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SCIENCE ADMINISTRATION
LECTURE 32
PARADIGM OF MECHANISM
CHANGE! – QUANTUM MECHANICS
ILLUSTRATION –
QUANTUM MODEL OF THE ATOM
FREDERICK BETZ
PORTLAND STATE UNIVERSITY
PHILOSOPHY OF SCIENCE ADMINISTRATION
PROCESS OF
KNOWLEDGE
TECHNICAL
OPERATIONS
SCIENTIFIC
METHOD
(EPISTEMOLOGY)
MANAGEMENT
SCIENCE
OPERATIONS ADMINISTRATION
(ORGANIZATION)
STATE OF
KNOWLEDGE
SCIENTIFIC
PARADIGMS
(ONTOLOGY)
SCIENCE
APPLICATION
(TECHNOLOGY)
SCIENCE ADMINISTRATORS MUST UNDERSTAND SCIENCE WITHOUT
BECOMING EXPERTS IN A SCIENTIFIC FIELD.
THE WAY TO DO THIS IS THROUGH UNDERSTANDING SCIENTIFIC
PARADIGMS – INTELLECTUAL FRAMEWORKS OF SCIENCE.
SCIENCE DISCIPLINES CONSTRUCT THEORY
WITHIN GENERAL FRAMEWORKS OF PARADIGMS –
SCIENTIFIC META-THEORIES.
DISCIPLINE
META-THEORY
(SCIENTIFIC PARADIGM)
THEORY
DISCOVERY OF THE ELECTRON AND FIRST MODEL OF AN ATOM
J.J. THOMSON
In 1897 J. J. Thomson at the Cavendish Laboratory of Cambridge University
demonstrated that the electron was a subatomic particle (for which he was
awarded the Nobel Prize in physics in 1906).
J. J. Thomson (1865-1940) was born in Manchester, England. Later he
attended Cambridge University, obtaining a master’s degree in 1883. He
became a professor at Cambridge the following year.
He studied the then new cathode tube in which ‘rays’ passed through the
gas of the tube when electrical voltages were placed across each end of the
tube. He demonstrated that these ‘rays’ were currents of electricity made up
of a flow of particles, which he called ‘electrons.
Thomson then suggested that the atom was made up of a combination
of electrons and protons (called the ‘Plum pudding model’, with electrons
embedded like plums in a positive pudding).
Ideas in science can occur far earlier in philosophy. But they still are only
philosophical ideas and not scientific ideas.
For example in ancient philosophy, the idea of an atom was proposed by a preSocratic philosopher, Democritus (460-370 BC). He was born in Thrace and
believed all matter is made up of small, permanent units which he called ‘atomon’,
or 'indivisable elements'.
But the Newtonian paradigm of mechanism includes spatial explanation. So
Thomson aimed at the divisability of atoms into electrons and a positive pudding.
THE ‘GEIGER-MARSDEN EXPERIMENT’–
THE FIRST SCIENTIFIC MODELING OF THE ATOM
RESEARCH PROJECT MANAGEMENT BY ERNEST RUTHERFORD
Ernest Rutherford (1871-1937) was born in New Zealand. he studied at Nelson
College and Canterbury College. In 1883, he graduated with degrees of BA, MA,
and BSc. He stayed on for two years to do research in electric technology.
In 1885, he went to England for graduate study at the Cavendish Laboratory of the
University of Cambridge.
He investigated radioactivity and was able to distinguish between alpha, beta, and
gamma rays in the radioactive phenomena of atoms. He introduced the terms of
'alpha' and 'beta' radiation.
RUTHERFORD DISTINGUISHED RADIOACTIVE DECAY RAYS INTO ALPHA
RAYS, BETA RAYS AND GAMMA RAYS
Alpha rays are stream of alpha particles from radioactive decay in atoms.
Beta rays are streams of electrons.
Gamma rays are high-energy electromagnetic wave-particles, photons.
Alpha rays are streams of helium nuclei, with two protons and two neutrons. They originate
from the radioactive decay of some elements (such as radium or uranium). A radioactive
nucleus of an atom such as radium can decay by ejecting an alpha particle.
The helium nucleus (alpha particle ) of two protons and two neurons are bound together by
the strong nuclear force of ‘gluons’ which attract together the quarks that make up the
protons and neutrons – strong nuclear force.
