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Imagine a rock in the shape of a chessboard with pieces in a certain configuration.

Throw the rock down a particular hill. The hill is shaped in such a way that, given the correct throw, the chessboard-rock will be chipped and flinted in a deterministic way as it rolls and bounces down.

At the end of this very large, very specific hill, the rock has been "carved" by the hill into the shape of a sentence "bishop to e4", which happens to be the "best" move.

Has the hill performed a computation corresponding to a chess algorithm?

And furthermore, are all rocks falling down hills performing some kind of computation, and is it only a matter of interpretation whether every falling rock could be said to be computing consciousness?

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13 Answers 13

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I think your example is overly complex for the question you are asking. Consider instead a pachinko-like device with a slot at the top, and 4 slots or holes at the bottom. In between the top and the bottom, are a series of trap doors which you can control. Depending on the ones you open or close, a marble dropped in the top will be directed into one of the holes. We can then label the slots at the bottom with the numbers 1,2,3, and 4. The levers can also be labelled with numbers 1, 2, and 3 and configured in a way that when you flip the levers labelled 1 and 2, the marble is directed to slot 3 and so on and so forth. Check out this wikipedia page for a real example of such a device.

If you are following this idea, you should see that we can use this device as a simple computer i.e.: it can be used to compute small sums. This is somewhat like your 'rock'. It's a device that can be designed to do the 'work' of calculations.

Moreover, classical electronic computers are not fundamentally different from such devices. Transistors work by having 'switches' that change the path of electrical signals through a circuit. That is, a transistor can close or open paths much like the levers above. It's simply a device where we label inputs and outputs as e.g.: 1 or 0. There's nothing about a digital computer that makes it inherently more or less a computer than a mechanical one. The reason we use electronics is because they are fast and small compared to known comparable mechanical solutions.

In other words, if you can build your system and it actually works, you could call it a special purpose computer. However, nothing about anything about it implies consciousness. And it's not clear how that fits in here.

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Computation is a deliberate mapping of inputs to outputs according to a finite list of specific instructions. An accidental process cannot be computation. A process with infinite or unknowable instructions (keep following the laws of physics, then keep following the laws of physics, then...) cannot be a computation. A computation can include processes with infinite numbers of steps only if it can categorize those steps into a finite list of specific instructions.

Digital computers do this by reducing all the infinite variation of how electrical signals can be to simply two states: "signal" and "no signal"; then passing the signal (or no signal) through circuits that are known in advance to output either "signal" or "no signal" on their various specific outputs depending on whether you feed them "signal" or "no signal" on their various specific inputs. Thus one doesn't need to know or care about the laws of physics that the signal follows as it goes through the circuits. In this way, "keep following the laws of physics, etc" is reduced to a finite list of specific instructions.

It may be possible to torture your hill analogy to the point where hills constitute logic gates and rocks constitute signals, but I'll leave that to the analogy torturer.

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    "An accidental process cannot be computation" ─ this is debatable. The cellular automaton known as Rule 30 appears to be implemented in nature, producing the patterns on the shells of a species of sea snail. This automaton isn't Turing complete, but nonetheless I would call it a kind of computation, and I don't think it really matters that the shell has no knowledge or intention of how its pattern forms.
    – kaya3
    May 18, 2023 at 6:46
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    Furthermore, our (and other animal) brains have happened through extinction of things less capable of existing: they were not made deliberately by an agent; however, (afaik) most people consider them as being capable of computation, or even doing it always as a part of being an acting agent (thus not being initiated or created by themselves).
    – user369070
    May 18, 2023 at 14:32
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Speaking as a computer scientist, I would say that every such hill is performing a computation. Namely, it computes the state that the rock is in once it reaches the bottom. More precisely, the input is the initial state of the rock (weight, shape, material, etc.) and the way it is thrown (position, force, direction, etc.) and the output is the final state of the rock (shape, position, etc.). Think about it like this: if you have a computer simulation of that precise hill that lets you throw rocks of arbitrary shape down, the simulation would be computing the result of throwing the rock down the hill. But the hill can be seen as a perfect simulation of itself, and therefore performs the same computation.

