BeingBeinga studenta studentthrough the years:through the years:the beauty ofthe beauty ofscientific results,scientific re...
~~ Introduction: the meaning of being a studentIntroduction: the meaning of being a student~~ The models to study the Miss...
Introduction:Introduction:the meaning ofthe meaning ofbeing a studentbeing a studentThis presentation was sparked byThis p...
Teaching & learningTeaching & learningsciencescience
My UniversityMy University19651965--96960926199509261995
LomonosovLomonosovMoscowMoscowStateStateUniversityUniversityDimaDimaGordevGordev,1980,1980
The modelsThe modelsused for theused for theMissouri RiverMissouri River
20062006PresentationPresentationon theon theWesternWesternSouth DakotaSouth DakotaconferenceconferenceApr 18, 2006Apr 18, ...
VariabilityVariabilityas mathas mathmodelsmodelsPresentation on the WesternPresentation on the WesternSouth Dakota confere...
The duration curvesThe duration curves
The curveThe curvefor Missourifor Missouri103, cfs%Empiricaldurational curve1911-2010 forUSGS 06191500YellowstoneRiver at ...
AnnualAnnualdistributiondistribution
Structure ofStructure ofthe seasonalthe seasonalvariabilityvariabilityFactor 1 Score-2.5-1.5-0.50.51.52.519111920192919381...
Shifts in the mean for Factor 2, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1-2.5-1.5-0.50.51.52.51...
ModelingModelingthe regimesthe regimes19111911--20102010(2021)(2021)1500.02500.03500.04500.05500.0191119211931194119511961...
The WaveletsThe Wavelets
The WaveletsThe Wavelets
Math models &Math models &TimeTimeVariabilityVariability-2.5-1.5-0.50.51.52.5191119211931194119511961197119811991200120112...
Annual15002500350045005500191119201929193819471956196519741983199220012010Year (Hydr)cfsShifts in the mean for Factor 2, 1...
The common senseThe common sense"... it is the very genius of Aristotle"... it is the very genius of Aristotle —— as it is...
The KnowledgeThe Knowledgeof the Variabilityof the Variabilityfor Watershedfor Watershed* The Knowledge about watershed co...
The StatisticalThe StatisticalLearningLearning
Philosophy of Data AnalysisPhilosophy of Data Analysis& the Natural Structures& the Natural StructuresFactor analysis is m...
From Data AnalysisFrom Data Analysisto Statistical Learningto Statistical Learning
Statistical LearningStatistical Learning
Statistical LearningStatistical LearningSUMMARYSUMMARY““1. With the appearance of computers the concept of natural scien1....
TheThemodelmodelforforstatisticalstatisticallearninglearning
The UncertaintyThe Uncertainty& Different& DifferentSystems of CoordinatesSystems of CoordinatesMathematical & physicalMat...
The Uncertainty &The Uncertainty &Systems of CoordinatesSystems of CoordinatesNatural objects may be classified inNatural ...
Vertical slice ofthe Geographical Sphere withtwo independent elements:System ofAnthropological Geography (SAG)&System of P...
TheTheComponentsComponentsof Landscapeof LandscapeThe System ofPhysical GeographySphere (SFG)with fiveindependentelements:...
The ComponentsThe Componentsof Landscape onof Landscape onMapMapEvery Sai & Saij may becharacterized bymatrix of input {Wi...
{Ri}is a matrix ofrelations betweenthe components ofthe landscape(after Krcho, 1978)RijThe StructureThe Structureof theof ...
{Ri}is a matrix of relationsbetween the components ofthe landscapeThe number of characteristics forelements of landscape i...
The gThe g22 -- stream runoff systemstream runoff systemas a part of aas a part of a22-- hydrospherehydrospheremay be pres...
xxititThe gThe g22 -- stream runoff systemstream runoff systemas a part of aas a part of a22-- hydrospherehydrospheremay b...
EducationEducationas communication onas communication onthe movement fromthe movement fromUncertainty to theUncertainty to...
The KnowledgeThe KnowledgeBertrand Russell“Human Knowledge.Its Scope & Limits.”1948““I. THE DEFINITION OF KNOWLEDGEI. THE ...
TheTheUncertaintyUncertaintyLotfiLotfi A. ZadehA. Zadeh(born Feb 4, 1921)(born Feb 4, 1921)Professor in the Graduate Schoo...
Zadeh:Zadeh:the fuzzy logicthe fuzzy logic
(The)(The) UncertaintyUncertainty““Uncertainty is a personalUncertainty is a personalmatter; it is notmatter; it is not th...
There is part ofThere is part ofscience looking in thescience looking in thecoinscoinsTheThemodelmodel
TheThemodelmodel
Statistics & UncertaintyStatistics & UncertaintyThe statisticians task isThe statisticians task isto articulate theto arti...
Statistics at workStatistics at work““Karl Pearson said The unity of all science consists alone in itKarl Pearson said The...
The UncertaintyThe Uncertainty& Information& Information
The Science &The Science &the Languagethe Language[In linguistic] ...[In linguistic] ...““the proper object of studythe pr...
EvolutionEvolutionCommunicationCommunication& language& language
Information in theInformation in theLanguageLanguage““In cognitive linguistics asIn cognitive linguistics asin cognitive s...
LearningLearningConceptConcept
The Uncertainty & The KnowledgeThe Uncertainty & The Knowledgethrough Modeling: Object,through Modeling: Object,Data, Anal...
The Uncertainty & The KnowledgeThe Uncertainty & The Knowledgethrough Modeling: Object,through Modeling: Object,Data, Anal...
