Basic biology of the nervous system

Basic biology of the nervous system

• Basic biology of the nervous system

• Motivations

• Senses

• Learning

• Perception

• Memory

• Thinking and mental representations

All of these topics give a basic sense of the structure and operation of our mind

• All of these topics give a basic sense of the structure and operation of our mind

• What kinds of tasks does our mind engage in?

• Language
• Problem Solving
• Decision Making
• Others

Everyday experiences

• Everyday experiences

• How to get to the airport?
• How to study for a quiz, complete a paper, and finish a lab before recitation?

• Domain specific problems

• Physics or math problems

• Puzzles/games

• Crossword, anagrams, chess

Well-defined vs. ill-defined problems: Problems where the goal or solution is recognizable--where there is a right answer (ex. a math or physics problem) vs. problems where there is no "right" answer but a range of more or less acceptable answers.

• Well-defined vs. ill-defined problems: Problems where the goal or solution is recognizable--where there is a right answer (ex. a math or physics problem) vs. problems where there is no "right" answer but a range of more or less acceptable answers.

• Knowledge rich vs. knowledge lean problems: problems whose solution depends on specialized knowledge.

• Insight vs. non-insight problems--those solved "all of a sudden" vs. those solved more incrementally--in a step by step fashion.

Does the contents of memory influence how easy a problem is?

• Does the contents of memory influence how easy a problem is?

• Knowledge rich problems
• Require domain knowledge to answer, physics problems
• Knowledge lean problems
• Can use a general problem solving method to solve, don’t need a lot of domain knowledge

• Tower of Hanoi

• Weighing problem

• Traveling salesman (100 cities = 100! or 10200 or each electron, 109 operations per sec. would take 1011 years!!) but

• 100,000 cities within 1% in 2 days via heuristic breakup (reduce search!)

• Missionaries & Cannibals

• Flashlight: 1, 2, 5, 10 min. walkers to cross bridge

• 21 link gold necklace/21 day stay

• Subway Problem

• Vases (or 3-door)

Zeigarnik effect, 1927

• Zeigarnik effect, 1927

• Participants were given a set of problems to solve
• On some problems, they were interrupted before they could finish the problem
• Participants were given a surprise recall test
• They remembered many more of the interrupted problems than the uninterrupted ones
• Moss et al. (2007) recent RAT results: open goals

Luchins water jug experiment, 1942

• Luchins water jug experiment, 1942

• Participants were given a series of water jug problems
• Example: You have three jugs, A holds 21 quarts, B holds 127, C holds 3. Your job is to obtain exactly 100 quarts from a well
• Solution is B – A – 2C
• Participants solved a series of these problems all having the same solution

Luchins water jug experiment, 1942

• Luchins water jug experiment, 1942

• New problem: Given 23, 49, and 3 quart jugs. Goal is to get 20 quarts.
• Given 28, 76, and 3 quart jugs, obtain 25 quarts
• Some failed to solve, others took a very long time
• Mental set
• People who solved series of problems using one method tended to over apply that method to new similar appearing problems
• Even when other methods were easier or where the learned method no longer could solve the problem

1 21 127 3 100

• 1 21 127 3 100

• 2 14 163 25 99

• 3 18 43 10 5

• 4 9 42 6 21

• 5 20 59 4 31

• 6 23 49 3 20

• 7 15 39 3 18

• 8 28 76 3 25

• 9 8 48 4 22

• 10 14 36 8 6

Duncker’s candle problem, 1945

• Duncker’s candle problem, 1945

• Problem: Find a way to fix a candle to the wall and light it without wax dripping on the floor.
• Given: Candle, matches, and a bow of thumbtacks
• Solution: Empty the box, tack it to the wall, place candle on box
• Have to think of the box as something other than a container
• People found the problem easier to solve if the box was empty with the tacks given separately

Duncker’s candle problem

• Duncker’s candle problem

Functional Fixedness

• Functional Fixedness

• Inability to realize that something familiar for a particular use may also be used for new functions
• But is this really a bad thing?
• We learn and generalize from our experience in order to be more efficient in most cases
• Is it really a good idea to sit around trying to figure out how many potential uses a pair of pliers has?
• How often do mental sets and functional fixedness save time and computation?

