Download e-book for kindle: A Calculus of Ideas: A Mathematical Study of Human Thought by Ulf Grenander

By Ulf Grenander

ISBN-10: 981438318X

ISBN-13: 9789814383189

This monograph studies a notion test with a mathematical constitution meant to demonstrate the workings of a brain. It provides a mathematical conception of human proposal in keeping with trend idea with a graph-based method of considering. the tactic illustrated and produced through large laptop simulations is said to neural networks. established quite often on introspection, it really is speculative instead of empirical such that it differs notably in perspective from the traditional knowledge of present cognitive technology.

Readership: Graduate scholars in utilized arithmetic, records and cognitive technology in addition to postgraduates and researchers in those fields.

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Extra resources for A Calculus of Ideas: A Mathematical Study of Human Thought

Example text

Interpretation: “Eduard says that Charlotte requires that she waits for him”. The next three figures show slightly more complicated thoughts. 11 with the interpretation: “Eduard follows the gardener who walks away fast”. 11: 33 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 2. 12: Interpretation: “The Captain came earlier and sent earlier a letter to calm Charlotte”. 5. Some Thoughts in Goethe Interpretation: “Charlotte plays the piano well”. Some of these examples show connected graphs, or, to use our terminology, they represent conscious thoughts.

The set of all regular configurations is called the (regular or completely regular) configuration space, the MIND, and is denoted by MIND(C(R)); it represents the set of all the thoughts that this mind is capable of. Note that the regularity requirement of an idea means that its constituent subthoughts (ideas) conform. Hence we view thoughts as geometric constructs, to wit graphs, whose composition expresses the personality of the individual. Following the wise Spinoza (1670), (“ordine geometrico”), we claim the CONCLUSION: Human thought has geometric structure.

For example, g1 = “John” and g2 = “Jim” may be equivalent but probably not g1 = “John” and g2 = “Mary”: this is an expression of the principle “arbitrariness of the sign” to quote de Saussure although he spoke of language rather than thought. e. abstract thinking, but preserving modalities, and avoiding incorrect references by not allowing primitive idea to be substituted for more than one other primitive idea. Hence the substitutions do indeed form a bijactive map: a permutation within modalities.

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A Calculus of Ideas: A Mathematical Study of Human Thought by Ulf Grenander

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