(The medium of computation is irrelevant. Computation can be performed by a digital circuit, a mechanical calculator, a human being with pen and paper, a cell membrane or a set of dominoes. See the Wikipedia page for Unconventional Computing. Nor does it matter if it's intentional or deliberate: if I generate a random sequence of computer instructions, it still computes something, even if I don't know what it is. All that matters is what output it produces for a given input.)

Now, does that computation correspond to a chess algorithm? That depends. Computation is not defined based on the result of a single input. To determine what an algorithm or a system computes, you need to know what the result is for every input. For example, let's say that I propose the following simple algorithm for determining if an integer is prime: given an integer, answer "yes". If you give this algorithm the integer 17, it will output the correct result, but that doesn't mean that it computes whether an integer is prime or not, because for many other inputs (for example, 18) it will give an output that doesn't correspond to the correct result of that computation.

Transposing this to the hill example, if you throw this chessboard-shaped rock in this way and it lands carved with the same move that a chess algorithm would come up with, it doesn't mean that it performs the same computation as the chess algorithm. But if for every board position you can determine a way of carving it on a rock and throwing it down this hill such that it lands with the best move (in computer science, this is what we call a reduction), then it would be reasonable to say that the hill computes the best move like a chess algorithm.

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    Yeah, my first thought was "It's an anlouge computer that can calculate exactly how fast a rock rolls down a hill and where it's final location will be, along with millions of other speed and angle calculations. Math is simply how we precisely describe nature, but is not required to preform the calculations.
    – Bill K
    May 18, 2023 at 21:46
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Computation is like meaning or beauty; it is something that we may see in physical objects but it really isn't in the object; it is in the mind of the observer. When you see marks on a screen, those marks are meaningful only in virtue of conventions that certain marks are to be interpreted in a certain way. The mark "dog" doesn't refer to dogs in virtue of anything physical about the mark itself, but only in virtue of the fact that we have learned that it refers to dogs. Someone who doesn't read English would have no idea what the mark refers to, and no possible examination of the physical characteristics of the mark could reveal what it refers to.

Beauty is a bit different because it isn't entirely conventional. When you see a configuration of pixels on a screen that resolves visually into a picture of some beautiful scene, you don't consider the scene beautiful just because of convention. Convention (or, more properly, social conditioning) may play a part, but there is also an aspect of biological response, so that another human who sees the image can often know that you would see the image as beautiful without knowing what your social conditioning is, but an alien with no knowledge of human biology or psychology would not be able to tell that the image is considered beautiful, and no amount of physical examination could reveal that.

Computation is different yet again, in that it is constrained by logic in such a way that if you can infer what aspects of a physical process are intended to be computational, then you can make reasonable assumptions about what function is being computed. Someone who has never seen a calculator before might be able to figure out what it does by examining how it operates. However, that is because it is clear what the inputs and the outputs are. In the case of the rock rolling down the hill, it would not be at all clear what the inputs and outputs are, and without that information, no physical examination of the process could reveal what calculation is being performed.

Furthermore, even in the case of the calculator, what the inputs and the outputs are is a matter of convention much like meaning. The only reason anyone could figure it out is by inferring the intentions of the designer and assuming the designer would have designed the device following certain rules of design such as making it as simple as possible to perform the desired function, and that the desired function is rational. Without such assumptions--which depend entirely on the mind of the designer--no amount of physical examination could reveal what functions even a calculator computes.

Any reasonably complex physical system can be interpreted in many ways so that it computes a very large number of functions. All you have to do is assign various measurements to various inputs and outputs. For example, when the temperature of this tiny area is X, and the temperature of this tiny area is Y, then eventually the temperature of this tiny area becomes Z where Z is the average of X and Y.

So meaning, beauty, and computation are not properties of physical systems alone; they are properties that the mind imposes on physical systems.

Now, something similar can be said about any property of physical systems. Any measurable property of a physical system such as color, mass, velocity, temperature, etc. depends on our sensory capabilities and on conventions of units and measurement techniques. No amount of physical investigation of a physical object can tell you how many kilograms that object is unless you know the convention for kilograms. Measurements are like meaning, beauty, and computation in this sense.

