# Computation is a Physical Process The theory of computation has traditionally been studied almost entirely in the abstract, as a topic in pure mathematics. This is to miss the point of it. *Computers are physical objects, and computations are physical processes*. What computers can or cannot compute is determined by the laws of physics alone, and not by pure mathematics Computation inherently involves a dynamic process: It's the step-by-step execution of instructions to transform input data into output data. A static program represents the algorithm or instructions, but the computation occurs when those instructions are actively carried out[^1]. ## The Relationship Between Computation and Physics When a computer performs computation it: * Starts with some *input* information * Which it then modifies according to definite *rules* (which are characteristic of the hardware of that computer) * Thus, the *output* depends on the input and the rules by which the computer operates There is a clear relationship with [Physics](notes/Physics.md): * A *Physical System* is some part of nature that could in principle be experimented on. This will make use of some *measuring instrument*. * They undergo *motion*, or change. We can perform an *experiment* and make a *measurement*. * We can find or prepare the system in an *initial state*, and we then prepare our *measuring instrument*. * The change follows the *Laws of Motion* (which are [The Laws of Physics](The%20Laws%20of%20Physics.md) specialized to that system) * And this leads to a *final state*. The system and the measuring instrument interact according to the laws of physics, which makes the measuring instrument display the outcome We can see that everything in the computer example is just a special case of the physics example. But we can also think of this the other way around: the motion of any physical system, because it obeys physical laws, can be regarded as [Information](Information.md) processing. --- Date: 20241215 Links to: [Fabric of Reality](Fabric%20of%20Reality.md) pg 98, [Beginning of Infinity](Beginning%20of%20Infinity.md) pg 188 Tags: References: * []() [^1]: TODO: determine if this is correct