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HOW TO GET A PH.D.: HOW TO GET A PH.D.: MethodsMethods and and PracticalPractical HintsHints II--II (2011II (2011--2012)2012)
Aarne Mämmelä, 22.9.2011
http://www.infotech.oulu.fi/to_phdhttp://www.infotech.oulu.fi/to_phd
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IV Research methods: Analytical approachIV Research methods: Analytical approachAarne Mämmelä Aarne Mämmelä
We will discuss the difference between research and development, and betweenscience and engineering. Scientific research is divided into discovery andverification. The research starts with the definition of the problem. After collectingsome data, a tentative solution that is also called a hypothesis or system modelshould be found, implying some kind of causal relationship or correlation. We willpresent the conventional scientific, analytical, or reductive approach of research.Not all problems can be solved analytically. Therefore a complementary systemsapproach will be presented in a later session. However, the analysis has been thereason for the success of the western culture since the 1600’s. Analysis is based onthe idea of dividing a large problem into several subproblems that are solvedseparately using induction, abduction, intuition, imagination, or any othermethods of discovery. (Continued)
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IV Research methods: Analytical approachIV Research methods: Analytical approachAarne Mämmelä Aarne Mämmelä
(Continued) Scientific theories are shown to be deductive and causal structureshaving internal and external coherence. Usually in engineering a construction ofthe system is implemented to show that the theory is “working”. Thecorrespondence of the theory with reality is verified by using the hypothetico-deductive method where some conclusions are deductively derived from thehypothesis and they are compared with reality. In engineering research we startfrom performance requirements and therefore the hypothetico-deductive methodmust be slightly modified. Conceptual analysis are emphasized before theories canbe formed. Causality and correlation, deductive, inductive and abductivereasoning, strong inference, and the problem of induction will be explained indetail. Philosophical discussions will improve your awareness of your work.
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Summary of my lectures Summary of my lectures
A doctor must be able to discover new scientific knowledge independently, which is shown with original conference and journal papers (lecture 1)
Existing knowledge in the literature is best found through databases, bibliographies, and citations (lecture 2)
All documents are written using a hierarchical top-down approach using the IMRAD structure (lecture 3)
In this lecture I show that the actual research is a learning process where the opposite bottom-up approach (analytical approach) is used (lecture 4)
In my next lecture I show that also top-down approach (systems approach) can be useful to foster creativity and support learning (lecture 5)
In my last lecture I present the history of research methods (lecture 6)
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Research methods: Analytical approachResearch methods: Analytical approach
Introduction
Research and development
Choosing a problem
Types of reasoning
Formation of concepts and theories
Methods of discovery
Methods of verification
Conclusions
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Introduction
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IntroductionIntroduction
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Christopher Columbus’s and Vasco Christopher Columbus’s and Vasco dada Gama’s Problem:Gama’s Problem:New Way to IndiaNew Way to India
Competing hypotheses: over the Atlantic (Columbus), around Africa (da Gama)
Toscanelli’s map [Suomalainen90][Suomalainen90]
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Methodological Approaches and Research Methods
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Bottom-Up and Top-Down ApproachesBottom-up approach (analytical approach)
Emphasis in details at the expense of the whole
System divided into parts which are weakly interrelated, system isolated from environment
Local optimization does not lead to global optimization
Good basis for mathematical analysis, results are general (even for the whole universe as in relativity theory) but valid only for quite simple idealized cases
Examples: evolution of ideas, learning
Top-down approach (systems approach)
Emphasis in the whole at the expense of the details
Relationships between parts taken into account, whole seen as a part of the environment
Analysis is difficult if not impossible, results are rough and descriptive
Global optimization attempted, contradictory goals
Examples: hierarchical management organizations, design of large systems (Apollo program, “man to the moon”)
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Methodological Approaches [Arbnor97]
1. Analytical approach (reductive approach)
developed in the 1600’s (Galileo, Francis Bacon, Descartes, Newton)
bottom-up approach, a whole is the sum of its parts and isolated from the environment
knowledge is independent of observer
interested in cause-effect relations in deterministic phenomena and correlations in stochastic phenomena
2. Systems approach (holistic approach)
developed in the 1950’s (Bertalanffy, Buckley, Churchman, Emery)
top-down approach, a whole differs from the sum of its parts (synergy, emergence), environment has an important role
knowledge is independent of observer
interested also in producer-product relations and final causes (purposes)
3. Actors approach
developed in the 1970’s (Silverman, earlier work by Husserl, Weber, Schutz)
top-down approach, actor is an active, reflective, and creative human being
interested in understanding social wholes
knowledge exists only as a social construction and is not independent of observers
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Research Methods (Research Approaches) [Iivari91]
1. Nomothetic research (explains with general laws, e.g. in physics)
Formal mathematical analysis
Experiments (laboratory and field)
Field studies and surveys
2. Constructive research (solution of the problem is constructed)
Conceptual development
Technical development
3. Idiographic research (describes unique events, e.g. in history)
Case study
Action research
Note 1. Action research can be classified also as nomothetic research.
