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## June 2002

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**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**The rate of technological change is increasing exponentially****Computers have doubled performance every 18 months**Source: www.intel.com