Rutherford had demonstrated that radioactivity was the spontaneous
disintegration of atoms, determining that different atoms had different times of a
constant rate-of-decay, which he called the ‘half-life’ of a radioactive atom. His
work was rewarded with a Noble Prize in physics in 1908.
In 1907, Rutherford moved back to England as the chair of physics at the
University of Manchester. As chair, Rutherford was given space by the University
and a budget to run a physics research laboratory. There he would conceive and
lead a team of researchers to perform the famous experiment on the structure of
the atom.
Hans Geiger (1882-1945) was born in Germany and earned his doctorate in
physics in 1906 at the University Erlangen. In 1907, he went to England to work
for Rutherford and, with Rutherford and with him invented the Geiger counter.
Geiger would return to Germany, becoming head of the Physical-Technical
Reichsanstalt in Berlin and then a professor at the University of Keil in 1925.
During World War II, he would be part of the German group attempting to make
an atomic bomb during World War II.
Ernest Marsden (1889-1970) was born in England and enrolled in the University
of Manchester as an undergraduate. In Rutherford’s lab, he worked under
Geiger, participating in the famous experiment as an undergraduate. Later in
1914, Marsden would move to Victoria University in New Zealand. He would
serve in World War I as a Royal Engineer and then return to New Zealand to
found New Zealand’s Department of Scientific and Industrial Research in 1924.
In 1909 in Rutherford’s lab, Geiger and Marsden bombarded a thin gold foil
with alpha particles. The experiment was performed in a darkened room
under a low-powered microscope.
Geiger and Marsden watched for tiny flashes of light as the scattered
particles struck a zinc sulfide scintillant screen. Most of the particles
penetrated the foils, passing through with some absorbed in the foil.
Rutherford had expected that most alpha particles would pass through the
foil, some slightly deflected. And most did.
But once in about 8000 times, the alpha particles bounced back from the foil
toward the source – as if these particles had hit a hard object in the foil!
This phenomenum was called a ‘back-scatter’.
Back-scattering in classical physics can occur when one hard object hits
another hard object and scatters backwards.
Such backscattering could not be explained by Thompson’s ‘plum pudding model’
of the atom. In the ‘plum pudding’ model, the alpha particles would be absorbed
by the pudding of the positive charges, and the electrons (raisins in the pudding)
were smaller than the alpha particles and too small to back scatter the much
heavier alpha particles.
So when alpha particle did hit a small, heavy and hard nucleus of the gold atom, it
would backscatter. That meant that the atom must have hit a small, heavy, and
hard nucleus at its core with electrons surrounding the core.
In 1911, Rutherford published his analysis of the alpha scattering as the
‘Rutherford model’ of the atom. His model looked like the model of the solar
system, with a core atomic nucleus (like the sun) orbited by electrons (like
planets). The atom was composed of a small atomic nucleus surrounded by a
cloud of electrons in orbits. Like the solar system, the atom was mostly space.
Rutherford used as a metaphor that earlier (1638) Copernican model of the solar
system
CLASSICAL SOLAR ANALOGY FOR A MODEL OF A HYDROGEN ATOM
..
Hydrogen Nucleus
Composed of a
Proton and Neutron
Orbiting
Electron
Of course, Rutherford did not believe such an analogy of the atomic system
to the solar system possible could be true because of the theory of
electromagnetism.
Because of electromagnetic theory, a real orbiting electron as a particle
would radiate electromagnetic energy -- thereby losing velocity and
eventually collapsing into the nucleus.
Electromagnetic theory predicted that accelerating electrons radiate energy.
And experiment had shown this was true. And constantly changing
directions in an orbit is a form of acceleration -- change of velocity as the
direction of the velocity changes.
Rutherford knew that the spatial model of an atom with electrons far out
circling an nucleus was experimentally correct. But how was it physically
possible? He knew that a new kind of model of the atom was needed.
And later one of his assistants-to-be, Niels Bohr, would soon devise an
answer – a quantum atom.
NATURE WOULD REQUIRE A PARADIGM SHIFT IN THE PARADIGM OF MECHANISM
Niels Bohr (1885-1962) was to solve the issue of how electrons orbit the nucleus
of an atom. Bohr was born in Denmark.
As a young man he went to England as an undergraduate at Trinity College,
Cambridge. He returned to Denmark and received a doctorate from Copenhagen
University in 1911.
