Modern computing is generally taken to consist primarily of symbol manipulation. But symbols are abstract, and computers are physical. How can a physical device manipulate abstract symbols? Neither Church nor Turing considered this question. My answer is that the bit, as a hardware-implemented abstract data type, serves as a bridge between materiality and abstraction. Computing also relies on three other primitive—but more straightforward—abstractions: Sequentiality, State, and Transition. These physically-implemented abstractions define the borderline between hardware and software and between physicality and abstraction. At a deeper level, asking how a physical device can interact with abstract symbols is the wrong question. The relationship between symbols and physical devices begins with the realization that human beings already know what it means to manipulate symbols. We build and program computers to do what we understand to be symbol manipulation. To understand what that means, consider a light switch. A light switch doesn’t turn a light on or off. Those are abstractions. Light switches don’t operate with abstractions. We build light switches (and their associated circuitry), so that when flipped, the world is changed in such a way that we understand the light to be on or off. Similarly, we build computers to perform operations that we understand as manipulating symbols.

中文翻译：

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位（和其他三个抽象）定义了硬件和软件之间的边界

现代计算通常主要由符号操作组成。但是符号是抽象的，而计算机是物理的。物理设备如何操作抽象符号？丘奇和图灵都没有考虑过这个问题。我的回答是，bit 作为硬件实现的抽象数据类型，充当了物质性和抽象性之间的桥梁。计算还依赖于其他三个原始但更直接的抽象：顺序性、状态和转换。这些物理实现的抽象定义了硬件和软件之间以及物理性和抽象之间的边界。在更深层次上，询问物理设备如何与抽象符号交互是错误的问题。符号和物理设备之间的关系始于人类已经知道操纵符号意味着什么的认识。我们构建和编程计算机来执行我们理解的符号操作。要了解这意味着什么，请考虑电灯开关。灯开关不会打开或关闭灯。这些都是抽象。电灯开关不以抽象方式运行。我们构建了电灯开关（及其相关电路），因此当翻转时，世界会以这样一种方式改变，即我们理解灯是打开还是关闭。同样，我们构建计算机来执行我们理解为操纵符号的操作。灯开关不会打开或关闭灯。这些都是抽象。电灯开关不以抽象方式运行。我们构建了电灯开关（及其相关电路），因此当翻转时，世界会以这样一种方式改变，即我们理解灯是打开还是关闭。同样，我们构建计算机来执行我们理解为操纵符号的操作。灯开关不会打开或关闭灯。这些都是抽象。电灯开关不以抽象方式运行。我们构建了电灯开关（及其相关电路），因此当翻转时，世界会以这样一种方式改变，即我们理解灯是打开还是关闭。同样，我们构建计算机来执行我们理解为操纵符号的操作。