Note 2. The term “method” refers to more concrete research principles than the term “approach”.
Note 3. Each method can be used in different methodological approaches.
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Scientific Methods
1. Nomothetic research (in natural sciences and engineering): the aim is to find general causal laws to explain phenomena, theories are usually axiomatic (deductive) systems or sets of models
2. Constructive research (in engineering): the solution of the problem is not only shown to exist but it is constructed [Pagels88]
3. Idiographic (ideographic) research trying to provide all possible explanations of a particular case, for example in history [Nagel79]
radio waves
receiver wherewaves are collected
wavesconverted intoelectro signals
computerreceived as signal
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Additional Scientific Methods
1. Action research (in social sciences): the problem is solved by certain actions whose consequences are evaluated and new actions are specified (iterative improvement, trial and error)
2. Case study (in social sciences): an in-depth, longitudinal examination of a single instance or event, which is called a case
3. Questionnaire study (in social sciences): a series of questions are used for the purpose of gathering information, which is usually analyzed statistically
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What is Research All About: Problem and HypothesisWhat is Research All About: Problem and Hypothesis
No general systematic deductive methods exist to discover hypotheses
A hypothesis is essentially a guess for the solution, which is then tested.
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Question and Answer – Related Terminology
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Research and development
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Research and Development [Jain97], Research and Development [Jain97], [Gell[Gell--Mann94]Mann94]
research: discover new knowledge (i.e., promote understanding by finding regularities and dynamical causal explanations)
basic research (no specific application in mind)
applied research (ideas into operational form)
development: systematic use of the existing knowledge
research and development are closely related
in research a prototype is often developed
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Intrinsic Values of ResearchIntrinsic Values of Research((KalevaKaleva 4.9.2011)4.9.2011)
Creativity
Criticalness
Objectivity (impartiality)
Publicity
Integrity (honesty)
Communication
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Science, Technology and Engineering [Jain97]
science: “organized knowledge of the physical or material world gained through observation and experimentation” [Random House79]
technology: “the sum of the ways in which social groups provide ourselves with the material objects of their civilization”, application of scientific knowledge for practical ends in engineering, medicine, agriculture, etc.
natural sciences and engineering sciences differ in the object of study
natural sciences (also called “science”, inc. physics, chemistry, and biology): objects in the nature
engineering sciences: objects (products, services, processes/methods) not found in the nature, using results of mathematics and natural sciences
in engineering an invention to be patented may be a new concept or implementation
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Difference of science and engineeringDifference of science and engineering
In science we develop a theory for a phenomenon in nature
In engineering we start from requirements (needs) and our aim is to have a product that fits these requirements, a theory is needed to explain and predict the performance
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Scientific MethodScientific Method
scientific method is “a method of research, in which a problemis identified, relevant data are gathered, a hypothesis is formulated [= discovery], and the hypothesis is empiricallytested [= verification]” [Random House99]
Problem is a question proposed for solution or discussion
Hypothesis is a provisional theory suggested as a solution to the problem: either a causal relationship or correlation (correlation is a weaker form of theory, correlation does not imply causality).
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Newton’s problem and hypothesis Newton’s problem and hypothesis
Idea: An apple and the moon are controlled by the same universal force called gravitational force.
Problem: How to unify the theories of terrestrial mechanics (Galileo) and celestial mechanics (Kepler)?
Hypothesis: Newtonian mechanics consisting of four axioms from which the terrestrial and celestial mechanics can be derived.
Verification: The moon follows the same laws as an apple. All planets also follow the same laws.
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Method of hypothesis Method of hypothesis
You must guess how the clock is build without actually seeing the interiorInitially you believe that only the second hand is moving, later you realize that the minute and hour hands are also moving and thus you improve the hypothesisWithout opening the clock you will never know how the clock is actually built, but you can develop models of it (models are instruments for making predictions, they do not necessarily represent the reality)
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Descartes’sDescartes’s Rules [Checkland99]Rules [Checkland99]
1. Avoid precipitancy [undue hastiness] and prejudice and accept only clear and distinct ideas.
2. Divide each of the difficulties [problems] into as many parts as possible and necessary in order best to solve it.
3. Progress orderly from the simple to the complex.
4. Use complete analysis, omit nothing.
Rule 2 is the principle of analytical reduction which characterizes the Western intellectual tradition.
