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

By Ulf Grenander

ISBN-10: 981438318X

ISBN-13: 9789814383189

This monograph studies a idea scan with a mathematical constitution meant to demonstrate the workings of a brain. It provides a mathematical conception of human proposal in line with trend thought with a graph-based method of pondering. the strategy illustrated and produced through broad computing device simulations is expounded to neural networks. established quite often on introspection, it's speculative instead of empirical such that it differs significantly in angle from the normal knowledge of present cognitive technological know-how.

Readership: Graduate scholars in utilized arithmetic, information and cognitive technological know-how in addition to postgraduates and researchers in those fields.

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41 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 3. b1336-ch03 A Mind Equation We shall now build a probability measure P over MIND and base the construction on the following: RATIONALE: For a regular thought regular c = thought ∈ MIND = C(R) thought = σ(g1 , g2 , . . 1) we shall assume its probability p = P (thought) 1) to be proportional to Q(gi ) for each node i in σ; 2) to be proportional to A[bj (gi ), bj (gi )] for each connected pair of bonds bj (gi ), bj (gi ) in σ; 3) to be proportional to κn where κn is a complexity parameter for size n of thought.

10. 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.

As the situation changes from one genre to another the Q-function will change; more about this later. But the specification of the Q-function does not describe how one simple idea is likely to associate with another. To do this we introduce a positive acceptor or association function A(g1 , g2 ): a large value of A(g1 , g2 ) means that the ideas g1 and g2 are likely to be associated (directly) with each other in the thinking of MIND and vice versa; see GPT, Chapter 7. 41 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 3.

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

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