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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

Boris Shmagin, profile picture
Boris Shmagin

The document discusses the evolving role of students and the importance of active engagement in learning, particularly in scientific fields. It emphasizes the significance of computational science and statistics in understanding the variability of natural systems, specifically through the study of watersheds and hydrological data. The conclusion highlights a paradigm shift brought about by computers, which alters traditional methods and methodologies in science and calls for new approaches to data analysis and model development.

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BeingBeing a studenta student through the years:through the years: the beauty ofthe beauty of scientific results,scientific results, mathematic &mathematic & other artsother arts Feb 15,Feb 15, 20122012 ComputationalComputational Science &Science & StatisticsStatistics SeminarSeminar South DakotaSouth Dakota State UniversityState University BorisBoris ShmaginShmagin WRI SDSUWRI SDSU
~~ 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 from uncertainty 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 personalities Topics:Topics:
Introduction:Introduction: the meaning ofthe meaning of being a studentbeing a student This presentation was sparked byThis presentation was sparked by DrDr AbcAbc De questionDe question during 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?””
Teaching & learningTeaching & learning sciencescience
My UniversityMy University19651965--9696 0926199509261995
LomonosovLomonosov MoscowMoscow StateState UniversityUniversity DimaDimaGordevGordev,1980,1980
The modelsThe models used for theused for the Missouri RiverMissouri River
20062006 PresentationPresentation on theon the WesternWestern South DakotaSouth Dakota conferenceconference Apr 18, 2006Apr 18, 2006 TheThe conferenceconference presentationpresentation
VariabilityVariability as mathas math modelsmodels Presentation on the WesternPresentation on the Western South Dakota conferenceSouth Dakota conference Apr 18, 2006Apr 18, 2006
The duration curvesThe duration curves
The curveThe curve for Missourifor Missouri 103, cfs % Empirical durational curve 1911-2010 for USGS 06191500 Yellowstone River at Corwin Springs, MT The hydrograph of hydrological year for USGS 06191500 1911-2010
AnnualAnnual distributiondistribution
Structure ofStructure of the seasonalthe seasonal variabilityvariability Factor 1 Score -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) Factor 2 Score -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) Factor 3 Score -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) More thatMore that oneone dimensiondimension
Shifts in the mean for Factor 2, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 1, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 3, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Annual Hydrologic Year, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 1500 2000 2500 3000 3500 4000 4500 5000 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 InterannualInterannual seasonal regime:seasonal regime: shiftsshifts Every seasonEvery season (dimension) has(dimension) has differentdifferent shifts.shifts. Annual reflectsAnnual reflects some shiftssome shifts
ModelingModeling the regimesthe regimes 19111911--20102010 (2021)(2021) 1500.0 2500.0 3500.0 4500.0 5500.0 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 AYH [cfs] Model -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F1 Model -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F2 Model -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F3 Model
The WaveletsThe Wavelets
The WaveletsThe Wavelets
Math models &Math models & TimeTime VariabilityVariability -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F1 Model Shifts in the mean for Annual Hydrologic Year, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 1500 2000 2500 3000 3500 4000 4500 5000 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010
Annual 1500 2500 3500 4500 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) cfs Shifts in the mean for Factor 2, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 1, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 3, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Annual Hydrologic Year, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 1500 2000 2500 3000 3500 4000 4500 5000 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 To put theTo put the knowledge forknowledge for work on thework on the engineering'sengineering's goalsgoals ?? ?? ??
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 great teacherteacher —— to make you think he is uncovering your ownto make you think he is uncovering your own thought in his."thought in his."
The KnowledgeThe Knowledge of the Variabilityof the Variability for Watershedfor Watershed * The Knowledge about watershed comes only from the analysis of the empirical data (instrumental observations) * Variability has to be defined in coordinates of particular watershed; with the number of factor’s axes the annual & seasonal structure of hydrologic time & space may be presented * The math model does not have criteria to verify itself (Gödel's incompleteness theorems) & multi models & scales studies with use of empirical data have to be completed
The StatisticalThe Statistical LearningLearning
Philosophy of Data AnalysisPhilosophy of Data Analysis & the Natural Structures& the Natural Structures Factor analysis is method for extraction that are regarded as thFactor analysis is method for extraction that are regarded as the basice basic variables that account for the interrelations observed in the davariables that account for the interrelations observed in the datata A factor is a portion of a quantity, usually an integer or polynA factor is a portion of a quantity, usually an integer or polynomialomial that, when multiplied by other factors, gives the entire quantitthat, when multiplied by other factors, gives the entire quantityy The main applications ofThe main applications of factor analytic techniques are:factor analytic techniques are: •• (1) to reduce the number of(1) to reduce the number of variables andvariables and •• (2) to detect structure(2) to detect structure inin the 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
From Data AnalysisFrom Data Analysis to Statistical Learningto Statistical Learning
Statistical LearningStatistical Learning
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
Statistical LearningStatistical Learning SUMMARYSUMMARY ““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 very different 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 factsfacts that 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 thethe classical concept of science: creating generative models of evenclassical concept of science: creating generative models of events & explaints & explain--ability ofability of obtained rules.obtained rules. 4. The new paradigm introduces direct search for solution (4. The new paradigm introduces direct search for solution (transductivetransductive inference, instead ofinference, instead of inductiveinductive), the meditative principle of decision making, & a unity), the meditative principle of decision making, & a unity of 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 thee computer 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 complexityomplexity of algorithms for inference rather than complexity of the functiof algorithms for inference rather than complexity of the function that theseon that these algorithms produce.algorithms produce. Algorithms with low complexity can create a complex functionAlgorithms with low complexity can create a complex function which will generalize well.which will generalize well.””
