einstein quotes

UHL Seminar, November 2008UHL Seminar, November 2008

Einstein QuotesEinstein QuotesFast alle die Kerle sehen nämlich nicht von den Tatbeständen aus die Theorie, sondern nur von der Theorie aus die Tatbestände; sie können aus dem einmal angenommenen Begriffsnetz nicht heraus, sondern nur possierlich darin herumzappeln.

Almost all those guys avoid viewing the theory from the point of view of the facts, but only view the facts from the point of view of the theory; they can’t escape the conceptual net they have accepted, but can only daintily wriggle in it.

Letter to Erwin Schrödinger, 8 August 1935

Da könnt mir halt der liebe Gott leid tun. Die Theorie stimmt doch. Antwort auf die Frage: „Wie würden sie reagieren, wenn die allgemeine Relativitätstheorie nicht empirisch bestätigt worden wäre?“

Then I would have to pity our dear God. The theory is correct anyway. Answer to the question: “How would you have reacted if the general theory of relativity had not been empirically confirmed?”

Various sources and versions

Chances are …Chances are …

Peter BryantPeter BryantThe Business SchoolThe Business School

University of Colorado DenverUniversity of Colorado DenverUHL Seminar November 2008UHL Seminar November 2008


Risky businessRisky business

In the last year, the world-wide stock In the last year, the world-wide stock market has lost about half its value.market has lost about half its value.

Risk has always been a problem:Risk has always been a problem:Shipments may get lostShipments may get lostPlanes and trains and cars may crashPlanes and trains and cars may crashYou or I might get sickYou or I might get sickSomeone might rob usSomeone might rob us

How do you feel about risk?How do you feel about risk?


Historically, risk was, well, just Historically, risk was, well, just therethere

Risk is just part of the human conditionRisk is just part of the human conditionThere’s nothing you can do about itThere’s nothing you can do about itBe fatalistic, take comfort in religion, avoid Be fatalistic, take comfort in religion, avoid

all risksall risksPretty limitingPretty limiting


The idea of insuranceThe idea of insurance

Aveducto wants to send Aveducto wants to send ten bales of woolens from ten bales of woolens from Pisa to Sicily.Pisa to Sicily. Such trips are dangerousSuch trips are dangerous

Robbers, brigands,…Robbers, brigands,… Storms at sea,…Storms at sea,… Aveducto is concernedAveducto is concerned

He contracts with Nicolao He contracts with Nicolao to ship the woolens to to ship the woolens to Sicily.Sicily. But what if there’s a But what if there’s a

problem?problem? Why not buy insurance?Why not buy insurance?


Insurance…Insurance…

Insurance:Insurance: Aveducto pays a fee to Aveducto pays a fee to Amigueto. Amigueto promises to pay Amigueto. Amigueto promises to pay Aveducto the price of his woolens if it Aveducto the price of his woolens if it should happen that the shipment doesn’t should happen that the shipment doesn’t get to Sicily.get to Sicily.

Aveducto has to pay a fee, but he’s sure Aveducto has to pay a fee, but he’s sure that he’ll get the price of his shipment. The that he’ll get the price of his shipment. The fee (the premium) is what he pays to be fee (the premium) is what he pays to be sure of his money.sure of his money.



Problem 1: What should the fee be?Problem 1: What should the fee be?How much are the bales worth? (easy)How much are the bales worth? (easy)What is the chance they won’t get there? What is the chance they won’t get there?

(hard)(hard)



Problem 2. This is 1343 A.D., and insurance is Problem 2. This is 1343 A.D., and insurance is illegal.illegal. The Roman Catholic Church considers it usury – you The Roman Catholic Church considers it usury – you

may not charge a fee for the use of money. may not charge a fee for the use of money. Since Aveducto is getting less money than his goods Since Aveducto is getting less money than his goods

are worth, that looks like usury.are worth, that looks like usury.

Effectively, unless you can specifically identify Effectively, unless you can specifically identify the value of the risk, you can’t charge a fee for it.the value of the risk, you can’t charge a fee for it.

This ban lasts (at least officially) until about 1840 This ban lasts (at least officially) until about 1840 A.D.A.D.


