{"product_id":"generative-theory-of-shape-book-michael-leyton-9783540427179","title":"A Generative Theory of Shape","description":"The purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence -(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis'es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52354623209745,"sku":null,"price":0.0,"currency_code":"USD","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52354626978065,"sku":"NLS9783540427179","price":133.39,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540427179.jpg?v=1758184068","url":"https:\/\/www.worldofbooks.com\/products\/generative-theory-of-shape-book-michael-leyton-9783540427179","provider":"World of Books ","version":"1.0","type":"link"}