Student Scientific Journey

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
-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
-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
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

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
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
-2.5
-1.5
-0.5
0.5
1.5
2.5
1911
1920
1929
1938
1947
1956
1965
1974
1983
1992
2001
2010
-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
-2.0
-1.0
0.0
1.0
2.0
3.0
1911
1920
1929
1938
1947
1956
1965
1974
1983
1992
2001
2010
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

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

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

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.””

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.

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

Student Scientific Journey

Recomendados

Recomendados

Más contenido relacionado

Destacado

Destacado (10)

Similar a Student Scientific Journey

Similar a Student Scientific Journey (20)

Último

Último (20)

Student Scientific Journey