TheThe modelmodel forfor statisticalstatistical learninglearning
The UncertaintyThe Uncertainty & Different& Different Systems of CoordinatesSystems of Coordinates Mathematical & physicalMathematical & physical objects are abstractionsobjects are abstractions && ““havehave”” the principle ofthe principle of uncertaintyuncertainty TechnologicalTechnological objects haveobjects have the errors ofthe errors of measurementmeasurement Natural objects have fuzzyNatural objects have fuzzy boundaries in their ownboundaries in their own coordinates ofcoordinates of nonstationarynonstationary axesaxes zz xx yy xx zz yy xx zz yy
The Uncertainty &The Uncertainty & Systems of CoordinatesSystems of Coordinates Natural objects may be classified inNatural objects may be classified in coordinates of multicoordinates of multi--dimensionaldimensional process & nonstationary axesprocess & nonstationary axes xx1t1t xx zz yy Natural objects have fuzzyNatural objects have fuzzy boundaries in their ownboundaries in their own coordinates of & nonstationarycoordinates of & nonstationary axesaxes xx2t2t xxitit xx zz yy
Vertical slice of the Geographical Sphere with two independent elements: System of Anthropological Geography (SAG) & System of Physical Geography (SFG). Arrows indicate vertical & horizontal components of matter, energy & information circulation (after Krcho, 1978) The Cybernetic ModelThe Cybernetic Model of theof the GeosphereGeosphere
TheThe ComponentsComponents of Landscapeof Landscape The System of Physical Geography Sphere (SFG) with five independent elements: a1- atmosphere, a2- hydrosphere, a3- lithosphere, a4- pedosphere, a5- biosphere. The elements of the Physical Geography System SFG are the Spheres Sa1, Sa2, Sa3, Sa4, Sa5 & they may be considered as Subsystems Sai (after Krcho, 1978)
The ComponentsThe Components of Landscape onof Landscape on MapMap Every Sai & Saij may be characterized by matrix of input {Wi}, matrix of output {Qi}, & matrix of states {Hi}. The System of Physical Geography Sphere (SFG) with five independent elements: a1- atmosphere, a2- hydrosphere, a3- lithosphere, a4- pedosphere, a5- biosphere Every element a1 – a5 of SFG is a System Sai & consists from units: a1(a11, a12, a13 …), a2(a21, a22 …), … a5 & those units may be considered as subsystems Saij.
{Ri} is a matrix of relations between the components of the landscape (after Krcho, 1978) Rij The StructureThe Structure of theof the RelationsRelations
{Ri} is a matrix of relations between the components of the landscape The number of characteristics for elements of landscape is unlimited & the number is unlimited for dependences too Rij The Structure of RelationsThe Structure of Relations & Reestablishment& Reestablishment of Dependencesof Dependences
The gThe g22 -- stream runoff systemstream runoff system as a part of aas a part of a22-- hydrospherehydrosphere may be presented as:may be presented as: SgSg22 = {= { ggjiji,, RRjiji },}, Any watershedAny watershed ggjiji for territory mayfor territory may be considered as a part of streambe considered as a part of stream runoff system Sgrunoff system Sg22.. c a b ggjiji Each of these components may beEach of these components may be characterized 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 of Hydrosphere (SaHydrosphere (Sa22)) with nine independentwith nine independent elements:elements: gg11-- atmosphere,atmosphere, gg22-- stream runoff filmstream runoff film (pellicle),(pellicle), gg33-- lithosphere,lithosphere, aa44-- pedosphere,pedosphere, aa55-- biospherebiosphere wherewhere ggJiJi-- watershedwatershed in specific coordinatesin specific coordinates yy Cybernetic 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) xx zz
xxitit The gThe g22 -- stream runoff systemstream runoff system as a part of aas a part of a22-- hydrospherehydrosphere may be presented as:may be presented as: SgSg22 = {= { ggjiji,, RRjiji },}, Any watershedAny watershed ggjiji for territory mayfor territory may be considered as a part of streambe considered as a part of stream runoff system Sgrunoff system Sg22.. c a b ggjiji Each of these components may beEach of these components may be characterized 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 of Hydrosphere (SaHydrosphere (Sa22)) with nine independentwith nine independent elements:elements: gg11-- atmosphere,atmosphere, gg22-- stream runoff filmstream runoff film (pellicle),(pellicle), gg33-- lithosphere,lithosphere, aa44-- pedosphere,pedosphere, aa55-- biospherebiosphere wherewhere ggJiJi-- watershedwatershed in specific coordinatesin specific coordinates yy The Watershed inThe Watershed in Multidimensional System ofMultidimensional System of Coordinate with DiversityCoordinate with Diversity LandscapesLandscapes xx zzxxitit xxitit
EducationEducation as communication onas communication on the movement fromthe movement from Uncertainty to theUncertainty to the KnowledgeKnowledge
The KnowledgeThe Knowledge Bertrand Russell “Human Knowledge. Its Scope & Limits.” 1948 ““I. THE DEFINITION OF KNOWLEDGEI. THE DEFINITION OF KNOWLEDGE The 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 the three 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 thought that 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. The trouble 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 knows what 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 DATA Animal Inference. Mental & Physical Data.Animal Inference. Mental & Physical Data. III. METHODS OF INFERENCEIII. METHODS OF INFERENCE Induction. Probability. Limitation of Variety. Grades of CertainInduction. Probability. Limitation of Variety. Grades of Certainty.ty.”” The book has sixThe book has six parts, & the partparts, & the part namednamed ““LanguageLanguage”” isis the biggest one withthe biggest one with eleven chapterseleven chapters
TheThe UncertaintyUncertainty LotfiLotfi 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 of Electrical Engineering & Computer SciencesElectrical Engineering & Computer Sciences Director, Berkeley Initiative in SoftDirector, Berkeley Initiative in Soft Computing University of CaliforniaComputing University of California Berkeley, CA 94720Berkeley, CA 94720 --17761776
Zadeh:Zadeh: the fuzzy logicthe fuzzy logic
(The)(The) UncertaintyUncertainty““Uncertainty is a personalUncertainty is a personal matter; it is notmatter; it is not thethe uncertainty butuncertainty but youryour uncertainty.uncertainty.”” Dennis LindleyDennis Lindley (2006)(2006) UnderstandingUnderstanding UncertaintyUncertainty Dennis 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
