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 experiences a inspiration test with a mathematical constitution meant to demonstrate the workings of a brain. It offers a mathematical concept of human idea in response to development concept with a graph-based method of pondering. the tactic illustrated and produced through wide computing device simulations is said to neural networks. established usually on introspection, it truly is speculative instead of empirical such that it differs significantly in angle from the traditional knowledge of present cognitive technology.

Readership: Graduate scholars in utilized arithmetic, records and cognitive technological know-how 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

Sample text

And, of course, some thinking takes the form of pictures. Hence ideas are not necessarily represented by words and sentences in a natural language, so that our approach is extra-linguistic. Thinking comes before language! Thoughts could be, for example, “John loves Mary” 15 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 2. b1336-ch02 Creating Thoughts: Algebra of Thinking “smell of Madeleine cake” “index finger hurts” “bell tolls” We shall limit ourselves in this book to outlining a mathematical representation theory but hope that sooner or later it will be applied to knowledge available to experimental neurologists/psychiatrists.

In Appendix C the regular modalities are shown as rectangular boxes, while the irregular ones are indicated as diamond shaped boxes. Modalities can be ordered by inclusion. For example, ANIMAL ⊂ ANIMATE . Note that this ordering is different from the partial order discussed above. It is clear that M forms a lattice, a POSET. This means that the ordering of modalities produces entities on different planes of modality. We have been denoting modalities (on the first plane) by capital letters and shall use bold faced capitals for the next plane.

If the thought chatter had been allowed to continue it may have led to a complete thought. 15 illustrates how Goethe makes a generalization, using A, B, C, D as modalities. 15: 35 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 2. 16: Interpretation: “Eduard says idea5”, with idea5 = “let the modality A contain Charlotte, the modality B contain Eduard, . ”. 16. Interpretation: the driver “thought1 to thought2” with thought1 = “A loves B and C loves D”; thought2 = “A loves C and B loves D”. It actually represents a thought transformation with a composite move, a double romantic relation changes into another.

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

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