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Criteria for Scientific Work
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Criteria for Scientific Theories [Barbour74], [Barbour97], [Wilson99], [Pagels88]
1. Simplicity
Parsimony or economy (Occam’s razor: select the simplest theory from competing equally good theories)
2. Coherence (= unity)
Internal and external coherence (deductive structure)
3. Correspondence (= agreement with reality)
Falsifiability (hypothetico-deductive method)
Repeatability and reproducibility
4. Generality
Theory is useful in many cases
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Critics Are Our FriendsCritics Are Our Friends
The aim of criticism is to show weaknesses and finally improve the quality of the work in international competition
Without criticism we would always compete in the “province league”
Do not prevent criticism although you may become angry because criticism hurts
Criticism must be objective and impersonal
Ideally you should show what should be improved and how
Start and finish with encouragement
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Novelty and ParadigmNovelty and Paradigm
Paradigm is an unquestioned theory or set of beliefs, existing world-view (concept introduced by T. Kuhn in 1962) [Honderich05]. Novel results outside the present paradigm are often rejected by the scientific community.
Example: If you try to show that Einsteinian mechanics is wrong, you are most probably rejected. You must very carefully present your methods. For example Pasteur explained with extreme detail his methods when he was showing that life is not spontanously developed [Day98].
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Choosing a problem
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Choosing a Problem [Loehle90]
For success in research you need right problem, right timing, right approach [Hamming93]Difficulty of the problem and its likely payoff must be balanced (not too easy, not too difficult)Opportunities for you
other person is wrong (do not tell that the person is wrong, but show what is right)contradictory experimentsterminological confusion
More experience needed to solve problemsdiscussions (most new ideas are generated by talking with others [Jain97])experiments (start them early, use experimental-inductive approach)literature (find out existing knowledge)
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Types of reasoning
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Induction and DeductionInduction and DeductionDeductive reasoning (inference):
All humans are mortal (assumption or premise 1)
Socrates is human (assumption or premise 2)
Socrates is mortal (conclusion)
In deduction the conclusions are implied by the premises. The truth is necessarily preserved. There is no new information in the conclusions that would not be in the premises.
Inductive reasoning (inference):
All crows observed so far have been black (assumption or premise)
All crows are black (conclusion)
In induction the truth is not necessarily preserved. The conclusions include more information than the premises. New theories must include this kind of generalizations developed from observations ,and induction cannot be avoided.
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Induction and DeductionInduction and Deduction
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Scientific and Mathematical InductionScientific and Mathematical Induction
Scientific induction
Scientific induction presented on the previous slides is incomplete: truth is not necessarily preserved
Scientific induction is based on regularity of the world (in time and space), thus generalizations and predictions are possible
Scientific induction should not be mixed with mathematical induction
Complete and mathematical induction:
Complete induction is induction where all the special cases of the generalization are enumerated. This is actually a form of deduction [Niiniluoto83].
Mathematical induction is a special case of complete induction, used in mathematical proofs (If a statement holds when n = 1 and if the statement holds for some n, and the statement also holds when n + 1 is substituted for n, then the statement holds for all n.)
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Abduction and Strong InferenceAbduction and Strong Inference
Abduction and deduction are opposites
Strong inference tries to simulate abduction
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Summary: Types of reasoningSummary: Types of reasoning
Deduction (top-down): if the premises are true, the conclusion must be true, i.e., deduction preserves the truth (often proceeds from general to particular)
Induction (bottom-up): the conclusion, though supported by the premises, does not follow from them necessarily, i.e., induction does not in general preserve the truth (often proceeds from particular to general)
abduction: inference to the best explanation, Russell’s chicken example
strong inference: use several competing hypotheses and select the best one, i.e., approximate of abduction
statistical inference (Bayesian inference): Bayes’ theorem is used to infer the probability that the hypothesis is true
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Analysis and Synthesis, Deduction and Induction [Random House99], [Hall62], [Honderich05]
Analysis (reduction): Separating of any material or abstract entity into its constituent elements.
Synthesis: Combining of the constituent elements or separate material or abstract entities into a single or unified entity.
Deduction: A form of inference; if the premises are true, the conclusion must be true, i.e., deduction preserves the truth (equivalent to analysis).
