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Title: GDST1013 The Power of Science and Technology

GDST1013 The Power of Science and Technology
An Introduction
  • Course Introduction
  • What is Science
  • A Brief Introduction to the Scientific Revolution
  • The Power and Limits of Science

Course Introduction
  • Course Code GDST1013
  • Title The Power of Science and Technology
  • Textbook none
  • Website ISpace

  • Instructor Prof. Ken Tsang
  • Office E409
  • Phone 3620606
  • Email
  • Teaching Assistant (TA)
  • Ms. Garbo Hu
  • Email

Time Venue (3)
  • 800-950am, Tuesday C208
  • 1300-1350pm, Thursday E301

Course Content schedule (subject to adjustment)
  • Week 1 Introduction
  • Week 24 Statistics Module
  • Week 5 Quiz
  • Week 6-7 Group presentation
  • Week 8-10 Computer Module
  • week 11 Guest Lecture or other activity?
  • Week 12-13 Group presentation
  • Week 14 Review for Final Exam

Assessment (from syllabus)
  • Class Participation 10
  • Written assignment/Project 40
  • Quiz/test (week 5) 10
  • Final Examination 40

Part I What is Science
What is Science
  • Can we describe what science is using your own
  • Can you give a few examples of what you consider
    to be science?
  • Can you name a few scientists?
  • And a few examples of what is NOT science?

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Science -- ??
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Definition Science
  • (knowledge from) the careful study of the
    structure and behavior of the physical world,
    especially by watching, measuring and doing
    experiments, and the development of theories to
    describe the results of these activities. from
    the Cambridge Dictionary

Science (From Wikipedia)
  • Science (from Latin scientia, meaning
    "knowledge") is a systematic enterprise that
    builds and organizes knowledge in the form of
    testable explanations and predictions about the
  • In an older and closely related meaning,
    "science" also refers to a body of knowledge
    itself, of the type that can be rationally
    explained and reliably applied.

Definition Measure Experiment
  • Measure to discover the exact size or amount of
    something, or to be of a particular size.
  • Experiment a test done in order to learn
    something or to discover is something works or is
    true (verification)
  • Can you give a few important scientific
    experiments in the history?

Definition Theory
  • Theory a formal statement of the rules on which
    a subject of study is based or of ideas that are
    suggested a fact of event or, more generally, an
    opinion or explanation
  • Theories are powerful explanations for a wide
    range of phenomena.

Definition Technology
  • Technology (the study and knowledge of) the
    practical, especially industrial, use of
    scientific discoveries
  • Can you give a few examples of technology?

Discussion Sharing
  • Is mathematics science? Why?
  • Is Chinese medicine science? Why?
  • Is Feng shui (??) science? Why?
  • Is Astrology science? Why?

Example of Scientific Study Free Falling Objects
  • Given two balls, one is ten-pound and the other
    one-pound. If dropping both balls off at the same
    time, which ball will hit the ground first? The
    heavier one, or the lighter one?

What Aristotle Said
  • Aristotle (384BC-322BC)
  • A Greek philosopher, student of Plato and teacher
    of Alexander the Great
  • He studied many subjects encompassing physics,
    logic, politics, ethics, aesthetics and
  • He had taught that heavy objects fall faster
    than lighter ones, in direct proportion to
  • Is this theory true or false? How to prove?

What Galileo Did
  • Galileo (1564-1642)
  • An Italian physicist, mathematician, astronomer
    and philosopher who played a major role in the
    Scientific Revolution. He is considered as the
    father of modern science
  • A biography by Galileo's pupil Vincenzo Viviani
    stated that Galileo had dropped balls of the same
    material, but different masses, from the Leaning
    Tower of Pisa to demonstrate that their time of
    descent was independent of their mass.

