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

By Ulf Grenander

This monograph studies a concept test with a mathematical constitution meant to demonstrate the workings of a brain. It provides a mathematical thought of human concept according to development conception with a graph-based method of considering. the strategy illustrated and produced via large desktop simulations is said to neural networks. dependent mostly on introspection, it's speculative instead of empirical such that it differs noticeably 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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We first introduce the concept of modality. The generator space will be partitioned into a family M of subsets, modalities M (m) ⊂ G; m = 1, 2, . . 1) together with a partial ordering so that m1 ↓ m2 for some, pairs m1 , m2 = 1, 2, . . , M while other pairs may not be ordered with respect to each other. A modality will contain generators with related meaning, for example color = {red, blue, green, yellow, . 2) movement = {run, jump, turn, still, . 3) or where the set of all modalities has been denoted by M and enumerated m = 1, 2, .

Following the wise Spinoza (1670), (“ordine geometrico”), we claim the CONCLUSION: Human thought has geometric structure. Note also the resemblance to chemistry. This has been observed and elaborated by Tarnopolsky (2003). Generators correspond to atoms, configurations (thoughts) to molecules, and bonds to bonds. Sometimes we shall use chemistry like notation as idealomega . We shall distinguish between different isotopes of ideas, for example give23 and g22 . This notation will be used only when clarity demands it.

The behavior of “self” is regulated by personality parameters greedy, scholastic, aggressive, selfish, . . The values of the parameters are in the interval (0,1) so that for example “generous” controls the value of A(self , g) with “g” = “give”, “lend”, . . Their values constitute a personality profile that remains fixed after having been set. 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.

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