)• Apply paint (SUBGOAL 2)• Paint the house (GOAL 1)
G1
Goal Stack: last in, first out
G1G2
G1G2G3
G1G2G3G4
Push Goal 1
on Stack
G1G2G3
G4
Push Goal 2
on Stack
Push Goal 3
on Stack
Push Goal 4
on Stack
Solved Goal 4:Popoff Stack
What about illdefined problems?
• No real mechanisms for dealing with these
• According to Gestalt psychologists, the problem may be solved suddenly by ‘seeing’ the problem differently
• Often requires developing a suitable representation
Six stick problem
Wrong solution:
With these six sticks:
Answer:
New Yorker Puzzle win an IPAD
Functional Fixedness
Maier’s (1931) twostring problem
Only 39% of subjects were able to see solution within 10 minutes
Duncker’s problem: support a candle on a wall
A box of tacks, some matches, and a candle
Why people get stuck solving problems
• Functional Fixedness– Subjects who utilize an object for a particular
function will have more trouble in a problemsolving situation that requires a new and dissimilar function for the object.
– Young children suffer less from functional fixedness Less experience might help...
Insight• Seemingly sudden understanding of a problem
• Often involves conceptualizing a problem in a totally different way (e.g. six stick problem, overcoming functional fixedness)
• How can we distinguish between problems requiring insight and problems requiring noninsightful problem solving?
Evidence for concept of insight: Metcalfe and Weibe (1987) experiment
1) Noninsight problem (algebra): - factor 16y^2 – 40yz + 25z^2
2) Insight problem (nonroutine):• A prisoner was attempting escape from a tower. He
found in his cell a rope which was half long enough to permit him to reach the ground safely. He divided the rope in half and tied the two parts together and escaped. How could he have done this?
Results (1)• First result: subjects “feelings of knowing”
(beforehand) only predicted eventual success of solving the problem for noninsight problems.
• At 15 seconds intervals, ss. rated how close they felt to solving the problem:
1=cold (nowhere close to solution) ….
7=hot (problem is virtually solved)
Results (2)
Number of times a particular warmth rating was given
Implicit and Explicit Problem Solving
Human problem-solving comes in two varieties: explicit and implicit.
These two modes differ sharply: explicit problem-solving has clear, conscious goals and clearly defined steps for getting from a starting point to a solution.
Mental arithmetic is an example of explicit problem-solving
Subtract 209-45=?.
Implicit
Human problem-solving comes in two varieties: explicit and implicit.
Implicit problem-solving may be more common than explicit since we learn and practice many kinds of skills from early on in life. These problem-solving skills become more proficient, implicit (unconscious), and automatic with practice.
Infants acquiring language is an example of implicit problem-solving.
Thinking and Problem Solving
Explicit problem-solving involves greater executive control, higher mental workload, more frequent conscious access, and wider recruitment of cortical regions in pursuit of explicit goals.
Implicit problem-solving takes less executive control than the explicit kind, less conscious access, lower cognitive load, and less cortical involvement.
Working Memory as part of a functional system
Working memory in the functional framework
Working memory is constantly involved in problem-solving, however working memory functions also make use of stored information shown in the gray boxes at the bottom of the functional framework diagram.
Working Memory
A schematic of brain areas in the frontal and parietal lobes that support working memory processes.
So What are these areas?
Working Memory
Brain regions supporting working memory overlap with those supporting attention, conscious events, and episodic recall. This widespread activation primarily includes frontal and parietal cortex.
Explicit Problem Solving
Problem-solving can be thought of as finding a path through a maze of choice-points between possible sub-goals toward a final goal. A puzzle called the Towers of Hanoi is frequently used to investigate brain areas involved in explicit problem-solving. The task is to move the disks between the rods, one step at a time, until that they match the goal.
Explicit Problem Solving
Brain areas activated during solving of the Towers of Hanoi include the dorsolateral prefrontal cortex.
Explicit Problem Solving
Flexibility is an important aspect of successful explicit problem-solving. People may get ‘fixed’ in problem-solving strategies: a standard task used to investigate flexibility in problem-solving strategies is the Wisconsin Card Sorting Task (WCS).
The basic task is for the subject to sort cards, however they are not instructed as to what the rules are for sorting -- they must extract the rules based on experimenter feedback regarding whether their sorting is correct or not.
Wisconsin Card Sorting Task
• Patient is given a deck of 64 different cards
Told to place each card under the one it best matches
Told correct or incorrect after each card
Row of 4 example cards set out
Must deduce what the underlying rule is.
Correct!
