Transcript The Power of Science and Technology

GDST1013
The Power of Science and Technology
An Introduction
Content
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Course Introduction
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What is Science
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A Brief Introduction to the Scientific
Revolution
The Power and Limits of Science
Course Introduction
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Course Code: GDST1013
Title: The Power of Science and Technology
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Textbook: none
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Website: ISpace
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Teachers
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Instructor: Prof. Ken Tsang
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Office: E409
Phone: 3620606
Email: [email protected]
Teaching Assistant (TA)
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Ms. Garbo Hu
Email: [email protected]
Time & Venue (3)
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8:00-9:50am, Tuesday
C208
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13:00-13:50pm, Thursday
E301
Course Content & schedule
(subject to adjustment)
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Week 1: Introduction
Week 2~4: 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)
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Class Participation
10%
Written assignment/Project 40%
Quiz/test (week ~5)
10%
Final Examination
40%
Part I: What is Science
What is Science
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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?
Science in Chinese-- 科学
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据说文解字，科，会意字：“从禾从斗，斗
者量也”；故“科学”一词乃取“测量之学问
”之义为名。
从唐朝到近代以前，“科学”作为“科举之
学”的略语，“科学”一词虽在汉语典籍中
偶有出现，但大多指“科举之学”。
“科学”一词由近代日本学界初用于对译
英文中的“Science”及其它欧洲语言中
的相应词汇。
Science -- 科学
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中国传统上将所有的知识统称“学问”，关
于自然物道理的学问称为“物理” 。因此古
代的物理即是自然科学， “数学”则独立于
“物理”。
自明代以后中国称研究自然物道理的学问
为格致学(王阳明)，即格物致知之学。
中国近代最早使用“科学”一词的学者大概
是康有为。他出版的《日本书目志》中就列
举了《科学入门》、《科学之原理》等书目。“
科学”一词才逐渐取代“格致学”。
Definition: Science
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(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)
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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.
Definition:
Measure & Experiment
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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?
Definition: Theory
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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
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Technology: (the study and knowledge
of) the practical, especially industrial,
use of scientific discoveries
Can you give a few examples of
technology?
Discussion & Sharing
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Is mathematics science? Why?
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Is Chinese medicine science? Why?
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Is Feng shui (风水) science? Why?
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Is Astrology science? Why?
Example of Scientific Study:
Free Falling Objects
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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
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Aristotle (384BC-322BC)
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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?
What Galileo Did
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Galileo (1564-1642)
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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
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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
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
Galileo’s On Motion (1590)
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“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
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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
Experiment Results
Galileo’s Result on Free Fall
Objects
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In the absence of air resistance, all
objects experience the same
acceleration due to gravity
V(t) = gt
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1
S(t) = gt 2
2
g is the acceleration due to gravity (9.81
m/s2 near the surface of the earth)
What Can We Predict
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Using Galileo’s theory, if we drop a
feather and a stone at the same time
from the Pisa’s Tower, which will hit the
ground first? Why?
What else can we predict?
What experiment condition do we need
to verify Galileo’s theory?
Hammer and Feather Drop
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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
Practical Application of the
Theory
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To estimate how deep the well is
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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 1+3+5=9*5m
or 45 metres down the shaft.
Summary: the Scientific Method
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Testing ideas with evidence gathered
from the natural world
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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
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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
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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.
Think Science
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Question what you observe
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Investigate further
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Why does an apple fall onto the ground?
Find out what is already known about your
observations (literature review)
Be skeptical
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Challenge existing ideas
Think Science
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Try to refute your own ideas
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Seek out more evidence
Be open-minded
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Look at things from the other side of the
argument
Change your mind if the evidence warrants
Think creatively
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Try to come up with alternate explanations
What Science Does Not Do
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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 isn’t everything.
Part II: A Brief History of
Science
A Brief History of Science
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The Origin of Classical Science
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The Scientific Revolution
Human History & technology
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Human history has always been shaped
by science & technology. In the prehistory, there were:
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The Stone Age
The Neolithic Era (New Stone age, the
Agricultural Revolution)
The Bronze Age
?? Beginning of history
The Iron Age
The Origin of Science
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Ancient Greeks are seen as the intellectual
forefathers of the western civilization
Greek philosophers made great discoveries
of theorems by deductive reasoning (logic)
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Pythagoras (570-495BC毕达哥拉斯): “number is
the ultimate nature of reality”
Euclid’s (欧几里德) Elements of Geometry
Plato: “let no one ignorant of Geometry enter”
The Origin of Science
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Greek scholars were in general mostly
theoretical thinkers in philosophy & logic …
With some exceptions:
