“Intelligence cannot be present without understanding. No computer has any awareness of what it does.”
英语
“没有理解就不可能有智能。没有任何计算机对自己所做之事有任何觉察。”
“There is something in the conscious act of understanding that eludes computation. Mathematical insight, the "Aha!" moment, is not the output of an algorithm — it is the recognition of truth that no formal system, by itself, can achieve.”
英语
“意识中的理解行为有某种东西是计算所无法捕捉的。数学洞察力——那个"顿悟"时刻——不是算法的输出，而是对真理的识别，这是任何形式系统本身都无法做到的。”
“It seems to me that we must make a distinction between what is computable and what is merely computational. The brain may use quantum-level processes that are not algorithmic, and consciousness may depend on physics that we do not yet understand.”
英语
“在我看来，我们必须区分可计算的和仅仅是计算性的。大脑可能使用非算法的量子层级过程，而意识可能依赖于我们尚未理解的物理学。”
“The world of mathematics is a Platonic reality every bit as genuine as the physical world we inhabit. Mathematical truths are not invented; they are discovered. They exist timelessly, whether or not anyone finds them.”
英语
“数学世界是一个柏拉图式的实在，与我们栖居的物理世界一样真实。数学真理不是发明的，而是发现的。它们超越时间地存在着，无论是否有人找到它们。”
“Do I dare to say that there are three worlds — physical, mental, and Platonic-mathematical — and that each seems to emerge mysteriously from one of the others?”
英语
“我敢说存在三个世界——物理的、心灵的、柏拉图数学的——而每一个似乎都神秘地从另一个中涌现出来？”