Explicit Problem Solving
Brain areas involved in adapting to new rules -- or task switching -- overlap with areas active for other executive tasks in frontal and parietal lobes.
Explicit Problem Solving
A current model for brain areas involved in explicit problem-solving: on the outer surface of each hemisphere, peak activity during problem-solving appears in the dorsolateral prefrontal cortex (DLPFC).
During task conflict or errors, we find high activity in the forward (anterior) part of cingulate cortex (ACC).
Mental Workload and Cortical Activity
Effortful tasks show a wide spread of brain activity, even beyond the executive regions of the frontal cortex.
In a classic fMRI study by Smith and Jonides, memory load was varied using an n-back task. In this task, the subject must hold in mind several trials in order to report the item that was presented in the n-preceding trials.
Mental Workload and Cortical Activity
Effortful tasks show a wide spread of brain activity, even beyond the executive regions of the frontal cortex
Results showed a dramatically expanded cortical activity as a function of memory load.
Semantic Memory
Semantic memory plays a key role in problem-solving. How and where are concepts represented in the brain?
A recent summary of semantic memory location in the left hemisphere provides evidence that semantic working memory involves constantly looping activity between the temporal and frontal lobes.
Short term vs Long term memory
Working memory constantly activates long-term storageCowan (2001) suggests that working memory may be thought of as active and time-limited neuronal activity playing on long-term patterns of structural connectivity.
Expertise
Expertise
Developing Expertise
• What are differences between novices and experts?
• How to become an expert?
See anything unusual?
• Experts need only a few seconds to see what is wrong (or what isn’t)
• Experts perceive large meaningful patterns in their domain
(collapse of the upper right lobe, upper left in picture) (normal)
Chess Studies• De Groot (1965)
• Instructed 5 chess grandmasters to think out loud
• Grandmasters only considered about 30 moves and only thought 6 moves ahead.
• Not that different from novices. However, The 30 moves considered by a grandmaster are really good moves
• Masters rely on extensive experience: 50,000 patterns
Chase & Simon (1973)
Number of pieces successfully recalled by chess players after the first study of a chess board.
(Chase & Simon, 1973)
Conclusion from Chase & Simon (1973)
• Chess masters only expert with real chess positions. They do not have better memory in general
• Expertise allows chunking of salient information to promote memory of good moves
• Experts organize knowledge differently – reflects a deep understanding.
What makes an expert an expert?• Talent? IQ? Practice? Genetic factors?
• Experts are masters mostly in their own domain; the skill does not cross into different domains
• Study exceptional feats: – Memory experts– Chess experts– Musicians– Athletes
(Voss et al., 1983)
10 year rule
• 10 years of deliberate practice needed to attain an international level
• Deliberate practice: practice that is highly motivated and involves careful selfmonitoring
• Master chess players spend 10,000 – 20,000 hours playing
What about talent?• Maybe exceptional performance in some area can be explained by
talent – an innate predisposition that predetermines performance in a domain.
• Anders Ericsson et al.
disagree that concept of talent is useful or explains anything
(genius is 90% perspiration and 10% inspiration)
this is controversial!
Difference between good and exceptional musicians is related to the amount of practice
Graph from Ericsson et al. (1996) showing the cumulative amount of practice by two groups of aspiring musical performers (experts and good violinists) and those who planned to teach music
6.0 Summary of Thinking and Problem Solving
Working memory is the domain of problem-solving
Completely explicit problem-solving is probably rare in the natural world—although is common in educational domains
Explicit puzzles like the Tower of Hanoi are quite sensitive to frontal lobe damage; the WSC task can be used to test for mental flexibility in problem-solving
Effective problem-solving likely entails a mixture of explicit and implicit processes along with a high degree of mental flexibility
LANGUAGE: THOUGHT, CULTURE, HUMANESSS
Language is the foremost tool of human thought and culture
It is also one of the major landmarks of child development, with no close parallel in other species.
Language is not unitary -- there are many levels of analysis and production. Each level is highly complex, but is processed by skilled speakers largely unconsciously and rapidly -- within seconds.
The Sounds of Spoken Language
It is amazing how many intricate sounds the human vocal tract can produce using air from the lungs and the articulators in the nose and mouth.
The vocal tract is basically a tube, with two flexible flaps just above the lungs and its diaphragm muscles, which together create air pressure when we breathe out.
The Sounds of Spoken Language
The sounds of a language are called phonemes, consisting basically of consonants and vowels. We produce consonants by closing the entire vocal tube at one of several places. In English, we use the lips at the front of the mouth to produce consonants such as /b/, /p/, and /m/, the tongue against the palate in the back or middle of the mouth to produce consonants like /g/ and /k/, and the teeth in the front to produce consonants such as /th/ and /v/.
