Hansjörg Neth, Gerd Gigerenzer
We distinguish between situations of risk, where all options, consequences, and probabilities are known, and situations of uncertainty, where they are not. Probability theory and statistics are the best tools for deciding under risk but not under uncertainty, which characterizes most relevant problems that humans have to solve. Uncertainty requires simple heuristics that are robust rather than optimal.
|The truths about numbers are in us; but still we learn them.|
|G.W. Leibniz (1765), Nouveaux essais sur l’entendement humain, p. 85|
[Copyright neth.de, 2010]:
Helen De Cruz, Hans Neth, Dirk Schlimm (2010). The cognitive basis of arithmetic.
Overview: Arithmetic is the theory of the natural numbers and one of the oldest areas of mathematics. Since almost all other mathematical theories make use of numbers in some way or other, arithmetic is also one of the most fundamental theories of mathematics. But numbers are not just abstract entities that are subject to mathematical ruminations — they are represented, used, embodied, and manipulated in order to achieve many different goals, e.g., to count or denote the size of a collection of objects, to trade goods, to balance bank accounts, or to play the lottery. Consequently, numbers are both abstract and intimately connected to language and to our interactions with the world. In the present paper we provide an overview of research that has addressed the question of how animals and humans learn, represent, and process numbers.
From the introduction: Although human thought may be possible in those floatation tanks that are used to encourage meditative states, in by far the majority of instances thought occurs in the context of some physical task environment. The physical environment can be as simple as a light and book. It can be as complex as the face of a mountain and the equipment of the climber. It may be as dynamic as the cockpit of an F-16 in supersonic flight and as reactive as a firefight in Iraq or as heated as an argument between lovers.