He returned to England did a post doctoral research under Ernest Rutherford in
the University of Manchester.
There Bohr learned of Rutherford’s experiments and devoted himself to
theoretically modeling the structure of the atom. In 1913, Bohr published his
model of the atom.
EXPERIMENTAL BASIS – RYDBERG SPECTRAL LINES
OF THE HYDROGEN ATOM
Photons are the quantum particles of an electromagnetic field. When light of a proper
frequency is shown on an atom, a photon of the light can be absorbed by one of the atom’s
orbiting electrons, jumping that electron into a higher orbit. Then subsequently that
electron can emit the same frequency proton and fall back into its lower orbit. This is the
phenomena of light absorption and emission by atoms. Experimental studies on hydrogen
gas were performed by Heinrich Rubens (1865-1922).
The mathematical study of the experiments on light emission by the hydrogen atom was
done by Johann Balmer in 1885. He devised an analytical formula summarizing the pattern
of wavelengths found in the spectral lines of lines of hydrogen -- Balmer's formula.
In 1890, Rydberg published an analytical formula which described the pattern of
wavelengths occuring in the spectral emission of light from heated alkali metals. Also,
Rydberg showed that the spectral lines from hydrogen (Balmer's formula) was a special
case of the more general alkali metal emission pattern.
Balmer
Rydberg
Balmer spectral lines from a deuterium lamp. Hydrogen has one proton and
one electron. Deuterium is an isotope of hydrogen with one proton plus one
neutron in its nucleus and one electron circling the nucleus.
The two spectral lines Db and Da are photons emitted in the transition of the
electron from a higher energy orbit to a lower energy orbit.
Bohr understood that the explanation of Balmer-Rydberg spectral formula
for hydrogen would be to show how jumps from higher to lower energetic
orbits around the atom would emit photons of light at just the frequencies
in the formula.
The emission of a light particle, photon, occurs in the transition of an
electron from higher to lower orbit. So this is the set of empirical
measurements which Bohr could use to judge whether or not his atomic
model was real.
But for Bohr to construct his model, he had to make a major conceptual
break with Newtonian mechanics – paradigm shift.
Bohr and Rutherford knew something had to be non-classical about the
electron if they were to orbit the nucleus of an atom – because of the
classical electromagnetic radiation by accelerating electrons.
Niels Bohr (1885-1962) was to solve the issue of how electrons orbit the nucleus
of an atom. Bohr was born in Denmark. As a young man he went to England as
an undergraduate at Trinity College, Cambridge. He returned to Denmark and
received a doctorate from Copenhagen University in 1911.
He returned to England did a post doctoral research under Ernest Rutherford in
the University of Manchester. There Bohr learned of Rutherford’s experiments
and devoted himself to theoretically modeling the structure of the atom.
The new philosophical idea of what is a fundamental particle at an atomic scale
required new phenomenological ideas (such as ‘matter waves’) along with new
mathematical ideas (such as ‘traveling wave packets’).
Where did Bohr get his new philosophical ideas for modeling the atom?
After Newton’s triumph of science in the late 1600s for mechanics and later
after Maxwell’s triumph of science in the middle 1800s, it seemed then to
contemporary observes that the science of physics may have completely laid
down its foundations. But this was not to be.
The research of Max Planck would establish the idea that atoms radiated light
in discrete quantized energy.
Max Planck (1858-1947) was born in Kiel, Germany, and attended the
University of Munich in 1874. He focused his research on the mechanical
theory of heat, and in 1894 began his studies of the physical phenomenon of
‘black body radiation’. An electricity company had asked him to research
how to gain the most light efficiently from the new light bulbs.
Then in 1905, four years after Planck’s law, Albert Einstein added to the new
quantum idea of mechanics:
that the quantization of the gas molecule’s oscillations was an example of
how light generally interacted with atomic matter -- traveling as a wave but
interacting with matter as a kind of particle (photon).
He wrote that in another physical phenomena, the photoelectric effect, the
absorption (in contrast to emission) of light by the electrons of an atom
occurred also as discrete packets (quantum of light) -- photons.
Einstein proposed that the energy of a photon (E) is proportional to its
frequency (v) by Planck’s constant (h): E = hv.
Albert Einstein (1879-1955) was born Wurttemberg, Germany.