French. English German Spanish Italian Portugeesesimple V. 14 14 19 5 7 14
simple C. 17 20 20 17 17 20
Total 34 44 46 24 49 38
11 in Rotokas to as many as 112 in !Xóõ
The Number of Languages
The difference between a language and a dialect is not always clear-cut. It has nothing to do with similarity of vocabulary, grammar, or pronunciation. Sometimes, the distinctions are based purely on geographical, political, or religious reasons. It is usually estimated that the number of languages in the world varies between 3,000 and 8,000.
The ten largest languages in the world are the first languages for nearly half of the world's population.
Here is a list of the top 10 languages
1. Mandarin 885 million speakers2. Spanish 332 million speakers3. English 322 million speakers4. Bengali 189 million speakers5. Hindi 182 million speakers6. Portuguese 170 million speakers6. Russian 170 million speakers8. Japanese 125 million speakers9. German 98 million speakers10. Wu 77 million speakers
Is language only a human feature?
Language as learned?
Language as developed?
Language Evolution?
What makes us Human?
Scientists Identify a Langauge Gene!FoxP2 KE family
Nature, 2001
• "The most obvious feature is that they are unintelligible both to naive listeners and to other KE family members without the disorder," said neurologist Faraneh VarghaKhadem of London's Institute for Child Health, who studied the family. The members of the family also have dyslexic tendencies, difficulty processing sentences, and poor spelling and grammar.
What else makes us Human?
• Language• Problem Solving?• Smart phones?• ?• ?•
What else makes us Human?
• Upright walking? Bipedalism• The other FOXP2 gene influence...•• Less clear that FoxP2 is about Language as
opposed to hominoid
LANGUAGE: Language Supporting Functions
Abstract concepts, prototypes,semantics and networks
How is semantic knowledge represented in the brain? Do we carry pictures in our heads that represent the perceptual world around us? Evidence suggests that we tend to use visual images that are prototypical reminders of categories like chair or movie star.
Concepts and Language
• Functions of conceptual categories:– Facilitate learning over non
identical events– Planning requires
generalization across individuals
– Communication cannot contain all detail
– Economy of knowledge storage and retrieval
The Nature of Language
Findings from the 19th and 20th centuries have been supported by neuroimaging studies in the 21st century
Syntax, Nesting, and Sequencing
Syntax -- or grammar -- is often said to be the most distinctive aspect of language.
Syntax is typically represented in ‘tree’ diagrams which show the relationship between individual words in a sentence and their grammatical case and structure.
Syntax, Nesting, and Sequencing
A sentence has a ‘surface‘ structure which is the word order and structure that you see when you hear or read it.
The ‘tree’ diagram reveals the ‘deep’ structure of the sentence, showing its grammatical parts and relationships.
S sentenceVP Verb phraseNP Noun phrase
How would the tree diagram for this sentence be changed if the sentence read “The dog that scratched the cat that killed the mouse … “
Syntax, Nesting, and Sequencing
What brain areas are involved in decoding syntax?
This is a complex question that is still being resolved: it is difficult to tease apart brain activity that is specific to syntax decoding and not related to phonological and semantic processes or working memory functions.
Results of a recent neuroimaging study show different brain areas in the frontal and temporal lobes that are involved in differing aspects of syntactic processing
Broca's
Wernicke's
Broca's aphasics struggle to speak more than one word at a time but shows signs of enormous effort; thus, patients with Broca's aphasia is characterized as "nonfluent aphasia" (4). Here is an example of a Broca's aphasic speech: Yes ... ah ... Monday ... er Dad and Peter H ... (his own name), and Dad ... er hospital ... and ah ... Wednesday ... Wednesday nine o'clock ... and oh ... Thursday ... ten o'clock, ah doctors ... two ... an' doctors ... and er ... teeth ... yah. (3) This passage shows the difficulty in interpreting a patient with Broca's aphasia. This particular aphasic may be trying to explain that he has a dental appointment at the hospital, or that his dad had an appointment.
Wernicke's aphasics have different types of symptoms. Individuals with Wernicke's aphasia speak extremely fluently but with no informative purpose (3). In this respect, Wernicke's aphasia is known as "fluent aphasia" (4). An example of a Wernicke's aphasic speaking is as follows: Well this is .... mother is away here working her work out o'here to get her better, but when she's looking, the two boys looking in other part. One their small tile into her time here. She's working another time because she's getting, too. (3)Clearly, the aphasic has problems expressing his thoughts to their audience.