Communicating theCommunicating theKnowledge for theKnowledge for theWatershedWatershedScientistScientistworking inworking ...
““VitruvianVitruvian ManMan””Albert Einstein wrote thatthe mind “always has triedto form for itself a simple& synoptic ima...
““VitruvianVitruvianManMan””The ancient Roman engineerThe ancient Roman engineerVitruvius opined in his magnum opus,Vitruv...
OurOurUniversityUniversity
RaphaelRaphael(1509(1509--1510)1510)Fresco (500*770 cm) Vatican City, Apostolic PalaceFresco (500*770 cm) Vatican City, Ap...
““VitruvianVitruvian ManMan””… “Vitruvian Man”ultimately offers a“synoptic image” of theRenaissance itself.Beforethe Pacio...
Renaissance of our daysRenaissance of our daysIn the search ofIn the search ofthethe““EnlightenmentEnlightenment’’ss””imag...
Maria MontessoriMaria Montessori(1870(1870--1952)1952)Scientific observation has established thatScientific observation ha...
Few biographical factsFew biographical factsMaria Montessori became a physician in 1896, she was the first wMaria Montesso...
Her methodHer methodas the answer toas the answer toDrDr AbcAbc DeDe’’s questions questionThe main principles of MariaThe ...
Tomasello, 51, previously taughtpsychology at Emory University in Atlanta& conducted research at Atlanta’s YerkesPrimate C...
A centuryA centurylaterlater
StudentsStudentsininthetheUniversityUniversity
Epilogue:Epilogue:the sciencethe scienceasascommunicationcommunicationof personalitiesof personalities
Isitthescience?Isitthescience?
““In place of scientific method, PolanyiIn place of scientific method, Polanyitrumpeted the importance oftrumpeted the imp...
Michael PolanyiMichael Polanyi(1891(1891 –– 19761976)Polanyi addressing the Congress ofPolanyi addressing the Congress ofC...
"In questions"In questionsof science,of science,the authority of a thousandthe authority of a thousandis not worthis not w...
QuestionsQuestions
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Seminar presentation: "Being a student for the years: the beauty of scientific results, mathematic & other arts"; Computational Science & Statistics Seminar South Dakota State, Feb 15 2012

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The presentation was sparked by question during one of seminars’ sessions last semester. “Why are the students not active, they don’t ask the questions?” Doing science, studying mathematics and teaching statistical learning for quite of few years I thought that have my answer and may bring it to students as the inside and outside view on study and collaboration, teaching and learning.

The scientific part of the presentations is about modeling of one time series for Missouri River (1911-2010), the discussion is about how the deal with the math modeling of natural system and communicate the results to the colleagues and the students.

Topics of the presentation:
~ Introduction: the meaning of being a student
~ The models used for the Missouri River
~ The Statistical Learning
~ Education as communication on the movement from uncertainty to the knowledge
~ “Vitruvian Man”
~ Maria Montessori (1870-1952) and her method as the answer “the question”
~ The epilogue – the science as communication of personalities

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Seminar presentation: "Being a student for the years: the beauty of scientific results, mathematic & other arts"; Computational Science & Statistics Seminar South Dakota State, Feb 15 2012

  1. 1. BeingBeinga studenta studentthrough the years:through the years:the beauty ofthe beauty ofscientific results,scientific results,mathematic &mathematic &other artsother artsFeb 15,Feb 15,20122012ComputationalComputationalScience &Science &StatisticsStatisticsSeminarSeminarSouth DakotaSouth DakotaState UniversityState UniversityBorisBorisShmaginShmaginWRI SDSUWRI SDSU
  2. 2. ~~ Introduction: the meaning of being a studentIntroduction: the meaning of being a student~~ The models to study the Missouri RiverThe models to study the Missouri River~~ The Statistical LearningThe Statistical Learning~~ Education as communication fromEducation as communication fromuncertainty to the knowledgeuncertainty to the knowledge~~ Maria Montessori (1870Maria Montessori (1870--1952) &1952) &her method as the answer to the questionher method as the answer to the question~~ ““VitruvianVitruvian ManMan””~~ The epilogueThe epilogue ––the science as communication of personalitiesthe science as communication of personalitiesTopics:Topics:
  3. 3. Introduction:Introduction:the meaning ofthe meaning ofbeing a studentbeing a studentThis presentation was sparked byThis presentation was sparked byDrDr AbcAbc De questionDe questionduring one of seminarsduring one of seminars’’ sessions last semester.sessions last semester.““Why are the students not active,Why are the students not active,they donthey don’’t ask the questions?t ask the questions?””