Einstein graduated with a teaching diploma from the Swiss Federal Institute
in Zurich, Switzerland in 1901. He looked for a teaching position.
But upon not finding one, he took a job as an assistant patent examiner in
the Swiss Federal Office for Intellectual Property in 1903.
Then in1905, the physics journal , Annalen der Physik, published four key
papers by the young Einstein:
(1) The photoelectric effect that demonstrated light interacted with
electrons in discrete energy packets;
(2) Brownian motion which explained the random paths of particles in
suspended in a liquid as direct evidence of molecules;
(3) Special relativity which postulated the speed of light was a constant in
the universe with the same value as seen by and observer and implied that
the mass of an object increased as the velocity neared the speed of light;
(4) Equivalence of matter and energy in that mass could be converted into
energy at the quantity E=mc2.
Thus nature’s answer to Newton’s puzzle about the nature of light, wave or
particle, turned out to both.
Light travels as an electromagnetic wave, according to Maxwell’s equations.
But when interacting with matter (atoms), light acts like a particle,
transmitting or receiving energy in discrete bundles (quanta), according to h=
E/v.
So that Planck’s constant h is a minimum ‘bundle/quantum’ of energy
transmitted between light and atoms.
At a macro-scale in classical physics, there can be a continuous range of
energy transfers between things (Newtonian mechanics).
But at a micro-scale (atomic level) there are only discrete transfers of energy
(quanta) between light and atoms (Quantum mechanics).
THE PARADIGM SHIFT IN PHYSICS FROM CLASSICAL NEWTONIAN MECHANICS TO
QUANTUM MECHANICS WAS REQUIRED BY A SCALE CHANGE IN PHYSICAL
PHENOMENA – FROM MACRO-SCALE TO ATOMIC-SCALE.
PARADIGM’S FOLLOW NATURE, AND NATURE DOES NOT FOLLOW PARADIGMS.
Now back to the story of Niels Bohr at Rutherford’s laboratory in Cambridge
in 1912.
Bohr knew of Planck’s quantization of the energy of radiant light (in 1900)
and Einstein’s interpretation of this quantization as particles, photons, of
light.
So Bohr knew that light traveled as wave in motion but interacted with
matter (atoms) as a particle – a wave/particle duality of the nature of light.
If the emission of light by an atom must be quantized, then perhaps the
orbits of electrons must also have quantum features.
And a quantum feature might explain the stable orbits of electrons in an
atom.
BOHR’S MODEL OF THE ATOM
(1) ELECTRONS TRAVEL IN ORBITS ABOUT THE NUCLEUS WITH DISCRETE (QUANTIZED)
ORBITS.
(2) ELECTRONS DO NOT LOSE ENERGY IN THEIR STABLE ORBITS.
BOHR’S MODEL
The electron in circular orbit is attracted to the positive nucleus by an
electrostatic attractive force (Fa = ke2/r2) with an potential energy (E = ke2/2r ).
(Where the energy E is the integral of the force F acting over distance r -- or the
Force is the differential of the Energy with respect to distance r. (Newton’s
calculus). To remain in orbit, the attractive force and centrifugal force must be
equal: Fa = Fg or ke2/r2 = mv2/r or v2 = ke2/mr or v = (ke2/mr)1/2
Centrifugal
Force
mv2/r
Velocity v
v=(ke2/mr)1/2
v
Centripetal
Force
2 2
Potential ke /r
Angular
Momentum
L = mvr
Energy
Ep=ke2/r
Radius
r
Nucleus
Positive Charged
Proton (e+)
Electron
Negatively Charged
eCircular Orbit
Of electron
Around
Nucleus
What feature of an electron orbit should be quantized? This was Bohr’s puzzle.
He made a great guess. Perhaps it was the angular momentum? The angular
momentum (mvr) is an essential feature of an orbit.
Bohr assumed that the angular momentum of the electron for a stable orbit is
quantized in units n of Planck’s constant: ( mvr = nh ) or (r = nh/mv),
where m is mass of electron, v is velocity, and r is radius of orbit and h is Planck’s
constant.
Then in a quantized orbit:
r = nh/mv or r= nh/m(ke2/mr)1/2
-- ( where v = (ke2/mr)1/2 )
nh = mr(ke2/mr)1/2 or nh = (m2r2ke2/mr)1/2 or nh= (mrke2)1/2
Squaring both sides gives: n2h2 = mrke2, so that
r = n2h2/mke2 .
