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(Author here.) > Do you believe that a hot bar of iron is a computer? This is the crux of it. The main objection to the triviality argument is that we've jus
by antognini 4y ago
(Author here.)
> Do you believe that a hot bar of iron is a computer?
This is the crux of it. The main objection to the triviality argument is that we've just used far too broad a definition of a "computer." If we're thinking that a hot iron bar is a computer, then this should suggest to us that it's the definition that's wrong. You are correct in saying that if the definition we use is wrong, the whole triviality argument falls apart.
But for me, the problem with this objection is that I've never seen any workable alternative definition for a computer besides the standard definition. (Namely that a computer is a mapping from physical states to Turing machine states.) Any alternative seems to introduce some measure of subjectivity. The hot iron bar doesn't seem like a computer to us because it requires a random mapping and is not repeatable. But a requirement that the mapping be "simple" or "low entropy" is not easy to rigorously define, nor is it easy to find a principled way to determine how "repeatable" or "deterministic" a computer's behavior should be.
- Imnimo 4y agoIs empty space also a computer, because while we might naively interpret it as "all zeros", with the proper location and time-dependent mapping, it can be seen to be running Doom?
- jamesrom 4y agoExactly this. You can encode a computer anywhere, given your own definition of "computer". Getting your computer to compute, there's the rub.
- 3g4o53g4o5 4y agoWell, there is still random quantum behavior in a complete vacuum a.k.a. empty space according to quantum field theory's findings. So yes, empty space is a computer as long as you notice that physics law is doing math all the time.
- dqpb 4y agoLet's say you can initialize the first N bits of the hot iron to the initial state of your program. By what process does the hot iron use that information to compute the next state of your program?
- antognini 4y agoIn the case of the hot iron bar, obviously there is no deterministic process that takes us from one state to the next. We just happen to get lucky and see that it randomly fluctuates from one state to the next state correctly. The trouble is that formal computation theory does not take into consideration the physical process by which the computer moves from one state to the next. That's what makes it so general. We can make computers out of transistors or vacuum tubes or Legos equally well and can be assured that whatever we make our computer out of the computational complexity of bubble sort is O(n^2). Requiring specific physical processes for computation would invalidate computation theory in a very fundamental kind of way.
- dqpb 4y agoI'm not requiring specific physical processes, I'm asking for any physical process in a hot iron bar that executes any model of computation that is capable of running an arbitrary program. But you're saying there is not one, we just get lucky one time. That's not computation.
- antognini 4y agoThe physical process is simply that the atoms in the bar of iron start in one Turing machine state, obey the laws of physics, and end up in another Turing machine state. But this is also true of any other physical computer. It sounds like your objection is that this is not a computer because it's not reproducible --- we just got lucky that the physical states mapped onto the appropriate Turing machine states one time. But then how deterministic does the physical system need to be to be considered a computer? It can't be 100% because no real-world physical computer is 100% deterministic. Is it a computer if the mapping is correct 50% of the time? 90%? 1%? I can't see any principled reason to choose any particular value.
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