"Good numeric representation is a key to effective thinking that is not limited to understanding risks. Natural languages show the traces of various attempts at finding a proper representation of numbers. [...] The key role of representation in thinking is often downplayed because of an ideal of rationality that dictates that whenever two statements are mathematically or logically the same, representing them in different forms should not matter. Evidence that it does matter is regarded as a sign of human irrationality. This view ignores the fact that finding a good representation is an indispensable part of problem solving and that playing with different representations is a tool of creative thinking." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"Ignorance of relevant risks and miscommunication of those risks are two aspects of innumeracy. A third aspect of innumeracy concerns the problem of drawing incorrect inferences from statistics. This third type of innumeracy occurs when inferences go wrong because they are clouded by certain risk representations. Such clouded thinking becomes possible only once the risks have been communicated." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"In my view, the problem of innumeracy is not essentially 'inside' our minds as some have argued, allegedly because the innate architecture of our minds has not evolved to deal with uncertainties. Instead, I suggest that innumeracy can be traced to external representations of uncertainties that do not match our mind’s design - just as the breakdown of color constancy can be traced to artificial illumination. This argument applies to the two kinds of innumeracy that involve numbers: miscommunication of risks and clouded thinking. The treatment for these ills is to restore the external representation of uncertainties to a form that the human mind is adapted to." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"Information needs representation. The idea that it is possible to communicate information in a 'pure' form is fiction. Successful risk communication requires intuitively clear representations. Playing with representations can help us not only to understand numbers (describe phenomena) but also to draw conclusions from numbers (make inferences). There is no single best representation, because what is needed always depends on the minds that are doing the communicating." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"Natural frequencies facilitate inferences made on the basis of numerical information. The representation does part of the reasoning, taking care of the multiplication the mind would have to perform if given probabilities. In this sense, insight can come from outside the mind." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"Overcoming innumeracy is like completing a three-step program to statistical literacy. The first step is to defeat the illusion of certainty. The second step is to learn about the actual risks of relevant events and actions. The third step is to communicate the risks in an understandable way and to draw inferences without falling prey to clouded thinking. The general point is this: Innumeracy does not simply reside in our minds but in the representations of risk that we choose." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"Statistical innumeracy is the inability to think with numbers that represent uncertainties. Ignorance of risk, miscommunication of risk, and clouded thinking are forms of innumeracy. Like illiteracy, innumeracy is curable. Innumeracy is not simply a mental defect 'inside' an unfortunate mind, but is in part produced by inadequate 'outside' representations of numbers. Innumeracy can be cured from the outside." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"The creation of certainty seems to be a fundamental tendency of human minds. The perception of simple visual objects reflects this tendency. At an unconscious level, our perceptual systems automatically transform uncertainty into certainty, as depth ambiguities and depth illusions illustrate." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"The key role of representation in thinking is often downplayed because of an ideal of rationality that dictates that whenever two statements are mathematically or logically the same, representing them in different forms should not matter. Evidence that it does matter is regarded as a sign of human irrationality. This view ignores the fact that finding a good representation is an indispensable part of problem solving and that playing with different representations is a tool of creative thinking." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"The possibility of translating uncertainties into risks is much more restricted in the propensity view. Propensities are properties of an object, such as the physical symmetry of a die. If a die is constructed to be perfectly symmetrical, then the probability of rolling a six is 1 in 6. The reference to a physical design, mechanism, or trait that determines the risk of an event is the essence of the propensity interpretation of probability. Note how propensity differs from the subjective interpretation: It is not sufficient that someone’s subjective probabilities about the outcomes of a die roll are coherent, that is, that they satisfy the laws of probability. What matters is the die’s design. If the design is not known, there are no probabilities." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"When does an uncertainty qualify as a risk? The answer depends on one’s interpretation of probability, of which there are three major versions: degree of belief, propensity, and frequency. Degrees of belief are sometimes called subjective probabilities. Of the three interpretations of probability, the subjective interpretation is most liberal about expressing uncertainties as quantitative probabilities, that is, risks. Subjective probabilities can be assigned even to unique or novel events." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"When natural frequencies are transformed into conditional probabilities, the base rate information is taken out (this is called normalization). The benefit of this normalization is that the resulting values fall within the uniform range of 0 and 1. The cost, however, is that when drawing inferences from probabilities (as opposed to natural frequencies), one has to put the base rates back in by multiplying the conditional probabilities by their respective base rates." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
"Why does representing information in terms of natural frequencies rather than probabilities or percentages foster insight? For two reasons. First, computational simplicity: The representation does part of the computation. And second, evolutionary and developmental primacy: Our minds are adapted to natural frequencies." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)
No comments:
Post a Comment