Bohr substituted this quantized radius for a stable orbit into the equation for the
potential energy of the electron in the orbit: E=ke2/2r.
Then the momentum-quantized orbit has energy:
E = ke2/2r or E = mke2ke2/2n2h2 or E = mk2e4/2h2n2 or E = R/n2
Bohr defined the Rydberg constant R as R = mk2m4/2h2 .
After Bohr defined the Rydberg constant as R = mk2m4/2h2 , he found the
calculated value matched the experimentally-measured value of R, which Rydberg
had analyzed from spectral experiments on light-emission from the hydrogen
atom.
Then Bohr had an equation for the stable orbits of an electron with quantized
angular momentum as depending upon the Rydberg number and differing from
energy level to energy level by the inverse square of integer numbers:
E = R/n2 .
The integers n give the different quantum energy levels of the stable orbits. The
energy of the orbits differ one from another by the inverse of squared integers
1/n2.
When an electron dropped from a stable higher-energy orbit En+1 to a stable lowerenergy orbit En, the difference of energy the electron could give up to an emitted
photon is:
En+1- E1 = R(1/(n+1)2 – 1/n2).
Bohr set this equal to the quantized energy (hf) of the photon emitted with
frequency f:
hf = R(1/n+1)2 – 1/n2).
Thus Bohr had derived the Rydberg’s formula – experiment grounding theory.
Transitions from one energy orbit to a higher energy orbit (discrete in energy
changes) occurred both when an electron absorbed a photon or when an
electron fell back into the lower energy orbit by emitting a photon.
These transitions were quantized both as angular momentum of stable
atomic orbits and as packets of photon energy. In calculating the series of
transitions, Bohr’s photon emission spectrum just matched that
experimentally seen in the hydrogen light emission spectrum. Bohr’s atomic
theory just matched experiment!
Bohr had successfully modeled Rutherford’s atom. But to do so, later physicists
learned that the electron (as well as the photon) must have a wave/particle duality!
Classical physics needed to be added to with quantum physics to explain nature
at both a micro-level and at a smaller atomic level.
THE PARADIGM SHIFT IN PHYSICAL MECHANICS WAS REQUIRED
FOR EXTENDING THE MECHANISM PARADIGM ACROSS
THE SPACIAL SCALES OF NATURE.
In the mechanistic paradigm, physical processes are depicted on different scales,
from very, very small spaces up toward very, very large spaces. This is the
microscopic-to-macroscopic explanatory strategy of science through special scale..
In the very smallest space we have to date, the sub-particle space, the fundamental
particles are made up of smaller particles, quarks and gluons
In the next spatial size up, the atomic nuclei and orbiting electrons form atoms. The
atom is constructed of negatively-charged electrons orbiting the positively-charged
nucleus.
In the next spatial size up, molecules are formed from combinations of atoms that
bond together by the exchanging outer electrons (valant bonding) or sharing outer
electrons (co-valant bonding
In the next spatial size up, atoms or molecules stabilize in liquid or solid
configurations as domains or polymeric structures. This is the domain-level scale of
space.
In the next spatial size up, we find the microscopic level of the organization of matter
as aggregates or organisms.
We humans exist on a macro scale of space of organism system.
Finally, there are two more scales of space above this macro-level -- the planetary
and cosmic levels.
TIME LINE FOR SCIENTIFIC PROGRESS AS QUANTUM MECHANICS
Technology
Scientific
Events
Theory:
Experiment:
Electromagnetism
Rutherford
Maxwell
Atom
1864
1909
Experiment:
Thomson
Electron
1897
Technology
Analysis:
Spectral Lines
Balmer/Rydberg
1890
Scientific
Events
Theory:
Quantum
Radiation
Planck
1901
Theory & Paradigm:
Quantum Mechanics
Schroedinger
Jordan
Born
Experiment:
Theory:
Heisenberg
Photoelectric
Quantum Atom Dirac
Effect
Theory:
Bohr
1913-1922
Photon
1913
Einstein
1905
Technology
Scientific
Events
Method
Method
Method
TIME
Administration
/ Paradigm
Administration
/Paradigm
Administration
/Paradigm
Bohr, Schroedinger, Heisenberg, Born, Dirac, Jordan
PHYSICAL THEORY
The paradigm of mechanism makes modern physical theory possible.