What characteristics do all problems share?

• What characteristics do all problems share?

• Start with an initial situation
• Want to end up in some kind of goal situation
• There are ways to transform the current situation into the goal situation

• Can we have a general theory of problem solving?

Newell & Simon proposed a general theory in 1972 in their book Human Problem Solving

• Newell & Simon proposed a general theory in 1972 in their book Human Problem Solving

• They studied a number of problem solving tasks

• Proving logic theorems
• Chess
• Cryptarithmetic

Verbal Protocols

• Verbal Protocols

• Record people as they think aloud during a problem solving task

• Computational simulation

• Write computer programs that simulate how people are doing the task
• Yields detailed theories of task performance that make specific predictions

Problem spaces

• Problem spaces

• Initial state
• Goal state(s)
• Operators that transform one state into another

Tower of Hanoi

• Tower of Hanoi

• Given a puzzle with three pegs and three discs
• Discs start on Peg 1 as shown below, and your goal is to move them all to peg 3
• You can only move one at a time
• You can never place a larger disc on a smaller disc

Missionaries and cannibals problem

• Missionaries and cannibals problem

• Six travelers must cross a river in one boat
• Only two people can fit in the boat at a time
• Three of them are missionaries and three are cannibals
• The number of cannibals on either shore of the river can not exceed the number of missionaries

How do we choose which operators to apply given the current state of the problem?

• How do we choose which operators to apply given the current state of the problem?

• Algorithm
• Series of steps that guarantee an answer within a certain amount of time
• Heuristic
• General rule of thumb that usually leads to a solution

Columnar algorithm for addition

• Columnar algorithm for addition

• Add the ones column
• Carry if necessary
• Add the next column, etc.

• People don’t have a simple algorithm for solving most problems

Hill climbing

• Hill climbing

• Just use the operator which moves you closer to the goal no matter what
• What about problems where you have to first move away from the goal in order to get to it (detour problems)?

• Fractionation and Subgoaling

• Break the problem into a series or hierarchy of smaller problems

Working Backwards from the goal

• Working Backwards from the goal

• Works well if there are fewer branches going from the goal to the initial state
• Only works if you can reverse the operators
• Ex. Lily Pond Problem

Means-ends analysis

• Means-ends analysis

• Always choose an operator that reduces the difference between your current state and the goal state
• Tests for their applicability of the operator on the current problem state
• Adopts subgoals if there is no move that will take you to the goal in one step
• Must have a difference-operator table or its equivalent
• Tells you what operator(s) to use given the current difference between the state of the problem and the goal. Might have to modify operator if none can be applied in current state

Newell & Simon (1956)

• Newell & Simon (1956)

• Logic Theorist (LT)
• LT completed proofs for a number of logic theorems
• General Problem Solver (GPS)
• GPS incorporated means-ends analysis, capable of solving a number of problems
• Planning problems
• Cryptarithmetic
• Logic proofs

Problem space and representation

• Problem space and representation

• Problem difficulty and representation

• The interaction of representation and processing limitations (problem isomorphs)

Number scrabble

• Number scrabble

• 1 2 3 4 5 6 7 8 9

What about problems where there is no explicit test for a goal state?

• What about problems where there is no explicit test for a goal state?

• Well-defined problems have a clearly defined goal state
• Ill-defined problems don’t have a clearly defined goal state

Engineering Design

• Engineering Design

• Architecture

• Painting

• Sculpture

• How to run a business?

• A number of other creative or difficult tasks that people engage in

Can AI programs be applied to ill-defined problems?

• Can AI programs be applied to ill-defined problems?

• Engineering Design (ex. A-Design, Campbell, Cagan, Kotovsky, 1999)

• AARON

• Program created by Harold Cohen
• Produces paintings using a number of heuristics and general conceptions of aesthtics

Large problem spaces are usually harder to search than small ones

• Large problem spaces are usually harder to search than small ones

• Compare playing tic-tac-toe to chess

• What factors from our architecture of mind play a role in determining how hard a problem is?

