1.0:Feynman's question
$\qquad$von Neuman, Einstein
1.1:Quantum language
$\qquad$Dsecartes, the philosophy of probability and statistics, the philosophy of quantum mechanics,
1.2(1):Axioms 1 and 2 (measurement and causality ) and interpretation
$\qquad$measurement, causal relation, Lord Kelvin, metaphysics, Descartes=Kant philosophy,
1.2(2):Linguistic interpretation
$\qquad$the interpretation of quantum mechanics, cookbook, Kolmogorov's extension theorem,
1.2(3):Summary
$\qquad$Kant, a priori judgment, sell, continental rationlism, British empiricism,
1.3:Example (Hot or Cold?)
$\qquad$ translation from ordinary language to quantum language
2.0: Axiom 1( measurement ); Abstract
$\qquad$ Newtonian mechanics, von Neumann's "Mathematical foundations of quantum mechanics"
2.1: Basic structure $[{\mathcal A} \subseteq$ $ \overline{\mathcal A} \subseteq B(H)]$( General Theory)
$\qquad$ Newtonian mechanics, von Neumann's "Mathematical foundations of quantum mechanics", Hilbert space, operator algebra, basic structure,
2.2: Quantum basic structure $[{\mathcal C}(H) \subseteq$ $ B(H) \subseteq B(H)]$
$\qquad$ Dirac notation, complete orthonormal sysyte, trace operator, compact operator,
2.3: Classical basic structure $[C_0(\Omega ) \subseteq$ $ L^\infty ( \Omega, \nu ) \subseteq B(H)]$
$\qquad$ commutative $C^*$-algebra, commutative $W^*$-algebra, Gelfand theorem, spectrum, point measure,
2.4: State and observable
$\qquad$ John Locke, the primary ( sencondary ) quality, Plato, Aristotle, dualism, observable (= measureing instrument), sample space
2.5: Examples of observables
$\qquad$ existence observable, Berkeley , Einstein and Tagore's conversation, exact observable,
2.6: System quantity
$\qquad$ system quantity, Hermite matrix, specral decomposition,
2.7: Axiom 1 ; No science without measurements
$\qquad$ Born, the probabilistic interpretation of quantum mechanics, Einstein, the god does not throw dice, The Bohr?Einstein debates
2.8: Classicalexamples ( urn problem, etc.)
$\qquad$ urn problem, Wonder of man's linguistic competence
2.9: Stern=Gerlach experiment
$\qquad$ spin observable,
2.10: de Broglie paradox
$\qquad$ there is something faster than ligh, non-locality, Stop being bothered!
3.0: Linguistic interpretation; Abstract
$\qquad$ fifth Solvay conference
3.1: The linguistic interpretation
$\qquad$Kant, a priori judgment, sell, continental rationlism, British empiricism,dualism, Descartes' figure, Parmenides, Whitehead,
3.2: Tensor operator algebra
$\qquad$ tensor Hilbert space, tensor basic structure,
3.3.1: Only one observable
$\qquad$ Kolmogorv's extension theore, simultaneous observable,
3.3.2: state doesnot move
$\qquad$ Parmenides, Herakleitos, quasi-product observable,
3.3.3: Only one state
$\qquad$ parallel measurement, erdodic,
4.0: Linguistic interpretation; quantum system
$\qquad$ Descartes' figure,
4.1: Kolmogorov extension theorem
$\qquad$ Parmenides, infinite simultaneous observable
4.2: The law of large numbers
$\qquad$ Bernoulli, Galileo, Mean,variance,unbiased variance, Robertson uncertainty relation
4.3.1: Why is Heisenberg's uncertainty principle famous?
