By Gary F. Marcus
Within the Algebraic brain, Gary Marcus makes an attempt to combine theories approximately how the brain works, one who says that the brain is a computer-like manipulator of symbols, and one other that says that the brain is a huge community of neurons operating jointly in parallel. Resisting the traditional knowledge that claims that if the brain is a big neural community it can't at the same time be a manipulator of symbols, Marcus outlines various ways that neural platforms might be equipped so that it will control symbols, and he exhibits why such platforms usually tend to supply an sufficient substrate for language and cognition than neural platforms which are inconsistent with the manipulation of symbols. Concluding with a dialogue of the way a neurally learned approach of symbol-manipulation may have advanced and the way one of these process may spread developmentally in the womb, Marcus is helping to set the longer term time table of cognitive neuroscience.
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Extra resources for The Algebraic Mind: Integrating Connectionism and Cognitive Science (Learning, Development, and Conceptual Change)
For example, a constraint of Hebrew word formation is that adjacent consonants in a root must not be identical; Berent and her colleagues (Berent, Everett & Shimron, 2000; Berent & Shimron, 1997) have shown that speakers freely generalize this constraint to novel items. My own recent research suggests that the ability to freely generalize patterns like reduplication has roots quite early in development. My colleagues and I have found that seven-month-old infants can freely generalize (Marcus, Vijayan, Bandi Rao & Vishton, 1999).
Does it have a way of representing variables and a way of representing relations between variables? Proponents of symbol-manipulation assume that the answer is yes—that we make use of open-ended schemas such as “form a progressive of any verb by adding -ing to its stem” (such as walk-walking). Because such schemas are much like algebraic equations (prog = stem + ing), I refer to them as relations between variables or algebraic rules. Although it seems clear enough that we can manipulate algebraic rules in “serial, deliberate reasoning”, not everybody agrees that such abstract relationships between variables play an important role in other aspects of language and cognition.
Hence the output node is not turned on. 5 The Need for Hidden Units Although functions like AND and OR are easily represented in simple two-layer networks, many other functions cannot be represented so easily. For example, our simple network could not represent the function of exclusive or (XOR), which is true only if exactly one input is true. 6, we can draw a straight line that divides the inputs that lead to a true output from the inputs that lead to a false output. 6 Illustrations of the logical functions OR and AND.
The Algebraic Mind: Integrating Connectionism and Cognitive Science (Learning, Development, and Conceptual Change) by Gary F. Marcus