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Einstein Quotes

Einstein Quotes. Fast alle die Kerle sehen n ämlich nicht von den Tatbest änden aus die Theorie, sondern nur von der Theorie aus die Tatbestände; sie k önnen aus dem einmal angenommenen Begriffsnetz nicht heraus, sondern nur possierlich darin herumzappeln.

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Einstein Quotes

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  1. Einstein Quotes • Fast 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 UHL Seminar, November 2008

  2. Chances are … Peter BryantThe Business SchoolUniversity of Colorado Denver UHL Seminar November 2008

  3. Risky business • In the last year, the world-wide stock market has lost about half its value. • Risk has always been a problem: • Shipments may get lost • Planes and trains and cars may crash • You or I might get sick • Someone might rob us • How do you feel about risk? UHL Seminar, November 2008

  4. Historically, risk was, well, just there • Risk is just part of the human condition • There’s nothing you can do about it • Be fatalistic, take comfort in religion, avoid all risks • Pretty limiting UHL Seminar, November 2008

  5. The idea of insurance • Aveducto wants to send ten bales of woolens from Pisa to Sicily. • Such trips are dangerous • Robbers, brigands,… • Storms at sea,… • Aveducto is concerned • He contracts with Nicolao to ship the woolens to Sicily. • But what if there’s a problem? • Why not buy insurance? UHL Seminar, November 2008

  6. Insurance… • Insurance: Aveducto pays a fee to Amigueto. Amigueto promises to pay Aveducto the price of his woolens if it should happen that the shipment doesn’t get to Sicily. • Aveducto has to pay a fee, but he’s sure that he’ll get the price of his shipment. The fee (the premium) is what he pays to be sure of his money. UHL Seminar, November 2008

  7. Insurance… • Problem 1: What should the fee be? • How much are the bales worth? (easy) • What is the chance they won’t get there? (hard) UHL Seminar, November 2008

  8. Insurance… • Problem 2. This is 1343 A.D., and insurance is illegal. • The Roman Catholic Church considers it usury – you may not charge a fee for the use of money. • Since Aveducto is getting less money than his goods are worth, that looks like usury. • Effectively, unless you can specifically identify the value of the risk, you can’t charge a fee for it. • This ban lasts (at least officially) until about 1840 A.D. UHL Seminar, November 2008

  9. Getting around the problem Policy 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, 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 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 re- ceived 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 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 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 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 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 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 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, 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 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 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 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. (Quoted in Humbert O. Nelli, “The Earliest Insurance Contract. A New Discovery,” Journal of Risk and Insurance, Vol. 39, No. 2 (Jun 1972), pp 215-220. UHL Seminar, November 2008

  10. Components of Risk • Consequences of a loss • Chance of loss • How did you feel about these in the public health director example? • Let’s see.. UHL Seminar, November 2008

  11. Components of Risk • Consequences of a loss • Chance of loss • Example 1: • We flip a coin. • If it comes up heads, I buy you coffee • If it comes up tails, you buy me coffee. • Probability of success = 0.5 • “Value of game” = Zero UHL Seminar, November 2008

  12. Components of Risk • Consequences of a loss • Chance of loss • Example 2: • We flip a coin. • If it comes up heads, I buy you coffee UHL Seminar, November 2008

  13. Components of Risk • Consequences of a loss • Chance of loss • Example 2: • We flip a coin. • If it comes up heads, I buy you coffee • If it comes up tails, you have to cut off your right arm with a lawnmower blade. UHL Seminar, November 2008

  14. Components of Risk • Consequences of a loss • Chance of loss • Example 2: • We flip a coin. • If it comes up heads, I buy you coffee • If it comes up tails, you have to cut off your right arm with a lawnmower blade. • Probability of success = 0.5 UHL Seminar, November 2008

  15. Components of Risk • Consequences of a loss • Chance of loss • Example 2: • We flip a coin. • If it comes up heads, I buy you coffee • If it comes up tails, you have to cut of your right arm with a lawnmower blade.. • Probability of success = 0.5 • “Value of game” = ??? UHL Seminar, November 2008

  16. Components of Risk • Consequences of a loss • Chance of loss • Example 2: • We flip a coin. • If it comes up heads, I buy you coffee • If it comes up tails, you have to cut of your right arm with a lawnmower blade.. • Probability of success = 0.5 • “Value of game” = One half of (The price of a cup of coffee - Value of right arm) UHL Seminar, November 2008

  17. To manage risk in a commerical, practical, reliable way… • You must be able to quantify the consequences • You must be able to quantify the chances • But humans are unreliable at doing this…at least intuitively UHL Seminar, November 2008

  18. Quantifying chances • In some situations, it’s easy • Coin flipping • Die rolling • Card drawing • Even then, though, minor modifications can make it tricky. UHL Seminar, November 2008

  19. Problem 1 • A (tiny) deck of cards has two cards: • A Red/Red card --- red on both sides • A Red/Black card – red on one side, black on the other. • The “deck” is shuffled, and one card is drawn at random, and randomly placed on the table. • 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. • 0 • 1/4 • 1/3 • 1/2 • 2/3 • 3/4 • 1 • Somethingelse UHL Seminar, November 2008