$\qquad$ Heisenberg's uncertainty principle is doubtful, Heisenberg's thought experiment due to γ-ray microscope
4.3.2: Mathematical formulation of Heisenberg's uncertainty principle
$\qquad$approximately simultaneous measurement
4.3.3: except approximately simultaneous measurement
$\qquad$Ozawa inequality, EPR-paradox,
4.4: EPR-paradox
$\qquad$entangled state, there is something faster than light, Bohr-Einstein debates
4.5: Bell's inequalirty
$\qquad$there is no relation between Bell's inequality and Bell's argument, hiden variable, Shut up and calculate
5.0: Fisher statistics (abstract)
$\qquad$measurement and inference are the two sides of a coin
5.1: Urn problem
$\qquad$Population(=system), paramenter (=state), normal measurement, student distribution, Gsset,
5.2: Fisher's maximum likrlihoof method
$\qquad$Born and Fisher,
5.3: Examples of Fisher's maximum likrlihoof method<
$\qquad$urn problem, normal measurement
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5.4: Moment method
$\qquad$ unnatual but useful
5.5: Monty Hall problem: High school student puzzle
$\qquad$measurement is the metaphysical concept
5.6: Two envelope problem: High school student puzzle
$\qquad$"symmetrical" is non-sense without world description, Copernican revolution, Heliocentrism, Geocentric model
6.0: Confidence interval and statistical hypothesis testing ( Abstract )
$\qquad$"null hypothesis vs. alternative hypothesis" and "one-sided test and two-sided test"
6.1: Review: classical quantum language
$\qquad$Gauss integral, image observable, $\chi^2$-distribution,
6.2: The reverse relation between confidence interval and statistical hypothesis
$\qquad$ semi-metric, estimator and system quantity, rejection region
6.3(1): Population mean (Confidence interval and statistical hypothesis testing)
$\qquad$simultaneous normal measurement, Gauss integral,
6.3(2): Population mean (Confidence interval and statistical hypothesis testing)
6.4(1): Population variance (Confidence interval and statistical hypothesis testing)
6.4(2): Population variance (Confidence interval and statistical hypothesis testing)
6.5: Difference of population means (Confidence interval and statistical hypothesis
6.6: Student $t$-distribution of population mean
$\qquad$"null hypothesis vs. alternative hypothesis" and "one-sided test and two-sided test
7.0: ANOVA(Analysis of variance) ( Abstract )
7.1: Zero way ANOVA (= Student $t$-distribution )
$\qquad$ $\;\;\; F$-distribution with $(1,n-1)$ degree of freedom= the student $t$-distribution with $(n-1)$ degree of freedom
7.2: The one way ANOVA
$\qquad$ $F$-distribution, Gayss integral,
7.3(1): The two way ANOVA
$\qquad$ $F$-distribution, Gayss integral,
7.3(2): The two way ANOVA
$\qquad$ $F$-distribution, Gayss integral,
7.4: Supplement (Gauss integral )
$\qquad$ $F$-distribution, Gayss integral,
8.0: Practical logic - Do you believe in syllogism?
$\qquad$Socrates is mortal
8.1: Marginal observable and quasi-product observable
$\qquad$quasi-product observable, projection observable,
8.2: Properties of quasi-product observables
$\qquad$ tomato
8.3: The definition of "implication "
$\qquad$ Contraposition
8.4: Cogito-- "I think, therefore I am" is doubtful
$\qquad$ Descartes figure, Heidegger, Augustinus, Bergson, What we cannot speak about we must pass over in silence.
8.5: Combined observable -- Only one measurement is permitted
$\qquad$ combined observable, Bell's inequality,
8.6: Syllogism-- Does Socrates die?
$\qquad$variants of syllogism,
8.7: Syllogism does not hold in quantum systems
$\qquad$ EPR-paradox, non-locality,
9.0: Mixed measurement theory ($\supset$Bayesian statistics)
9.1: Mixed measurement theory ( Bayesian statistics )
9.2: Simple examples in mixed measurements
$\qquad$ urn problem,
9.3: St. Petersburg two envelope problem
$\qquad$symmetricity
9.4: Bayesian statistics is to use Bayes theorem
$\qquad$Bayes theorem
9.5: Two envelope problem (Bayes' method)
$\qquad$Bayes theorem
9.6:Monty Hall problem ( Bayesian approach )
$\qquad$Bayes theorem
9.7:Monty Hall problem ( The principle of equal weight )
$\qquad$ the case that you throw dice
9.8: Averaging information ( Entropy )
$\qquad$ Shanon
9.9: Fisher statistics: Monty Hall problem [three prisoners problem]
$\qquad$ Descartes figure
9.10:Bayesian statistics: Monty Hall problem [three prisoners problem]
$\qquad$ Descartes figure
9.11: Equal probability: Monty Hall problem [three prisoners problem]
$\qquad$ Descartes figure
9.12: Bertrand's paradox( "randomness" depends on how you look at)
10.0: Causality (Abstract)
$\qquad$ Anti-realism
10.1: The most important unsolved problem---what is causality?
