June 2002 Creative Problem Solving and Critical Reasoning Douglas Abrams - Parallax Consulting
What is the difference between creativity and creative problem solving? • All creativity is creative problem solving • Not sure? • Be creative
Creativity = Problem-solving • You can’t be creative without a problem • Problem-solving causes you to stretch your thinking • If no solution exists, you must be creative to find one • If a solution exists, you can still create a better one
Even creative artists are solving problems • Blank canvas • Block of marble • Using perspective to create dimensionality • Communicating a vision
The QWERTY keyboard • Why are the keys on the typewriter keyboard arranged the way that they are? • QWERTY, ASDFG, etc. • Do you think this is the optimal layout?
It was designed to reduce typing speed • The arrangement was chosen to maximize the distance between the most frequently typed letters • Early typewriters used mechanical arms which would jam when two were struck at the same time • Alternative keyboards improve typing speed by 5-10% • Bandwagon effect maintains the inferior standard
Calendars and clocks • Why is the day divided into twenty-four hours? • Why are there only twelve hours on a clock face? • Why are there seven days in a week? • Were the concepts of time different before calendars and clocks?
Twenty-four hours • Egyptians used sexagesimal number system developed by Babylonians, based on multiple of sixes • 60 was a special number to the Babylonians • Early clocks measured daylight hours separately from nighttime, resulting in 12 hour clock faces
Why a seven-day week? • The ancient Greeks had no week • Ancient Romans had an eight-day week; farmers worked for 7 days and came to town on the eighth day for market • The Romans changed to a seven-day week around the third century A.D. • Days of the week still bear the names of the then-known seven planets in European languages • Seven is a special number in many cultures
Before clocks and calendars • People marked time only by the cycles of nature • Changing seasons • Waxing and waning moon • Time was only kept during the day • The length of sundial “hours” varied throughout the year
How can everyone be above average? • Those who score in the lowest quartile on tests of logic, English grammar and humor are also the most likely to "grossly overestimate" how well they had performed. • The most able subjects are likely to underestimate their own competence • Vast majority of people rate themselves as "above average" on a wide array of abilities • “He who knows best knows how little he knows” - Thomas Jefferson
Why is it so difficult to predict the weather? • The Butterfly Effect • Sensitive dependence on initial conditions • Aperiodic systems that repeat themselves but never quite • Weather, animal populations, epidemics • Non-linear systems
Why is it so difficult to predict cotton prices? • Individual price changes appear random and unpredictable • But the sequence of changes is independent of scale • Curves for daily price changes and monthly price changes match perfectly • Fractals
Why are apples red? • What does an apple tree do? • Creates more apple trees • Leaves are green • Highest contrast color to green is red • Animals eat apples • Animals deposit seeds far from tree • More new apple trees
Why do trees grow tall? • Trees grow tall to reach the sunlight • Trees compete against one another for sunlight • Trees can spend energy either in growing tall or living longer • If they could all agree to stay shorter, they could all live longer • Why can’t they cooperate?
The Prisoner’s Dilemma • Two criminals are arrested by the police • They are held separately and cannot communicate with one another. The police offer each of them a deal: • If one informs on his partner and the other does not inform, the informant will go free, while the partner be sentenced to three years in prison. • If both inform on one another, both will be sentenced to two years. • If neither informs on the other, both will be sentenced to one year. • Both know that the other is offered the same deal.
Answer: You should always inform • In a one-shot Prisoner’s dilemma, you do better by informing, no matter what the other person does • If he informs, and you inform, you receive 2 years instead of the 3 you would have received if you did not inform • If he does not inform, you receive 0 years, instead of the 1 you would have received it you also did not inform
Is this a zero-sum or non-zero sum game? • Would your answer be the same if you knew that you would have to play this game repeatedly with the same person? Why or why not? • What roles do communication and trust play? • Why is this a dilemma?
Question: Define: what is a computer? • You are answering this question for someone who has never seen or heard of a computer before but in all other respects is in possession of a full range of knowledge and understanding. • Hint: "A computer is a labor-saving device" is not a good answer. • Bonus question 1: How does a computer work? • Bonus question 2: Is it theoretically possible to create a computer that is conscious in the same way that human beings are conscious? • In answering the bonus questions, you can assume that the questioner already knows what a computer is.