  4. 4. Teaching & learningTeaching & learningsciencescience
  5. 5. My UniversityMy University19651965--96960926199509261995
  6. 6. LomonosovLomonosovMoscowMoscowStateStateUniversityUniversityDimaDimaGordevGordev,1980,1980
  7. 7. The modelsThe modelsused for theused for theMissouri RiverMissouri River
  8. 8. 20062006PresentationPresentationon theon theWesternWesternSouth DakotaSouth DakotaconferenceconferenceApr 18, 2006Apr 18, 2006TheTheconferenceconferencepresentationpresentation
  9. 9. VariabilityVariabilityas mathas mathmodelsmodelsPresentation on the WesternPresentation on the WesternSouth Dakota conferenceSouth Dakota conferenceApr 18, 2006Apr 18, 2006
  10. 10. The duration curvesThe duration curves
  11. 11. The curveThe curvefor Missourifor Missouri103, cfs%Empiricaldurational curve1911-2010 forUSGS 06191500YellowstoneRiver at CorwinSprings, MTThe hydrograph ofhydrological year forUSGS 061915001911-2010
  12. 12. AnnualAnnualdistributiondistribution
  13. 13. Structure ofStructure ofthe seasonalthe seasonalvariabilityvariabilityFactor 1 Score-2.5-1.5-0.50.51.52.5191119201929193819471956196519741983199220012010Year (Hydr)Factor 2 Score-2.5-1.5-0.50.51.52.5191119201929193819471956196519741983199220012010Year (Hydr)Factor 3 Score-2.0-1.00.01.02.03.0191119201929193819471956196519741983199220012010Year (Hydr)More thatMore thatoneonedimensiondimension
  14. 14. Shifts in the mean for Factor 2, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1-2.5-1.5-0.50.51.52.5191119201929193819471956196519741983199220012010Shifts in the mean for Factor 1, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1-3.0-2.0-1.00.01.02.03.0191119201929193819471956196519741983199220012010Shifts in the mean for Factor 3, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1-2.0-1.00.01.02.03.0191119201929193819471956196519741983199220012010Shifts in the mean for Annual Hydrologic Year, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1150020002500300035004000450050005500191119201929193819471956196519741983199220012010InterannualInterannualseasonal regime:seasonal regime:shiftsshiftsEvery seasonEvery season(dimension) has(dimension) hasdifferentdifferentshifts.shifts.Annual reflectsAnnual reflectssome shiftssome shifts
  15. 15. ModelingModelingthe regimesthe regimes19111911--20102010(2021)(2021)1500.02500.03500.04500.05500.0191119211931194119511961197119811991200120112021AYH [cfs] Model-2.5-1.5-0.50.51.52.5191119211931194119511961197119811991200120112021F1 Model-2.5-1.5-0.50.51.52.5191119211931194119511961197119811991200120112021F2 Model-2.0-1.00.01.02.03.0191119211931194119511961197119811991200120112021F3 Model
  16. 16. The WaveletsThe Wavelets
  17. 17. The WaveletsThe Wavelets
  18. 18. Math models &Math models &TimeTimeVariabilityVariability-2.5-1.5-0.50.51.52.5191119211931194119511961197119811991200120112021F1 ModelShifts in the mean for Annual Hydrologic Year, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1150020002500300035004000450050005500191119201929193819471956196519741983199220012010
  19. 19. Annual15002500350045005500191119201929193819471956196519741983199220012010Year (Hydr)cfsShifts in the mean for Factor 2, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1-2.5-1.5-0.50.51.52.5191119201929193819471956196519741983199220012010Shifts in the mean for Factor 1, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1-3.0-2.0-1.00.01.02.03.0191119201929193819471956196519741983199220012010Shifts in the mean for Factor 3, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1-2.0-1.00.01.02.03.0191119201929193819471956196519741983199220012010Shifts in the mean for Annual Hydrologic Year, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1150020002500300035004000450050005500191119201929193819471956196519741983199220012010To put theTo put theknowledge forknowledge forwork on thework on theengineeringsengineeringsgoalsgoals ??????
  20. 20. The common senseThe common sense"... it is the very genius of Aristotle"... it is the very genius of Aristotle —— as it is of every greatas it is of every greatteacherteacher —— to make you think he is uncovering your ownto make you think he is uncovering your ownthought in his."thought in his."
  21. 21. The KnowledgeThe Knowledgeof the Variabilityof the Variabilityfor Watershedfor Watershed* The Knowledge about watershed comes only from theanalysis of the empirical data (instrumental observations)* Variability has to be defined in coordinates ofparticular watershed; with the number of factor’s axesthe annual & seasonal structure of hydrologic time &space may be presented* The math model does not have criteria to verify itself(Gödels incompleteness theorems) & multi models &scales studies with use of empirical data have to becompleted
  22. 22. The StatisticalThe StatisticalLearningLearning
  23. 23. Philosophy of Data AnalysisPhilosophy of Data Analysis& the Natural Structures& the Natural StructuresFactor analysis is method for extraction that are regarded as thFactor analysis is method for extraction that are regarded as the basice basicvariables that account for the interrelations observed in the davariables that account for the interrelations observed in the datataA factor is a portion of a quantity, usually an integer or polynA factor is a portion of a quantity, usually an integer or polynomialomialthat, when multiplied by other factors, gives the entire quantitthat, when multiplied by other factors, gives the entire quantityyThe main applications ofThe main applications offactor analytic techniques are:factor analytic techniques are:•• (1) to reduce the number of(1) to reduce the number ofvariables andvariables and•• (2) to detect structure(2) to detect structure ininthe relationships between variables,the relationships between variables,that is to classify variables.that is to classify variables.(From: Wolfram(From: Wolfram MathWorldMathWorld))The variables selected after factor analysis are considered as tThe variables selected after factor analysis are considered as typical &ypical &may be used for timemay be used for time--series analysisseries analysis
