{"resolved":true,"match_type":"uuid","source_type":"original_book","book_id":"a6cc7da8-99f2-4538-8a66-26787f7481a3","title":"资本主义与精神分裂(卷2)：千高原(修订译本)","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787208178977","requested_by":"printed_page","book":{"source_type":"original_book","book_id":"a6cc7da8-99f2-4538-8a66-26787f7481a3","id":"a6cc7da8-99f2-4538-8a66-26787f7481a3","uuid":"a6cc7da8-99f2-4538-8a66-26787f7481a3","title":"资本主义与精神分裂(卷2)：千高原(修订译本)","normalized_title":"资本主义与精神分裂卷2千高原修订译本","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787208178977","isbns":["9787208178977"],"parsed":true,"ai_readable":true,"document_type":"book","page_count":515,"navigation_url":"https://workshop.closeclaw.top/ai/book/a6cc7da8-99f2-4538-8a66-26787f7481a3","title_url":"https://workshop.closeclaw.top/ai/title/%E8%B5%84%E6%9C%AC%E4%B8%BB%E4%B9%89%E4%B8%8E%E7%B2%BE%E7%A5%9E%E5%88%86%E8%A3%82(%E5%8D%B72)%EF%BC%9A%E5%8D%83%E9%AB%98%E5%8E%9F(%E4%BF%AE%E8%AE%A2%E8%AF%91%E6%9C%AC)","fixed_page_url_template":"https://workshop.closeclaw.top/ai/book/a6cc7da8-99f2-4538-8a66-26787f7481a3/page/{printed_page}","path_api_url_template":"https://workshop.closeclaw.top/api/ai/book/a6cc7da8-99f2-4538-8a66-26787f7481a3/page/{printed_page}","read_url":"https://workshop.closeclaw.top/api/ai/read/a6cc7da8-99f2-4538-8a66-26787f7481a3","page_url":"https://workshop.closeclaw.top/api/ai/books/a6cc7da8-99f2-4538-8a66-26787f7481a3/page","search_url":"https://workshop.closeclaw.top/api/ai/books/a6cc7da8-99f2-4538-8a66-26787f7481a3/search"},"page":{"printed_page":456,"pdf_page":474,"physical_index":474,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"422bef1e5b3b6a79454e065a2c3e90779706547a6c64224f289a8ede8837455b"},"chapter":"Capitalisme et Schizophré Mille Plat Dilles Del ix Gu","content":"是否有可能对平滑空间给出一种极为普遍的数学界定？伯努瓦·曼德勃罗(Benoit Mandelbrot)的“分形客体（objets fractals)”似乎正是朝向这个方向。分形客体构成了这样的集合，在其中，维度的数目是分数、而非整数，或虽然是整数，但其方向却处于连续流变之中。比如，我们用一个等边三角形的角来取代一个线段的中点，在由此得到的四条线段上重复此种操作，如此以至无穷，遵循着一种位似（homothétie）的关系，—一条这样的线段将构成一条无限的直线或曲线，它的维度大于1，但却小于一个表面(=2)。相似的结果也可以通过穿孔，通过在一个圆之上挖出“窗洞”(baies)、而非在一个三角形上增加“点”(caps）的方式来形成；同样，当我们根据位似法则在一个立方体上挖出洞孔之时，它就越来越变成一个面、而非体（这就是对于自由空间和穿孔空间之间的近缘性的数学表达)。还存在其他的形式，布朗运动，涡流，天穹都是这类的“分形客体”。②\n\n资本主义与精神分裂（卷2）：千高原（修订译本）\n\n① 关于此种真正的欧式几何的结合(与积聚的过程迥然有别)，参见 Lautman，Les schémas de structure，pp.45—48。\n\n② Benoit Mandelbrot, Les objets fractals, Flammarion.\n\n456","previous_page":455,"next_page":457}