Book Review: Mechanizing hypothesis formation. Mathematical foundations for a general theory

Good, I. J.

doi:10.1090/s0273-0979-1979-14650-0

Cited by 1 publication

(2 citation statements)

References 5 publications

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“…Chess endgames can be analyzed with Kronecker tensor product and direct sums. They discussed the work of Friedrich Amelung and Theodor Molien, the founder of group representation, and the first person that analyzed a pawnless endgame [11] [12]. High-performance parallel computing can be solved from the endgame analysis.…”

Section: Related Workmentioning

confidence: 99%

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Computation and Information Theory of Chess Games

Hwang¹,

Gilbert²,

Huang³

et al. 2023

Preprint

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<p>We provide two methodologies in the area of computation theory to solve optimal strategies for games such as Watermelon chess and Go. From experimental results, we find relevance to graph theory, group representation, and mathematical consciousness. We prove that the decision strategy of movement for Watermelon chess and Chinese checker games belongs to a matrix that is a noncommutative ring or an abelian group over set Y={-1,0,1}. Additionally, the movement for any chess game with two players belongs to a noncommutative ring or an abelian group from Occam’s razor principle. We derive the closed form of the transition matrix for any chess game with two players and discover that the element of the transition matrix belongs to a rational number. We propose a different methodology based on abstract algebra to analyze the complexity of chess games in their entirety, instead of being limited solely to endgame results. It is probable that similar decision processes of people may also belong to a noncommutative ring or an abelian group.</p>

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Section: Related Workmentioning

confidence: 99%

“…(2, 1), (2, 3), (2,6), (3, 0), (3,7), (3,4), (4, 0), (4, 1), (4, 3), (4, 8), (5, 1), (5,10), (5,9), (5,20), (6,2), (6,11), (6,12), (6,13), (7,3), (7,14), (7,15), (7,16), (8,4), (8,17), (8,18), (8,19), (9,5), (9,10), (9,20), (10,5), (10,9), (10,11), (11,6), (11,12), (11,<...…”

Section: Introductionmentioning

confidence: 99%