  24. 24. From Data AnalysisFrom Data Analysisto Statistical Learningto Statistical Learning
  25. 25. Statistical LearningStatistical Learning
  26. 26. Statistical LearningStatistical LearningSUMMARYSUMMARY““1. With the appearance of computers the concept of natural scien1. With the appearance of computers the concept of natural science,ce,its methodology & philosophy started a process of aits methodology & philosophy started a process of a paradigm changeparadigm change::The concepts, methodology, & philosophy of aThe concepts, methodology, & philosophy of a Simple WorldSimple World move to verymove to verydifferent concepts, philosophy & methodology of adifferent concepts, philosophy & methodology of a Complex WorldComplex World..2. In such changes an important role belongs to the mathematical2. In such changes an important role belongs to the mathematical factsfactsthat were discovered by analyzing thethat were discovered by analyzing the ““Drosophila flyDrosophila fly”” of cognitive science theof cognitive science the““Pattern recognition problemPattern recognition problem”” & attempts to obtain their philosophical interpretation.& attempts to obtain their philosophical interpretation.3. The results of these analyzes lead to methods that go beyond3. The results of these analyzes lead to methods that go beyond thetheclassical concept of science: creating generative models of evenclassical concept of science: creating generative models of events & explaints & explain--ability ofability ofobtained rules.obtained rules.4. The new paradigm introduces direct search for solution (4. The new paradigm introduces direct search for solution (transductivetransductiveinference, instead ofinference, instead of inductiveinductive), the meditative principle of decision making, & a unity), the meditative principle of decision making, & a unityof two languages for pattern description: technical (rational) &of two languages for pattern description: technical (rational) & holistic (irrational).holistic (irrational).This leads to the convergence of the exact science with humanitiThis leads to the convergence of the exact science with humanities.es.5. The main difference between the new paradigm (developed in th5. The main difference between the new paradigm (developed in theecomputer era) & the classical one (developed before the computercomputer era) & the classical one (developed before the computer era) is the claim:era) is the claim:To guarantee the success of inference one needs to control the cTo guarantee the success of inference one needs to control the complexityomplexityof algorithms for inference rather than complexity of the functiof algorithms for inference rather than complexity of the function that theseon that thesealgorithms produce.algorithms produce. Algorithms with low complexity can create a complex functionAlgorithms with low complexity can create a complex functionwhich will generalize well.which will generalize well.””
  27. 27. TheThemodelmodelforforstatisticalstatisticallearninglearning
  28. 28. The UncertaintyThe Uncertainty& Different& DifferentSystems of CoordinatesSystems of CoordinatesMathematical & physicalMathematical & physicalobjects are abstractionsobjects are abstractions&& ““havehave”” the principle ofthe principle ofuncertaintyuncertaintyTechnologicalTechnologicalobjects haveobjects havethe errors ofthe errors ofmeasurementmeasurementNatural objects have fuzzyNatural objects have fuzzyboundaries in their ownboundaries in their owncoordinates ofcoordinates ofnonstationarynonstationary axesaxeszzxxyyxxzzyyxxzzyy
  29. 29. The Uncertainty &The Uncertainty &Systems of CoordinatesSystems of CoordinatesNatural objects may be classified inNatural objects may be classified incoordinates of multicoordinates of multi--dimensionaldimensionalprocess & nonstationary axesprocess & nonstationary axesxx1t1txxzzyyNatural objects have fuzzyNatural objects have fuzzyboundaries in their ownboundaries in their owncoordinates of & nonstationarycoordinates of & nonstationaryaxesaxesxx2t2txxititxxzzyy
  30. 30. Vertical slice ofthe Geographical Sphere withtwo independent elements:System ofAnthropological Geography (SAG)&System of Physical Geography(SFG).Arrows indicatevertical & horizontal componentsof matter, energy & informationcirculation(after Krcho, 1978)The Cybernetic ModelThe Cybernetic Modelof theof theGeosphereGeosphere
  31. 31. TheTheComponentsComponentsof Landscapeof LandscapeThe System ofPhysical GeographySphere (SFG)with fiveindependentelements:a1- atmosphere,a2- hydrosphere,a3- lithosphere,a4- pedosphere,a5- biosphere.The elements of thePhysical GeographySystem SFG are theSpheresSa1, Sa2, Sa3, Sa4, Sa5& they may beconsidered asSubsystems Sai(after Krcho, 1978)
  32. 32. The ComponentsThe Componentsof Landscape onof Landscape onMapMapEvery Sai & Saij may becharacterized bymatrix of input {Wi},matrix of output {Qi}, &matrix of states {Hi}.The System ofPhysical GeographySphere (SFG)with fiveindependentelements:a1- atmosphere,a2- hydrosphere,a3- lithosphere,a4- pedosphere,a5- biosphereEvery element a1 – a5 of SFGis a System Sai & consists fromunits: a1(a11, a12, a13 …), a2(a21, a22 …),… a5 & those units may be consideredas subsystems Saij.