There is part ofThere is part of science looking in thescience looking in the coinscoins TheThe modelmodel
TheThe modelmodel
Statistics & UncertaintyStatistics & Uncertainty The statistician's task isThe statistician's task is to articulate theto articulate the scientist's uncertaintiesscientist's uncertainties in thein the languagelanguage ofof probabilityprobability…… A model is merely yourA model is merely your reflection of reality &,reflection of reality &, like probability,like probability, it describes neither youit describes neither you nor the world,nor the world, but only a relationshipbut only a relationship between 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 are needed 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 'you''you' of the analysis is the client, not the statistician.of the analysis is the client, not the statistician.”” (p. 318)(p. 318)
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 material's 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)
The UncertaintyThe Uncertainty & Information& Information
The Science &The Science & the Languagethe Language [In linguistic] ...[In linguistic] ... ““the proper object of studythe proper object of study waswas the speaker'sthe speaker's underlyingunderlying knowledge of the languageknowledge of the language,, his "linguistic competence"his "linguistic competence" that enables him to producethat enables him to produce & understand sentences& understand sentences he has never heard beforehe has never heard before”” From:From: "Chomsky's Revolution"Chomsky's Revolution In Linguistics"In Linguistics" by John R. Searleby John R. Searle The New York Review of Books,The New York Review of Books, June 29, 1972June 29, 1972
EvolutionEvolution CommunicationCommunication & language& language
Information in theInformation in the LanguageLanguage ““In cognitive linguistics asIn cognitive linguistics as in cognitive science, the humanin cognitive science, the human mind is considered to be anmind is considered to be an informationinformation--processing deviceprocessing device ((StillingsStillings 1995),1995), & language is viewed as& language is viewed as a vehicle for communicatinga vehicle for communicating information.information.”” From: J. Van deFrom: J. Van de WalleWalle, 2008, 2008 Six communication functions distinguished by Jakobson, (from Wiki)
LearningLearning ConceptConcept
The Uncertainty & The KnowledgeThe Uncertainty & The Knowledge through Modeling: Object,through Modeling: Object, Data, Analysis & ResultsData, Analysis & Results Photo picture Photo picture as presentation as presentation of the natural of the natural objectobject The conceptual model The conceptual model (Cybernetic Model) (Cybernetic Model) is the way to use is the way to use previously obtained previously obtained KnowledgeKnowledge The knowledge (K)= 0,The knowledge (K)= 0, about a new object forabout a new object for the considerationthe consideration the uncertainty (U)= 1the uncertainty (U)= 1 KKpp = 1 & we have the= 1 & we have the direction for thedirection for the research, the task,research, the task, U = 0, but theU = 0, but the Knowledge isKnowledge is previous (previous (KKpp)) The Statistical LearningThe Statistical Learning is the way to obtainis the way to obtain ((““extractextract””) the structure) the structure of a natural objectof a natural object AfterAfter StatisticalStatistical LearningLearning K > UK > U The Uncertainty from The Uncertainty from Analysis obtained for Analysis obtained for every model.every model. For Factor Analysis For Factor AnalysisU=1U=1-- explained variability explained variability
The Uncertainty & The KnowledgeThe Uncertainty & The Knowledge through Modeling: Object,through Modeling: Object, Data, Analysis & ResultsData, Analysis & Results Photo picture Photo picture as presentation as presentation of the natural of the natural objectobject The conceptual model The conceptual model (Cybernetic Model) (Cybernetic Model) is the way to use is the way to use previously obtained previously obtained KnowledgeKnowledge The knowledge (K)= 0,The knowledge (K)= 0, about a new object forabout a new object for the considerationthe consideration the uncertainty (U)= 1the uncertainty (U)= 1 KKpp = 1 & we have the= 1 & we have the direction for thedirection for the research, the task,research, the task, U = 0, but theU = 0, but the Knowledge isKnowledge is previous (previous (KKpp)) The Statistical LearningThe Statistical Learning is the way to obtainis the way to obtain ((““extractextract””) the structure) the structure of a natural objectof a natural object AfterAfter StatisticalStatistical LearningLearning K > UK > U The Uncertainty from The Uncertainty from Analysis obtained for Analysis obtained for every model.every model. For Factor Analysis For Factor AnalysisU=1U=1-- explained variability explained variability
Communicating theCommunicating the Knowledge for theKnowledge for the WatershedWatershed ScientistScientist working inworking in Hydrology haveHydrology have to handle theto handle the Uncertainty &Uncertainty & communicatecommunicate the Knowledgethe Knowledge aboutabout timetime--spatialspatial variability ofvariability of the Watershedthe Watershed characteristicscharacteristics
““VitruvianVitruvian ManMan””Albert Einstein wrote that the mind “always has tried to form for itself a simple & synoptic image of the surrounding world.” During the Renaissance, when the ancient Greek idea of man as the measure of all things leapt to the forefront of intellectual life, the human body became a preferred object for this type of “synoptic” speculation. … “Vitruvian Man” ultimately offers a “synoptic image” of the Renaissance itself. Leonardo’s most famous images, “Vitruvian Man” (circa 1490).
““VitruvianVitruvian ManMan”” The ancient Roman engineerThe ancient Roman engineer Vitruvius 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 the principle relating the members of aprinciple relating the members of a wellwell--shaped man.shaped man.”” He thenHe then enumerated the ideal proportions ofenumerated the ideal proportions of the male physique & posited that athe male physique & posited that a manman’’s outstretched body could bes outstretched body could be made 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.””
