GDST1013 The Power of Science and Technology

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GDST1013 The Power of Science and Technology
An Introduction
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Content

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

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Course Introduction

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

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Teachers

• Instructor Prof. Ken Tsang
• Office E409
• Phone [phone]
• Email kentsang_at_uic.edu.hk
• Teaching Assistant (TA)
• Ms. Garbo Hu
• Email garbohu_at_uic.edu.hk

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Time Venue (3)

• 800-950am, Tuesday C208
• 1300-1350pm, Thursday E301

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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

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Assessment (from syllabus)

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

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Part I What is Science
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What is Science

• Can we describe what science is using your own
  language?
• 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 in Chinese-- ??

• ?????,?,???????,?????????????????????
• ????????,???????????,???????????????,??????
  ???
• ????????????????????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

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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
  universe.
• 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.

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Definition Measure Experiment

• Measure to discover the exact size or amount of
  something, or to be of a particular size.
  (quantification)
• 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?

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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.

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Definition Technology

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

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Discussion Sharing

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

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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?

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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
  metaphysics
• He had taught that heavy objects fall faster
  than lighter ones, in direct proportion to
  weight.
• Is this theory true or false? How to prove?

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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.

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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
  mathematical

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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

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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.

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Galileo's Inclined Plane Experiments

• Start the ball rolling at time t-zero and count
  equal intervals of time as it rolls down the
  plane.
• Take the distance covered in the first time
  interval as a unit of measure

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Experiment Results
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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)

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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?

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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
  simultaneously

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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.

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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

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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.

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The Scientific Community

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

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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

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Think Science

• Try to refute your own ideas
• Look at things from the other side of the
  argument
• 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.

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Part II A Brief History ofScience
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A Brief History of Science

• The Origin of Classical Science
• The Scientific Revolution

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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
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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

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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.

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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
Greek
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
Augustulus
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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.
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Alexander the Great (356 323 BC)
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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.
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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
  science
• Fate in Greek Tragedy becomes the order of nature
  in modern thought
• The laws of physics are the decrees of fate

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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.

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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

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Precursors to the Scientific Revolution

• Fall of Constantinople 1453 the migration of
  Greek scholars and texts to Italy
• Renaissance
• Leonardo da Vinci 14521519, Michelangelo
  14751564
• The Printing Press Gutenberg Bible 1450
• Discovery of America Christopher Columbus 1492

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Renaissance rediscovery of the Greek spirit
Venus de Milo Created 130 - 100 BC
Statue of David Michelangelo 1504
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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.

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Wine Press Screw
Carolingian Script
Paper
Moveable type
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The Printing Press

• First book ever printed on a printing press using
  moveable type
• The Gutenberg Bible 1450

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Why Printing Press is so important to the
Scientific Revolution

• Books became more affordable to ordinary people
  (cost producing a book becomes 300 times
  cheaper).
• No more transcription errors, making knowledge
  accumulation much easier.
• nothing new under the sun, ancient discoveries
  soon became forgotten.

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Books produced per Year
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Economic Impact of the Printing Press
1776 The Wealth of Nations published
1945-Atomic bomb
1687-Newton published Principia Mathematica
1905-Special Relativity
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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

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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
  Universe.

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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.
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Copernicus Revolution
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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

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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
  death.
• 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
  hypothesis

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Giordano Bruno (1548-1600)

• Italian philosopher mathematician, poet and
  astronomer
• 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.

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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

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The Laws of Planetary Motion
Later, Sir Isaac Newton utilized Kepler's
theories and observations in formulating his
theory of gravitational force.
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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.

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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.

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After Galileos Death

• The weight of papal authority which had succeeded
  in halting the growth of the new science in
  Italy.
• 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.

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1642 as a Significant Year

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

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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."

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Occams Razor (?????)

• a principle first developed by the Franciscan
  friar and philosopher, William of Ockham (1287
  1347)
• 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
  selected.

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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.

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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
  own.
• Francis Bacon The New Organon Book One. 1620.

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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.

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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,"

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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)

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Rene Descartes (1596-1650)

• He is considered as the father of modern
  philosophy
• 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

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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

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Henry VIII his children The family that
changed the History of England
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Under Queen Elizabeth Is leadership, England
defeated the Spanish Armada in 1588 and enjoyed
prosperity.
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The irony of history
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Queen Elizabeth Is contribution
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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

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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

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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

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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

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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.

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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
  religion.

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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.

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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)
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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.

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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?

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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?

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Scientists Were Very Optimistic

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

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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)

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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

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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

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Fortunately

• 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)

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Part III The Power and Limits of
ScienceAdvances of science in the 20th Century
101
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

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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)
103
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.

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The Invention of the Computer

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

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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)"

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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
  protocols.
• 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.

107
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.

108
The Limits of Science

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

109
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

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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
  theory
• such a system cannot demonstrate its own
  consistency

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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//en.wikipedia.org/wiki/Chaos_theory

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Discussion and Sharing

• Is the stock market predictable? Why?
• Is your own behavior predictable? Why?

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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

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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.

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Summary

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

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The Rest of the Course

• Science has many fields
• We will not cover all of them

117
The Rest of the Course

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