  33. 33. {Ri}is a matrix ofrelations betweenthe components ofthe landscape(after Krcho, 1978)RijThe StructureThe Structureof theof theRelationsRelations
  34. 34. {Ri}is a matrix of relationsbetween the components ofthe landscapeThe number of characteristics forelements of landscape is unlimited& the number is unlimited fordependences tooRijThe Structure of RelationsThe Structure of Relations& Reestablishment& Reestablishmentof Dependencesof Dependences
  35. 35. The gThe g22 -- stream runoff systemstream runoff systemas a part of aas a part of a22-- hydrospherehydrospheremay be presented as:may be presented as:SgSg22 = {= { ggjiji,, RRjiji },},Any watershedAny watershed ggjiji for territory mayfor territory maybe considered as a part of streambe considered as a part of streamrunoff system Sgrunoff system Sg22..cabggjijiEach of these components may beEach of these components may becharacterized by matrix of input {characterized by matrix of input {WiWi},},matrix of output {matrix of output {QiQi}, & matrix of states {Hi}.}, & matrix of states {Hi}.Subsystem ofSubsystem ofHydrosphere (SaHydrosphere (Sa22))with nine independentwith nine independentelements:elements:gg11-- atmosphere,atmosphere,gg22-- stream runoff filmstream runoff film(pellicle),(pellicle),gg33-- lithosphere,lithosphere,aa44-- pedosphere,pedosphere,aa55-- biospherebiospherewherewhere ggJiJi-- watershedwatershedin specific coordinatesin specific coordinatesyyCybernetic Model (a)Cybernetic Model (a)for Watershed in Landscape,for Watershed in Landscape,with Map of Conditions (b)with Map of Conditions (b)& Models of Multilayer Map (c)& Models of Multilayer Map (c)xxzz
  36. 36. xxititThe gThe g22 -- stream runoff systemstream runoff systemas a part of aas a part of a22-- hydrospherehydrospheremay be presented as:may be presented as:SgSg22 = {= { ggjiji,, RRjiji },},Any watershedAny watershed ggjiji for territory mayfor territory maybe considered as a part of streambe considered as a part of streamrunoff system Sgrunoff system Sg22..cabggjijiEach of these components may beEach of these components may becharacterized by matrix of input {characterized by matrix of input {WiWi},},matrix of output {matrix of output {QiQi}, & matrix of states {Hi}.}, & matrix of states {Hi}.Subsystem ofSubsystem ofHydrosphere (SaHydrosphere (Sa22))with nine independentwith nine independentelements:elements:gg11-- atmosphere,atmosphere,gg22-- stream runoff filmstream runoff film(pellicle),(pellicle),gg33-- lithosphere,lithosphere,aa44-- pedosphere,pedosphere,aa55-- biospherebiospherewherewhere ggJiJi-- watershedwatershedin specific coordinatesin specific coordinatesyyThe Watershed inThe Watershed inMultidimensional System ofMultidimensional System ofCoordinate with DiversityCoordinate with DiversityLandscapesLandscapesxxzzxxititxxitit
  37. 37. EducationEducationas communication onas communication onthe movement fromthe movement fromUncertainty to theUncertainty to theKnowledgeKnowledge
  38. 38. The KnowledgeThe KnowledgeBertrand Russell“Human Knowledge.Its Scope & Limits.”1948““I. THE DEFINITION OF KNOWLEDGEI. THE DEFINITION OF KNOWLEDGEThe question how knowledge should be defined is perhaps the mostThe question how knowledge should be defined is perhaps the most important and difficult of theimportant and difficult of thethree with which we shall deal. This may seem surprising: at firthree with which we shall deal. This may seem surprising: at first sight it might be thoughtst sight it might be thoughtthat knowledge might be defined as belief which is in agreementthat knowledge might be defined as belief which is in agreement with the facts. Thewith the facts. Thetrouble is that no one knows what a belief is, no one knows whattrouble is that no one knows what a belief is, no one knows what a fact is, & no one knowsa fact is, & no one knowswhat sort of agreement between them would make a belief true.what sort of agreement between them would make a belief true.Belief. Words. Truth in Logic.Belief. Words. Truth in Logic.II. THE DATAII. THE DATAAnimal Inference. Mental & Physical Data.Animal Inference. Mental & Physical Data.III. METHODS OF INFERENCEIII. METHODS OF INFERENCEInduction. Probability. Limitation of Variety. Grades of CertainInduction. Probability. Limitation of Variety. Grades of Certainty.ty.””The book has sixThe book has sixparts, & the partparts, & the partnamednamed ““LanguageLanguage”” isisthe biggest one withthe biggest one witheleven chapterseleven chapters
  39. 39. TheTheUncertaintyUncertaintyLotfiLotfi A. ZadehA. Zadeh(born Feb 4, 1921)(born Feb 4, 1921)Professor in the Graduate School,Professor in the Graduate School,Computer Science Division Department ofComputer Science Division Department ofElectrical Engineering & Computer SciencesElectrical Engineering & Computer SciencesDirector, Berkeley Initiative in SoftDirector, Berkeley Initiative in SoftComputing University of CaliforniaComputing University of CaliforniaBerkeley, CA 94720Berkeley, CA 94720 --17761776
  40. 40. Zadeh:Zadeh:the fuzzy logicthe fuzzy logic
  41. 41. (The)(The) UncertaintyUncertainty““Uncertainty is a personalUncertainty is a personalmatter; it is notmatter; it is not thetheuncertainty butuncertainty but youryouruncertainty.uncertainty.””Dennis LindleyDennis Lindley(2006)(2006)UnderstandingUnderstandingUncertaintyUncertaintyDennis Victor LindleyDennis Victor Lindley(born 25 July 1923)(born 25 July 1923)Professor Emeritus of Statistics,Professor Emeritus of Statistics,& past Head of Department,& past Head of Department,at University College London (UK).at University College London (UK).He is a British statistician, decision theorist &He is a British statistician, decision theorist &leading advocate of Bayesian statisticsleading advocate of Bayesian statistics
  42. 42. There is part ofThere is part ofscience looking in thescience looking in thecoinscoinsTheThemodelmodel
  43. 43. TheThemodelmodel