Getting around the problemGetting around the problemPolicy of February 13, 1343Policy of February 13, 1343

In the name of God, Amen. I, Amigueto Pinello, free son, I swear, of Johannus (Giovanni) Pinello, do promise to you, In the name of God, Amen. I, Amigueto Pinello, free son, I swear, of Johannus (Giovanni) Pinello, do promise to you, Tomaso Grillo, agent and with the title of agent for Aveducto Guillelmo, citizen and merchant of Panormo (concerning Tomaso Grillo, agent and with the title of agent for Aveducto Guillelmo, citizen and merchant of Panormo (concerning which agency there is agreement in public docu ment written at Pisa by the hand of a citizen of Pisa and notary on the which agency there is agreement in public docu ment written at Pisa by the hand of a citizen of Pisa and notary on the bank of the Arno, Henry, the son of a certain Bonincontro, on Saturday the 13th of February, in the year of our Lord, 1343 bank of the Arno, Henry, the son of a certain Bonincontro, on Saturday the 13th of February, in the year of our Lord, 1343 eleventh year of the indictio) * that I have and have received from you with mutual favor and love-you giving and sharing eleventh year of the indictio) * that I have and have received from you with mutual favor and love-you giving and sharing in the said name of agent-680 gold florins of money, the money, you swear, of the said Aveducto. Renouncing acceptance in the said name of agent-680 gold florins of money, the money, you swear, of the said Aveducto. Renouncing acceptance of the said 680 gold florins for the said case from you under the said agency as above if they were not held, received and of the said 680 gold florins for the said case from you under the said agency as above if they were not held, received and counted in accordance with all law; and these very 680 gold florins, or their equivalent with all the same power of money, I counted in accordance with all law; and these very 680 gold florins, or their equivalent with all the same power of money, I promise and agree with you, with the said title of agent, to receive under solemn contract, and furthermore, I promise to promise and agree with you, with the said title of agent, to receive under solemn contract, and furthermore, I promise to give, pay, return and restore them to you under the said title of agent, or to the said Aveductus or to his sure agent or give, pay, return and restore them to you under the said title of agent, or to the said Aveductus or to his sure agent or messenger at your good pleasure under the title of agent and whensoever it might please you; and I acknowledge this messenger at your good pleasure under the title of agent and whensoever it might please you; and I acknowledge this completely, that if Nicolao Pinello or other for him will have given, handed over, and consigned to the said Aveductus or completely, that if Nicolao Pinello or other for him will have given, handed over, and consigned to the said Aveductus or other lawful person for him in any part inhabited of the island Sicily ten bales of woolens of the said Aveductus which he other lawful person for him in any part inhabited of the island Sicily ten bales of woolens of the said Aveductus which he promised to have transported and to see that they were transported from the port of Pisa to the said island Sicily on a promised to have transported and to see that they were transported from the port of Pisa to the said island Sicily on a galley called Santa Catalina whose lord and master is Valentino Pinello, son of the said Nicolao, and if he will have taken galley called Santa Catalina whose lord and master is Valentino Pinello, son of the said Nicolao, and if he will have taken care and seen to on behalf of the said Aveducto that the ten bales are safe on land, each and every one, which he care and seen to on behalf of the said Aveducto that the ten bales are safe on land, each and every one, which he promised to do, and further which he promised to the said same Aveducto according to the form of public document promised to do, and further which he promised to the said same Aveducto according to the form of public document written at Pisa by the hand of Henry, son of Bonincontro, citizen of Pisa and notary on the bank of the Arno on Saturday, written at Pisa by the hand of Henry, son of Bonincontro, citizen of Pisa and notary on the bank of the Arno on Saturday, February 13, in the year of our Lord, 1343, the eleventh year of the indictio, according to the use and custom of the people February 13, in the year of our Lord, 1343, the eleventh year of the indictio, according to the use and custom of the people of Pisa-if he does this: then, and in that case the present document is null and of no force as if it had never been made, if of Pisa-if he does this: then, and in that case the present document is null and of no force as if it had never been made, if the said Nicolao see to and takes care of the aforesaid, in the aforesaid manner contained in the said document. the said Nicolao see to and takes care of the aforesaid, in the aforesaid manner contained in the said document. Otherwise, I, the said Amigueto do pro mise to give and pay to you, the said Tomaso, under the said title of agent Otherwise, I, the said Amigueto do pro mise to give and pay to you, the said Tomaso, under the said title of agent receiving, a penalty double the said amount of 680 gold florins, with restitution of damages and loss which might be receiving, a penalty double the said amount of 680 gold florins, with restitution of damages and loss which might be incurred additionally, or lawsuits, or in accordance with the terms remaining as pre viously said. + And to thus observe incurred additionally, or lawsuits, or in accordance with the terms remaining as pre viously said. + And to thus observe this, I bind over as a pledge to you, receiving under the title of agent, all my goods that I have and will have. Done as this, I bind over as a pledge to you, receiving under the title of agent, all my goods that I have and will have. Done as above in toto. above in toto.

