Posts Tagged: CogSci

Paper: Arithmetic with Arabic vs. Roman numerals


… 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

Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals

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.

Paper: Immediate interactive behavior (IIB)


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.

Hansjörg Neth, Richard A. Carlson, Wayne D. Gray, Alex Kirlik, David Kirsh, Stephen J. Payne

Immediate interactive behavior: How embodied and embedded cognition uses and changes the world to achieve its goals

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.

Chapter: The functional task environment


Human beings, viewed as a behaving system, are quite simple.
The apparent complexity of our behavior over time is largely a reflection
of the complexity of the environment in which we find ourselves.
(Simon, 1996, p. 53)

Wayne D. Gray, Hansjörg Neth, Michael J. Schoelles

The functional task environment

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.

Paper: Melioration dominates maximization

There is no reason to suppose that most human beings are
engaged in maximizing anything unless it be unhappiness,
and even this with incomplete success.
R.H. Coase (1980), The Firm, the Market, and the Law, p. 4

[Copyright neth.de, 2006]:

Hans Neth, Chris Sims, Wayne Gray (2006). Melioration dominates maximization: Stable suboptimal performance despite global feedback. Paper presented at CogSci 2006.

Hansjörg Neth, Chris R. Sims, Wayne D. Gray

Melioration dominates maximization: Stable suboptimal performance despite global feedback

Abstract:  Situations that present individuals with a conflict between local and global gains often evoke a behavioral pattern known as melioration — a preference for immediate rewards over higher long-term gains.  Using a variant of a binary forced- choice paradigm by Tunney & Shanks (2002), we explored the potential role of global feedback as a means to reduce this bias.