theoretical, mathematical or formal analysis
The truths about numbers are in us; but still we learn them. |
G.W. Leibniz (1765), Nouveaux essais sur l’entendement humain, p. 85 |
Helen De Cruz, Hansjörg Neth, Dirk Schlimm
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.
If an organism is confronted with the problem of behaving approximately rationally, or adaptively, in a particular environment, the kinds of simplifications that are suitable may depend not only on the characteristics—sensory, neural, and other—of the organism, but equally on the nature of the environment. |
H.A. Simon (1956), Rational choice and the structure of the environment, p. 130 |
Hansjörg Neth, Sangeet S. Khemlani, Wayne D. Gray
Objective: We distinguish outcome feedback from control feedback to show that suboptimal performance in a dynamic multitasking system may be caused by limits inherent to the information provided rather than human resource limits.
The solution to a problem changes the problem. |
Peer’s Law |
Hansjörg Neth, Thomas Müller
Abstract: Taking a lead from existing typologies of actions in the philosophical and cognitive science literatures, we present a novel taxonomy of actions.