((Quoted in Humbert O. Nelli, “The Earliest Insurance Contract. A New Discovery,” Quoted in Humbert O. Nelli, “The Earliest Insurance Contract. A New Discovery,” Journal of Risk and InsuranceJournal of Risk and Insurance, , Vol. 39, No. 2 (Jun 1972), pp 215-220.Vol. 39, No. 2 (Jun 1972), pp 215-220.


Components of RiskComponents of Risk

Consequences of a lossConsequences of a lossChance of lossChance of lossHow did you feel about these in the public How did you feel about these in the public

health director example?health director example?Let’s see..Let’s see..



Consequences of a lossConsequences of a lossChance of lossChance of lossExample 1:Example 1:

We flip a coin.We flip a coin. If it comes up heads, I buy you coffeeIf it comes up heads, I buy you coffee If it comes up tails, you buy me coffee.If it comes up tails, you buy me coffee.Probability of success = 0.5Probability of success = 0.5 ““Value of game” = ZeroValue of game” = Zero




We flip a coin.We flip a coin. If it comes up heads, I buy you coffeeIf it comes up heads, I buy you coffee




We flip a coin.We flip a coin. If it comes up heads, I buy you coffeeIf it comes up heads, I buy you coffee If it comes up tails, you have to cut off your If it comes up tails, you have to cut off your

right arm with a lawnmower blade.right arm with a lawnmower blade.




We flip a coin.We flip a coin. If it comes up heads, I buy you coffeeIf it comes up heads, I buy you coffee If it comes up tails, you have to cut off your If it comes up tails, you have to cut off your

right arm with a lawnmower blade.right arm with a lawnmower blade.Probability of success = 0.5Probability of success = 0.5




We flip a coin.We flip a coin. If it comes up heads, I buy you coffeeIf it comes up heads, I buy you coffee If it comes up tails, you have to cut of your If it comes up tails, you have to cut of your

right arm with a lawnmower blade..right arm with a lawnmower blade..Probability of success = 0.5Probability of success = 0.5 ““Value of game” = ???Value of game” = ???



Consequences of a lossConsequences of a loss Chance of lossChance of loss Example 2:Example 2:

We flip a coin.We flip a coin. If it comes up heads, I buy you coffeeIf it comes up heads, I buy you coffee If it comes up tails, you have to cut of your right arm If it comes up tails, you have to cut of your right arm

with a lawnmower blade..with a lawnmower blade.. Probability of success = 0.5Probability of success = 0.5 ““Value of game” = Value of game” =

One half of (The price of a cup of coffee - Value of right arm)One half of (The price of a cup of coffee - Value of right arm)


To manage risk in a commerical, To manage risk in a commerical, practical, reliable way…practical, reliable way…

You must be able to quantify the You must be able to quantify the consequencesconsequences

You must be able to quantify the chancesYou must be able to quantify the chancesBut humans are unreliable at doing this…But humans are unreliable at doing this…

at least intuitivelyat least intuitively


Quantifying chancesQuantifying chances

In some situations, it’s easy In some situations, it’s easy Coin flippingCoin flippingDie rollingDie rollingCard drawingCard drawing

Even then, though, minor modifications Even then, though, minor modifications can make it tricky.can make it tricky.


Problem 1Problem 1 A (tiny) deck of cards has two cards:A (tiny) deck of cards has two cards:

A Red/Red card --- red on both sidesA Red/Red card --- red on both sides A Red/Black card – red on one side, black on the other.A Red/Black card – red on one side, black on the other.

The “deck” is shuffled, and one card is drawn at random, and The “deck” is shuffled, and one card is drawn at random, and randomly placed on the table.randomly placed on the table.

We observe that the upper face of the card is red.We observe that the upper face of the card is red. What is the probability that the other side of the card is red, too.What is the probability that the other side of the card is red, too.

00 1/41/4 1/31/3 1/21/2 2/32/3 3/43/4 11 SomethingSomething elseelse


CARD FACE SHOWING

R/B B COUNT 5000

R/R R

R/R R #RED/RED 2467 49.3%

R/B R #REB/BLACK 2533 50.7%

R/R R

R/R R #RED SHOW 3735 74.7%

R/B R #BLACK SHOW 1265 25.3%

R/R R

R/B B #REDRED|RED SHOW 2467 66.1%

R/R R

SimulationSimulation


The “right” answerThe “right” answer

Red Face Red Face ShowingShowing

Black Black Face Face ShowingShowing

Red-Red Red-Red CardCard

1/21/2

Red-Red-Black Black CardCard

1/21/2

11


The “right” answerThe “right” answerRed Face Red Face ShowingShowing



1/21/2 00 1/21/2


1/21/2

11





1/21/2 00 1/21/2


1/41/4 1/41/4 1/21/2

11





1/21/2 00 1/21/2


1/41/4 1/41/4 1/21/2

3/43/4 1/41/4 11


The “right” answerThe “right” answerRed Red Face Face ShowingShowing



1/21/2 00 1/21/2


1/41/4 1/41/4 1/21/2

3/43/4 1/41/4 11

Probability of Red/Red card, given Red face showing = (1/2)/(3/4) =2/3


Problem 2Problem 2 3 prisoners, you, Joe, and Gladys, are in a dungeon.3 prisoners, you, Joe, and Gladys, are in a dungeon. The guard appears, saying “One of you has been chosen at The guard appears, saying “One of you has been chosen at