Discovering the Laws of Nature
  • Galileo was willing to change his views in
    accordance with observation.
  • Galileo was one of the first modern thinkers to
    clearly state that the laws of nature are

Galileo physics should be mathematical
  • Philosophy i.e. physics is written in this
    grand book I mean the universe
  • but it cannot be understood unless one first
    learns to comprehend the language and interpret
    the characters in which it is written. It is
    written in the language of mathematics, and its
    characters are triangles, circles, and other
    geometrical figures

Galileos On Motion (1590)
  • Some superficial observations have been made as,
    for instance, that the free motion of a heavy
    falling body is continuously accelerated. But to
    just what extent this acceleration occurs has not
    yet been announced. For so far as I know, no one
    has yet pointed out the distances traversed
    during equal intervals of time by a body falling
    from rest stand to one another in the same ratio
    as the odd numbers beginning with unity.

Galileo's Inclined Plane Experiments
  • Start the ball rolling at time t-zero and count
    equal intervals of time as it rolls down the
  • Take the distance covered in the first time
    interval as a unit of measure

Experiment Results
Galileos Result on Free Fall Objects
  • In the absence of air resistance, all objects
    experience the same acceleration due to gravity
  • g is the acceleration due to gravity (9.81 m/s2
    near the surface of the earth)

What Can We Predict
  • Using Galileos theory, if we drop a feather and
    a stone at the same time from the Pisas Tower,
    which will hit the ground first? Why?
  • What else can we predict?
  • What experiment condition do we need to verify
    Galileos theory?

Hammer and Feather Drop
  • In 1971, Apollo 15 astronaut David Scott on the
    Moon recreating Galileo's famous experiment.
  • A 1.32-kg aluminum geological hammer) and a light
    object (a 0.03-kg falcon feather) were released
    simultaneously from approximately the same height
    (1.6 m)
  • the objects were observed to undergo the same
    acceleration and strike the lunar surface

Practical Application of the Theory
  • To estimate how deep the well is
  • Count the number of seconds (n) taken for the
    stone to hit the water at the bottom of the well.
  • Add up the first n odd numbers starting at 1.
  • Multiply the result by 5 metres.
  • For example, the stone takes three seconds to
    fall. That means the water is 13595m or 45
    metres down the shaft.

Summary the Scientific Method
  • Testing ideas with evidence gathered from the
    natural world
  • Ask a question
  • Formulate a hypothesis
  • Perform experiments
  • Collect and analyze data
  • Draw conclusion (Induction)
  • Make predictions (deduction)
  • Further Verification to confirm

The Scientific Community
  • The progress of science depends on interactions
    within the scientific community that is,
  • the community of people and organizations that
    generate scientific ideas, test those ideas,
    publish scientific journals, organize
    conferences, train scientists, distribute
    research funds, etc.

The Scientific Community
  • This scientific community provides the cumulative
    knowledge base that allows science to build on
  • It is also responsible for the further testing
    and scrutiny of ideas and for performing checks
    and balances on the work of community members.

Think Science
  • Question what you observe
  • Why does an apple fall onto the ground?
  • Investigate further
  • Find out what is already known about your
    observations (literature review)
  • Be skeptical
  • Challenge existing ideas

Think Science
  • Try to refute your own ideas
  • Look at things from the other side of the
  • Seek out more evidence
  • Be open-minded
  • Change your mind if the evidence warrants
  • Think creatively
  • Try to come up with alternate explanations

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What Science Does Not Do
  • make moral judgments,
  • make aesthetic judgments,
  • tell you how to use scientific knowledge,
  • draw conclusions about supernatural explanations.
  • Science is an important part of human knowledge,
    but it isnt everything.