OurOur UniversityUniversity
RaphaelRaphael (1509(1509--1510)1510) Fresco (500*770 cm) Vatican City, Apostolic PalaceFresco (500*770 cm) Vatican City, Apostolic Palace The School of Athens:The School of Athens: all togetherall together ““Sky is limitSky is limit”” there were people in SDthere were people in SD who saw the connectionswho saw the connections
““VitruvianVitruvian ManMan”” … “Vitruvian Man” ultimately offers a “synoptic image” of the Renaissance itself. Before the Pacioli collaboration, the idea had inspired what has since become one of Leonardo’s most famous images, “Vitruvian Man” (circa 1490), a careful line drawing of a nude male figure whose outstretched arms and legs 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 engineer Vitruvius opined in his magnum opus, “Ten Books on Architecture” (circa 25 B.C.), that a temple cannot be built properly “unless it conforms exactly to the principle relating the members of a well-shaped man.” He then enumerated the ideal proportions of the male physique and posited that a man’s outstretched body could be made to fit within a circle and a square. “Ancient philosophers, mathematicians and mystics had long invested those two shapes with special symbolic powers,” Lester writes. “The circle represented the cosmic and the divine; the square represented the earthly and the secular.”
Renaissance of our daysRenaissance of our days In the search ofIn the search of thethe ““EnlightenmentEnlightenment’’ss”” imageimage
Maria MontessoriMaria Montessori (1870(1870--1952)1952) Scientific observation has established thatScientific observation has established that education is not what the teacher gives;education is not what the teacher gives; education is a natural process spontaneouslyeducation is a natural process spontaneously carried 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 by experiences upon the environment.experiences upon the environment. The task of the teacher becomes that ofThe task of the teacher becomes that of preparing a series of motives of culturalpreparing a series of motives of cultural activity, spread over a specially preparedactivity, spread over a specially prepared environment, & then refraining from obtrusiveenvironment, & then refraining from obtrusive interference. Humaninterference. Human teachers can only helpteachers can only help the great work that is being done, as servantsthe great work that is being done, as servants help the master.help the master. Doing soDoing so, they will be witnesses to the, they will be witnesses to the unfolding of the human soul & to the risingunfolding of the human soul & to the rising of a New Manof a New Man who will not be a victim ofwho will not be a victim of events, but will have the clarity of vision toevents, but will have the clarity of vision to direct & 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””
Few biographical factsFew biographical facts Maria 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 receive a 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 an interest 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 fifty poor 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 of Rome. 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. Montessori spoke 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 went to this class. (From:to this class. (From: http://http://www.montessori.eduwww.montessori.edu).).
Her methodHer method as the answer toas the answer to DrDr AbcAbc DeDe’’s questions question The main principles of MariaThe main principles of Maria MontesoryMontesory teaching methodteaching method are applicable for college/university level course inare applicable for college/university level course in research seminar format:research seminar format: * students are not blank slates, but that they each* students are not blank slates, but that they each has 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 these gifts, 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 of specific discipline & encourage independence, selfspecific discipline & encourage independence, self-- directed learning (+ Web), & learning from peers.directed learning (+ Web), & learning from peers.
Tomasello, 51, previously taught psychology at Emory University in Atlanta & conducted research at Atlanta’s Yerkes Primate Center. Through his studies of learning in human children ages 1 to 4 years old, as well as in chimpanzees, gorillas, & orangutans, he found that, unlike other great apes, humans are specially adapted to learn cooperatively, even before developing language. This collaborative approach to learning leads to shared intellectual creations such as language, & shared cultural creations such as social norms &institutions.. A centuryA century laterlater TomaselloTomasello’’s work has clear applications in education, by highlightings work has clear applications in education, by highlighting thethe importance of peer learningimportance of peer learning, says Anne Peterson, a psychologist at the Center, says Anne Peterson, a psychologist at the Center for 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.
A centuryA century laterlater
StudentsStudents inin thethe UniversityUniversity
Epilogue:Epilogue: the sciencethe science asas communicationcommunication of personalitiesof personalities
Isitthescience?Isitthescience?
““In place of scientific method, PolanyiIn place of scientific method, Polanyi trumpeted the importance oftrumpeted the importance of ““tacit knowledge.tacit knowledge.”” No practicing scientist learned the craft of researchNo practicing scientist learned the craft of research from books or articlesfrom books or articles, Polanyi argued. Rather,, Polanyi argued. Rather, they had tothey had to practice craftpractice craft like skills, which they internalized via sociallike skills, which they internalized via social relationships like apprenticeship training.relationships like apprenticeship training. Scientists often formed their beliefs from an immersion inScientists often formed their beliefs from an immersion in particulars that resisted explicit articulation;particulars that resisted explicit articulation; he likened the experience tohe likened the experience to religious conversion.religious conversion. To Polanyi,To Polanyi, the routines of scientific research could never bethe routines of scientific research could never be captured 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 speech 2 :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
Michael PolanyiMichael Polanyi (1891(1891 –– 19761976) Polanyi addressing the Congress ofPolanyi addressing the Congress of Cultural Freedom in Milan aboutCultural Freedom in Milan about 19561956 It 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 ofof scientificscientific knowledgeknowledge..”” [M. Polanyi 1963][M. Polanyi 1963] ““The system of scientificThe system of scientific knowledge isknowledge is a 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 of science 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 framework of beliefs or dogmas that provide the problems & answersof beliefs or dogmas that provide the problems & answers for ordinary scientific work.for ordinary scientific work.”” ““Science remains objective, not in the detachmentScience remains objective, not in the detachment of the knower from the known,of the knower from the known, but inbut in the power of sciencethe power of science to establish contact with a hidden realityto establish contact with a hidden reality based in the skills & commitment of the knowerbased in the skills & commitment of the knower..”” [M. Polanyi 1964][M. Polanyi 1964]
