|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.
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.
|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.
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.