By Ulf Grenander

This monograph reviews a idea scan with a mathematical constitution meant to demonstrate the workings of a brain. It offers a mathematical concept of human suggestion in keeping with development idea with a graph-based method of considering. the tactic illustrated and produced by means of large laptop simulations is expounded to neural networks. dependent generally on introspection, it's speculative instead of empirical such that it differs notably in perspective from the normal knowledge of present cognitive technological know-how.

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

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**A Calculus of Ideas: A Mathematical Study of Human Thought**

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**Additional info for A Calculus of Ideas: A Mathematical Study of Human Thought**

**Sample text**

Gi , . . 7) and a weaker concept: DEFINITION: A conﬁguration, or thought, c = σ(g1 , g2 , . . , gi , . . , gn ) is said to be REGULAR if any connected jth down-bond βj (gi ) satisﬁes the bond relation ρ : gi ∈ βj (gi ). 8) In other words, a completely regular conﬁguration has all its down-bonds connected, but an incomplete has some down-bond left open. 2 the second conﬁguration is complete but if the connection question ↓ cat is broken it is incomplete (assuming that ω(question) = 2). We shall use the terms complete and incomplete thoughts when talking about conﬁgurations.

A given set {MIND(R), P } is called a personality, where P is a probability measure on MIND(R). 6 Thought Patterns A subset P ⊂ MIND(R) is called a thought pattern if it is invariant with respect to the modality group S. 7 Completion Thoughts are made meaningful by the application of the COMPLETE operation that closes out-bonds. 8 Generalization Thoughts are generalized by the application of the MOD operation from a semi-group GENERALIZATION. 9 Abstraction The device of encapsulation abstracts thoughts to ideas that can be referred to as independent units; they are automatically added to the generator space G.

Since binomial coeﬃcients are always bigger than (or equal to) one, it follows that energy is superadditive. Combining thoughts demand more and more mental power as the sizes increase: the MIND is limited in the complexity of thoughts. We should think of Q as specifying the constitution of the mental soup in which the MIND is immersed at the time. This soup will depend upon the external world that we shall later characterize in terms of themes (or genres). This is likely to change during over time.