Scientific induction: a form of inference in which the conclusion, though supported by the premises, does not follow from them necessarily, i.e., induction does not necessarily preserve the truth (equivalent to synthesis).
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Criticism on Inductivism [Niiniluoto83]Criticism on Inductivism [Niiniluoto83]
Induction does not preserve the truth as deduction does (Hume’s problem of induction)
Strictly speaking, we cannot verify but only falsify hypotheses (Popper’s “solution” to the problem of induction).
Often the new theory (hypothesis) is in conflict with the old theory and thus cannot be induced from the old theory (Kuhn’s revolutionary science).
Hypothetico-deductive method is presently seen as the standard view of scientific reasoning. There are no systematic methods to find hypotheses.
Induction is needed in everyday life (based on regularities in space and time).
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Formation of concepts and theories
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Formation of Concepts and TheoriesFormation of Concepts and Theories
We learn by induction (bottom up, generalization from examples to models) [Felder88]
We present theories by deduction (top down, from models to results)
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Concept Formation [Niiniluoto02] Concept Formation [Niiniluoto02]
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Definitions [Honderich05]Classes of definitions
Ostensive definition (“pseudodefinition”, elementary terms are explained by examples to avoid an endless loop of definitions (Locke), “blue is the color of the sky”) [Rosenberg00] Dictionary definition (meaning explained as established in a language, “complexity refers to the number of parts and their interconnections”)Stipulative definition (definition by agreement, “complexity is measured by size/weight, delay, energy, and cost”)
A definition names a wider class to which something belongs and distinguishing properties (“triangle is a closed plane figure [wider class] having three angles and three sides [distinguishing properties]”)Standardization organizations such as ISO, IEC, ITU, and SFS define general terms, see for example
Electropedia, www.electropedia.org (IEC’s electrotechnical vocabulary)SFS-verkkokauppa, sales.sfs.fiISO Guide 99:2007 International vocabulary metrology: Basic and general concepts and associated terms (VIM)
Definitions can be found also from textbooks and review papers
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Assumptions
By using assumptions, we simplify the problem, we eliminate or ignore unnecessary factors and focus on major ones, and we enable mathematical formulation.
Typical simplifying assumptions: linearity, slow changes, isolated from other systems and environment, normal (Gaussian) statistics for random variables, tractable criteria (for example power or energym of error signal), modularity, hierarchy
Sometimes it is difficult to say whether a statement is a definition or assumption, for example the second law F = ma in Newtonian mechanics (F is force, m is mass and a is acceleration) [Nagel79]
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Comparison of Theories Comparison of Theories [Honderich05], [Rosenberg00][Honderich05], [Rosenberg00]
Theories are based on analogies, without a theory all situations look completely different, but theories reveal the underlying relationships and improve understanding
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Taxonomy of Theories [Rosenberg00]Taxonomy of Theories [Rosenberg00]
1. Axiomatic systems – ideal form of theorytheorems are derived deductively (= analysis) from definitions and axiomstwo forms: Hilbertian axiomatic systems in formal sciences (mathematics, logic, set theory, computer science) and hypothetico-deductive systems in empirical sciences
2. Theories based on sets of theoretical modelsresults are derived by analysis (deduction, equations) from the definitions and assumptions of the model usually used in science and engineering, for example ideal gas, Bohr model of atomComplicated systems cannot be understood without models, which are simplified presentations of those systemsTheoretical model can often be simulated
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Theoretical Model and IMRAD Structure [Day98], Theoretical Model and IMRAD Structure [Day98], [Rosenberg00][Rosenberg00]
• From here we can see what should be put in the materials and methods section.
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Classification of models [Barbour74]Classification of models [Barbour74]
1. Experimental models (physical models)
a) Scale models (show spatial relationships, for example a globe), b) working models (show temporal relationships), c) analogue models (a physical system, often electronic system, as a model for another)
2. Logical models
Set of entities that satisfy axioms and theorems in axiomatic systems (e.g., points and lines in Euclidean geometry, the Sun and planets in Newtonian mechanics)
3. Mathematical models
Symbolic representation of a physical or social system, basis for computer models, no physical similarities with the actual system (model for supply and demand, growth of population)
4. Theoretical models
Symbolic representation of a physical system, represents also underlying structure (billiard-ball model of a gas, Bohr model of atom)
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Methods of Solution in a Mathematical Model [Chestnut65]
1. Analytic methods
Deduction is used in a theoretical model, usually desirable since an exact answer is derived, useful for relatively simple cases.
2. Numerical or deterministic methods
Direct solution, for example by using the Gaussian elimination method, can be found especially for matrix equations.