  44. 44. Statistics & UncertaintyStatistics & UncertaintyThe statisticians task isThe statisticians task isto articulate theto articulate thescientists uncertaintiesscientists uncertaintiesin thein the languagelanguage ofofprobabilityprobability……A model is merely yourA model is merely yourreflection of reality &,reflection of reality &,like probability,like probability,it describes neither youit describes neither younor the world,nor the world,but only a relationshipbut only a relationshipbetween you &between you &that world.that world.”” (p. 303)(p. 303)“…“… data analysis assists in the formulation of a modeldata analysis assists in the formulation of a model &&is an activity that precedes the formal probability calculationsis an activity that precedes the formal probability calculations that arethat areneeded for inference.needed for inference.”” (p. 305)(p. 305)““Statisticians are not masters in their own house.Statisticians are not masters in their own house.Their task is to help the client to handle the uncertainty thatTheir task is to help the client to handle the uncertainty that they encounter.they encounter.TheThe youyou of the analysis is the client, not the statistician.of the analysis is the client, not the statistician.”” (p. 318)(p. 318)
  45. 45. Statistics at workStatistics at work““Karl Pearson said The unity of all science consists alone in itKarl Pearson said The unity of all science consists alone in its method, not in its materials method, not in its material(Pearson, 1892).(Pearson, 1892). It is not true to say that physics is science whereas literatureIt is not true to say that physics is science whereas literature is notis not..””(p. 316)(p. 316)
  46. 46. The UncertaintyThe Uncertainty& Information& Information
  47. 47. The Science &The Science &the Languagethe Language[In linguistic] ...[In linguistic] ...““the proper object of studythe proper object of studywaswas the speakersthe speakersunderlyingunderlyingknowledge of the languageknowledge of the language,,his "linguistic competence"his "linguistic competence"that enables him to producethat enables him to produce& understand sentences& understand sentenceshe has never heard beforehe has never heard before””From:From: "Chomskys Revolution"Chomskys RevolutionIn Linguistics"In Linguistics"by John R. Searleby John R. SearleThe New York Review of Books,The New York Review of Books,June 29, 1972June 29, 1972
  48. 48. EvolutionEvolutionCommunicationCommunication& language& language
  49. 49. Information in theInformation in theLanguageLanguage““In cognitive linguistics asIn cognitive linguistics asin cognitive science, the humanin cognitive science, the humanmind is considered to be anmind is considered to be aninformationinformation--processing deviceprocessing device((StillingsStillings 1995),1995),& language is viewed as& language is viewed asa vehicle for communicatinga vehicle for communicatinginformation.information.””From: J. Van deFrom: J. Van de WalleWalle, 2008, 2008Six communicationfunctionsdistinguishedby Jakobson,(from Wiki)
  50. 50. LearningLearningConceptConcept
  51. 51. The Uncertainty & The KnowledgeThe Uncertainty & The Knowledgethrough Modeling: Object,through Modeling: Object,Data, Analysis & ResultsData, Analysis & ResultsPhoto picturePhoto pictureas presentationas presentationof the naturalof the naturalobjectobjectThe conceptual modelThe conceptual model(Cybernetic Model)(Cybernetic Model)is the way to useis the way to usepreviously obtainedpreviously obtainedKnowledgeKnowledgeThe knowledge (K)= 0,The knowledge (K)= 0,about a new object forabout a new object forthe considerationthe considerationthe uncertainty (U)= 1the uncertainty (U)= 1KKpp = 1 & we have the= 1 & we have thedirection for thedirection for theresearch, the task,research, the task,U = 0, but theU = 0, but theKnowledge isKnowledge isprevious (previous (KKpp))The Statistical LearningThe Statistical Learningis the way to obtainis the way to obtain((““extractextract””) the structure) the structureof a natural objectof a natural objectAfterAfterStatisticalStatisticalLearningLearningK > UK > UThe Uncertainty fromThe Uncertainty fromAnalysis obtained forAnalysis obtained forevery model.every model.For Factor AnalysisFor Factor AnalysisU=1U=1-- explained variabilityexplained variability
  52. 52. The Uncertainty & The KnowledgeThe Uncertainty & The Knowledgethrough Modeling: Object,through Modeling: Object,Data, Analysis & ResultsData, Analysis & ResultsPhoto picturePhoto pictureas presentationas presentationof the naturalof the naturalobjectobjectThe conceptual modelThe conceptual model(Cybernetic Model)(Cybernetic Model)is the way to useis the way to usepreviously obtainedpreviously obtainedKnowledgeKnowledgeThe knowledge (K)= 0,The knowledge (K)= 0,about a new object forabout a new object forthe considerationthe considerationthe uncertainty (U)= 1the uncertainty (U)= 1KKpp = 1 & we have the= 1 & we have thedirection for thedirection for theresearch, the task,research, the task,U = 0, but theU = 0, but theKnowledge isKnowledge isprevious (previous (KKpp))The Statistical LearningThe Statistical Learningis the way to obtainis the way to obtain((““extractextract””) the structure) the structureof a natural objectof a natural objectAfterAfterStatisticalStatisticalLearningLearningK > UK > UThe Uncertainty fromThe Uncertainty fromAnalysis obtained forAnalysis obtained forevery model.every model.For Factor AnalysisFor Factor AnalysisU=1U=1-- explained variabilityexplained variability
  53. 53. Communicating theCommunicating theKnowledge for theKnowledge for theWatershedWatershedScientistScientistworking inworking inHydrology haveHydrology haveto handle theto handle theUncertainty &Uncertainty &communicatecommunicatethe Knowledgethe Knowledgeaboutabouttimetime--spatialspatialvariability ofvariability ofthe Watershedthe Watershedcharacteristicscharacteristics
  54. 54. ““VitruvianVitruvian ManMan””Albert Einstein wrote thatthe mind “always has triedto form for itself a simple& synoptic image of thesurrounding world.”During the Renaissance,when the ancient Greekidea of man as themeasure of all things leaptto the forefront ofintellectual life, the humanbody became a preferredobject for this type of“synoptic” speculation.… “Vitruvian Man”ultimately offers a“synoptic image” of theRenaissance itself.Leonardo’s most famous images, “Vitruvian Man” (circa 1490).
