“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
“We chose to do this work mathematically, which has the advantage of precision but is not always appreciated by readers. It is perhaps for this reason that anthropologists have not shown much interest in these models, unlike economists, for example, for whom the use of mathematics poses no problem. However, one could reach the same conclusions by using just a bit of common sense.” ReasonUseProblemBitsInterestCommonExampleReaderModelsAdvantageMathematicsCommon SenseConclusionEconomistNo ProblemAppreciatedPrecisionAnthropologists Author:Luigi Luca Cavalli-Sforza
“Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes.” MenMindEyeTogetherHistoryCreationWasteEternalModelsMathematicsGeometryThrough The Eyes Author:Johannes Kepler
“Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music. Art, on the other hand, begins with the world we construct, not with the world we see. It starts with the imagination, and then works toward ordinary experience.” WorldWayTryingArtHandsMovingLawScienceLiteratureSpeakLanguageImaginationAcceptingModelsOrdinaryMathematicsDataConstructsInterpretingLiterature And Music Author:Northrop Frye
“The standard model gives us an accuracy of ten decimal digits, this is an amazing success that has never been achieved before in science.” GivingScienceTenModelsStandardsMathematicsAccuracyDecimals Author:Nathan Seiberg
“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
“General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines. Mathematics attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge.” WorldDoeRealUseBodyLyingNamesLevelsSituationStudyBuildingTheoryDisciplinePureModelsConnectionsMathematicsReal WorldConstructionConcreteOrganizeTheoreticalThinkableSystems Theory Author:Kenneth E. Boulding
“The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.” WorldMindHumansStoriesRealityLyingValuesDifficultCreationModelsMathematicsPatternsFeaturesCollectivesHuman MindEquationsOutside WorldCorrespondence Book:Seventeen Equations that Changed the World Source: Seventeen Equations that Changed the World
“I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.” ThinkingImportantCreationProveBenefitsModelsMathematicsTheorems Author:David Mumford
“Do not trust financial market risk models. Despite the predilection of some analysts to model the financial markets using sophisticated mathematics, the markets are governed by behavioral science, not physical science.” RiskModelsMathematicsFinancialDespiteSophisticatedAnalystsFinancial MarketsPhysical ScienceMarket Risk Author:Seth Klarman
“If you go through the list of things that are not possible you're left with a very finite amount of possibilities. The fancy name for this is constraint theory. It's a nonquantitative model, but it's a field of mathematics.” IfsNamesLeftFieldsPossibilityTheoryAmountModelsMathematicsListsFancyFiniteConstraints Author:George Friedman
“Henceforth, whilst there are a great many theories and models proposed as to how, or why, magic works (based on subtle energies, animal magnetism, psychological concepts, quantum theory, mathematics or the so-called anthropomorphic principle) it is not a case that one of them is more 'true' than others, but a case of which theory or model you choose to believe in, or which theory you find most attractive. Indeed, from a Chaos Magic perspective, you can selectively believe that a particular theory or model of magical action is true only for the duration of a particular ritual or phase of work.” BelieveActionEnergyAnimalPrinciplesCasesMagicParticularTheoryPerspectiveModelsConceptsMathematicsChaosPsychologicalAttractiveGreat MenSubtleRitualYou ChooseQuantumPhasesDurationQuantum TheoryMagnetismAnimal Magnetism Author:Phil Hine
“I recognize that I have a unique position to be a role model to young girls because I am doing something that they consider glamorous, which is acting, and yet I took a time to really get my education and study mathematics, and I think math is the cat's meow.” ThinkingYoungGirlActingRolesStudyPositionUniqueModelsCatMathematicsMathRole ModelsGlamorous Author:Danica McKellar