By Gary F. Marcus
An try and combine theories approximately how the brain works, person who says that the brain is a computer-like manipulator of symbols, and one other that says that the brain is a big community of neurons operating jointly in parallel.
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Extra resources for Algebraic Mind: Integrating Connectionism and Cognitive Science
To make the strongest possible case that the mind does in fact implement operations over variables, I focus on what I call universally quantified one-to-one mappings (UQOTOM). The terms universally quantified and one-to-one come from logic and mathematics. A function is universally quantified when it applies to all instances in its domain. ” A function is one-to-one if each output maps onto a single input in its domain. For example, in the function f(x) = x, the output 6 corresponds to the input 6 (and no other); the output 3,252 corresponds to the input 3,252 (and no other); and so forth.
Algebraic rules are not finite tables of memorized facts or relationships between specific instances but open-ended relationships that can be freely generalized to all elements within some class. 3 Implementing Operations over Variables in a Physical System How might a system that can perform operations over variables be implemented in a physical system? One simple way to do this is to use a set of buckets. One bucket represents the variable x, and another bucket represents the variable y. The instantiation of a given bucket is indicated by the bucket’s contents.
For researchers drawn to views in which a child enters the world with relatively little initial structure, multilayer perceptrons offer a way of making their view computationally explicit. Elman et al. (1996, p. 115), for instance, see multilayer perceptron models as providing a way to “simulate developmental phenomena in new and . . exciting ways . . ” Multilayer perceptrons are also appealing because of their intrinsic ability to learn (Bates & Elman, 1993) and because of their ability to gracefully degrade: they can tolerate limited amounts of noise or damage without dramatic breakdowns (Rumelhart & McClelland, 1986b, p.