“The space that we're looking through is nine-dimensional. If you build a mathematical model, the amount of searching that we've done in 50 years is equivalent to scooping one 8-ounce glass out of the Earth's ocean, looking and seeing if you caught a fish. No, no fish in that glass? Well, I don't think you're going to conclude that there are no fish in the ocean. You just haven't searched very well yet. That's where we are.” IfsThinkingYearsWellsDoneEarthSpaceSeeingHavensAmountOceanModelsGlassesCaughtFishesNineMathematicalMathematical Models Author:Jill Tarter
“In the popular mind, if Hoyle is remembered it is as the prime mover of the discredited Steady State theory of the universe. "Everybody knows" that the rival Big Bang theory won the battle of the cosmologies, but few (not even astronomers) appreciate that the mathematical formalism of the now-favoured version of Big Bang, called inflation, is identical to Hoyle's version of the Steady State model.” IfsKnowsMindStatesBigsUniverseTheoryBattleModelsAppreciateVersionsMathematicalRememberedPrimeSteadyInflationBangsRivalsIdenticalCosmologyAstronomers Author:Fred Hoyle
“If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.” IfsMayUseActionModelsMethodStructureObjectivesAlternativesMathematicalProgrammingSchedulesExhibitsMathematical Models Book:Linear Programming and Extensions Source: Linear Programming and Extensions
“As soon as a thought or word becomes a tool, one can dispense with actually 'thinking' it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics - the model of all neo-positivistic thinking - lies in just this 'intellectual economy.' Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. ... Reason ... becomes a fetish, a magic entity that is accepted rather than intellectually experienced.” ThinkingHas BeensReasonLyingEconomyMagicInvolvedIntellectualModelsAdvantageToolsPerformancesMathematicsComplicatedAcceptedSymbolsMathematicalOperationsLogicalEntityFetish Author:Max Horkheimer
“The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.” MayProblemCertainSpeakEasyDifficultAbilityLevelsEconomicMastersModelsRelationIncludingIntellectMathematicalDevicesMasteryRequirementsCompetenceIncompetentScreeningAbility To Speak Author:John Kenneth Galbraith
“The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke.” FirstsScienceExistenceFourModelsJokesMathematicsMathematicalSurprisingAxiomsEuclid Author:John Allen Paulos
“It is clear that the building of models is not a purely mechanical process but requires skill of a high order - not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.” DifferentOrderProcessEconomyClearBuildingSkillsModelsImportanceCriticalFactorsArtisticMathematicalReasonableFacultyRelativeBehaviourSensitivityHypothesisSelectionEquationsExplaining Author:Kenneth E. Boulding
“The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?” ShouldDoeFaithUniverseAnswersApproachModelsMathematicalBotherUsualMathematical Models Author:Stephen Hawking
“The good news is that, at least in economics, I've seen movement away from its overemphasis on mathematical models of purely rational behavior to a more eclectic and commonsense approach: research that is, among other things, more respectful of insights from psychology.” PsychologyMovementBehaviorApproachNewsModelsResearchEconomicsInsightRationalMathematicalGood NewsRespectfulEclecticMathematical Models Author:Robert J. Shiller
“Is war an inevitable outcome of competing interests in a complex society? In other words, would war be the same even if human nature were very different? There are mathematical models of large groups working together that lead to conflict on a reliable basis. So there's a whole other view of war that is not psychological at all.” IfsHumansDifferentWarWholeTogetherInterestViewsGroupsHuman NatureConflictModelsBasesComplexesPsychologicalMathematicalInevitableOutcomesWorking TogetherCompetingLarge GroupsMathematical Models Author:Jaron Lanier
“As a graduate student, I wrote a long paper connecting the dots between mathematical models of learning and language development in children. It was published in a major journal.” ChildrenLongLanguageStudentsDevelopmentPaperMajorsModelsMathematicalGraduatesJournalConnectingDotsGraduate StudentsConnecting The DotsMathematical ModelsLanguage Development Author:Steven Pinker