|The solution to a problem changes the problem.|
[Copyright neth.de, 2008]:
Hans Neth and Thomas Mueller (2008). Thinking by doing and doing by thinking: A taxonomy of actions. Paper presented at CogSci 2008.
Hansjörg Neth, Thomas Müller
|… how information is represented can greatly affect how easy it is
to do different things with it. (…) it is easy to add, to subtract,
and even to multiply if the Arabic or binary representations are used,
but it is not at all easy to do these things — especially multiplication —
with Roman numerals. This is a key reason why the Roman culture failed
to develop mathematics in the way the earlier Arabic cultures had.
|D Marr (1982): Vision, p. 21
[Copyright neth.de, 2008]:
Dirk Schlimm and Hans Neth (2008).
Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals. Paper presented at CogSci 2008.
Dirk Schlimm, Hansjörg Neth
Abstract: To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar — a claim that is widely disputed. An analysis of our models’ elementary processing steps reveals intricate trade-offs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps.
|… immediate behavior, responses that must be made to some stimulus
within very approximately one second (that is, roughly from ~300 ms to ~3 sec). (…)
… immediate behavior is where the architecture shows through — where you can see
the cognitive wheels turn and hear the cognitive gears grind. Immediate behavior is
the appropriate arena in which to discover the nature of the cognitive architecture.
|A. Newell (1990), Unified theories of cognition, p. 235f.|
[Copyright neth.de, 2007]:
Hans Neth, Rich Carlson, Wayne Gray, Alex Kirlik, David Kirsh, and Steve Payne (2007): Immediate interactive behavior: How embodied and embedded cognition uses and changes the world to achieve its goals. Symposium held at CogSci 2007.
Summary: We rarely solve problems in our head alone. Instead, most real-world problem solving and routine behavior recruits external resources and achieves its goals through an intricate process of interaction with the physical environment. Immediate interactive behavior (IIB) entails all adaptive activities of agents that routinely and dynamically use their embodied and environmentally embedded nature to augment cognitive processes. IIB also characterizes an emerging domain of cognitive science research that studies how cognitive agents exploit and alter their task-environments in real-time. Examples of IIB include arranging coins when adding their values, solving a problem with paper and pencil, arranging tools and ingredients while preparing a meal, programming a VCR, and flying an airplane.
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.