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I have read three questions about algorithms and their relation to the human brain.

Two recent ones:
Question on Godel's Remark on Algorithmic Nature of Mind

and:
Why doesn't Searle's argument apply against humans?

And an old one:

Could the Qualia of differring subjective impressions be compared?

They made me wonder. Can a physical process be replaced by its algorithm-based computation in the first place? So not only in relation to brains but to general physical processes in general. What does it even mean to say they are identical? They are clearly not identical when their physical Nature is considered.

Any physical process can be represented by a set of parallel or series operations on parallel or series data. The computer can do this in faster and more sophisticated ways as time grows. The question still remains if this somehow is identical to the process itself. How? For sure the computed process of color perception doesb't see. Or does it?

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    If you get shot, is the actual process of surgery to remove the bullet from your body identical to having a computer compute the state of your body once it is done? If I had to pick one or the other, I know which one I would chose...
    – armand
    Aug 6, 2021 at 5:31
  • An algorithm will calculate that after N seconds, the state of the system will be X. The actual process will always show a different result; even if the difference is infinitesimal, it will be different. But if you want to call processes "algorithms", you're free to do it.
    – RodolfoAP
    Feb 4 at 3:50

4 Answers 4

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They are not identical; one is a physical process involving atoms, the other is a formal computation involving an abstract machine changing state, which may run on a second physical process involving atoms (the computer).

But they can share similar structure. The computation can do things that are logically analogous to what the physical process does. A rubber ball bounces off the wall, and in the computer, a simulation of a rubber ball bounces off a simulation of a wall. Events in the physical process correspond to events in the simulation, and objects in the physical process correspond to objects in the simulation.

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No one knows what an "algorithm" is. See here for a catalogue of attempts at a definition: https://en.wikipedia.org/wiki/Algorithm_characterizations. But I think most, if not all, of those attempted characterizations characterize it as a formal structure. Physical processes embody formal structures. I don't think you can say a physical process "is" the formal structure it embodies, but everyone would say that two different physical processes can embody the same formal structure. So then it comes down to the question of whether you consider "consciousness" a physical process or a formal structure embodied by a physical process. The computational theory of mind takes the approach that consciousness is akin to the program/software and the brain is akin to the hardware; you can run the same program on different hardware; so, with consciousness, it doesn't matter whether it's being "run" by organically grown neurons in a carbon-based life-form or "run" by some other sort of machinery composed of some other sort of particles. ("Embody" might not be the best term for it, but I think and hope my intended meaning is clear enough here.)

As for the question you concluded with: I think we should replace questions about whether something is consciousness (e.g. "Does the computer computing the process of red color perception actually see red?") with questions about when we would attribute consciousness to something (e.g. "Under what conditions would we say that the computer does actually see red?"). Because consciousness is a construct of attributions of consciousness (including self-attributions), so there's no fact of the matter beyond the attributions and their justifications. I'm deeply indebted to Dan Dennett on this view.

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One interesting point in relation to this:

The set of computable numbers is a subset of the set of real numbers of measure zero.

The extremely non-rigorous and technically incorrect but intuitively clear significance of this is - numbers that can ever be produced by an algorithmic process are an infinitesimally small proportion of the set of states that a given physical process could be in, if these are continuous.

So if the physical world is continuous such that its states are analogous to real numbers (or complex numbers where the components a and b in the complex number a+ib can take real values and are not confined to computable values) then the answer to this question is straightforwardly no - the world absolutely cannot be precisely identical to any algorithm.

Couple of further points: this is I think an interesting philosophical observation, but it isn't a practical constraint of any sort because any number is arbitrarily close to a computable number; also, in Quantum Computing since Democritus, Scott Aaronson uses precisely this observation to motivate his hunch that the world probably isn't really continuous.

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The algorithm is just the recipe --- the physical system is the bowl, flour, eggs, sugar, mixing spoon, etc.

An algorithm is just a description of a process to be performed --- it does not implement itself. Even when we are talking about computing algorithms, these are all implemented using some physical machine. So no, an algorithm is not identical to a physical process. Computing algorithms are written so that they can be implemented on a range of possible physical systems (e.g., different computers) but the "algorithm" doesn't do any computing itself --- it is just the description for how the physical system should operate.

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