"In questions"In questions of science,of science, the authority of a thousandthe authority of a thousand is not worthis not worth the humble reasoning ofthe humble reasoning of a single individual.a single individual.““ Galileo GalileiGalileo Galilei TheThe Scientist Scientist “A model is merely your reflection of reality &, like probability, it describes neither you nor the world, but only a relationship between you & that world” Dennis Lindley
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

  • 1. BeingBeing a studenta student through the years:through the years: the beauty ofthe beauty of scientific results,scientific results, mathematic &mathematic & other artsother arts Feb 15,Feb 15, 20122012 ComputationalComputational Science &Science & StatisticsStatistics SeminarSeminar South DakotaSouth Dakota State UniversityState University BorisBoris ShmaginShmagin WRI SDSUWRI SDSU
  • 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 from uncertainty 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 personalities Topics:Topics:
  • 3. Introduction:Introduction: the meaning ofthe meaning of being a studentbeing a student This presentation was sparked byThis presentation was sparked by DrDr AbcAbc De questionDe question during 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. Teaching & learningTeaching & learning sciencescience
  • 7. The modelsThe models used for theused for the Missouri RiverMissouri River
  • 8. 20062006 PresentationPresentation on theon the WesternWestern South DakotaSouth Dakota conferenceconference Apr 18, 2006Apr 18, 2006 TheThe conferenceconference presentationpresentation
  • 9. VariabilityVariability as mathas math modelsmodels Presentation on the WesternPresentation on the Western South Dakota conferenceSouth Dakota conference Apr 18, 2006Apr 18, 2006
  • 10. The duration curvesThe duration curves
  • 11. The curveThe curve for Missourifor Missouri 103, cfs % Empirical durational curve 1911-2010 for USGS 06191500 Yellowstone River at Corwin Springs, MT The hydrograph of hydrological year for USGS 06191500 1911-2010
  • 13. Structure ofStructure of the seasonalthe seasonal variabilityvariability Factor 1 Score -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) Factor 2 Score -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) Factor 3 Score -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) More thatMore that oneone dimensiondimension
  • 14. Shifts in the mean for Factor 2, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 1, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 3, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Annual Hydrologic Year, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 1500 2000 2500 3000 3500 4000 4500 5000 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 InterannualInterannual seasonal regime:seasonal regime: shiftsshifts Every seasonEvery season (dimension) has(dimension) has differentdifferent shifts.shifts. Annual reflectsAnnual reflects some shiftssome shifts
  • 15. ModelingModeling the regimesthe regimes 19111911--20102010 (2021)(2021) 1500.0 2500.0 3500.0 4500.0 5500.0 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 AYH [cfs] Model -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F1 Model -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F2 Model -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F3 Model
  • 18. Math models &Math models & TimeTime VariabilityVariability -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011 2021 F1 Model Shifts in the mean for Annual Hydrologic Year, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 1500 2000 2500 3000 3500 4000 4500 5000 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010
  • 19. Annual 1500 2500 3500 4500 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Year (Hydr) cfs Shifts in the mean for Factor 2, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.5 -1.5 -0.5 0.5 1.5 2.5 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 1, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Factor 3, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 -2.0 -1.0 0.0 1.0 2.0 3.0 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 Shifts in the mean for Annual Hydrologic Year, 1911-2010 Probability = 0.1, cutoff length = 10, Huber parameter = 1 1500 2000 2500 3000 3500 4000 4500 5000 5500 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001 2010 To put theTo put the knowledge forknowledge for work on thework on the engineering'sengineering's goalsgoals ?? ?? ??
  • 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 great teacherteacher —— to make you think he is uncovering your ownto make you think he is uncovering your own thought in his."thought in his."
  • 21. The KnowledgeThe Knowledge of the Variabilityof the Variability for Watershedfor Watershed * The Knowledge about watershed comes only from the analysis of the empirical data (instrumental observations) * Variability has to be defined in coordinates of particular watershed; with the number of factor’s axes the annual & seasonal structure of hydrologic time & space may be presented * The math model does not have criteria to verify itself (Gödel's incompleteness theorems) & multi models & scales studies with use of empirical data have to be completed
  • 23. Philosophy of Data AnalysisPhilosophy of Data Analysis & the Natural Structures& the Natural Structures Factor analysis is method for extraction that are regarded as thFactor analysis is method for extraction that are regarded as the basice basic variables that account for the interrelations observed in the davariables that account for the interrelations observed in the datata A factor is a portion of a quantity, usually an integer or polynA factor is a portion of a quantity, usually an integer or polynomialomial that, when multiplied by other factors, gives the entire quantitthat, when multiplied by other factors, gives the entire quantityy The main applications ofThe main applications of factor analytic techniques are:factor analytic techniques are: •• (1) to reduce the number of(1) to reduce the number of variables andvariables and •• (2) to detect structure(2) to detect structure inin the 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. From Data AnalysisFrom Data Analysis to Statistical Learningto Statistical Learning
  • 27. Statistical LearningStatistical Learning SUMMARYSUMMARY ““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 very different 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 factsfacts that 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 thethe classical concept of science: creating generative models of evenclassical concept of science: creating generative models of events & explaints & explain--ability ofability of obtained rules.obtained rules. 4. The new paradigm introduces direct search for solution (4. The new paradigm introduces direct search for solution (transductivetransductive inference, instead ofinference, instead of inductiveinductive), the meditative principle of decision making, & a unity), the meditative principle of decision making, & a unity of 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 thee computer 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 complexityomplexity of algorithms for inference rather than complexity of the functiof algorithms for inference rather than complexity of the function that theseon that these algorithms produce.algorithms produce. Algorithms with low complexity can create a complex functionAlgorithms with low complexity can create a complex function which will generalize well.which will generalize well.””