$\qquad$ Parmenides, Herakleitos, Aristotle, purpose, Galileo, Bacon, Hume, Kant, Copernican revolution,
10.2: Causality---Mathematical preparation
$\qquad$Causal operator, Heisenberg picture and the Schrödinger picture
10.2.2: Simple example---Finite causal operator is represented bymatrix
$\qquad$ Causal map, Heisenberg picture and the Schrödinger picture
10.3:Axiom 2---Smoke is not located on the place which does not have fire
$\qquad$ final cause, evolution theory, dialectic, entropy increase, multiple markov process, time-lag process
10.4: Kinetic equation (in classical mechanics and quantum mechanics)
$\qquad$Newtonian equation(=Hamilton's canonical equation), Schrödinger equation,Heisenberg's kinetic equation
10.5: Exercise:Solve Schrödinger equation by variable separation method
$\qquad$Schrödinger equation in a box
10.6:Random walk and quantum decoherence
$\qquad$non-deterministic causal operator
10.7: Leibniz=Clarke Correspondence: What is space-time?
$\qquad$ realistic view vs. linguistic view, Newton's absolutism , Leibniz's relationalism, McTaggart's paradox, Einstein=Bohr debates
11.0: Measurement and causality (Abstract)
$\qquad$ the relationship between measurement and causality
11.1: The Heisenberg picture and the Schrödinger picture
$\qquad$ Parmenides, there is no movement
11.2:Wave function collapse (= Projection postulate )
11.3:de Broglie's paradox(non-locality=faster-than-light)
$\qquad$ there is something faster than light
11.4: Quantum Zeno effect
$\qquad$ watched pot effect
11.5: Schrödinger's cat, Wigner's friend and Laplace's demon
$\qquad$Schrödinger's cat( quantum decoherence), Wigner's friend(What we cannot speak about we must pass over in silence)
11.6: Wheeler's Delayed choice experiment: "Particle or wave?" is a foolish question
$\qquad$What we cannot speak about we must pass over in silence
11.7: quantum eraser experiment
12.0: Realized causal observable in general theory
$\qquad$ the relationship between measurement and causality
12.1: Finite realized causal observable
$\qquad$ existence observable, Berkeley , Einstein and Tagore's conversation, exact observable,
12.2 Double-slit experiment
$\qquad$seni-ordered tree
12.3: Wilson cloud chamber in double slit experiment
$\qquad$approximately simultaneous measurement
12.4: Two kinds of absurdness ---idealism and dualism
$\qquad$A spectator does not go up to the stage, Fit feet to shoes, There are no facts, only interpretations. Click,
13.0: Fisher statistic (II)
$\qquad$ regression analysis, "inference" in the relation of "measurement" and "causality"
13.1: "Inference = Control" in quantum language
13.2: Regression analysis
$\qquad$ regression analysis $=$ inference $+$ realized causal operator
14.0: Classical causal relation
$\qquad$ Zeno's paradox
14.1: Infinite realized causal observable in classical systems
$\qquad$Kolmogorov extension theorem
14.2: Is Brownian motion a motion?
$\qquad$non-deterministic causal operator
14.3: The Schrödinger picture of the sequential deterministic causal operator
$\qquad$Why does Newtonian mechanics have measurement?
14.4 : Zeno's paradoxes---Flying arrow is not moving
$\qquad$ Zeno's pardox $\Leftrightarrow$ quantum language
15.0 :Least-squares method and Regression analysis
$\qquad$ explanational variable, response variable
15.1 The least squares method
$\qquad$ too easy, thus somewhat difficult
15.2: Regression analysis in quantum language
$\qquad$ classical deterministic causality, parallel measurement,
15.3: Regression analysis(distribution , confidence interval and statistical hypothesis testing)
$\qquad$ student-distribution
15.4: Generalized linear model
$\qquad$ explanational variable, response variable
16.0: Abstract (16.0: Kalman filter)
$\qquad$ classical non-deterministic causality in Bayesian statistics
16.1: Bayes=Kalman method (in $L^\infty(\Omega, m)$)
16.2: Problem establishment (concrete calculation)
16.3: Bayes=Kalman operator
16.4: Calculation: prediction part
16.5: Calculation: Smoothing part
17.0:The reliability in psychological test
$\qquad$ system error, measurement error, reliability
17.1: Reliability in psychological tests
$\qquad$ group test (=parallel measurement), test observable
17.1.3: Reliability coefficient
17.2: Correlation coefficient: How to calculate the reliability coefficient
18.0: how to describe "brief"
$\qquad$ odds
18.1: Belief, probability and odds
$\qquad$the " probability" that Japan will win the victory in the next FIFA World Cup
18.2: The principle of equal odds weight
$\qquad$Monty Hall problem
19.1 Two kinds of ( realistic and linguistic ) world- views
$\qquad$The necessariness of the philosophy of dualistic idearism
19.2: The summary of quantum language
$\qquad$The linguistic interpretation
19.3: Quantum language is located at the center of science
$\qquad$Dr. Hawking, Quantum language is only one useful philosophy
