Thinking and problem solving

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Thinking and problem solving

• Are you smart?
• Would you like to be?
• What does smart mean anyway?

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Admin

• How is your reading going?
• Insights?
• Comments on The Code Book

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What does smart mean?

• Witty, clever in conversation, quick with a
  come-back
• Solve math problems
• Taking a tough major at college (IT!)
• High IQ
• Excellent snowboarder

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Multiple intelligences

• Dr Howard Gardner proposes
• Linguistic intelligence ("word smart")
• Logical-mathematical intelligence
  ("number/reasoning smart")
• Spatial intelligence ("picture smart")
• Bodily-Kinesthetic intelligence ("body smart")
• Musical intelligence ("music smart")
• Interpersonal intelligence ("people smart")
• Intrapersonal intelligence ("self smart")
• Naturalist intelligence ("nature smart")

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IQ can be trained

• Each of the types of IQ can be trained
• We will focus on thinking styles for
  problem-solving

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Problem Solving Phases

• Expansion then Contraction

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Learning to think for problem solving

• Thinking and problem solving skills can be
  learned and improved
• Understanding thinking approaches will prepare
  you.
• Insight
• Logical Thinking
• Abstraction
• Sequential
• Strategic

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Insight Aha

• The solution is obviously correct, it requires no
  justification
• Before the solution is found there is no obvious
  way to get you to it
• EG Two Indians are walking through the desert
  carrying bows and arrows. The little Indian is
  the big Indians son but the big Indian is not
  the little Indians father. Who is the big Indian?

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EG Analysis

• Superficial resemblance to logic
• But different
• Suggest solutions "his uncle," "his stepfather,"
  "his grandfather,"
• Test them against the given information
• Exotic suggestions tend to arise
• "his spirit guide" , "his brother who married his
  mother," etc.
• Lateral thinking?

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Solution

• Words mislead
• Clichés stereotypes channel thinking
• "Indians," "bows and arrows," father/son
• Conditioned by popular media to think of Indians
  with bows and arrows as warriors, big strong men.
  
• Once the correct answer is perceived then all
  this becomes meaningless.
• The correct answer is, of course, his mother.

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Insight thinking

• Insight takes us in a single jump from conclusion
  to solution
• See things in a different way
• May be wrong check with logic
• Humor often associated with insight creativity

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There are 11 human faces in this picture. Can you
find them all? Most people can find 4 or 5,
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Humor in Insight Thinking

• EG 1.
• Time flies."
• "You cant, They move too fast"
• EG 2
• "If the auto industry had advanced as computers
  have then a Cadillac would cost 10 and give 1000
  miles to the gallon today."
• "That Cadillac would be two inches long and would
  crash and delete its contents every year
  especially if it had Windows"
• Punch line changes your perspective (insight)

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Characteristics of Insight Thinking

• Lateral thinking (thinking sideways)
• Edward de Bono
• Explore impossible ideas
• Reserve judgment (not yes, not No Po)
• Humor and paradoxes
• Generate lots of solutions (group brainstorm)
• Test results with logical thinking
• Mathematical proofs
• Pull the ladder up behind you

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Logical thinking

• Logical thinking is proceeding from sound
  premises in a strictly controlled way to a
  definite conclusion.
• Example A man is looking at a picture and he
  says "Brothers and sisters have I none. This
  mans father is my fathers son. Who am I"

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Logical ? Deconstruction

• Relationship can be deduced by strictly logical
  rules.
• Problem is reduced to sub-problems
• EG If no siblings, "my fathers son" is me.
  Substitute "me" for "my fathers son" and
• Statement becomes, "This mans father is me. Who
  am I".
• If necessary re-arrange the statement to "I am
  this man's father
• problem is solved.

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More logic problems

• Elementary school "story problems".
• A train is traveling east from LA at 97 mph
• remove superfluous verbiage
• reduced to a strictly logical problem
• unique solution (in elementary school)
• Mathematics is a sub-branch of logic.
• this category includes all story problems,
  Sudoku, Kenken etc.

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Logic characteristics

• Set of data (premises)
• Strictly logical deductions
• Build from premises to conclusion.
• Often has form of if-then-else evaluations.
• Used to solve problems which have direct, unique
  (sets of) solutions
• Also used to check the validity of a hunch or
  Lateral thinking

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Abstraction

• To extract from one situation a general
  understanding that can be applied to other
  situations

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Math models

• What does this represent? What does it imply?
  What can you use it for?
• y ax b
• How about these?
• x A sin (T) a

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Prototypes

• In what way is a prototype an abstraction?
• Paper prototypes
• Wizard of Oz prototypes
• Façade prototypes
• etc.

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Abstraction within IT

• ?

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Sequential Thinking

• Very useful in debugging computers (SW HW)
• Successively modify a solution
• History of Technology
• EG Twenty Questions
• EG Eight balls or twelve balls
• EG de Bono Five day course in thinking

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12 8 ball problems

• 12 balls There are twelve balls. Think of them
  as similar to billiard or snooker balls. Eleven
  of the balls are identical is size and weight and
  appearance the twelfth is the same size and
  appearance but a different weight. It is either
  lighter or heavier.
• Using a set of scales (old fashioned weight
  balances with two pans) a maximum of three times,
  
• find the different ball and
• state whether it is lighter or heavier.
• You may only compare the weight of balls to
  balls, no other weights may be used. 

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8 Ball Problem

• A slightly easier variant the eight balls
  problem There are 8 balls. One of them is
  heavier. Using a set of scales a maximum of twice
  find the odd ball.

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• E.G. de Bono proposed series of problems to
  demonstrate sequential thinking. Using a set of
  six rectangular blocks solve the following
  problems in the order given. For these problems a
  touching box is one that share a common boundary
  for some distance. The corner of one box
  intersecting another at one point is not
  "touching.

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Arrange the boxes such that each box

• is touching 2 and only 2 other boxes.
• is touching 3 and only 3 other boxes.
• is touching 4 and only 4 other boxes.
• is touching 5 and only 5 other boxes.
• one box is touching only 1 other box, one box is
  touching only 2 other boxes, one box is touching
  only 3 other boxes, one box is touching only 4
  other boxes, one box is touching only 5 other
  boxes.

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Sequential boxes contd

• Working through these six problems and
  contemplating the thinking processes used helps
  you develop creative and sequential thinking
  techniques that can be applied to later problems.
  
• In particular the last problem can be
  sequentially solved in stages but the stages are
  not the obvious order that you may expect.
• De Bono's book, The Five-Day Course in Thinking,
  gives other exercises and problems

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Sequential Characteristics

• Combinations of insight and logical thinking
• Step by step progression
• See strategic thinking

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Strategic Thinking

• Expert chess players do not predict the game many
  moves ahead.
• They strive for powerful positions on the board
• Strategic thinking Pursue intermediate goals
  with a clear long-term goal in mind
• Do not to plan every detail
• EG Project management.

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Strategy
The objective is to start at state 1 and end at
state 2. There are many alternative paths
possible. Some intermediate states are absolutely
necessary, such as state 3, while others can be
avoided. Some states such as state 4, are
dead-ends although this might not be apparent
until the dead-end is reached.
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Elegant Solutions?

• Optimal in one or more ways
• Succinct
• Covers every case with one algorithm
• Fastest solution
• EG
• 1e-ip0
• The most beautiful equation in the world
• Richard Feynmann as a teenager
• Contains 1, 0, , -, fundamental constants e, i, p

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Problems

• See class notes
• Do problems 1, 3, 4b in class
• State what style(s) of thinking is (are) involved
  for each problem.
• Finish for HW