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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 STATE OF KNOWLEDGE KNOWLEDGE.

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slide1

SCIENCE ADMINISTRATION

LECTURE 32

PARADIGM OF MECHANISM

CHANGE! – QUANTUM MECHANICS

ILLUSTRATION –

QUANTUM MODEL OF THE ATOM

FREDERICK BETZ

PORTLAND STATE UNIVERSITY

slide2

PHILOSOPHY OF SCIENCE ADMINISTRATION

PROCESS OF STATE OF

KNOWLEDGE KNOWLEDGE

TECHNICAL SCIENTIFIC SCIENTIFIC

OPERATIONS METHOD PARADIGMS

(EPISTEMOLOGY) (ONTOLOGY)

MANAGEMENT SCIENCE SCIENCE

OPERATIONS ADMINISTRATION APPLICATION

(ORGANIZATION) (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.

slide3

SCIENCE DISCIPLINES CONSTRUCT THEORY WITHIN GENERAL FRAMEWORKS OF PARADIGMS – SCIENTIFIC META-THEORIES.

DISCIPLINE

THEORY

META-THEORY

(SCIENTIFIC PARADIGM)

slide4

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.

slide5

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 pre-Socratic 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.

slide6

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.

slide7

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.

slide8

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.

slide9

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.

slide10

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

. .

Orbiting

Electron

Hydrogen Nucleus

Composed of a

Proton and Neutron

slide11

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

slide12

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.

slide13

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

slide14

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.

slide15

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.

slide16

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?

slide17

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.

slide18

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.

slide19

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.

slide20

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.

slide21

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
  • ELECTRONS TRAVEL IN ORBITS ABOUT THE NUCLEUS WITH DISCRETE (QUANTIZED) ORBITS.
  • ELECTRONS DO NOT LOSE ENERGY IN THEIR STABLE ORBITS.
slide22

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

Angular

Momentum

L = mvr

Electron

Negatively Charged

e-

Centripetal

Force

ke2/r2

Circular Orbit

Of electron

Around

Nucleus

Potential

Energy

Ep=ke2/r

Radius

r

Nucleus

Positive Charged

Proton (e+)

slide23

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 .

slide24

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 lower-energy 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.

slide25

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.

slide26

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.

slide27

TIME LINE FOR SCIENTIFIC PROGRESS AS QUANTUM MECHANICS

Theory & Paradigm:

Quantum Mechanics

Schroedinger

Jordan

Born

Heisenberg

Dirac

1913-1922

Scientific

Events

Technology

Scientific

Events

Scientific

Events

Technology

Technology

Theory:

Electromagnetism

Maxwell

1864

Experiment:

Rutherford

Atom

1909

Experiment:

Photoelectric

Effect

Theory:

Quantum Atom

Bohr

1913

Theory:

Quantum

Radiation

Planck

1901

Theory:

Photon

Einstein

1905

Experiment:

Thomson

Electron

1897

Analysis:

Spectral Lines

Balmer/Rydberg

1890

Method

Method

Method

TIME

Administration

/ Paradigm

Administration

/Paradigm

Administration

/Paradigm

slide29

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.

slide30

FOUR PARADIGMS IN SCIENCE

WORLD SELF

MECHANISM FUNCTION

SYSTEMS LOGIC

MATTER

MIND

ILLUSTRATION:

NESSI SEMANTIC TECHNOLOGIES WORKING GROUP ROADMAP

SESA = SEMANTIC ENABLED SERVICE APPLICATION SYSTEM

slide31

 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

 Zero Emission Fossil Fuel Power Plants - ZEP

slide32

SCIENTIFIC METHODOLOGY

IN PHYSICAL SCIENCE PROPOSALS

OBSERVATION:

PHYSICAL

INSTRUMENT:

SENSORY

EXPERIMENT:

PHYSICAL

PARADIGM:

MECHANISM

THEORY:

PHYSICAL

ANALYSIS:

MATHEMATICAL

MODALITY:

PREDICTION

slide33

SCIENTIFIC METHODOLOGY IN MULTI-DISCIPLINARY PROPOSALS

OBSERVATION:

PHYSICAL

OBSERVATION:

PURPOSE

INSTRUMENT:

SENSORY

EXPERIMENT:

PHYSICAL

INSTRUMENT:

EXPERIMENT:

PARADIGM:

MECHANISM

PARADIGM:

FUNCTION

THEORY:

PHYSICAL

THEORY:

BIOLOGICAL

ANALYSIS:

MATHEMATICAL

ANALYSIS:

MODALITY:

PREDICTION

MODALITY:

PRESCRIPTION

OBSERVATION:

PROCESS

OBSERVATION:

LINGUISTIC

INSTRUMENT:

EXPERIMENT:

INSTRUMENT:

EXPERIMENT:

PARADIGM:

SYSTEM

PARADIGM:

LOGIC

THEORY:

DESIGN

THEORY:

REASON

ANALYSIS:

ANALYSIS:

MODALITY:

SUFFICIENCY

MODALITY:

NECESSITY