Part II A Brief History ofScience
A Brief History of Science
  • The Origin of Classical Science
  • The Scientific Revolution

Human History technology
  • Human history has always been shaped by science
    technology. In the pre-history, there were
  • The Stone Age
  • The Neolithic Era (New Stone age, the
    Agricultural Revolution)
  • The Bronze Age
  • The Iron Age

??? Beginning of history
The Origin of Science
  • Ancient Greeks are seen as the intellectual
    forefathers of the western civilization
  • Greek philosophers made great discoveries of
    theorems by deductive reasoning (logic)
  • Pythagoras (570-495BC?????) number is the
    ultimate nature of reality
  • Euclids (????) Elements of Geometry
  • Plato let no one ignorant of Geometry enter

The Origin of Science
  • Greek scholars were in general mostly theoretical
    thinkers in philosophy logic
  • With some exceptions
  • Aristotle (?????, 384BC 322 BC)
  • Archimedes (????, 287 BC 212 BC)
  • Euclid ( ????, "Father of Geometry" 300BC)
  • They sowed the seed of modern science.

A brief history of ancient Western Civilization
800 BC (Greek epic poem) Iliad Odyssey Socrates
470? 399 BC Plato 424? 348 BC Aristotle 384?
322 BC
First Roman Emperor Augustus 63 BC-14 AD
Roman Empire
Constantine I legalized Christianity in Roman
Empire, 330 AD moved the capital to Constantinople
395 AD Christianity became official state religion
Byzantine Empire 330-1453 AD
476 AD End of the western Roman Empire Germanic
Roman general Odoacer deposed Emperor Romulus
Homer's Iliad and the Odyssey Trojan War
The Trojan War was waged against the city of Troy
by the Achaeans (Greeks) after Paris of Troy took
Helen from her husband Menelaus, king of Sparta.
The ancient Greeks thought that the Trojan War
was a historical event that had taken place in
the 13th or 12th century BC, and believed that
Troy was located in modern-day Turkey.
Alexander the Great (356 323 BC)
Shakespearean tragedy Antony and Cleopatra
The last pharaoh of Ancient Egypt, Cleopatra,
consummated a liaison with Julius Caesar that
solidified her power.
After Caesar's assassination in 44 BC, she
aligned with Mark Antony (Roman general and
important supporter of Julius Caesar) in
opposition to Caesar's legal heir, Gaius Julius
Caesar Octavianus (Augustus). After losing the
Battle of Actium to Octavian's forces, Antony
Cleopatra committed suicide.
Greek Fate and Order of Nature
  • The Greek view of nature was dramatic
  • Their vision of fate, remorseless and
    indifferent, urging a tragic incident to its
    inevitable end, is the vision possessed by
  • Fate in Greek Tragedy becomes the order of nature
    in modern thought
  • The laws of physics are the decrees of fate

Medieval Europe
  • After centuries of civil war and corruption the
    western Roman Empire disappeared when Odoacer
    deposed the last Roman Emperor in 476AD.
    Barbarian hordes swept over the west and razed
    the last vestiges of this once mighty empire.
    Europe entered what is commonly called "The Dark
    Ages". Most major city centers lay in ruins,
    however, monasteries, because they were remote
    and hard to access, remained and within them were
    retained the culture and book knowledge lost
    everywhere else.
  • In medieval Europe only the monks and nobility
    could read and write and study knowledge.
    Monasteries became the keeper of knowledge and
    center of education, until Johann Gutenberg
    invented the first printing press in the 1450's
    and changed the situation so that knowledge was
    made available to everyone.

Medieval Europe Rationality God
  • In the Middle Ages, there was a belief in the
    rationality of God (Christianity)
  • There is a secret in the nature that can be
    unveiled every detailed occurrence can be
    correlated with its antecedents in a perfectly
    definite manner, exemplifying general principles
  • The search of natural laws could result in the
    vindication of the faith in rationality

Precursors to the Scientific Revolution
  • Fall of Constantinople 1453 the migration of
    Greek scholars and texts to Italy
  • Renaissance
  • Leonardo da Vinci 14521519, Michelangelo
  • The Printing Press Gutenberg Bible 1450
  • Discovery of America Christopher Columbus 1492

Renaissance rediscovery of the Greek spirit
Venus de Milo Created 130 - 100 BC
Statue of David Michelangelo 1504
The Printing Press
  • The world's first movable type printing
    technology was invented and developed in China by
    Bi Sheng (?? ?-1051) between the years 1041 and
    1048. ??????
  • Re-invented and improved by a goldsmith from
    Mainz, Germany, Johannes Gutenberg, 1450.

