What is the difference between a Turing machine and the modern computer? It's the same as that between Hillary's ascent of Everest and the establishment of a Hilton hotel on its peak.
图灵机和现代计算机之间有什么区别?这与希拉里(Hillary)登上珠穆朗玛峰(Everest)和在高峰期建立希尔顿酒店之间的过程相同。
What I think I've been talking about really is success and failure. And one of the interesting things about success is that we think we know what it means. If I said that there's somebody behind the screen who's very successful, certain ideas would immediately come to mind. You'd think that person might have made a lot of money, achieved renown in some field. My own theory of success -- I'm somebody who's very interested in success, I really want to be successful, always thinking, how can I be more successful? But as I get older, I'm also very nuanced about what that word "success" might mean.
Mathematics is not just about numbers, equations, computations, or algorithms: it is about understanding.
真相很少是纯粹的,也从来不简单。