Simpler iterative procedures, for example Newton’s method, are often used to find optimum or worst case state.
3. Monte Carlo simulation methods (random or stochastic sampling)
Simulations are only descriptive, model is not “solved” or “optimized”, optimization can be done by varying the parameters or configuration, but the number of parameters is usually too large.
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Deduction and Reduction [Rosenberg00] (1)
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Deduction and Reduction [Rosenberg00] (2)
Newtonian mechanics (Newton, 1684, 1687)
Terrestrial mechanics (Galileo, 1638)
Celestial mechanics (Kepler, 1619-21)
Theory of relativity (Einstein, 1905, 1915)
D R
RDD R
D = deductionR = reduction
Observations
D RDR
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Hypothetico-Deductive (HD) System: Newtonian Mechanics [Rosenberg00], [Young04], [Nagel79]
A. Primitive (undefined) concepts: Mass m, space (length s or d), and time t.
B. Definitions: Velocity v = ds/dt, acceleration a = dv/dt = d2s/dt2, and impulse p = mv, G is constant of gravity.
C. Axioms (assumptions): 1. Law of inertia (F = 0), 2. Relationship of force and acceleration (F = dp/dt = ma), 3. Law of action and reaction F1 = -F2 (equivalent to conservation of momentum p = mv), 4. Law of gravitation F = Gm1m2/d2.
D. Theorems (consequences, some examples):
I. Galileo’s terrestrial mechanics: 1. Projectiles follow the path of a parabola. 2. Period of a simple pendulum is proportional to the square root of the length of the wire and is independent of the weight of the bob. 3. Law of free fall: all bodies fall with an acceleration that is constant and independent of their weights.
II. Kepler’s celestrial mechanics: 1. Orbits of planets are elliptical. 2. A line from the sun to a planet sweeps out equal areas in equal times. 3. The squares of the periods of planets are directly proportional to the cubes of the major axes of their orbits.
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Axiomatic SystemsAxiomatic Systems
The term hypothesis has a different meaning in these two axiomatic systems.
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Taxonomy of Axiomatic Systems [Niiniluoto02]
Hilbertian axiomatic systemsused on formal sciences
no interpretation made (no relationship to reality)
the axioms are assumptions and initially the theorems arehypotheses or conjectures, which are proved by deriving them deductively from axioms
examples: logic, arithmetics, geometry, set theory, probability theory
Hypothetico-deductive systemsused in empirical sciences
interpretations made (correspondence with reality)
initially axioms arehypotheses that are verified indirectly by comparing the results with reality
examples: Newtonian mechanics, quantum mechanics, hypothetico-deductive systems are used also in biology and social sciences
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Scientific Explanations [Rosenberg00]
1. Deductive explanation (deductive-nomological)
every explanation includes a deductive argument containing at least one deterministic law and is empirically testable
laws in science may be 1) causal (cause-effect relations), 2) static (Boyle’s law) or 3) dynamic (Galileo’s law of falling bodies) [Nagel79]
2. Statistical explanation (inductive-statistical)
statistical generalizations instead of strict laws (for example quantum mechanics, statistical mechanics, opinion survey)
Note. Free will does not have a scientific explanation that all scientists could accept. Teleological explanations based on final causes (purpose) are suspected in the analytical approach. Not all laws in deductive explanation are causal although causality may be behind the law.
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Methods of discovery
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Scientific Method [Honderich05], [Pagels88]Scientific Method [Honderich05], [Pagels88]
Scientific method is divided into two parts: Discovery: divide and conquer (reduction), iterative improvement, empirical-inductive method, systems approach (next lecture)Verification: hypothetico-deductive method
Modern scientific method by Galileo includes mathematical analysis (coherence of the theory) and experiments (correspondence with reality), in engineering the solution must also be practical (pragmatic)
Best theories are deductive systems (either axiomatic systems or causal theoretical models)
Methods of discovery are controversial (no systematic method of discovery exists)
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Creativity: On the Edge of Order and ChaosCreativity: On the Edge of Order and Chaos
You must have something on which to build (order, systematic work) and something to move (chaos, flexibility)
Ways to improve creativity: analogies, symmetries, relations, extremes, opposites
Working habits: well defined problem, quiet time (“lazyness”), new environment, mental barriers avoided [Loehle90]
Order Chaos
Creativity
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Isomorphism in Science: Analogies and Isomorphism in Science: Analogies and Homologies [Bertalanffy98]Homologies [Bertalanffy98]
Analogy is “a form of reasoning in which one thing is inferred to be similar to another thing in a certain respect, on the basis of known similarities in other respects” [Random House99]
Analogies may be sometimes superficial similarities and misleading (growth of an organism as compared with that of a crystal, consideration of a forest as an organism).
