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2 years ago in Philosophy By Prithvi Patel

In what precise sense are modern personal computers computationally equivalent to a Turing Machine, and where do they differ in philosophically important ways?

 In my philosophy of mind class, we often hear "the brain is a computer" or "the mind is software." This relies on the Church-Turing thesis. But a Turing Machine has an infinite tape and operates serially. A modern PC has finite memory, parallel processing, and interacts with the world in real-time. Are these practical limitations or fundamental differences? Does the equivalence hold only for what is computable (functions), not how it's computed (efficiency, embodiment)? What are the philosophical implications for claims about computational theories of mind?

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By Abeden Answered 1 year ago

They are equivalent in the class of functions they can compute (computability theory): any function computable by a modern PC is Turing-computable, and vice versa. This is the heart of the Church-Turing thesis. The differences are profound but often considered "implementation details": 1) Finiteness: A PC has finite memory, but we idealize this as sufficient (or extendable) for any given task, approximating infinity. 2) Architecture: Parallel processing, GPUs, etc., can be simulated on a serial Turing machine (though possibly with exponential slowdown). 3) Interaction: A standard Turing machine doesn't interact with an environment during computation; a PC does via I/O. This last point is philosophically crucial for embodied and embedded cognition. A Turing machine models closed-form calculation, not real-time, embodied agency. So, while they are equivalent for what is computable, they differ radically in how computation is realized and what it means for a system to be intelligent in a world.

                             

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