Words and Meanings
Recognizing synonyms
What brain areas activate for heard words? For seen words? An fMRI experiment recorded activation for words that were homonyms (words with different spellings but the same pronunciation such as ‘rain’ and ‘reign’) and synonyms (words with different pronunciations and related meanings such as ‘ship’ and ‘boat’).
Homonyms activated left hemisphere posterior central sulcus and inferior frontal gyrus. Meaning-related activation for synonyms activated broader regions in the inferior temporal and frontal lobes
What is Meaning?
How is it organized in the Brain
Long Term Memory?
Logic & Probability Meet
Wittgenstein: The Problems with the Classical View
Wittgenstein introduces family resemblances and Polymorphy to help us understand how some concepts actually work, how they function in language. Take the classic example of a GAME.
“What is a game? How do we decide if this is or isn't a game? Why is this a game but that not? And so on. In short, how do we define ``game''? Solitaire is a game, so is basketball, chess, bingo, poker, pickupsticks, Parcheesi, .... If these are all games, we want to say that they MUST have something in common, something in virtue of which they are games. But what would that be? 66. ...For if you look at them you will not see something that is common 66. ...For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: to all, but similarities, relationships, and a whole series of them at that. To repeat: don't think, but look! don't think, but look!
What emerges is the picture of overlapping sets of features which come together to What emerges is the picture of overlapping sets of features which come together to form an interlinked array.form an interlinked array.” ”
Probabilistic Categories
Members of a category do not possess members that have necessaryand sufficient features
Implications that follow:
1. Some members of the category are better members (more representative) then other members
2. Category boundaries are graded and “fuzzy”
3. Learning a category does not involve learning a “rule”
4. Abstraction is moving higher in a natural taxonomy of category types
E. Rosch (1976) Natural Categories
E. Rosch revives the concerns of Wittgenstein:
“The world is structured because realworld attributes do not occurindependently of one another. Creatures with features are likely to wings then creatures with fur, and objects with the visual apperance of chairs are more likely to have functional sitonableness then objectswith the appearance of cats. That is combinations of attributesof real objects do not occur uniformly. Some pairs, triples, or ntuplesare quite probable , appearing in combination sometimes with one,sometimes with another attribute; others are rare; others logically cannot or empirically donot occur. “
Kinds of Categories
82
Rosch et al. (1976)
* Average number of features listed
Stimulus ComplexityPosner & Keele (1968)
Prototype Results
More errors with high distortion or average distance from prototype
More errors with new patterns then old patterns
More errors with new patterns then Prototype
And after several days Prototype no worse then old patterns and is with many subjects better than old or new patterns.
“The Genesis of Abstraction”.
Homa HOMA:ProtoidsThe eraof PrototypeStudies
Homa (1975,1978,1980)
Learning About Categories in the Absence of Memory, by Larry R. Squire and Barbara J. Knowlton © 1995 National Academy of Sciences.
Abstract
A fundamental question about memory and cognition concerns how information is acquired about categories and concepts as the result of encounters with specific instances. We describe a profoundly amnesic patient (E.P.) who cannot learn and remember specific instancesi.e., he has no detectable declarative memory. Yet after inspecting a series of 40 training stimuli, he was normal at classifying novel stimuli according to whether they did or did not belong to the same category as the training stimuli. In contrast, he was unable to recognize a single stimulus after it was presented 40 times in succession....
....E.P. could also properly classify the prototype of the category even after 1 week, but has trouble with novel exemplars..
Using Existing Knowledge
Knowledge comes in networks
Mental representations, including words, concepts, and images, are thought to be organized in the brain in elaborate networks of knowledge.
Ideas appear to be represented in the cortex in terms of complex webs of learned connectivities, rather than localized filing systems with neatly arranged conceptual categories.
Overlapping semantic networks for concepts ‘tiger’ and ‘elephant’.
Basic levelanimals in zoos
Using Existing Knowledge
Conceptual deficits
Some of what we have learned about cortical representation of concepts comes from patients with brain damage in regions that are involved in semantic memory and conceptual representation.
The specific deficits that these patients have following brain damage informs us as to the role of those brain regions in semantic memory.
Selective Conceptual Deficits
Conceptual deficits
Patient EW had a selective deficit in naming animals but not in naming members of other categories, such as faces.
Her deficits were not only in recognizing pictures of animals, but also in recognizing spoken animal names, indicating that visual and sound representations of animals might be located in the same brain areas.
The fact that her deficit was limited to the animal category indicates that different semantic categories -- like animals and faces -- may be stored in differing brain regions.
Summary
(1) Language Depends Semantics and Long term memory storage
(2) Working memory
(3) Unknown Language Networks