Wine Press Screw
Carolingian Script
Moveable type
(No Transcript)
The Printing Press
  • First book ever printed on a printing press using
    moveable type
  • The Gutenberg Bible 1450

Why Printing Press is so important to the
Scientific Revolution
  • Books became more affordable to ordinary people
    (cost producing a book becomes 300 times
  • No more transcription errors, making knowledge
    accumulation much easier.
  • nothing new under the sun, ancient discoveries
    soon became forgotten.

Books produced per Year
Economic Impact of the Printing Press
1776 The Wealth of Nations published
1945-Atomic bomb
1687-Newton published Principia Mathematica
1905-Special Relativity
The Historical Revolt
  • Consequence of the invention of movable type
    printing press
  • In 1517, Martin Luther started the Protestant
    Reformation (????)
  • In science, the spread of Heliocentric cosmology
    and the inductive method of reasoning with
    experimental data

The Scientific Revolution
  • The "Scientific Revolution" refers to historical
    changes in thought belief that unfolded in
    Europe between roughly 1550-1700
  • Beginning with Nicholas Copernicus (1473-1543),
    who asserted a heliocentric (sun-centered)
    cosmos, it ended with Isaac Newton (1642-1727),
    who proposed universal laws and a Mechanical

Before Copernicus
The accepted geocentric Aristotelian system,
which placed the earth at the center of the solar
system, with the sun and planets in orbit.
Copernicus Revolution
Why Did Copernicus put the Sun at the center?
  • As improvements were made in the skills of
    observation, more and more circles and epicycles
    were called for to explain the movement of
    heavenly bodies.
  • A simple, regular, ordered and hierarchical
    system had, over time, become very complicated.
  • Copernicus wanted a simpler model

On the Revolutions of the Heavenly Bodies (1543)
  • He began to believe that the earth went round the
    sun about 1507.
  • Realizing his theory would offend, he decided to
    publish his findings in 1543, the year of his
  • The knowledge of the time was not sufficient to
    prove his theory his great argument for it was
    from its simplicity as compared to the epicycle

Giordano Bruno (1548-1600)
  • Italian philosopher mathematician, poet and
  • executed by the Roman Catholic Church because of
    his Copernican view and belief the Sun was just
    another star moving in space.
  • Remembered as the martyr of free thought and
    modern scientific ideas.

Johannes Kepler (1571-1630)
  • A German mathematician and astronomer
  • Kepler was forced to the realization that the
    orbits of the planets were not the circles
    demanded by Aristotle and assumed implicitly by
    Copernicus, but were instead the "flattened
    circles" that geometers call ellipses

The Laws of Planetary Motion
Later, Sir Isaac Newton utilized Kepler's
theories and observations in formulating his
theory of gravitational force.
Galileo Galilei (1564-1642)
  • The key to all of Galileo's discoveries was the
    accurate measurement of time.
  • Galileo used the uniform motion of the pendulum
    to measure time
  • Galileo experimented with various sorts of
    motions and falling bodies.
  • He formulated the basic law of falling bodies,
    which he verified by careful measurement.

Galileis Confession
  • In 1610 Galileo pointed his telescope at Jupiter
    and observed the orbits of four of its moons.
  • On the basis of his scientific observations
    Galileo became a heliocentrist.
  • On 22 June 1633 Galileo was forced to make a
    'confession' to the Cardinals of the Holy Office
    of the Church.

After Galileos Death
  • The weight of papal authority which had succeeded
    in halting the growth of the new science in
  • Following Galileo's death in 1642 that the
    greatest advances in science would come from
    outside Italy in Protestant countries (with a
    tradition of protest and toleration) like
    England, Holland and Germany.