Analogies where the laws are formally identical are called homologies, for example electrical flow and flow of a fluid (water)
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Creativity Can Be ImprovedCreativity Can Be Improved
Define your problem carefully.
Respect criticism and follow the instructions. Avoid group think by criticism.
Follow ethical rules. Emphasize integrity.
Appreciate publicity. Do not accept wildcat business.
Respect independence and accept dissimilarity and diversity.
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Sources of Knowledge [Honderich05]
deductive and inductive reasoning
experience, observation and experiment, improved instruments [Derry99]
analogy [Bohm87], [Feynman98]
abduction (Russel’s chicken [Deutsch98]), intuition, imagination, dream (Descartes: reductionism [Wilson99], Kekulé: benzene [Hudson92], Mendeleyev: periodic system of elements [Strathern00])
patterns and discrepancies in data, serendipity [Derry02]
wild guess [Losee01], brainstorming [Davis97], telepathy, clairvoyance, precognition, etc.
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Theory Construction in ScienceTheory Construction in Science
The finding of the hypothesis is a nonlinear process (it can be made systematic only in very specific cases)
There are several possible hypotheses that are good approximations of the reality (for example Aristotle’s circles and Ptolemy’s epicycles, Galileo/Kepler, Newton, Einstein)
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System Design in EngineeringSystem Design in Engineering
Natural object is replaced by requirements that describe user needs.
The requirements describe the properties of the expected system. The system is verified against the requirements, but finally validated in the field tests (perhaps not all needs are not included in the requirements).
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Methods of DiscoveryMethods of Discovery
Traditional methods of problem solving [Pagels88]
Divide and conquer (reduction, break a large problem into simpler subproblems and try to solve them, and finally combine the solutions)
Iterative improvement (guess a solution and then try to improve it)
Traditional methods need a complementary “holistic” method that is also called systems approach(example: working of an airplane)
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Reductive Method of Discovery [Wilson99], [Pagels88]Reductive Method of Discovery [Wilson99], [Pagels88]
Break the problem down and then generalize the results (“divide and conquer”)
“Practical people often balk at this approach [reduction, idealizations] since the idealized situations may be so far removed from those of use as to appear highly academic.” [Wilson90]
We present the results explicitly by deduction (top down), but we learn through induction (bottom up)
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EmpiricalEmpirical--Inductive Method of Discovery [Kragh02]Inductive Method of Discovery [Kragh02]
Problem is divided into subproblems (this is called reduction)
Hypothesis (system model) is derived by using experience (often analogies and homologies used).
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Iterative Method of Discovery [Pagels88]Iterative Method of Discovery [Pagels88]
You must work iteratively since the problem and hypotheses are initially not very clear (a chicken and egg problem)
In the beginning it is difficult to understand the literature
Experience is gained by own experiments and discussions
Reporting and publishing will improve the quality of research
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Iterative Method of DiscoveryIterative Method of Discovery
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CausalityCausality
Scientific theories are deterministic and deductive (relativity theory) or probabilistic (quantum theory) [Nagel79].
Scientific theories describe (question how?) but do not strictly speaking explain (question why?).
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Different Explanations Why Something Happens
Philosophical question with no answer: If everything is deterministic, how can we change anything (break the causality chain)?
Deterministic cause, free will, and chance are different explanations that cannot be presently unified.
Causality is not present in the microworld (quantum mechanics ) although the macroworld seems to work largely deterministically.
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Division of a System into Parts and PropertiesDivision of a System into Parts and Properties
Reduction is defined as a search for causes and therefore it proceeds in the opposite direction to causality (upwards causality and forwards causality).
Reduction may be analysis or synthesis depending on the situation.
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Reality and Theory [Wohlin00]Reality and Theory [Wohlin00]
In engineering a hypothesis (defined in system specifications) is usually an idea of the relationship between the cause and effect (defined in system requirements)
Theoretical model is always only an approximation of observation in real world
Prototypes include tacit or silent knowledge by Polanyi [Leppälä03], e.g., Stradivarius violin
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Example: Factors Affecting PerformanceExample: Factors Affecting Performance
Reductionism helps you to test your models.
Use reference data from simplified analysis or literature (lower and upper bounds often used).
