Recursive Worlds

Here and elsewhere in the dialogue, there is no place where we can find Socrates providing direct instruction in the form of here is the answer. But the boy does come to the correct answer. In the dialogue, Socrates draws the conclusion that the boy must have already known the answer, remembered from a previous life since he had not learned it in this life. To avoid a recursion problem, Plato also asserts that the knowledge does get a start, though through divine inspiration, not from the world, at some point in the soul s journeys through the world. 

When Stephen used his recursive program to perform an exhaustive search for longest paths in Worm World 1, he found a range of path lengths as follows (R=right, L=left, U=up, D=down) ... 

In this section, we introduce situation theoretical notions and objects that are fundamental for fine-grained modelling of information and information components. Situation Theory takes some set-theoretic objects as its basic objects. These basic objects then are used in the recursive construction of more complex situation theoretic objects. Informally, the basic informational pieces, called infons, are composite objects carrying information about relations and objects filling the arguments of the relations, at certain time and space locations. Infons can be basic or complex, by recursively defined system of objects. Infons are the ground, informational content of basic and complex informational objects, the informational content of situated propositions (introduced in Sect. 3), and other objects that carry information about situations. Infons are facts when supported by actual situations, e.g., in real or virtual worlds, theoretical models, or computerized models. 

Descriptions of the simplest data structure entities and explanations of their nature follow in succeeding sections. Basic data structures are stack, queue, and other linear lists multiple-dimension arrays (recursive) lists and trees (including forests and binary trees). Pointer or link simply means computer data constituting a memory location. Level indicates position in a structure that is hierarchical. Link, level, and the elementary structures are almost intuitive concepts. They are fairly easily understood by reference to their names or to real-life situations to which they relate. Evolving computer practice has had two effects. First, the impact of the World Wide Web and Internet browsers has acquainted many computer users with two basic ideas link (pointer) and level. Second, computer specialists have increased their use of advanced data structures. These may be understandable from their names or descriptive properties. Some of these terms are tries, quad-trees (quadtrees, quaternary trees), leftist-trees, 2-3 trees, binary search trees, and heap. While they are less common data structures and unlikely to be part of a first course in the field, they enable algorithmic procedures in applications such as image transmission, geographic data, and library search. 

At present, data are transferred manually between the LP and the optimizers. This is beneficial because the models allow us to increase the accuracy of LP shift vectors. A recent publication describes the benefits of running steady-state models in recursion with Aspen PIMS, a widely used LP program. This method may offer the best of both worlds— the practicality of LP technology augmented by the rigor of non-linear, unit-specific models. 

WF Rauschenberger. Recursive modelling of the fibre spinning process. Proc World Textile Congress on Polypropylene in Textiles, Huddersfield, 1996, pp 50-59. 

Armstrong, W. W., 1979, Recursive Solution to the Equations of Motion of an N-Link Manipulator , 5th World Congress on Theory of Machines and Mechanisms, vol. 2, pp. 1343-1346. 

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