What do you mean by "What is?" • Definition • Description
What is a definition? • Essential qualities • Exclusive • General, not specific • Description is not definition • Electronic, CPU, keyboard, mouse, store data
Why are definitions important? • Definition precedes classification • Classification enables analysis • Analysis allows critical reasoning • Critical reasoning contributes to creative problem-solving
Definitions divide the world into two sets • All computers and only computers are members of the computer set • All non-computers and only non-computers are members of the non-computer set Computer Non-Computer
What is a computer? • A programmable information-processing device • Program is internally stored and modifiable • Input/Output • Logical operations • Algorithms • A universal Turing Machine • Can emulate multiple devices
What is an algorithm? • 9th century Persian mathematician al-Kohwarizm (book titled: al jabr) • Systematic procedure for solving a problem • For any specific case the procedure will definitely terminate • A definite answer will be obtained in a finite number of steps • At each step it is perfectly clear what the operation is to be performed • Termination point also perfectly clear
What algorithmic procedure does this flow-chart represent? From The Emperor's New Mind by Roger Penrose
Obtaining the remainder from a division of two natural numbers, A and B
What is a Turing Machine? • Alan Turing - British mathematician • Concept of a general algorithm • A general mathematical procedure which could solve all the problems of mathematics
Characteristics of a Turing Machine • Discrete set of different possible internal states • Finite in number • Can deal with input unlimited in size • Can call upon unlimited storage space • Can produce an output of unlimited size • Must examine only those parts of the data or previous calculation that it is immediately dealing with
What does a Turing Machine look like? • Infinitely long tape with marks on it • Tape called upon by the device and read; moved forward and backward as necessary • Device can place new marks on the tape and obliterate old ones • Same tape is used as output • Tape runs back and forth through the device until the calculation is complete; then device halts and answer is displayed on the tape From The Emperor's New Mind by Roger Penrose
What does the tape look like? • Linear sequence of squares, marked with 0s or 1s • Device reads tape one square at a time, then moves one square to the right or left From The Emperor's New Mind by Roger Penrose
What can a Turning Machine do? • Behavior is determined by its internal state and the input • It changes its state to some other, or possibly the same internal state • It replaces the 0 or the 1 with the same or different symbol • It moves one square either to left or right • It decides whether to continue the calculation or come to a halt
How does a Turing Machine calculate? • Beginning internal state • Reads first symbol on the tape • If internal state=0 and input=1 then, go to internal state 13, change the 1 to a zero and move one square to the right • Instructions and data are fed in together; data demarcated through contraction
Example of a Turing Machine: UN+1 1 From The Emperor's New Mind by Roger Penrose
Universal Turing Machine • Turing machines can be constructed to perform any mechanical operation whatever • Computable, recursive, effective • Universal Turing Machine • Takes a specific Turing Machine as initial input • Can mimic any other Turing Machine • Modern general purpose computers are Universal Turing Machines • Computers can mimic each other and now other devices
How does a computer work? • Hardware on/off switches and memory registers (not 0s and 1s) drive • Software logical and simple mathematical operations which • Perform algorithmic operations • Which are incorporated into programs • Which take input information, process it and output the results to the user
Is it theoretically possible to create a conscious computer? • What is consciousness? • Mind/brain problem • Chess-playing machines in the 19th Century • Edgar Allen Poe • What is the source of consciousness? • Reductionism - Yes • Dualism - No • Vitalism - No • Complexity theory/quantum physics - Maybe • Computers have no senses
Machine intelligence is growing exponentially • Machine intelligence will approach and possibly surpass human intelligence, as it continues to grow at an exponential rate. • Exponential increase in the rate of change itself that will drive the rapid growth of the new economy beyond what appear to be today's most optimistic projections.
Information-processing technologies create feedback loops Which produces new information technologies more quickly New information technologies create more new technologies Which increases the rate of change Which increase the speed of the global brain
Mis-understanding change • Over-estimation of the short-term rate of technological change • The internet will change everything • Video-conferencing will replace business travel • Video-on-demand will replace video rental • Under-estimation of the mid-to-long term rate of technological change • All of the above are actually true in the mid-to-long term
Linear versus exponential rates of change • Short-term change is linear, but mid-to-long-term technological change is exponential • Most changes we observe in daily life are linear changes • Lengthening and shortening of the day • Seasonal changes in temperature • Growth in height • Increases in life-span
Computers have doubled performance every 18 months Source: www.intel.com