random to be executed tomorrow morning. I’m not allowed to tell random to be executed tomorrow morning. I’m not allowed to tell you which.”you which.”

You ask the guard “tell me the name of one of the others (Joe or You ask the guard “tell me the name of one of the others (Joe or Gladys) who will be spared.”Gladys) who will be spared.”

The guard, who is truthful and unbiased, says “OK,” and tells you The guard, who is truthful and unbiased, says “OK,” and tells you that Joe (say) will be spared.that Joe (say) will be spared.

Given all this, the probability that you will be executed tomorrow is:Given all this, the probability that you will be executed tomorrow is: 00 1/41/4 1/31/3 1/21/2 2/32/3 3/43/4 11 Something elseSomething else


PCT

Number of trials 5000 100.0%

#(DIE = you) 1722 34.4%

#(DIE = Joe) 1621 32.4%

#(DIE = Gladys) 1657 33.1%

#(G SAY Joe) 2494 49.9%

#(G SAY Gladys) 2506 50.1%

#(DIE=you | G Say Joe) 837 33.6%

#(DIE=Gladys | G Say Joe) 1657 66.4%

#(DIE=you| G Say Gladys) 885 35.3%

#(DIE=Joe| G Say Gladys) 1621 64.7%

SimulationSimulation



To be To be ExecutedExecuted

Guard says Guard says “Joe “Joe

spared”spared”

Guard says Guard says “Gladys “Gladys spared”spared”

YouYou 1/31/3

JoeJoe 1/31/3

GladysGladys 1/31/3

11





spared”spared”


YouYou 1/31/3

JoeJoe 00 1/31/3 1/31/3

GladysGladys 1/31/3

11


The “right” answerThe “right” answerTo be To be

ExecutedExecutedGuard says Guard says

“Joe “Joe spared”spared”


YouYou 1/31/3

JoeJoe 00 1/31/3 1/31/3

GladysGladys 1/31/3 00 1/31/3

11


The “right” answerThe “right” answerTo be To be

ExecutedExecutedGuard says Guard says

“Joe “Joe spared”spared”


YouYou 1/61/6 1/61/6 1/31/3

JoeJoe 00 1/31/3 1/31/3


11





spared”spared”


YouYou 1/61/6 1/61/6 1/31/3

JoeJoe 00 1/31/3 1/31/3


1/21/2 1/21/2 11

Probability you get executed given guard says “Joe to be spared” = (1/6)/(1/2) = 1/3 (unchanged!)


Problem 3Problem 3

In a room of 40 people, the probability that In a room of 40 people, the probability that there is at least one pair of matching there is at least one pair of matching birthdays (Month and Day) is:birthdays (Month and Day) is:

00 1/401/40 40/36640/366 40/36540/365 Between 15% and 25%Between 15% and 25% Between 25% and 50%Between 25% and 50% Between 50% and 75%Between 50% and 75% More than 75%More than 75%



Pr[At least one match] = 1 – Pr[no match] Pr[At least one match] = 1 – Pr[no match] = = 1- (365/365)(364/365)(363/365)…(326/365)1- (365/365)(364/365)(363/365)…(326/365)

= 0.891= 0.891


ThemesThemes

Do we know what we Do we know what we mean mean by chance? by chance? Probability? Uncertainty? Ignorance? Are Probability? Uncertainty? Ignorance? Are they the same?they the same?

Do we confuse probability with Do we confuse probability with consequences? Combine them?consequences? Combine them?

We’re not usually any good at intuitively We’re not usually any good at intuitively guessing probabilities – don’t guess: guessing probabilities – don’t guess: compute!compute!

Probability is a percentage: Probability is a percentage: of what?of what?


When is probability relevant?When is probability relevant?

If 95% of all couples who jump off Lover’s If 95% of all couples who jump off Lover’s Leap survive, that gives me guidance.Leap survive, that gives me guidance.



If 95% of all couples who jump off Lover’s If 95% of all couples who jump off Lover’s Leap survive, that gives me guidance.Leap survive, that gives me guidance.

