I decided to put this post here as this is where such posts normally go (rather than e.g., the "Science & Technology" section, which isn't a debate forum, or the "General Debates" section). I have, more than once, taken issue with comparisons between the mind or brain and computers. Also, computers are about as close as we can get to a wholly reducible system as
1) We build them, from the theoretical designs of Church and Turing to the actual implementations from the ENIAC to the computer/smartphone/tablet/etc. you are using to access this post.
2) They are quite literally physical instantiations of formal logic.
3) They are modularly and hierarchically organized (unlike most natural systems and in particular all living systems), especially with respect to function (unlike the brain, where memory systems are not only--at least somewhat--indistinct from one another, but are also indistinct from any would-be processor). So RAM, for example, is a particular type of memory located in a specific place that interacts with other likewise functionally organized components of the system in deliberate, pre-defined ways.
4) Everything about computers is rule-based, finite, discrete, and just generally the seeming epitome of a reducible system in basically all senses of the term.
So I found it interesting when, in the volume
Aguirre, A., Foster, B., & Merali, Z. (Eds.). (2015). Questioning the Foundations of Physics: Which of Our Fundamental Assumptions are Wrong? (The Frontiers Collection). Springer.
I found computers used as an example not only of non-physical entities but anti-reductionism in the contributing paper "Recognizing Top-Down Causation" by Ellis. I've included a summary of his use of this example, and for those who wish for an even more minimal amount of information part A is the most relevant:
"Definition 1 (Causal Effect) If making a change in a quantity X results in a reliable demonstrable change in a quantity Y in a given context, then X has a causal effect on Y...
Definition 2 (Existence) If Y is a physical entity made up of ordinary matter, and X is some kind of entity that has a demonstrable causal effect on Y as per Definition 1, then we must acknowledge that X also exists (even if it is not made up of such matter)...
A: Causal Efficacy of Non Physical entities: Both the program and the data are non-physical entities, indeed so is all software. A program is not a physical thing you can point to, but by Definition 2 it certainly exists. You can point to a CD or flashdrive where it is stored, but that is not the thing in itself: it is a medium in which it is stored. The program itself is an abstract entity, shaped by abstract logic. Is the software nothing but its realisation through a specific set of stored electronic states in the computer memory banks? No it is not because it is the precise pattern in those states that matters: a higher level relation that is not apparent at the scale of the electrons themselves. Its a relational thing (and if you get the relations between the symbols wrong, so you have a syntax error, it will all come to a grinding halt). This abstract nature of software is realised in the concept of virtual machines, which occur at every level in the computer hierarchy except the bottom one. But this tower of virtual machines causes physical effects in the real world, for example when a computer controls a robot in an assembly line to create physical artefacts.
B: Logical relations rule at the higher levels: The dynamics at all levels is driven by the logic of the algorithms employed in the high level programs. They decide what computations take place, and they have the power to change the world. This abstract logic cannot be deduced from the laws of physics: they operate in a completely different realm. Furthermore the relevant higher level variables in those algorithms cannot be obtained by coarse graining any lower level physical states. They are not coarse-grained or emergent variables: they are assigned variables, with specific abstract properties that then mediate their behaviour.
C: Underlying physics allows arbitrary programs and data: Digital computers are universal computers. The underlying physics does not constrain the logic or type of computation possible, which Turing has shown is universal. Physics does not constrain the data used, nor what can be computed (although it does constrain the speed at which this can be done). It enables the higher level actions rather than constraining them. The program logic dictates the course of things.
D: Multiple realisability at lower levels. The same high level logic can be implemented in many different ways: electronic (transistors), electrical (relays), hydraulic (valves), biological (interacting molecules) for example. The logic of the program can be realised by any of these underlying physical entities, which clearly demonstrates that it is not the lower level physics that is driving the causation. This multiple realisability is a key feature characterising top-down action: when some high level logic is driving causation at lower levels, it does not matter how that logic is physically instantiated: it can be realised in many different ways."