1642 as a Significant Year
  • Isaac Newton (1642-1727????), the man most
    responsible for producing modern science was
  • 1620. Francis Bacon published Novum Organum
  • 1644. René Descartes (Principles of Philosophy)
    I think, therefore I am
  • 1644. The Manchu conquer China ending the Ming
  • 1760 beginning of Industrial Revolution

The Scientific Methodology
  • By the 17th century, science, scientific thinking
    had spread to the rest of Europe
  • Occam's razor ( 1300)
  • The Baconian method empiricism
  • René_Descartes rationalism "That we cannot
    doubt of our existence while we doubt, and that
    this is the first knowledge we acquire when we
    philosophize in order."

Occams Razor (?????)
  • a principle first developed by the Franciscan
    friar and philosopher, William of Ockham (1287
  • The simplest answer is most often correct.
  • If you have more than one hypotheses that could
    explain an observation, the hypothesis with the
    fewest and simplest assumptions should be

Sir Francis Bacon (1561-1626)
  • Bacon has been called the creator of empiricism.
  • He established and popularized inductive
    methodologies for scientific inquiry.
  • Bacon's empirical approach helped to clearly
    separate science from philosophy.

Bacons Bee Metaphor
  • Those who have handled sciences have been either
    men of experiment or men of dogmas. The men of
    experiment are like the ant, they only collect
    and use the reasoners resemble spiders, who make
    cobwebs out of their own substance. But the bee
    takes a middle course it gathers its material
    from the flowers of the garden and of the field,
    but transforms and digests it by a power of its
  • Francis Bacon The New Organon Book One. 1620.

Bacons Bee Metaphor
  • Good scientists are not like ants (mindlessly
    gathering data) or spiders (spinning empty
    theories). Instead, they are like bees,
    transforming nature into a useful product.
  • Not unlike this is the true business of
    philosophy for it neither relies solely or
    chiefly on the powers of the mind, nor does it
    take the matter which it gathers from natural
    history and mechanical experiments and lay it up
    in the memory whole, as it finds it, but lays it
    up in the understanding altered and digested.
    Therefore from a closer and purer league between
    these two faculties, the experimental and the
    rational (such as has never yet been made), much
    may be hoped.

Knowledge(Science) is Power
  • Bacon was one of the first to fully understand
    that knowledge is power.
  • He believed science would serve to improve the
    human condition and create a better world
  • Bacon noted in his Novum Organum Scientiarum
    (1620) "printing, gunpowder, and the nautical
    compass . . . have altered the face and state of
    the world first, in literary matters second, in
    warfare third, in navigation,"

Rene Descartes (1596-1650)
  • A French philosopher and mathematician
  • He invented the Cartesian Coordinate System,
    credited as the father of analytical geometry
  • A major figure in the 17th-century Continental
    rationalism (deduction)

Rene Descartes (1596-1650)
  • He is considered as the father of modern
  • Best known for his philosophical statement
    "Cogito ergo sum" (I think, therefore I am)
  • Dualism he suggested that the body works like a
    machine and the mind was a nonmaterial and does
    not follow the laws of nature

English Reformation
  • Henry VIII (1531) sole protector and Supreme
    Head of the Church of England
  • Edward VI (1547-1553) more Reformation
  • Mary I (1553-1558) Catholic Restoration
  • Elizabeth I (1558-1603) Supreme Governor of the
    Church of England
  • James I King James Bible, most widely printed
  • book in history

Henry VIII his children The family that
changed the History of England
Under Queen Elizabeth Is leadership, England
defeated the Spanish Armada in 1588 and enjoyed
The irony of history
Queen Elizabeth Is contribution
Isaac Newton (1642-1727)
  • Born when the Church of England was totally
    independent from Rome
  • In 1687, Newton finished his greatest work, The
    Mathematical Principles of Natural Philosophy
  • The most influential book
  • in the history of science