Physical theory allows all physical morphologies of any technology to be
represented as mechanisms and enable manipulations of nature by the
technology to be predictable.
In the paradigm of mechanism, a generic technology strategy for the physical
aspects of all technologies can be devised as a scaling strategy -- improve
technology by better understanding nature at a smaller or greater scale.
Physical phenomenon at one spatial scale can be explained by physical
mechanisms at a smaller spatial scale. A generic technology strategy for
improving any physical technology is to understand nature mechanically at a
smaller scale.
The scientific paradigm of mechanism provides the intellectual perspective
(framework) for observing physical nature and understanding nature as
physical mechanisms.
A theoretical representation of a mechanism has (1) a description of nature as
special and temporal kinematics and (2) an explanation of nature as energy
dynamics, which in mathematical form allows (3) prediction of nature.
Physical theory provides a scientific representation of nature as mechanism -consisting of description, explanation, and prediction of nature.
FOUR PARADIGMS IN SCIENCE
WORLD
SELF
MATTER
MECHANISM
FUNCTION
MIND
SYSTEMS
LOGIC
ILLUSTRATION:
NESSI SEMANTIC TECHNOLOGIES WORKING GROUP ROADMAP
SESA = SEMANTIC ENABLED SERVICE APPLICATION SYSTEM
Advanced Engineering Materials and Technologies - EuMaT
Advisory Council for Aeronautics Research in Europe - ACARE
Embedded Computing Systems - ARTEMIS
European Biofuels Technology Platform - Biofuels
European Construction Technology Platform - ECTP
European Nanoelectronics Initiative Advisory Council - ENIAC
European Rail Research Advisory Council - ERRAC
European Road Transport Research Advisory Council - ERTRAC
European Space Technology Platform - ESTP
European Steel Technology Platform - ESTEP
European Technology Platform for the Electricity Networks of the Future - SmartGrids
European Technology Platform for Wind Energy - TPWind
European Technology Platform on Smart Systems Integration - EPoSS
Food for Life - Food
Forest based sector Technology Platform - Forestry
Future Manufacturing Technologies - MANUFUTURE
Future Textiles and Clothing - FTC
Global Animal Health - GAH
Hydrogen and Fuel Cell Platform - HFP
Industrial Safety ETP - IndustrialSafety
Innovative Medicines for Europe - IME
Integral Satcom Initiative - ISI
Mobile and Wireless Communications - eMobility
Nanotechnologies for Medical Applications - NanoMedicine
Networked and Electronic Media - NEM
Networked European Software and Services Initiative - NESSI
Photonics21 - Photonics
Photovoltaics - Photovoltaics
Plants for the Future - Plants
Robotics - EUROP
Sustainable Chemistry - SusChem
Water Supply and Sanitation Technology Platform - WSSTP
Waterborne ETP - Waterborne
SCIENTIFIC METHODOLOGY
IN PHYSICAL SCIENCE PROPOSALS
OBSERVATION:
PHYSICAL
INSTRUMENT:
SENSORY
EXPERIMENT:
PHYSICAL
PARADIGM:
MECHANISM
THEORY:
PHYSICAL
ANALYSIS:
MATHEMATICAL
MODALITY:
PREDICTION
SCIENTIFIC METHODOLOGY IN MULTI-DISCIPLINARY PROPOSALS
OBSERVATION:
PHYSICAL
INSTRUMENT:
SENSORY
OBSERVATION:
PURPOSE
EXPERIMENT:
PHYSICAL
INSTRUMENT:
PARADIGM:
MECHANISM
THEORY:
PHYSICAL
EXPERIMENT:
PARADIGM:
FUNCTION
ANALYSIS:
MATHEMATICAL
THEORY:
BIOLOGICAL
ANALYSIS:
MODALITY:
PREDICTION
MODALITY:
PRESCRIPTION
OBSERVATION:
PROCESS
OBSERVATION:
LINGUISTIC
INSTRUMENT:
EXPERIMENT:
INSTRUMENT:
PARADIGM:
SYSTEM
THEORY:
DESIGN
PARADIGM:
LOGIC
ANALYSIS:
MODALITY:
SUFFICIENCY
EXPERIMENT:
THEORY:
REASON
ANALYSIS:
MODALITY:
NECESSITY