  55. 55. ““VitruvianVitruvianManMan””The ancient Roman engineerThe ancient Roman engineerVitruvius opined in his magnum opus,Vitruvius opined in his magnum opus,““Ten Books on ArchitectureTen Books on Architecture””(circa 25 B.C.),(circa 25 B.C.),that a temple cannot be built properlythat a temple cannot be built properly““unless it conforms exactly to theunless it conforms exactly to theprinciple relating the members of aprinciple relating the members of awellwell--shaped man.shaped man.”” He thenHe thenenumerated the ideal proportions ofenumerated the ideal proportions ofthe male physique & posited that athe male physique & posited that amanman’’s outstretched body could bes outstretched body could bemade to fit within a circle & a square.made to fit within a circle & a square.Lester writes:Lester writes:““The circle represented the cosmic &The circle represented the cosmic &the divine;the divine;the square represented the earthly &the square represented the earthly &the secular.the secular.””
  56. 56. OurOurUniversityUniversity
  57. 57. RaphaelRaphael(1509(1509--1510)1510)Fresco (500*770 cm) Vatican City, Apostolic PalaceFresco (500*770 cm) Vatican City, Apostolic PalaceThe School of Athens:The School of Athens:all togetherall together““Sky is limitSky is limit””there were people in SDthere were people in SDwho saw the connectionswho saw the connections
  58. 58. ““VitruvianVitruvian ManMan””… “Vitruvian Man”ultimately offers a“synoptic image” of theRenaissance itself.Beforethe Pacioli collaboration, the idea had inspired what has since becomeone of Leonardo’s most famous images, “Vitruvian Man” (circa 1490), acareful line drawing of a nude male figure whose outstretched arms andlegs fit perfectly in the bounds of a circle and a square. “Vitruvian Man”has entered popular culture as an emblem of Leonardo’s genius —redolent of secret knowledge …The story, in some respects, is simple. The ancient Roman engineerVitruvius opined in his magnum opus, “Ten Books on Architecture” (circa25 B.C.), that a temple cannot be built properly “unless it conformsexactly to the principle relating the members of a well-shaped man.” Hethen enumerated the ideal proportions of the male physique and positedthat a man’s outstretched body could be made to fit within a circle and asquare. “Ancient philosophers, mathematicians and mystics had longinvested those two shapes with special symbolic powers,” Lester writes.“The circle represented the cosmic and the divine; the square representedthe earthly and the secular.”
  59. 59. Renaissance of our daysRenaissance of our daysIn the search ofIn the search ofthethe““EnlightenmentEnlightenment’’ss””imageimage
  60. 60. Maria MontessoriMaria Montessori(1870(1870--1952)1952)Scientific observation has established thatScientific observation has established thateducation is not what the teacher gives;education is not what the teacher gives;education is a natural process spontaneouslyeducation is a natural process spontaneouslycarried out by the human individualcarried out by the human individual, &, &is acquired not by listening to words but byis acquired not by listening to words but byexperiences upon the environment.experiences upon the environment.The task of the teacher becomes that ofThe task of the teacher becomes that ofpreparing a series of motives of culturalpreparing a series of motives of culturalactivity, spread over a specially preparedactivity, spread over a specially preparedenvironment, & then refraining from obtrusiveenvironment, & then refraining from obtrusiveinterference. Humaninterference. Human teachers can only helpteachers can only helpthe great work that is being done, as servantsthe great work that is being done, as servantshelp the master.help the master.Doing soDoing so, they will be witnesses to the, they will be witnesses to theunfolding of the human soul & to the risingunfolding of the human soul & to the risingof a New Manof a New Man who will not be a victim ofwho will not be a victim ofevents, but will have the clarity of vision toevents, but will have the clarity of vision todirect & shape the future of human society.direct & shape the future of human society.Maria Montessori,Maria Montessori, 1946.1946.””Education for a New WorldEducation for a New World””
  61. 61. Few biographical factsFew biographical factsMaria Montessori became a physician in 1896, she was the first wMaria Montessori became a physician in 1896, she was the first woman in Italy to receiveoman in Italy to receivea medical degree. She worked in the fields of psychiatry, educata medical degree. She worked in the fields of psychiatry, education & anthropology.ion & anthropology.In her work at the University of Rome psychiatric clinic Dr. MonIn her work at the University of Rome psychiatric clinic Dr. Montessori developed antessori developed aninterest in the treatment of special needs children, for severalinterest in the treatment of special needs children, for several years, she worked, wrote,years, she worked, wrote,and spoke on their behalf.and spoke on their behalf.In 1907 she was given the opportunity to study "normal" childrenIn 1907 she was given the opportunity to study "normal" children, taking charge of fifty, taking charge of fiftypoor children of the dirty, desolate streets of the San Lorenzopoor children of the dirty, desolate streets of the San Lorenzo slum on the outskirts ofslum on the outskirts ofRome. The news of the unprecedented success of her work soon sprRome. The news of the unprecedented success of her work soon spread around the world,ead around the world,people coming from far & wide to see the children for themselvespeople coming from far & wide to see the children for themselves..Invited to the USA by Alexander Graham Bell, Thomas Edison, & otInvited to the USA by Alexander Graham Bell, Thomas Edison, & others, Dr. Montessorihers, Dr. Montessorispoke at Carnegie Hall in 1915.spoke at Carnegie Hall in 1915.She was invited to set up a classroom at the PanamaShe was invited to set up a classroom at the Panama--Pacific ExpositionPacific Exposition in San Francisco,in San Francisco,where spectators watched twentywhere spectators watched twenty--one children, allone children, all new to this Montessori method,new to this Montessori method,behind abehind a glass wall for four months. The only two gold medals awarded forglass wall for four months. The only two gold medals awarded for education wenteducation wentto this class. (From:to this class. (From: http://http://www.montessori.eduwww.montessori.edu).).