Newtons Contributions to Science mathematics
  • Three laws of motion
  • Theory of universal gravitation
  • The first practical reflecting telescope
  • A theory of color
  • Shares the credit for the development of the
    differential and integral calculus
  • The generalized binomial theorem, the study of
    power series

Newtons Quote
  • If I have seen further it is by standing on the
    shoulders of giants
  • I do not know what I may appear to the world, but
    to myself I seem to have been only like a boy
    playing on the sea-shore, and diverting myself in
    now and then finding a smoother pebble or a
    prettier shell than ordinary, whilst the great
    ocean of truth lay all undiscovered before me

The Newtonian Worldview
  • Reductionism
  • to understand any complex phenomenon, you need to
    take it apart properties of a system are
    explainable by explaining the individual behavior
    of its smallest parts.
  • Materialism
  • all phenomena, whether physical, biological are
    ultimately constituted of matter

The Newtonian Worldview
  • Determinism/mechanism
  • If you know the initial positions and velocities
    of the particles constituting a system together
    with the forces acting on those particles (which
    are themselves determined by the positions of
    these and other particles), then you can in
    principle predict the further evolution of the
    system with complete certainty and accuracy.

The Newtonian Worldview
  • Dualism
  • The Newtonian worldview considers the physical
    and spiritual realms to be entirely separate.
  • while material objects obey mechanical laws, the
    mind does not
  • This way physics can avoid conflicting with

The Clockwork Universe
  • The Universes is like a giant clock that was
    assembled and wound up by God, but no longer
    needs anything else to keep functioning according
    to its rule of operation.

if we conceive of an intelligence that at a
given instant comprehends all the relations of
the entities of this universe, it could state the
respective position, motions, and general affects
of all these entities at any time in the past or
future. Pierre-Simon Laplace (1749 1827)
Influence of NewtonianWorldview
  • Newtonian thinking has had a profound
  • influence on society the concept of
  • natural law inspired democracy
  • The mechanistic and deterministic view of nature
    also inspired communism.
  • Dualism has had a profound impact on the way we
    see ourselves in relation to nature.

The Expectation of the Newtonian Worldview
  • PHYSICS would eventually explain CHEMISTRY
    CHEMISTRY would explain BIOLOGY and BIOLOGY
    would explain PSYCHOLOGY.
  • Love, joy and courage had been reduced to
    chemical reactions within the brain and the body
  • Do you agree, yes or not? Why?

Discussion Sharing
  • Do you agree that love can be eventually reduced
    to some physical movements of the chemicals
    within your body? Why?
  • Do you agree that the universe is a huge machine,
    or an organism? Why?

Scientists Were Very Optimistic
  • In the late 1800s, most physicists believed that
    physics was complete, described by classical
    mechanics, thermodynamics, and the Maxwell
  • All that remains to do in physics is to fill in
    the sixth decimal place (Albert Michelson, 1894)

Nothing New to be Discovered
  • There is nothing new to be discovered in physics
    now. All that remains is more and more precise
    measurement. (Lord Kelvin, an influential British
    physicist, 1900)

The Two Clouds of Physics
  • But Lord Kelvin also mentioned two clouds on
    the horizon of physics The beauty and clearness
    of the dynamical theory, which asserts heat and
    light to be modes of motion, is at present
    obscured by two clouds.
  • 1) Blackbody radiation
  • 2) Michelson-Morley experiment

Modern Physics
  • Kelvin's two "clouds" instead represented
    fundamental limits to a classical approach to
    understanding the universe.
  • Their resolution introduced whole new (and
    clearly unanticipated) realms of physics, known
    collectively as "modern physics.
  • The first cloud Quantum Physics
  • The second cloud Relativity

  • No matter how we may single out a complex from
    nature...its theoretical treatment will never
    prove to be ultimately conclusive... I believe
    that this process of deepening of theory has no
    limits. (Albert Einstein, 1917)

