Lecture 7 - Exactness & Gene

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History and Philosophy of Science and Technology
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Chen- Pang Yeang

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HPS211 Lecture 7 JUN052011 ExactnessNatural philosophers had used numerical valuesinformation in disciplines like astronomy and navigationQuality of measurement and calculations has longstanding issues especially in astronomyConcerned with the precision accuracy and exactness of their calculation th Issues became pressing in the 18 cContext sprit of quantificationI Spirit of QuantificationNewtonian mechanics and physical astronomyCloser fit between data and predictionLunar table orbits of Saturn and Jupiter figure of earthNavigation mapmaking and explorationQuantitative experiments in chemistry optics pneumatics hydraulics elasticitythese experiments were thimposed by scientists in the 18 cQuantitative administration of stateImpose the cause of reason into government administrationutilize statisticalnumerical dataDemography forestry metric units standardizing manufacturingCommerce and trade with more exact numbersAccounting actuaries insurance businessQuestions with NumbersWhich numbers are more trustworthyHow to improve the fit between data and theoryHow to make results of measurement or calculation consistentIn particular Observers measurers or experiments often obtained multiple sets of data under same conditionhow to best represent the dataII The Single Best MeasurementDominant Approach Single Best MeasurementMake multiple measurements but only present the best data setEpistemic and moral implicationsThere was a perfect figure for a measurement a golden event for experiment or observationThe perfect figure was attainable by improving instruments or skills No fundamental reason to prevent the acquisition of the perfect figuresThe failure to obtain the perfect figure was thus measurers faultsymptom of laziness carelessness incompetenceArtisans mentalityLavoisier represented an example of best measurement approachUsed weight balance to demonstrate that hydrogen and oxygen compose water 1780sPrecise measurements of hydrogen oxygen and water 8 decimal figuresBut Lavoisiers precision did not convince phlogiston chemistsWilliam Nicholson estimated that Lavoisiers instruments were only sensitive within 3 decimal figures Extra digits were meaninglessIn other words Lavoisier lacked a concept of significant figures and a theory of errorsAlternative ApproachAveragingDo not choose one data set among multiple sets combine all setsDates back to Newton th Became more popular in the late 18 centuryBreakthrough with the introduction of the least squares methodIII Least Squares MethodLeast square method was invented by French mathematician AdrienMarie Legendre in 1805
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