• Memory constraints
• Memory contents
• Types of mental representations we use

Work on isomorphs of the Tower of Hanoi (Kotovsky, Hayes & Simon, 1985)

• Work on isomorphs of the Tower of Hanoi (Kotovsky, Hayes & Simon, 1985)
• An isomorph of a problem is one in which the structure of the problem space is the same but the appearance of the problem is different
• Remember the Tower of Hanoi?

In the original Tower of Hanoi and in the condition with monster models there was an external memory aid

• In the original Tower of Hanoi and in the condition with monster models there was an external memory aid

• Change problems are harder than move problems

• Takes more processing to assess whether a change is valid than it does for a move
• Spatial proximity of the information
• Working with unchanging discs (stable representation) vs. changing discs

Tested understanding via a computer model that was:

• Tested understanding via a computer model that was:

• Goal driven, subgoaling, limited memory capable of perfect behavior except for limited working memory
• To see if we were in right “ballpark”
• To separate actions of various mechanisms to see which had the most control/influence
• To be able to experiment with the separate postulated mechanisms

Chinese Ring Puzzle

• Chinese Ring Puzzle

Hayes on ten year rule

• Hayes on ten year rule

• (Also encoded as 10,000 hours of practice)

DeGroot and Chase & Simon’s work on chunking and chess

• DeGroot and Chase & Simon’s work on chunking and chess

• Estimates of knowledge base size

• Ericsson: idea of deliberate practice

Power law of practice: Ta = cPb + d

• Power law of practice: Ta = cPb + d

Physics (Simon et al., 1980, Chi Feltovich & Glaser, 1981)

• Physics (Simon et al., 1980, Chi Feltovich & Glaser, 1981)

• Physics experts approach physics problems differently than do novices

• Chess (Chase & Simon, 1973)

• Given a mid-game chessboard, grandmasters can reconstruct it almost perfectly after studying it for only 5 seconds
• Novices can only place 3-5 pieces correctly after the same amount of study
• However, if the pieces are randomly placed on the board, novices and experts perform at the same level

Why do experts and novices perform differently?

• Why do experts and novices perform differently?

• Experts have more knowledge and experience
• But the organization of this knowledge is crucial
• Experts can chunk the chess board into meaningful units that are already in memory
• Novices have no such chunking mechanism
• Random placement of pieces eliminates this chunking from an expert’s performance

Working forward (physics experts) (Chi et al.)

• Working forward (physics experts) (Chi et al.)

• Deliberate Practice (Ericcsson et al.)

• McComb, Cagan & Kotovsky)

Insight problems

• Insight problems

• Insight is a seemingly sudden understanding of a problem or strategy that aids in solving the problem
• Sometimes require a change in mental representation before the problem can be solved

Place dominoes on the mutilated checkerboard until it is entirely covered

• Place dominoes on the mutilated checkerboard until it is entirely covered

• Taken from Kaplan & Simon, 1990

Subjects had difficulty solving this problem

• Subjects had difficulty solving this problem

• Average of 38 minutes

• Requires parity to be part of the representation

• Taken from Kaplan & Simon, 1990

Can knowledge learned on one problem be transferred to another problem?

• Can knowledge learned on one problem be transferred to another problem?

• Sometimes, if people notice a similarity between the source and target problems

• How do people map knowledge from a source problem to a target problem

• Analogy

Classic example (Gick & Holyoak, 1983, Based on Dunker)

• Classic example (Gick & Holyoak, 1983, Based on Dunker)

• Army problem
• Cancer problem
• Mapping between the two leads to a solution for the cancer problem

Problem solving is an everyday activity

• Problem solving is an everyday activity

• We can use findings from problem solving to further our understanding of the mind and its processes

• We can use our knowledge of the mind’s structure and operation to understand elements of problem solving

• Different types of problems and different contributions to problem difficulty