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Some examples with SOLVE

Some examples with SOLVE. QRG Meeting Friday, April 16, 2004. Back of the Envelope Reasoning. Numeric answers Specificity-Resources tradeoff Only thing you can do in many domains Environmental science, Biophysics, etc. New, unfamiliar domains. Useful

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Some examples with SOLVE

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  1. Some examples with SOLVE QRG Meeting Friday, April 16, 2004

  2. Back of the Envelope Reasoning • Numeric answers • Specificity-Resources tradeoff • Only thing you can do in many domains • Environmental science, Biophysics, etc. • New, unfamiliar domains. • Useful • Engineers, Scientists, Policymakers, everyone who reads a newspaper • Problem solving + feel for numbers

  3. Some examples 0. How many dentists are there in the US? • How many K-8 elementary school teachers are in the USA? • How much money is spent on newspapers in USA per year? • How much time would be saved per year nationwide by increasing the speed limit from 55 to 65 mph? • What is the annual cost of healthcare in USA? • How much tea (weight) is there in China? • Last summer, the US Army bought Microsoft Windows/Office/Server software for 500,000 computers. The deal included the software and six years of support. How much did the army pay for this?

  4. How many K-8 elementary school teachers are in the USA? Number of teachers = number of students / students per teacher Number of students = population * fraction in the age range of K-8 students * fraction of kids who go to school Number of students = 300 mil * 9/75 * 1 Number of teachers = 40 mil / 25 = 1.6 mil 1.9 million, source: Statistical Abstracts.

  5. How much money is spent on newspapers in USA per year? Total money spent = Money spent per buyer * number of buyers Annual expense per buyer = Units bought per year * cost per unit Annual expense per buyer = 365 * 0.75 = 250 Number of buyers = 300 mil * ¼ = 75 mil Total money spent = 75 mil * 250 = 20 billion 26 billion, source: Statistical abstracts

  6. How much time would be saved per year nationwide by increasing the speed limit from 55 to 65 mph? Total time spent driving = time spent driving per person * number of drivers Time spent driving per person = Total distance driven per person /Speed Total distance driven per person = Distance per day * number of days driving Number of drivers: assume one driver per household = 1/3 * population = 100 mil Total distance driven per person = 20 * 365 = 8000 Time spent per person = 8000/55 = 150 hours Time spent if it was 65 mph = 8000/65 = 120 hours Time saved per person = 30 hrs Total time saved = 3 billion hours = 300,000 years.

  7. Tea in china 1 billion people 5 cups a day 5 grams a cup Lets say they stock an years supply 25 billion grams = 25 million kilos per day In an year 365*25 million ~ 10 billion kilos

  8. SOLVE • Suggestions based problem solver • Represent problem solving progress in an and/or tree structure • Incremental solution generation, get-next-solution • Ordered subgoals

  9. An example (defSuggestion VolumeFormulaForSphere (volumeOfObject ?obj ?vol) :test (shapeOfObject ?obj SphereShape) :subgoals ((radius ?obj ?radius)) :result-step (evaluate ?vol (TimesFn 4.187 ;;4/3*Pi (ExponentFn ?radius 3))))

  10. (annualSales NewspaperCopy UnitedStatesOfAmerica (YearFn 2003) ?money) (defSuggestion PerBuyerStrategy (annualSales ?obj ?place ?time ?money) :subgoals ((annualExpensePerBuyer ?obj ?place ?time ?money-per-buyer) (numberOfBuyers ?obj ?place ?time ?number)) :result-step (evaluate ?money (TimesFn ?money-per-buyer ?number))) (defSuggestion UnitaryStrategyForCost (annualExpensePerBuyer ?obj ?place ?time ?money-per-buyer) :subgoals ((annualUnitsBoughtPerBuyer ?obj ?place ?time ?units) (cost ?obj ?unit-cost)) :result-step (evaluate ?money-per-buyer (TimesFn ?units ?unit-cost))) (defSuggestion FractionOfTotalStrategy (numberOfBuyers ?obj ?place ?time ?number) :subgoals ((populationDuring ?place ?any-time ?total) (percentOfBuyers ?obj ?place ?percent)) :result-step (evaluate ?number (QuotientFn (TimesFn ?total ?percent) 100)))

  11. (cardinality K-8SchoolTeacher ?numteachers) (defSuggestion StudentsPerTeacherStrategy (cardinality K-8SchoolTeacher ?numteachers) :subgoals ((cardinality K-8SchoolStudent ?numstudents) (studentsPerTeacher K-8School ?perteacher)) :result-step (evaluate ?numteachers (TimesFun ?numstudents ?perteacher))) (defSuggestion UniformAgeDistributionStrategy (cardinality K-8SchoolStudent ?numstudents) :subgoals ((populationDuring UnitedStatesOfAmerica (YearFn 1997) ?population) (minimumAge K-8SchoolStudent ?min) (maximumAge K-8SchoolStudent ?max) (lifeExpectancyForGroupInRegion UnitedStatesOfAmerica Person (YearsDuration ?life))) :result-step (evaluate ?numstudents (TimesFn (QuotientFn (DifferenceFn ?max ?min) ?life) ?population))))

  12. What next • Represent 20-30 problems, with the goal of re-usable representations, in strategies and theoretical knowledge added. • Provide support for units. ________________________________ • Feel for numbers • Build symbolic representations for numbers • Large, expensive, upper class, etc. • Analogical estimator: makes guesses for a numeric parameter based on analogy.

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