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Aristotle （亚理斯多德, 384BC ~ 322 BC）
Archimedes （阿基米德, 287 BC ~ 212 BC）
Euclid （ 欧几里得, "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
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
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
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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
Medieval Europe
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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
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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
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Fall of Constantinople 1453: the
migration of Greek scholars and texts to Italy
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Renaissance
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Leonardo da Vinci 1452–1519,
Michelangelo 1475–1564
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
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The world's first movable type
printing technology was
invented and developed in China
by Bi Sheng (毕升 ？-1051)
between the years 1041 and
1048. [沈括《梦溪笔谈》]
Re-invented and improved by a
goldsmith from Mainz, Germany,
Johannes Gutenberg, ~1450.
Wine Press Screw
Carolingian Script
Paper
Moveable type
The Printing Press
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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
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Books became more affordable to
ordinary people (cost producing a book
becomes 300 times cheaper).
No more transcription errors, making
knowledge accumulation much easier.
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“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
1687-Newton published
Principia Mathematica
1945-Atomic bomb
1905-Special Relativity
The Historical Revolt
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Consequence of the invention of movable
type printing press
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In 1517, Martin Luther started the Protestant
Reformation (宗教改革)
In science, the spread of Heliocentric cosmology
and the inductive method of reasoning with
experimental data
The Scientific Revolution
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The "Scientific Revolution" refers to historical
changes in thought & belief that unfolded in
Europe between roughly 1550-1700;
Beginning with Nicholas Copernicus (14731543), who asserted a heliocentric (suncentered) cosmos, it ended with Isaac
Newton (1642-1727), who proposed
universal laws and a Mechanical Universe.
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?
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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)
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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
Giordano Bruno (1548-1600)
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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.
Johannes Kepler
（1571－1630）
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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)
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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.
Galilei’s Confession
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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 Galileo’s Death
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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.
1642 as a Significant Year
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Isaac Newton (1642-1727雍正五年), the
man most responsible for producing
modern science was born.
1620. Francis Bacon published Novum Organum
Scientiarum
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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
The Scientific Methodology
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By the 17th century, science, scientific
thinking had spread to the rest of Europe
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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."
Occam’s Razor (奥卡姆剃刀)
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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.
Sir Francis Bacon (1561-1626)
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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.
Bacon’s 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.
Bacon’s 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
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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)
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A French philosopher and
mathematician
He invented the Cartesian
Coordinate System, credited
as the “father of analytical
geometry”
A major figure in the 17thcentury Continental
rationalism (deduction)
Rene Descartes (1596-1650)
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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
English Reformation
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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 I’s leadership, England defeated the
Spanish Armada in 1588 and enjoyed prosperity.
The irony of history
Queen Elizabeth I’s contribution
Isaac Newton (1642-1727)
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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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Newton’s Contribution’s to
Science & mathematics
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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
Newton’s Quote
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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
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Reductionism
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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
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all phenomena, whether physical, biological
are ultimately constituted of matter
The Newtonian Worldview
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Determinism/mechanism
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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
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Dualism
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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.
The Clockwork Universe
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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 Newtonian
Worldview
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
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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
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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
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
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)
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
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)
Part III
The Power and Limits of Science:
Advances 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 generalpurpose 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 protocols.
In 1982, the Internet Protocol Suite (TCP/IP)
was standardized and the concept of a worldwide 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 Observer Effect:


the more precisely the position of some particle is
determined, the less precisely its momentum can
be known, and vice versa.
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
1.
2.
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
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
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.
Summary



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 areas:



Statistics & Financial Mathematics
Computer science
You will learn to appreciate the power
of beauty of science and technology