Class 2

β employee of the month

235 A.C.

Hellenism - After Alexander The centuries after Alexander's death are known as the era of Hellenism. One might argue Hellenism lasted from the years of Alexander's reign until 146 BC, when Greece was annexed by the Roman empire; or even until 30 BC, when the famous Greek-Egyptian Queen Cleopatra died, the last Hellenistic ruler. In any case, Hellenism was the new world order shaped by Alexander's conquests. Trade The campaigns of Alexander had opened up gigantic areas to world trade and economic development. The conquering Greeks had aroused the sleeping masses of the east and profitable industries and agricultural enterprises sprung up everywhere. Because Alexander had started to mint the gold reserves of the Persian kings, huge amounts of money came into circulation. For centuries the Persian dynasts had safeguarded the treasures stored in their palaces. Alexander tried to spend them all within a matter of years. These factors combined, Hellenism can be seen as the world's first major economic boom. The system of economics and trade that developed after Alexander's death would remain basically unchanged for over two thousand years, until the industrial revolution of the 19th century. When the Romans began to expand their empire around 200 BC they inherited a world of florishing trade contacts for which Alexander had laid the foundations. http://www.pothos.co.uk/alexander.asp?ParaID=67

The Pillars of Rationality

The Rationality Paradigm
Artificial Intelligence
Economics
Management Science

What? Artificial Intelligence AND Economics?!? Never mind… These people are crazy.

Pillars of rationality Management Science Economics Artificial Intelligence Search Symbols Enumeration Logic Expected Utility Transitive ordering of alternatives Invariance Continuity Maximizing & satisficing Game theory Mathematical programming Equilibrium Inference reasoning

Historical Momentum

2 nd World War
Dresden
Auschwitz
Pearl Harbor
Hiroshima
London
Stalingrad
…

2 nd world war
Einstein’s theory and Atomic bombs
Operations research (ORSA)
Management science (TIMS)
Cryptography (Enigma), & the BOMBE
Alan Turing, Claude Shannon and computers
Von Newmann & Morgenstern (1944) Theory of games and economic behavior

Scientists usually fall for the attractor of “rigorous scientific results”

Economics Artificial Intelligence Management Science Pillars of rationality Search Symbols Enumeration Logic Expected Utility Transitive ordering of alternatives Invariance Continuity Maximizing & satisficing Game theory Mathematical programming Equilibrium Inference reasoning

Symbols, logic, and search

Logic
George Boole published his famous “Laws of thought”, which postulated a rigorous framework for inferences, now called Boolean logic. Boolean logic is the key mechanism behind the information processing of modern computers.
Example: Bongard problems and RF4

Bongard problems

RF4 project
K. Saito, and R. Nakano, Adaptive concept learning algorithm, IFIP Transactions A – Computer Science and Technology 51 (1994) 294-299
TRIANGLE (coordinates, line_width, … remaining properties) LINE_SEGMENT (coordinates, … remaining properties) ?

RF4: Symbols, logic, and search

 B  boxes ,  x 1  B , shape ( x 1)= polygon  class 1.
FALSE
Symbol

FALSE
BP#38:  B  boxes ,  x 1, x 2  B , shape ( x 1)= polygon  shape ( x 2)= oval  class 1.
FALSE
Logical statement

FALSE
FALSE
BP#38:  B  boxes ,  x 1, x 2, x3  B , shape ( x 1)= polygon  shape ( x 2)= oval  shape ( x 3)= line  class 1.
FALSE

FALSE
FALSE
BP#38:  B  boxes ,  x 1, x 2, x3  B , shape ( x 1)= polygon  shape ( x 2)= oval  shape ( x 3)= line  class 1.
FALSE
BP#38:  B  boxes ,  x 1, x 2  B , shape ( x 1)= polygon  shape ( x 2)= oval  size ( x 1)> size ( x 2)  class 1.
TRUE

The structure of management science

Management Science
Methodology
1. Problem identification & modelling
2. Determination of the set of possible alternatives
3. Determination of an evaluation criterion for these alternatives
4. Evaluation of the alternatives
5. Selection of an alternative as a final decision

Knapsack Problem
decision : for any item i , if i is taken, then Selection i =1
but if i is abandoned, then Selection i =0
Maximize
Subject to the constraint that total weight does not exceed capacity

Knapsack problem of a truck driver ? Capacity: 10 meters 9 meters, $111/m 3 meters, $100/m 5 meters, $100/m 2 meters, $100/m

Mystery #1 How many possibilities for a 100 item knapsack problem? Be the mind!

Chess
Game theory and the minimax algorithm

The Rabaul-Lae Convoy (1943)

The Rabaul-Lae convoy (1943)

The complexity of the chess game
In 1989 the game known as connect-four was solved (the first to play wins). The space of possibilities of this game holds 10^13 positions, and it was solved by exhaustive search.
Chess holds 10^44 positions, which demands 10,000,000,000,000,000,000,000,000,000,000 times the computational complexity of solving connect-four.
In practical terms, chess cannot be solved.

