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Against the Gods
Transcript of Against the Gods
BEGINNINGS When Greeks wanted a prediction about future, they turned to oracles... They believed that the order is to be found only in the skies...
The precision was the monopoly of the Gods... God"s"... Future is still a mystrey but it is determined by ONE power whose intensions and standards are clear to all... The will of single God... But calculation was very hard ... pebble: calculus sand-tray: abacus ????? Greeks had a system... Without numbers, there are no odds and no probabilities; without odds and probabilities, the only way to deal with risk is to appeal to the gods and the fates. Crusades... West met Middle East... Roman numerals met Arab-Hindu numbering system... The centerpiece was the invention of "zero" Liber Abaci: The Book of Abacus Fibonacci Al-Khowarizmi First mathematician to establish rules for adding, substracting, multiplying and dividing Omar Hayyam Reformed calendar. Figured squares, cubes. Higher powers of mathematics Resistance to change:
Fraud is easier Infidel numbers!
Disguising as Muslims if you want to learn! Recap (~ to 1200)
New numbering system
Mathematical achievements but...
The missing ingredients:
- The freedom of thought
- The passion for experimentation
- The desire to control the future Girolamo Cardano (mathematician, physicist and gambler's gambler) The Great Art The first major work of the Renaissance to concentrate on algebra. Book on Games of Chance The first serious effort to develop the statistical principles of probability. We will never know whether Cardano wrote the Book on Games of Chance as a primer on risk management for gamblers or as a theoretical work on the laws of probability. Cardano
Chavalier de Mere SAMPLING Briefy history of sampling
Neither a staticitian, nor a demographer.
Not a mathematician, an actuary, a scientist, a university don or a politician...
A rich businessman with interest in COUNTING...
Inventor of SAMPLING... Natural and Political Observations made upon Bills of Mortality Essential to risk taking... Statisticians joke:
a man with his feet in the oven and his head in the refrigerator, on the average, feels pretty good 1700-1900 Daniel Bernoulli "The value of an item must not be based on its price, but rather on its utility" Exposition of a New Theory on the Measurement of Risk How people make decisions (what we said so far)
Expected values are computed by multiplying each possible gain by the number of ways in which it can occur, and then dividing the sum of these products by the total numbers of cases....PURE math! What Bernoulli thinks:
It focuses only on the facts; it ignores the consequences of a probable outcome for a person who has to make a decision when the future is uncertain.
Gut rules the measurement! What we say:
Human beings employ both measurement and gut in making decisions when outcome is uncertain Recap 1200-1700:
Sampling The problem is that we never have all the information we would like.
Nature has established patterns, but only for the most part. Uncertainity can be measured...
Jacop Bernouilli: Law of Large Numbers (Average)
Abraham de Moivre: Bell Shaped Curve (Standard Deviation)
Thomas Bayes: Inverse Probability (Prior-Posterior)
Gauss: Normal Distribution (Universe)
Galton: Regression to the Mean (What goes up must come down) by Peter L. Bernstein Senem Acet Coskun 1 2 3 4 5 6 7 8 9 0 Past frequencies can collide with degrees of belief when risky choices must be made. Then why is forecasting so frustrating??? Regression to the mean...
1. So slow pace that a shock will disrupt the process
2. So strong that matters do not come to rest once they reach the mean.
3. The mean itself is not stable. What was normal yesterday may not be normal today 1900-1960 Up to now:
Measurement and gut
Gut and measurement John Maynard Keynes:
Most of our decisions can only be taken as a result of animal spirits, not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities. Frank Knight:
A priori reasoning cannot eliminate indeterminateness from the future. The world of pure probability does not exist except on paper
Our decisions matter Game Theory Earlier theories accepted uncertainity as a fact of life and did little to identify its source.
Game theory says that the true source of uncertainity lies in the intentions of "others". Prospect Theory Game theory:
How people "should" make decisions in the face of risk
Not everyone rational.
Emotions often destroys self-control
People often unable to understand fully what they are dealing with Chaos Theory Relatively new
Rejects the symmetry of the bell curve
Sensitive dependence on intial conditions Butterfly Effect Recap:
Game theory: People are not isolated
Prospect theory: Not everyone is rational
Chaos theory: Not everythig is linear TODAY Genetic Algorithms
Neural Networks Bottom-line:
Likeness to truth is not the same as truth
No data about future THANK YOU! 1200-1700 MUMBO JUMBO What about uncertainity? No numbers, no odds, no probabilities
Laws of Probability (with known rules)
Sampling (without known rules)
Human effect into measurement
Uncertainity (can be measured)
First Measurement and Then Gut
No, the other way around...
Chaos Theory What about new risks created by risk management? hahaha What I think? We sometimes use measurement And sometimes gut... John von Neumann Amos Tversky & Daniel Kahneman What do you do when a decision leads to a result that was not even in your set of probabilities?
Or when low-probability outcomes seem to occur more frequently than they should?