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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 stories a inspiration scan with a mathematical constitution meant to demonstrate the workings of a brain. It offers a mathematical conception of human notion according to development concept with a graph-based method of pondering. the tactic illustrated and produced by way of vast computing device simulations is expounded to neural networks. established mostly on introspection, it's speculative instead of empirical such that it differs greatly in perspective from the traditional knowledge of present cognitive technological know-how.

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

Occasionally we shall make use of the TERM modality mixes, meaning unions of modalities. An example of a modality mix is action1 ∪ action2. An extreme modality is m = mod = M itself, all modalities together. 4. An Algebra of Human Thought capital letters in contrast to the primitive ideas which are written with lower case letters. The generators g1 = bark and g2 = dog are naturally ordered, g1 ↓ g2 , but g3 = yellow and g4 = smooth do not appear to have any natural order. Thus the ordering is partial rather than completely.

In a similar way we could handle the situation when MIND is also allowed to delete elementary ideas in THOUGHT but we shall not go into this here. To continue evaluating the conditional probabilities we shall cancel factors occurring in both numerator and denominator. This gives us the simpler expressions Pnormal (THOUGHT new |THOUGHT ) m 1/T Qnormal (gi ) = t=1 added Anormal [bj (gi ), bj (gi )], (k,k )∈σ(added) Pabnormal (THOUGHT new |THOUGHT ) m 1/T Qabnormal (gi ) = t=1 added Aabnormal [bj (gi ), bj (gi )].

Gn . With some probability pcreate (n) we shall abstract thought 27 July 2, 2012 9:55 9in x 6in A Calculus of Ideas 2. 4a: to a new idea ideak ∈ G, where k is a counter that will be successively updated as new ideas are created. The probability distribution {pcreate (·)} expresses the sophistication of MIND: if it allows big values of n with considerable probabilities, the MIND is capable of powerful abstraction and vice versa. If the MIND’s decision is “create”, a new idea is created and it will be put in a new modality COMPLEX on level 1, since it can stand alone, with the in-bond idea.

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

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