“ What is emerging, therefore, from research on games like chess, is a computational theory of games: a theory of what is reasonable to do when it is impossible to determine what is best – a theory of bounded rationality . The lessons taught by this research may be of considerable value for understanding and dealing with situations in real life that are even more complex than the situations we encounter in chess – in dealing, say, with large organizations, with the economy, or with relations between nations”
H. Simon, The game of chess,
in Handbook of game theory with economic applications

Bounded rationality
Bounded rationality is rationality as exhibited by decision makers of limited abilities. The ideal of RATIONAL DECISION MAKING formalized in RATIONAL CHOICE THEORY, UTILITY THEORY, and the FOUNDATIONS OF PROBABILITY requires choosing so as to maximize a measure of expected utility that reflects a complete and consistent preference order and probability measure over all possible contingencies. This requirement appears too strong to permit accurate description of the behavior of realistic individual agents studied in economics, psychology, and artificial intelligence. Because rationality notions pervade approaches to so many other issues, finding more accurate theories of bounded rationality constitutes a central problem of these fields.
MIT ENCYCLOPEDIA OF COGNITIVE SCIENCES

Expected Utility Theory

Legal Disclaimer: This talk will not teach you how to predict the stock market or get rich quick.

What is a stock? Owning stock in a company indicates ownership of the assets and the future earnings of that company. A company’s stock is divided into many small pieces called shares.

Example: Microsoft (MSFT) The total market value of Microsoft’s assets and potential future earnings is about $272,000,000,000. (2003) There are about 11,000,000,000 shares of Microsoft stock available to buy. Therefore, the price of one share is about $25. (By the way, Bill Gates owns more than a billion shares of Microsoft stock!)

Price of one share of Microsoft Jan 1996 to Dec 1999

Price of one share of Microsoft Jan 2000 to Nov 2003

The trade
In buying such assets, we trade certainty for uncertainty.
HOW MUCH SHOULD A RATIONAL PERSON PAY?

St. Petersburg Paradox
From Nicolas Bernoulli’s letter
Consider the following game
Peter flips a coin and will give Paul:
$2 if the first flip is a head
$2 k if the k th flip is the first head

Mystery #2 How much should we pay to enter the St. Petersburg paradox? Be the mind!

Remember the law of large numbers!
2

St. Petersburg Paradox (cont)
The expectation is infinitely great but no one would be willing to purchase it at a moderately high price.

If you could some how measure happiness, the average person would likely be much happier to win $1,000 than $1. On the other hand, that same person would probably be equally happy to win $1,001,000 and $1,000,000. That is, happiness generally does not increase linearly with wealth.

Some Premises of EUT
Transitive ordering of alternatives
Dominance
Cancellation
Continuity
Invariance

Transitive ordering of alternatives
For any two alternatives A and B:
Either one is preferred; or
The decision maker is indifferent
If an outcome A is preferred over outcome B, and B is preferred over outcome C, then:
Outcome A is preferred over outcome C.

Dominance
If a car A is superior in mileage, cost, and looks then car B, then A strongly dominates B .
If a car A is superior in mileage, but equivalent in cost and looks, then A weakly dominates B .

Continuity
A rational decision maker should prefer a gamble, instead of a sure gain, if the odds of the best outcome are “good enough”.

Invariance
A rational decision maker is not affected by the way or the order in which alternatives are presented.
If the mathematics do not change, then the decision does not change.

Economics Artificial Intelligence Management Science Pillars of rationality Search Symbols Enumeration Logic Expected Utility Transitive ordering of alternatives Invariance Continuity Maximizing & satisficing Game theory Mathematical programming Equilibrium Inference reasoning

Thomas Schelling
2005 Nobel prize in economic sciences
“ for having enhanced our understanding of conflict and cooperation through game-theory analysis”

Theory of Nuclear Deterrence
Nuclear deterrence refers to the strategic concept that a country can remain at peace by using the threat of nuclear weapons to forestall acts of invasion by its enemies. A country relying on this concept must possess a more powerful nuclear weapons structure than that of its enemies. The pursuit of "parity of force" and "peace based on strength" was behind the aggressive race toward nuclear expansion.

Little Boy (Hiroshima) Fat Man (Nagasaki)
The 15,000 tons of TNT equivalent unleashed by little boy emanated from the fission of a single Kg of its 10—35 kgs of Uranium 235.

2 a World War firepower  3 Megatons
3 Millions of Tons of TNT ~ 3 Billions suicide bombers

300 Megatons
Firepower capable of destructing all the large and medium sized cities on the planet

1 Trident Submarine (10) 24 Megatons 1 Poseidon Submarine (41) 9 Megatons 2 a World War (3 Megatons) Planet Earth, 1981: 18,000 MEGATONS

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Class 2

by Alexandre Linhares on Oct 16, 2006

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