  62. 62. Her methodHer methodas the answer toas the answer toDrDr AbcAbc DeDe’’s questions questionThe main principles of MariaThe main principles of Maria MontesoryMontesory teaching methodteaching methodare applicable for college/university level course inare applicable for college/university level course inresearch seminar format:research seminar format:* students are not blank slates, but that they each* students are not blank slates, but that they eachhas inherent, individual gift;has inherent, individual gift;* the professor* the professor’’s job is to help students find theses job is to help students find thesegifts, rather than dictating what a student should know;gifts, rather than dictating what a student should know;* the professor has to provide a framework of* the professor has to provide a framework ofspecific discipline & encourage independence, selfspecific discipline & encourage independence, self--directed learning (+ Web), & learning from peers.directed learning (+ Web), & learning from peers.
  63. 63. Tomasello, 51, previously taughtpsychology at Emory University in Atlanta& conducted research at Atlanta’s YerkesPrimate Center. Through his studies oflearning in human children ages 1 to 4years old, as well as in chimpanzees,gorillas, & orangutans, he found that,unlike other great apes, humans arespecially adapted to learn cooperatively,even before developing language. Thiscollaborative approach to learning leadsto shared intellectual creations such aslanguage, & shared cultural creations suchas social norms &institutions..A centuryA centurylaterlaterTomaselloTomasello’’s work has clear applications in education, by highlightings work has clear applications in education, by highlighting thetheimportance of peer learningimportance of peer learning, says Anne Peterson, a psychologist at the Center, says Anne Peterson, a psychologist at the Centerfor Human Growth & Development at the University of Michigan, Anfor Human Growth & Development at the University of Michigan, Ann Arbor, &n Arbor, &the chair of the jury that awarded Tomasello the prize.the chair of the jury that awarded Tomasello the prize.
  64. 64. A centuryA centurylaterlater
  65. 65. StudentsStudentsininthetheUniversityUniversity
  66. 66. Epilogue:Epilogue:the sciencethe scienceasascommunicationcommunicationof personalitiesof personalities
  67. 67. Isitthescience?Isitthescience?
  68. 68. ““In place of scientific method, PolanyiIn place of scientific method, Polanyitrumpeted the importance oftrumpeted the importance of ““tacit knowledge.tacit knowledge.””No practicing scientist learned the craft of researchNo practicing scientist learned the craft of researchfrom books or articlesfrom books or articles, Polanyi argued. Rather,, Polanyi argued. Rather, they had tothey had topractice craftpractice craft like skills, which they internalized via sociallike skills, which they internalized via socialrelationships like apprenticeship training.relationships like apprenticeship training.Scientists often formed their beliefs from an immersion inScientists often formed their beliefs from an immersion inparticulars that resisted explicit articulation;particulars that resisted explicit articulation;he likened the experience tohe likened the experience toreligious conversion.religious conversion.To Polanyi,To Polanyi,the routines of scientific research could never bethe routines of scientific research could never becaptured by recipes,captured by recipes,& therefore any effort to steer the direction of research,& therefore any effort to steer the direction of research,or subject science to central planning, was bound to fail.or subject science to central planning, was bound to fail.””TheThe““tacit knowledgetacit knowledge””Tacit 1:Tacit 1: expressed or carried on without words or speechexpressed or carried on without words or speech2 :2 : impliedimplied or indicated (as by an act or by silence) but not actually expreor indicated (as by an act or by silence) but not actually expressedssed
  69. 69. Michael PolanyiMichael Polanyi(1891(1891 –– 19761976)Polanyi addressing the Congress ofPolanyi addressing the Congress ofCultural Freedom in Milan aboutCultural Freedom in Milan about19561956It is theIt is the social scientific communitysocial scientific community,,not a rational scientific method,not a rational scientific method,thatthat is the determining conditionis the determining condition ofofscientificscientific knowledgeknowledge..”” [M. Polanyi 1963][M. Polanyi 1963]““The system of scientificThe system of scientific knowledge isknowledge isa social systema social system of authority & apprenticeshipof authority & apprenticeship,,which imposes discipline & which values tradition,which imposes discipline & which values tradition,while teaching expert skills. In contrast to histories ofwhile teaching expert skills. In contrast to histories ofscience which emphasize the work of revolutionary heroes,science which emphasize the work of revolutionary heroes,most scientific work is accomplished within the frameworkmost scientific work is accomplished within the frameworkof beliefs or dogmas that provide the problems & answersof beliefs or dogmas that provide the problems & answersfor ordinary scientific work.for ordinary scientific work.””““Science remains objective, not in the detachmentScience remains objective, not in the detachmentof the knower from the known,of the knower from the known,but inbut in the power of sciencethe power of scienceto establish contact with a hidden realityto establish contact with a hidden realitybased in the skills & commitment of the knowerbased in the skills & commitment of the knower..””[M. Polanyi 1964][M. Polanyi 1964]
  70. 70. "In questions"In questionsof science,of science,the authority of a thousandthe authority of a thousandis not worthis not worththe humble reasoning ofthe humble reasoning ofa single individual.a single individual.““Galileo GalileiGalileo GalileiTheTheScientistScientist“A model is merely yourreflection of reality &,like probability,it describes neither younor the world,but only a relationship betweenyou & that world”Dennis Lindley
  71. 71. QuestionsQuestions
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