  • 29. The UncertaintyThe Uncertainty & Different& Different Systems of CoordinatesSystems of Coordinates Mathematical & physicalMathematical & physical objects are abstractionsobjects are abstractions && ““havehave”” the principle ofthe principle of uncertaintyuncertainty TechnologicalTechnological objects haveobjects have the errors ofthe errors of measurementmeasurement Natural objects have fuzzyNatural objects have fuzzy boundaries in their ownboundaries in their own coordinates ofcoordinates of nonstationarynonstationary axesaxes zz xx yy xx zz yy xx zz yy
  • 30. The Uncertainty &The Uncertainty & Systems of CoordinatesSystems of Coordinates Natural objects may be classified inNatural objects may be classified in coordinates of multicoordinates of multi--dimensionaldimensional process & nonstationary axesprocess & nonstationary axes xx1t1t xx zz yy Natural objects have fuzzyNatural objects have fuzzy boundaries in their ownboundaries in their own coordinates of & nonstationarycoordinates of & nonstationary axesaxes xx2t2t xxitit xx zz yy
  • 31. Vertical slice of the Geographical Sphere with two independent elements: System of Anthropological Geography (SAG) & System of Physical Geography (SFG). Arrows indicate vertical & horizontal components of matter, energy & information circulation (after Krcho, 1978) The Cybernetic ModelThe Cybernetic Model of theof the GeosphereGeosphere
  • 32. TheThe ComponentsComponents of Landscapeof Landscape The System of Physical Geography Sphere (SFG) with five independent elements: a1- atmosphere, a2- hydrosphere, a3- lithosphere, a4- pedosphere, a5- biosphere. The elements of the Physical Geography System SFG are the Spheres Sa1, Sa2, Sa3, Sa4, Sa5 & they may be considered as Subsystems Sai (after Krcho, 1978)
  • 33. The ComponentsThe Components of Landscape onof Landscape on MapMap Every Sai & Saij may be characterized by matrix of input {Wi}, matrix of output {Qi}, & matrix of states {Hi}. The System of Physical Geography Sphere (SFG) with five independent elements: a1- atmosphere, a2- hydrosphere, a3- lithosphere, a4- pedosphere, a5- biosphere Every element a1 – a5 of SFG is a System Sai & consists from units: a1(a11, a12, a13 …), a2(a21, a22 …), … a5 & those units may be considered as subsystems Saij.
  • 34. {Ri} is a matrix of relations between the components of the landscape (after Krcho, 1978) Rij The StructureThe Structure of theof the RelationsRelations
  • 35. {Ri} is a matrix of relations between the components of the landscape The number of characteristics for elements of landscape is unlimited & the number is unlimited for dependences too Rij The Structure of RelationsThe Structure of Relations & Reestablishment& Reestablishment of Dependencesof Dependences
  • 36. The gThe g22 -- stream runoff systemstream runoff system as a part of aas a part of a22-- hydrospherehydrosphere may be presented as:may be presented as: SgSg22 = {= { ggjiji,, RRjiji },}, Any watershedAny watershed ggjiji for territory mayfor territory may be considered as a part of streambe considered as a part of stream runoff system Sgrunoff system Sg22.. c a b ggjiji Each of these components may beEach of these components may be characterized 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 of Hydrosphere (SaHydrosphere (Sa22)) with nine independentwith nine independent elements:elements: gg11-- atmosphere,atmosphere, gg22-- stream runoff filmstream runoff film (pellicle),(pellicle), gg33-- lithosphere,lithosphere, aa44-- pedosphere,pedosphere, aa55-- biospherebiosphere wherewhere ggJiJi-- watershedwatershed in specific coordinatesin specific coordinates yy Cybernetic 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) xx zz
  • 37. xxitit The gThe g22 -- stream runoff systemstream runoff system as a part of aas a part of a22-- hydrospherehydrosphere may be presented as:may be presented as: SgSg22 = {= { ggjiji,, RRjiji },}, Any watershedAny watershed ggjiji for territory mayfor territory may be considered as a part of streambe considered as a part of stream runoff system Sgrunoff system Sg22.. c a b ggjiji Each of these components may beEach of these components may be characterized 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 of Hydrosphere (SaHydrosphere (Sa22)) with nine independentwith nine independent elements:elements: gg11-- atmosphere,atmosphere, gg22-- stream runoff filmstream runoff film (pellicle),(pellicle), gg33-- lithosphere,lithosphere, aa44-- pedosphere,pedosphere, aa55-- biospherebiosphere wherewhere ggJiJi-- watershedwatershed in specific coordinatesin specific coordinates yy The Watershed inThe Watershed in Multidimensional System ofMultidimensional System of Coordinate with DiversityCoordinate with Diversity LandscapesLandscapes xx zzxxitit xxitit
  • 38. EducationEducation as communication onas communication on the movement fromthe movement from Uncertainty to theUncertainty to the KnowledgeKnowledge
  • 39. The KnowledgeThe Knowledge Bertrand Russell “Human Knowledge. Its Scope & Limits.” 1948 ““I. THE DEFINITION OF KNOWLEDGEI. THE DEFINITION OF KNOWLEDGE The 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 the three 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 thought that 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. The trouble 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 knows what 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 DATA Animal Inference. Mental & Physical Data.Animal Inference. Mental & Physical Data. III. METHODS OF INFERENCEIII. METHODS OF INFERENCE Induction. Probability. Limitation of Variety. Grades of CertainInduction. Probability. Limitation of Variety. Grades of Certainty.ty.”” The book has sixThe book has six parts, & the partparts, & the part namednamed ““LanguageLanguage”” isis the biggest one withthe biggest one with eleven chapterseleven chapters
  • 40. TheThe UncertaintyUncertainty LotfiLotfi 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 of Electrical Engineering & Computer SciencesElectrical Engineering & Computer Sciences Director, Berkeley Initiative in SoftDirector, Berkeley Initiative in Soft Computing University of CaliforniaComputing University of California Berkeley, CA 94720Berkeley, CA 94720 --17761776
  • 42. (The)(The) UncertaintyUncertainty““Uncertainty is a personalUncertainty is a personal matter; it is notmatter; it is not thethe uncertainty butuncertainty but youryour uncertainty.uncertainty.”” Dennis LindleyDennis Lindley (2006)(2006) UnderstandingUnderstanding UncertaintyUncertainty Dennis 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