  20. Simulation UHL Seminar, November 2008

  21. The “right” answer UHL Seminar, November 2008

  22. The “right” answer UHL Seminar, November 2008

  23. The “right” answer UHL Seminar, November 2008

  24. The “right” answer UHL Seminar, November 2008

  25. The “right” answer Probability of Red/Red card, given Red face showing = (1/2)/(3/4) =2/3 UHL Seminar, November 2008

  26. Problem 2 • 3 prisoners, you, Joe, and Gladys, are in a dungeon. • The guard appears, saying “One of you has been chosen at random to be executed tomorrow morning. I’m not allowed to tell you which.” • You ask the guard “tell me the name of one of the others (Joe or Gladys) who will be spared.” • The guard, who is truthful and unbiased, says “OK,” and tells you that Joe (say) will be spared. • Given all this, the probability that you will be executed tomorrow is: • 0 • 1/4 • 1/3 • 1/2 • 2/3 • 3/4 • 1 • Something else UHL Seminar, November 2008

  27. Simulation UHL Seminar, November 2008

  28. The “right” answer UHL Seminar, November 2008

  29. The “right” answer UHL Seminar, November 2008

  30. The “right” answer UHL Seminar, November 2008

  31. The “right” answer UHL Seminar, November 2008

  32. The “right” answer Probability you get executed given guard says “Joe to be spared” = (1/6)/(1/2) = 1/3 (unchanged!) UHL Seminar, November 2008

  33. Problem 3 • In a room of 40 people, the probability that there is at least one pair of matching birthdays (Month and Day) is: • 0 • 1/40 • 40/366 • 40/365 • Between 15% and 25% • Between 25% and 50% • Between 50% and 75% • More than 75% UHL Seminar, November 2008

  34. The “right” answer • Pr[At least one match] = 1 – Pr[no match] = 1- (365/365)(364/365)(363/365)…(326/365) = 0.891 UHL Seminar, November 2008

  35. Themes • Do we know what we mean by chance? Probability? Uncertainty? Ignorance? Are they the same? • Do we confuse probability with consequences? Combine them? • We’re not usually any good at intuitively guessing probabilities – don’t guess: compute! • Probability is a percentage: of what? UHL Seminar, November 2008

  36. When is probability relevant? • If 95% of all couples who jump off Lover’s Leap survive, that gives me guidance. UHL Seminar, November 2008

  37. When is probability relevant? • If 95% of all couples who jump off Lover’s Leap survive, that gives me guidance. • If we jumped, and we’re now in mid-air, what does that 95% mean to us now? UHL Seminar, November 2008

  38. When is probability relevant? • If a marriage counselor tells you that based on your characteristics your proposed marriage has only a 25% chance of lasting ten years, how do you feel? UHL Seminar, November 2008

  39. When is probability relevant? • If a marriage counselor tells you that based on your characteristics your proposed marriage has only a 25% chance of lasting ten years, how do you feel? • If the marriage counselor now tells you that the chances for any marriage surviving ten years are only 15%, does that change how you feel? UHL Seminar, November 2008

  40. When is probability relevant? • If a marriage counselor tells you that based on your characteristics your proposed marriage has only a 25% chance of lasting ten years, how do you feel? • If the marriage counselor now tells you that the chances for any marriage surviving ten years are only 15%, does that change how you feel? • Should it change how you feel? UHL Seminar, November 2008

  41. Final Exam question • A 95% reliable screening test is administered to check for the presence of an icky condition. That is, of all the people who actually have the icky condition, 95% are labeled “icky,” while 5% are labeled “healthy.” Further, of all the people who don’t actually have the icky condition, 95% are labeled “healthy,” while 5% are labeled “icky.” • All those people who test positive for the condition (i.e. all those whom the test labels “icky”) are sent to a clinic, where a 100% reliable test is administered to check for the condition. • Of all those people sent to the clinic, what percentage really have the condition? UHL Seminar, November 2008

  42. Final Exam question Pr(Really icky given labeled “icky”) = (.95X)/(5+.90X) But we don’t know X. So we don’t know the probability. UHL Seminar, November 2008

  43. So what?? • Be suspicious of guesses about probability. • If it’s your money – don’t guess, compute! • If it’s something more valuable than money --- think even harder. UHL Seminar, November 2008

  44. Some References • Peter L. Bernstein, Against the Gods. The Remarkable Story of Risk, 1996, John Wiley and Sons • Darrel Huff (with Irving Geis), How to Lie With Statistics, 1954, W. W. Norton • Darrell Huff (with Irving Geis), How to Take a Chance, 1959, W. W. Norton • Deborah J. Bennett, Randomness, 1998, Harvard University Press • Theodore M. Porter, The Rise of Statistical Thinking 1820-1900, Princeton University Press • Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900, 1986, Belknap Press of Harvard University. UHL Seminar, November 2008

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