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

By Ulf Grenander

ISBN-10: 981438318X

ISBN-13: 9789814383189

This monograph experiences a concept test with a mathematical constitution meant to demonstrate the workings of a brain. It offers a mathematical concept of human idea in keeping with trend idea with a graph-based method of considering. the tactic illustrated and produced by means of large laptop simulations is said to neural networks. dependent commonly on introspection, it really is speculative instead of empirical such that it differs substantially in perspective from the traditional knowledge of present cognitive technology.

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

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The environment contains things, but also events that are happening or have happened, and other non-physical facts. Recall Wittgenstein’s dictum: “the world consists of facts, not of things”, Tractatus Logicus-Philosophicus (see References). We shall include physical things like {dog, cat, human, John, table, car, . } ⊂ G but also non-physical ideas like {thought, hate, walk, fear , say, . } ⊂ G and events like {wedding, fight, transaction} ⊂ G to mention but a few. 19 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 2.

Most of the elements in this taxonomy are self-explanatory, with one exception: note that the generator “canineM” is a generic symbol for male dogs in general, while “Rufus” signifies a particular dog. The observant reader will notice, however, that in order that this represent a real partition, the set “canineM” must be defined as different from “Rufus”. We shall return to this later. Non-physical generators are at least as important as things. For example, g = think representing someone’s thinking, or g = say meaning a statement is being made by someone.

The concept of personality should be compared to that of “genre” (or “theme”) which can vary quickly over time and controls the values of “Q”. The genre is not associated with any “self”; it describes the current mental environment. 45 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 3. 1 b1336-ch03 A Mind Equation The Pathological Mind So far we have been studying a normal mind with no pronounced abnormalities. In the opposite case, however, the mind parameters including Q and A but also channel properties (to be discussed later) will have to be modified considerably.

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

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