  • 43. There is part ofThere is part of science looking in thescience looking in the coinscoins TheThe modelmodel
  • 45. Statistics & UncertaintyStatistics & Uncertainty The statistician's task isThe statistician's task is to articulate theto articulate the scientist's uncertaintiesscientist's uncertainties in thein the languagelanguage ofof probabilityprobability…… A model is merely yourA model is merely your reflection of reality &,reflection of reality &, like probability,like probability, it describes neither youit describes neither you nor the world,nor the world, but only a relationshipbut only a relationship between 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 are needed 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 'you''you' of the analysis is the client, not the statistician.of the analysis is the client, not the statistician.”” (p. 318)(p. 318)
  • 46. 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 material's 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)
  • 47. The UncertaintyThe Uncertainty & Information& Information
  • 48. The Science &The Science & the Languagethe Language [In linguistic] ...[In linguistic] ... ““the proper object of studythe proper object of study waswas the speaker'sthe speaker's underlyingunderlying knowledge of the languageknowledge of the language,, his "linguistic competence"his "linguistic competence" that enables him to producethat enables him to produce & understand sentences& understand sentences he has never heard beforehe has never heard before”” From:From: "Chomsky's Revolution"Chomsky's Revolution In Linguistics"In Linguistics" by John R. Searleby John R. Searle The New York Review of Books,The New York Review of Books, June 29, 1972June 29, 1972
  • 50. Information in theInformation in the LanguageLanguage ““In cognitive linguistics asIn cognitive linguistics as in cognitive science, the humanin cognitive science, the human mind is considered to be anmind is considered to be an informationinformation--processing deviceprocessing device ((StillingsStillings 1995),1995), & language is viewed as& language is viewed as a vehicle for communicatinga vehicle for communicating information.information.”” From: J. Van deFrom: J. Van de WalleWalle, 2008, 2008 Six communication functions distinguished by Jakobson, (from Wiki)
  • 52. The Uncertainty & The KnowledgeThe Uncertainty & The Knowledge through Modeling: Object,through Modeling: Object, Data, Analysis & ResultsData, Analysis & Results Photo picture Photo picture as presentation as presentation of the natural of the natural objectobject The conceptual model The conceptual model (Cybernetic Model) (Cybernetic Model) is the way to use is the way to use previously obtained previously obtained KnowledgeKnowledge The knowledge (K)= 0,The knowledge (K)= 0, about a new object forabout a new object for the considerationthe consideration the uncertainty (U)= 1the uncertainty (U)= 1 KKpp = 1 & we have the= 1 & we have the direction for thedirection for the research, the task,research, the task, U = 0, but theU = 0, but the Knowledge isKnowledge is previous (previous (KKpp)) The Statistical LearningThe Statistical Learning is the way to obtainis the way to obtain ((““extractextract””) the structure) the structure of a natural objectof a natural object AfterAfter StatisticalStatistical LearningLearning K > UK > U The Uncertainty from The Uncertainty from Analysis obtained for Analysis obtained for every model.every model. For Factor Analysis For Factor AnalysisU=1U=1-- explained variability explained variability
  • 53. The Uncertainty & The KnowledgeThe Uncertainty & The Knowledge through Modeling: Object,through Modeling: Object, Data, Analysis & ResultsData, Analysis & Results Photo picture Photo picture as presentation as presentation of the natural of the natural objectobject The conceptual model The conceptual model (Cybernetic Model) (Cybernetic Model) is the way to use is the way to use previously obtained previously obtained KnowledgeKnowledge The knowledge (K)= 0,The knowledge (K)= 0, about a new object forabout a new object for the considerationthe consideration the uncertainty (U)= 1the uncertainty (U)= 1 KKpp = 1 & we have the= 1 & we have the direction for thedirection for the research, the task,research, the task, U = 0, but theU = 0, but the Knowledge isKnowledge is previous (previous (KKpp)) The Statistical LearningThe Statistical Learning is the way to obtainis the way to obtain ((““extractextract””) the structure) the structure of a natural objectof a natural object AfterAfter StatisticalStatistical LearningLearning K > UK > U The Uncertainty from The Uncertainty from Analysis obtained for Analysis obtained for every model.every model. For Factor Analysis For Factor AnalysisU=1U=1-- explained variability explained variability
  • 54. Communicating theCommunicating the Knowledge for theKnowledge for the WatershedWatershed ScientistScientist working inworking in Hydrology haveHydrology have to handle theto handle the Uncertainty &Uncertainty & communicatecommunicate the Knowledgethe Knowledge aboutabout timetime--spatialspatial variability ofvariability of the Watershedthe Watershed characteristicscharacteristics
  • 55. ““VitruvianVitruvian ManMan””Albert Einstein wrote that the mind “always has tried to form for itself a simple & synoptic image of the surrounding world.” During the Renaissance, when the ancient Greek idea of man as the measure of all things leapt to the forefront of intellectual life, the human body became a preferred object for this type of “synoptic” speculation. … “Vitruvian Man” ultimately offers a “synoptic image” of the Renaissance itself. Leonardo’s most famous images, “Vitruvian Man” (circa 1490).
  • 56. ““VitruvianVitruvian ManMan”” The ancient Roman engineerThe ancient Roman engineer Vitruvius 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 the principle relating the members of aprinciple relating the members of a wellwell--shaped man.shaped man.”” He thenHe then enumerated the ideal proportions ofenumerated the ideal proportions of the male physique & posited that athe male physique & posited that a manman’’s outstretched body could bes outstretched body could be made 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.””
