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94 Appendix B

the roll. Your chances of winning are roughly 1 in 6, assuming the game is fair. Now consider
the following “information” about the next roll:

• Scenario a: Someone tells you the die is loaded and the next roll will come up odd. You’ll
pick 1, 3, or 5, and your chances of winning increase to 1 in 3. You’ve been informed.
• Scenario b: Someone tells you the die is loaded and will come up odd when it will really
come up even. You’ve been misinformed.
• Scenario c: Someone tells you that the dealer is spinning a roulette wheel, not rolling a die.
Your chances of winning are greatly reduced, but your understanding of the game comes
closer to reality. You will almost certainly try to withdraw your bet. You’ve been informed.
• Scenario d: Someone tells you that the die is red. Nothing changes. You’ve been neither
informed nor misinformed.

Information, then, teaches you about the world. Sometimes it does so by reducing your uncer-
tainty about future events, other times by enlarging your perspective. Defining information
based on the reduction of uncertainty, such as occurs in this test scenario, has a rich tradition.
Claude Shannon (1948) of Bell Labs first introduced the notion for communications and
developed a measure for the quantity of information, based on how much the uncertainty was
reduced. Bayesian statisticians also use this concept.
Two subtleties are frequently important. First, although information can indeed be derived
from data, it can arise in other ways as well. A train whistle that warns you of an approaching
train is certainly informative. It qualifies as soft data, but it is hardly data (yet anyway).
Second, information is intensely personal. For example, the person standing next to you, having
seen the approaching train, views the whistle as an annoying blast, not information.