Part III The Power and Limits of
ScienceAdvances of science in the 20th Century
The Discovery of DNA
  • 1953, James Watson and Francis Crick deduced the
    double helix structure of DNA Nobel Prize for
    Physiology or Medicine (1962)
  • One of the most important scientific discovery of
    the 20th century

Atom Bomb
  • First Atomic Bomb, codenamed Trinity, tested near
    Alamogordo, New Mexico, on July 16, 1945

Atomic bomb mushroom clouds over Hiroshima (left
August 6, 1945) and Nagasaki (right August 9)
Manned Moon Landing
  • The Apollo 11 mission astronauts Neil Armstrong
    and Buzz Aldrin landed their Lunar Module (LM) on
    the Moon on July 20, 1969, and walked on its
    surface while Michael Collins remained in lunar
    orbit in the command spacecraft, and all three
    landed safely on Earth on July 24.

The Invention of the Computer
  • The ENIAC, 1946 the first general-purpose
    electronic computer.

Transistor Integrated Circuit
  • John Bardeen, Walter Brattain William Shockley
    Nobel Prize in Physics (1956) "for their
    researches on semiconductors and their discovery
    of the transistor effect (1947)
  • Jack Kilby ( Robert Noyce) Nobel Prize in
    Physics (2000) "for his part in the invention of
    the integrated circuit (1958)"

The Internet
  • Packet switched networks in US, such as ARPANET,
    Tymnet, and Telenet, were developed in the late
    1960s and early 1970s using a variety of
  • In 1982, the Internet Protocol Suite (TCP/IP)
    was standardized and the concept of a world-wide
    network of fully interconnected TCP/IP networks
    called the Internet was introduced.

Discovery of Quantum Mechanics
  • In 1929, theoretical physicist Paul Dirac
    announced "The general theory of quantum
    mechanics is now complete. . . . The underlying
    physical laws necessary for the mathematical
    theory of a large part of physics and the whole
    of chemistry are thus completely known." The
    discipline at the point was four years old. Dirac
    himself was just 27.

The Limits of Science
  • The limit of measurement
  • The limit of mathematics
  • The limit of prediction
  • The limit of computation

The Limit of Measurement
  • The Uncertainty (Heisenberg) Principle
  • the more precisely the position of some particle
    is determined, the less precisely its momentum
    can be known, and vice versa.
  • The Observer Effect
  • measurements of certain systems cannot be made
    without affecting the systems
  • the uncertainty principle is inherent in the
    properties of all wave-like systems

The Limit of Mathematics
  • Gödel's incompleteness theorems
  • Any effectively generated theory capable of
    expressing elementary arithmetic cannot be both
    consistent and complete. There is an arithmetical
    statement that is true, but not provable in the
  • such a system cannot demonstrate its own

The Limit of Prediction
  • Chaos Theory
  • When the present determines the future, but the
    approximate present does not approximately
    determine the future.
  • Tiny difference of the input will produce totally
    different output
  • Therefore the future is unpredictable
  • http//

Discussion and Sharing
  • Is the stock market predictable? Why?
  • Is your own behavior predictable? Why?

The Limit of Computation
  • Most real world problems are not computable,
    i.e., there does not exist a step-by-step
    procedure to solve it
  • For example, the halting problem to decide
    whether a computer program will halt or not
  • For most computable problems, there is no known
    efficient way to solve them
  • NP-complete problems, for example, the travelling
    salesman problem

The travelling salesman problem
  • Given a list of cities and the distances between
    each pair of cities, what is the shortest
    possible route that visits each city exactly once
    and returns to the origin city?
  • The problem was first formulated in 1930 and is
    one of the most intensively studied problems in
    optimization. It is used as a benchmark for many
    optimization methods.

  • What is Science
  • A Brief Introduction to the Scientific Revolution
  • The Power and Limits of Science

The Rest of the Course
  • Science has many fields
  • We will not cover all of them

The Rest of the Course
  • We will focus on the following two very useful
  • Statistics Financial Mathematics
  • Computer science
  • You will learn to appreciate the power of beauty
    of science and technology
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