If we jumped, and we’re now in mid-air, If we jumped, and we’re now in mid-air, what does that 95% mean to us now?what does that 95% mean to us now?



If a marriage counselor tells you that If a marriage counselor tells you that based on your characteristics your based on your characteristics your proposed marriage has only a 25% proposed marriage has only a 25% chance of lasting ten years, how do you chance of lasting ten years, how do you feel?feel?


When is probability relevant?When is probability relevant? If a marriage counselor tells you that If a marriage counselor tells you that

based on your characteristics your based on your characteristics your proposed marriage has only a 25% proposed marriage has only a 25% chance of lasting ten years, how do you chance of lasting ten years, how do you feel? feel?

If the marriage counselor now tells you If the marriage counselor now tells you that the chances for that the chances for anyany marriage marriage surviving ten years are only 15%, does surviving ten years are only 15%, does that change how you feel?that change how you feel?


When is probability relevant?When is probability relevant? If a marriage counselor tells you that based on If a marriage counselor tells you that based on

your characteristics your proposed marriage has your characteristics your proposed marriage has only a 25% chance of lasting ten years, how do only a 25% chance of lasting ten years, how do you feel? you feel?

If the marriage counselor now tells you that the If the marriage counselor now tells you that the chances for any marriage surviving ten years are chances for any marriage surviving ten years are only 15%, does that change how you feel?only 15%, does that change how you feel?

ShouldShould it change how you feel? it change how you feel?


Final Exam questionFinal Exam question A 95% reliable screening test is administered to check A 95% reliable screening test is administered to check

for the presence of an icky condition. That is, of all the for the presence of an icky condition. That is, of all the people who actually have the icky condition, 95% are people who actually have the icky condition, 95% are labeled “icky,” while 5% are labeled “healthy.” Further, of labeled “icky,” while 5% are labeled “healthy.” Further, of all the people who all the people who don’t don’t actually have the icky condition, actually have the icky condition, 95% are labeled “healthy,” while 5% are labeled “icky.” 95% are labeled “healthy,” while 5% are labeled “icky.”

All those people who test positive for the condition (i.e. All those people who test positive for the condition (i.e. all those whom the test labels “icky”) are sent to a clinic, all those whom the test labels “icky”) are sent to a clinic, where a 100% reliable test is administered to check for where a 100% reliable test is administered to check for the condition.the condition.

Of all those people sent to the clinic, what percentage Of all those people sent to the clinic, what percentage really have the condition?really have the condition?


Final Exam questionFinal Exam questionLabeled Labeled “icky”“icky”

Labeled Labeled “healthy”“healthy”

Really ickyReally icky .95(X)%.95(X)% .05(X)%.05(X)% X%X%

Really Really healthyhealthy

.05(100-X)%.05(100-X)% .95(100-X)%.95(100-X)% (100-X)%(100-X)%

(5+.90X)%(5+.90X)% (95-90X)%(95-90X)% 100%100%

Pr(Really icky given labeled “icky”) = (.95X)/(5+.90X)

But we don’t know X. So we don’t know the probability.


So what??So what??

Be suspicious of guesses about Be suspicious of guesses about probability.probability.

If it’s your money – don’t guess, compute!If it’s your money – don’t guess, compute! If it’s something more valuable than If it’s something more valuable than

money --- think even harder.money --- think even harder.


Some ReferencesSome References Peter L. Bernstein, Peter L. Bernstein, Against the Gods. The Remarkable Against the Gods. The Remarkable

Story of RiskStory of Risk, 1996, John Wiley and Sons, 1996, John Wiley and Sons Darrel Huff (with Irving Geis), Darrel Huff (with Irving Geis), How to Lie With StatisticsHow to Lie With Statistics, ,

1954, W. W. Norton1954, W. W. Norton Darrell Huff (with Irving Geis), Darrell Huff (with Irving Geis), How to Take a ChanceHow to Take a Chance, ,

1959, W. W. Norton1959, W. W. Norton Deborah J. Bennett, Deborah J. Bennett, RandomnessRandomness, 1998, Harvard , 1998, Harvard

University PressUniversity Press Theodore M. Porter, Theodore M. Porter, The Rise of Statistical Thinking The Rise of Statistical Thinking

1820-19001820-1900, Princeton University Press, Princeton University Press Stephen M. Stigler, Stephen M. Stigler, The History of Statistics: The The History of Statistics: The

Measurement of Uncertainty Before 1900Measurement of Uncertainty Before 1900, 1986, Belknap , 1986, Belknap Press of Harvard University.Press of Harvard University.

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