Einstein Quotes

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 cant 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
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?

4
Historically, risk was, well, just there

• Risk is just part of the human condition
• Theres nothing you can do about it
• Be fatalistic, take comfort in religion, avoid
  all risks
• Pretty limiting

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 theres a problem?
• Why not buy insurance?

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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
  doesnt get to Sicily.
• Aveducto has to pay a fee, but hes sure that
  hell get the price of his shipment. The fee (the
  premium) is what he pays to be sure of his money.

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Insurance

• Problem 1 What should the fee be?
• How much are the bales worth? (easy)
• What is the chance they wont get there? (hard)

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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 cant charge a fee for
  it.
• This ban lasts (at least officially) until about
  1840 A.D.

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.

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Components of Risk

• Consequences of a loss
• Chance of loss
• How did you feel about these in the public health
  director example?
• Lets see..

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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

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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

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.

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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

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 ???

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)

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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 thisat least
  intuitively

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Quantifying chances

• In some situations, its easy
• Coin flipping
• Die rolling
• Card drawing
• Even then, though, minor modifications can make
  it tricky.

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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
• Something else

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Simulation
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The right answer
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The right answer
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The right answer
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The right answer
25
The right answer
Probability of Red/Red card, given Red face
showing (1/2)/(3/4) 2/3
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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.
  Im 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

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Simulation
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The right answer
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The right answer
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The right answer
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The right answer
32
The right answer
Probability you get executed given guard says
Joe to be spared (1/6)/(1/2) 1/3
(unchanged!)
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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

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The right answer

• PrAt least one match 1 Prno match 1-
  (365/365)(364/365)(363/365)(326/365)
• 0.891

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Themes

• Do we know what we mean by chance? Probability?
  Uncertainty? Ignorance? Are they the same?
• Do we confuse probability with consequences?
  Combine them?
• Were not usually any good at intuitively
  guessing probabilities dont guess compute!
• Probability is a percentage of what?

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When is probability relevant?

• If 95 of all couples who jump off Lovers Leap
  survive, that gives me guidance.

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When is probability relevant?

• If 95 of all couples who jump off Lovers Leap
  survive, that gives me guidance.
• If we jumped, and were now in mid-air, what does
  that 95 mean to us now?

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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?

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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?

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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?

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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
  dont 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?

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Final Exam question
Pr(Really icky given labeled icky)
(.95X)/(5.90X) But we dont know X. So we dont
know the probability.
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So what??

• Be suspicious of guesses about probability.
• If its your money dont guess, compute!
• If its something more valuable than money ---
  think even harder.

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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.