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Methods of verification
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Experiment (Set of Tests) [Wohlin00]Experiment (Set of Tests) [Wohlin00]
Tests are either deterministic or statistical
One independent variable is changed and other independent variables are set at a fixed level
In this way the factors affecting the system can be determined
This idea works only for linear systems
Linear: ”having the same effect on the sum as on each part of the sum” [Random Hoouse99]
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Testing of hypothesis (theory)Testing of hypothesis (theory)
In strong inference we compare several different theories and select the best (this is abduction, inference to the best explanation). If the theories are equally good, we select the simplest theory (this is Occam’s razor).
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Einstein’s Hypothetico-Deductive Method [Baeyer05]
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Method of verification: Method of verification: HypotheticoHypothetico--deductive methoddeductive method
Newton: = 0.875”Einstein: = 1.75”Measured (1973): = 1.66” ± 0.19”
Source: www.mathpages.com/rr/s6-03/6-03.htm
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HypotheticoHypothetico--Deductive Method of Deductive Method of VerificationVerification
The scientific verification method is called hypothetico-deductive method [Honderich05]: the theoretical model acts as a hypothesis, which is verified indirectly by comparing the results given by the theoretical model with the corresponding experimental results given by the reality. (Deduction internal coherence, verification correspondence with reality.)
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Verification, Validation, and Certification [Calvez93], [VIM], [VIML]
verification is establishing the truth of a hypothesis, usually by experiment or observation (in science), “provision of objective evidence that a given item fulfils specified requirements,” or a design step satisfies the requirements of the higher hierarchy level in a laboratory environment (in engineering)
legal verification is verification of a measuring instrumentvalidation “verification, where the specified requirements are adequate for an intended use,” i.e., verification of system requirements that may be incomplete, or confirmation that a design step satisfies the requirements at the same hierarchy level
certification is an external validation given by an accredited authority
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Repeatability and Reproducibility [ISO Guide 99:2007]
Scientific results must be reproducible
Repeatability: the same results are obtained in the same laboratory, information may be exchanged by oral discussions, nobody knows exactly what information was exchanged
Reproducibility: the same results are obtained in different laboratories (more strict requirement), information is exchanged strictly through explicit documents
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Structure of Science [Barbour97]
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Typical mistakes of a doctoral student
Research problem is not defined properly and the work is too wide. The hypothesis is not concrete enough. The student does not discuss with people with different backgrounds to find new ideas.
Existing literature is either not studied or all time is used for studying literature. The student either does not present intermediate results at all or concentrates on writing comprehensive technical reports.
The student does not concentrate on own original results. The start of writing papers is postponed to wait for better times. The student is all the time publishing at low-level conferenceswhere the requirements are modest and thus the possible problems are not noticed.
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Conclusions
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Conclusions (1)Conclusions (1)
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Conclusions (2)Conclusions (2)
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Conclusions (3)Conclusions (3)
use bottom-up (“inductive”) approach in research, which is essentially a learning processuse top-down (deductive) approach in technical documents (reviews, monographs), this will make the presentation compact and easy to follow for experts (use IMRAD structure)use bottom-up approach in teaching (tutorials, textbooks), and integrate results by using the top-down approachremember that a doctoral thesis is not a textbook (writing a textbook is a large challenge), write the thesis for experts in the field
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Conclusions (4): Iterative research methodConclusions (4): Iterative research method
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Conclusions (5): Theory and practiceConclusions (5): Theory and practice
A good research project emphasizes theoretical results (usually system models) and uses prototypes for verification and validation of the new results
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AbbreviationsAbbreviations
AWGN, additive white Gaussian noise
DNA, deoxyribonucleic acid
ENIAC, Electronic Numerical Integrator and Computer
HD, hypothetico-deductive
IEC, International Electrotechnical Commission
IMRAD, introduction, materials and methods, results, and discussion
ISO, International Organization for Standardization
ITU, International Telecommunication Union
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References (1)References (1)
I. Arbnor and B. Bjerke, Methodology for Creating Business Knowledge, 2nd ed. Sage Publications, 1997.
I. G. Barbour, Myths, Models, and Paradigms. Harper & Row, 1974.
I. G. Barbour, Religion and Science: Historical and Contemporary Issues. HarperSanFrancisco, 1997.
H. C. von Baeyer, Informaatio: Tieteen uusi kieli [Information: The New Language of Science]. Terra Cognita, 2005.
L. von Bertalanffy, General System Theory. George Braziller, 1998.
P. Bock, Getting It Right: R&D Methods for Science and Engineering. Academic Press, 2001.
D. Bohm and F. D. Beat, Science, Order and Creativity. Bantam Books, 1987.
H. Chestnut, Systems Engineering Tools. New York: Wiley, 1965.
M. Davis, Scientific Papers and Presentations. Academic Press, 1997.
R. A. Day, How to Write and Publish a Scientific Paper, 5th ed. Oxyx Press, 1998.
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References (2)References (2)
G. N. Derry, What Science is and How It Works, reprint. Princeton University Press, 2002.
D. Deutsch, Fabric of Reality. Penguin, 1998.
R. M. Felder and L. K. Silverman, “Learning and teaching styles in engineering education,” Engineering Education, pp. 674-681, April 1988.