  • 58. RaphaelRaphael (1509(1509--1510)1510) Fresco (500*770 cm) Vatican City, Apostolic PalaceFresco (500*770 cm) Vatican City, Apostolic Palace The School of Athens:The School of Athens: all togetherall together ““Sky is limitSky is limit”” there were people in SDthere were people in SD who saw the connectionswho saw the connections
  • 59. ““VitruvianVitruvian ManMan”” … “Vitruvian Man” ultimately offers a “synoptic image” of the Renaissance itself. Before the Pacioli collaboration, the idea had inspired what has since become one of Leonardo’s most famous images, “Vitruvian Man” (circa 1490), a careful line drawing of a nude male figure whose outstretched arms and legs 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 engineer Vitruvius opined in his magnum opus, “Ten Books on Architecture” (circa 25 B.C.), that a temple cannot be built properly “unless it conforms exactly to the principle relating the members of a well-shaped man.” He then enumerated the ideal proportions of the male physique and posited that a man’s outstretched body could be made to fit within a circle and a square. “Ancient philosophers, mathematicians and mystics had long invested those two shapes with special symbolic powers,” Lester writes. “The circle represented the cosmic and the divine; the square represented the earthly and the secular.”
  • 60. Renaissance of our daysRenaissance of our days In the search ofIn the search of thethe ““EnlightenmentEnlightenment’’ss”” imageimage
  • 61. Maria MontessoriMaria Montessori (1870(1870--1952)1952) Scientific observation has established thatScientific observation has established that education is not what the teacher gives;education is not what the teacher gives; education is a natural process spontaneouslyeducation is a natural process spontaneously carried 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 by experiences upon the environment.experiences upon the environment. The task of the teacher becomes that ofThe task of the teacher becomes that of preparing a series of motives of culturalpreparing a series of motives of cultural activity, spread over a specially preparedactivity, spread over a specially prepared environment, & then refraining from obtrusiveenvironment, & then refraining from obtrusive interference. Humaninterference. Human teachers can only helpteachers can only help the great work that is being done, as servantsthe great work that is being done, as servants help the master.help the master. Doing soDoing so, they will be witnesses to the, they will be witnesses to the unfolding of the human soul & to the risingunfolding of the human soul & to the rising of a New Manof a New Man who will not be a victim ofwho will not be a victim of events, but will have the clarity of vision toevents, but will have the clarity of vision to direct & 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””
  • 62. Few biographical factsFew biographical facts Maria 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 receive a 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 an interest 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 fifty poor 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 of Rome. 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. Montessori spoke 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 went to this class. (From:to this class. (From: http://http://www.montessori.eduwww.montessori.edu).).
  • 63. Her methodHer method as the answer toas the answer to DrDr AbcAbc DeDe’’s questions question The main principles of MariaThe main principles of Maria MontesoryMontesory teaching methodteaching method are applicable for college/university level course inare applicable for college/university level course in research seminar format:research seminar format: * students are not blank slates, but that they each* students are not blank slates, but that they each has 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 these gifts, 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 of specific discipline & encourage independence, selfspecific discipline & encourage independence, self-- directed learning (+ Web), & learning from peers.directed learning (+ Web), & learning from peers.
  • 64. Tomasello, 51, previously taught psychology at Emory University in Atlanta & conducted research at Atlanta’s Yerkes Primate Center. Through his studies of learning in human children ages 1 to 4 years old, as well as in chimpanzees, gorillas, & orangutans, he found that, unlike other great apes, humans are specially adapted to learn cooperatively, even before developing language. This collaborative approach to learning leads to shared intellectual creations such as language, & shared cultural creations such as social norms &institutions.. A centuryA century laterlater TomaselloTomasello’’s work has clear applications in education, by highlightings work has clear applications in education, by highlighting thethe importance of peer learningimportance of peer learning, says Anne Peterson, a psychologist at the Center, says Anne Peterson, a psychologist at the Center for 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.
  • 69. ““In place of scientific method, PolanyiIn place of scientific method, Polanyi trumpeted the importance oftrumpeted the importance of ““tacit knowledge.tacit knowledge.”” No practicing scientist learned the craft of researchNo practicing scientist learned the craft of research from books or articlesfrom books or articles, Polanyi argued. Rather,, Polanyi argued. Rather, they had tothey had to practice craftpractice craft like skills, which they internalized via sociallike skills, which they internalized via social relationships like apprenticeship training.relationships like apprenticeship training. Scientists often formed their beliefs from an immersion inScientists often formed their beliefs from an immersion in particulars that resisted explicit articulation;particulars that resisted explicit articulation; he likened the experience tohe likened the experience to religious conversion.religious conversion. To Polanyi,To Polanyi, the routines of scientific research could never bethe routines of scientific research could never be captured 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 speech 2 :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
  • 70. Michael PolanyiMichael Polanyi (1891(1891 –– 19761976) Polanyi addressing the Congress ofPolanyi addressing the Congress of Cultural Freedom in Milan aboutCultural Freedom in Milan about 19561956 It 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 ofof scientificscientific knowledgeknowledge..”” [M. Polanyi 1963][M. Polanyi 1963] ““The system of scientificThe system of scientific knowledge isknowledge is a 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 of science 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 framework of beliefs or dogmas that provide the problems & answersof beliefs or dogmas that provide the problems & answers for ordinary scientific work.for ordinary scientific work.”” ““Science remains objective, not in the detachmentScience remains objective, not in the detachment of the knower from the known,of the knower from the known, but inbut in the power of sciencethe power of science to establish contact with a hidden realityto establish contact with a hidden reality based in the skills & commitment of the knowerbased in the skills & commitment of the knower..”” [M. Polanyi 1964][M. Polanyi 1964]
  • 71. "In questions"In questions of science,of science, the authority of a thousandthe authority of a thousand is not worthis not worth the humble reasoning ofthe humble reasoning of a single individual.a single individual.““ Galileo GalileiGalileo Galilei TheThe Scientist Scientist “A model is merely your reflection of reality &, like probability, it describes neither you nor the world, but only a relationship between you & that world” Dennis Lindley