R. P. Feynman, The Meaning of It All. Perseus Publishing, 1998.
M. Gell-Mann, The Quark and the Jaguar. W. H. Freeman and Company, 1994.
A. D. Hall, A Methodology for Systems Engineering. Princeton, NJ: D. Van Nostrand Company, 1962.
R. W. Hamming, “You and your research,” IEEE Potentials, pp. 37-40, October 1993.
Honderich (Ed.), The Oxford Companion to Philosophy, 2nd ed. Oxford Univ Press, 2005.
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References (3)References (3)
J. Hudson, The History of Chemistry. Chapman and Hall, 1992.
J. Iivari, “A paradigmatic analysis of contemporary schools of IS development,” European Journal of Information Systems, vol. 1, no. 4, 1991, pp. 249-272. R. K. Jain and H. C. Triandis, Management of Research and Development Organizations. John Wiley & Sons, 1997.
H. Kragh, Quantum Generations: A History of Physics in the Twentieth Century, reprint ed. Princeton University Press, 2002.
K. Leppälä et al., Professional Virtual Design of Smart Products. IT Press, 2003.
C. Loehle, “A guide to increased creativity in research - inspiration or perspiration?” BioScience, vol. 40, pp. 123-129, February 1990, limnology.wisc.edu/courses/zoo955/publications/Wk04_Research/Loehle_1990_Guide_to_Creativity.pdf.
J. Losee, A Historical Introduction to the Philosophy of Science, 4th ed. Oxford Univ Press, 2001.
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References (4)References (4)E. Nagel, Structure of Science: Problems in the Logic of Scientific Explanation. Hackett Pub Co, 1979.I. Niiniluoto, Johdatus tieteenteoriaan: Käsitteen- ja teorianmuodostus, 3rd ed. Otava, 2002.I. Niiniluoto, Tieteellinen päättely ja selittäminen. Otava, 1983H. Pagels, The Dreams of Reason. Simon and Schuster, 1988.G. Pahl, W. Beitz, J. Feldhusen, and K.-H. Grote, Engineering Design: A Systematic Approach, 3rd ed. Springer, 2007.A. Rosenberg, Philosophy of Science. Routledge, 2000.Random House Webster’s Concise College Dictionary. New York: Random House, 1999.P. Strathern, Mendeleyev‘s Dream: The Quest for the Elements. Thomas Dunne Books, 2001.Suomalainen tietosanakirja, vol. 4. Weilin+Göös, 1990, p. 351.[VIM] ISO Guide 99:2007 International vocabulary metrology: Basic and general concepts and associated terms (VIM).[VIML] International Vocabulary of Terms in Legal Metrology (VIML). OIML, 2000.
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References (5)References (5)
E. B. Wilson, An Introduction to Scientific Research, rev. ed. Dover Publications, 1990. E. O. Wilson, Consilience: The Unity of Knowledge. Random House, 1999.C. Wohlin et al., Experimentation in Software Engineering: An Introduction, Springer, 1999. H. D. Young and R. A. Freedman, Sears and Zemansky’s University Physics with Modern Physics, 11th ed. Pearson - Addison Wesley, 2004.
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Recommended ReadingRecommended Reading
A. Rosenberg, Philosophy of Science, 2nd ed. Routledge, 2005. (A nice introduction to philosophy of science.)
I. Niiniluoto, Johdatus tieteenteoriaan: Käsitteen- ja teorianmuodostus, 3rd ed. Otava, 2002. (Extensive two-part summary of philosophy of science. This first part is about formation of concepts and theories.)
I. Niiniluoto, Tieteellinen päättely ja selittäminen. Otava, 1983. (This second part is about scientific inference and explanation.)
Honderich (Ed.), Oxford Companion to Philosophy, 2nd ed. Oxford Univ Press, 2005. (A standard encyclopedia that includes many topics in philosophy of science.)
R. M. Felder and L. K. Silverman, “Learning and teaching styles in engineering education,” Engineering Education, pp. 674-681, April 1988. (Emphasizes inductive generalizations in learning and teaching.)
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VTT creates business from technology