However, the number of units is not the significant feature of the mass. What is significant is how the mass compares to the mass of other objects, and that is something that can be determined by any human or alien simply by examining the object psychically, with no knowledge of any human conventions. Such an examination can reveal how an object is going to interact in collisions with other objects, for example.

Therefore, physical properties like mass can enter into physical causality, because it is an encoding of an aspect of the physical world. But subjective properties like meaning, beauty, computation, and unit conventions cannot enter into physical causality because they are not aspects of the physical world itself, but aspects of a mind.

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    +1 recognizing the dualism inherent in physical computation. "In the case of the rock rolling down the hill, it would not be at all clear what the inputs and outputs are, and without that information, no physical examination of the process could reveal what calculation is being performed." Che bravo. So explicitly, it depends on the details of implementation of the hardware.
    – J D
    May 16, 2023 at 17:34
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In this thought experiment no computation occurs during the rolling of the rock.

If the hill, the rock and the throwing action are deliberately designed to bring that particular result, then some serious computation must have taken place during the design phase.

If the shape of the hill and the rock and the throwing action are random, then no computation has taken place and the result is a mere coincidence.

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I would argue that there is indeed a computation happens as a state is transformed to another state, following a (presumably) determenistic set of rules.

The real questions here are: What is YOUR definition of computation? and whether such computation is useful: if it is knowable and known(to a user agent), that the hill does exactly that, then it can be used by said agent to do exactly that(convert a rock saying a very specific position into a rock saying a very specific move). It would be more useful if it was also known that it could convert any position into a determined move using a throw (a set of inputs) that themselves require less computation to achieve than to get to the result of the hill.

The hill can be said to have computed a chess algorithm so long that its inputs and outputs can be converted to chess values, even if the algorithm itself is useless.

If a computation is knowable but not known, then it can be measured to become known, and thus useful. The computation does not even need to be always exact same: if the correctnesss to error ratio is non-zero, then a useful computation can be measured, and utilised.

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  • Another way to rephrase this answer is to simply say that a computation models something else.
    – DKNguyen
    May 17, 2023 at 21:22
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Pareidolia

Your chessboard example sounds similar to pareidolia, which is roughly speaking when you see meaningful patterns in seemingly random data.

Just because you ended up with something that looks like what a chess algorithm would give you, doesn't mean that a chess algorithm was performed.

What is a computation?

Firstly, I wouldn't say "the hill performed" anything, because the hill is an inanimate object incapable of "performing" anything. If anything, the "computation" would've been performed by the system containing the hill, the rock and physical forces acting on them.

Okay, so we have a physical system containing a rock in the shape of a chessboard, which follows some deterministic process to turn that rock into the shape of a sentence. Would that be a computation? This may be a question of how you define "computation", rather than a question of philosophy. The important question is how this process works (e.g. whether it's deterministic), rather than what we call it.

I probably wouldn't in general call it a computation, though, because computation tends to imply some structured process, often with a particular goal, which would not apply to a rock arbitrarily rolling down a hill. If we were to call that a computation, this would make the definition of far too broad, and have it encompass roughly all of existence, which would not really be a useful definition. If someone were to have specifically crafted the hill and rock in order to go through that process and end up with the rock in a different shape, this may be closer to a computation (although perhaps still distinct from that). But one could also argue that computations are computations regardless of goals, so either both should be a computation, or neither should be. It's also worth keeping in mind that the bounds of categories tend to be blurry.

every falling rock could be said to be computing consciousness

No. Even if you hold that consciousness is purely computational, this does not mean that every computation is consciousness. That would be like saying an apple (consciousness) is a fruit (computation), and an orange (falling rock) is a fruit, therefore an orange is an apple. That reasoning would be very flawed.

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  • Not downvoting, but complements of CriglCragl, tumbling objects selecting strings is not only a computer but manufactured as such: "Although it resembles a pachinko machine in its aesthetic use of gravity-fed metal balls, it is primarily a teaching device in the fundamentals of logic-computer programming, and as such is an example of gamification." Turing Tumble
    – J D
    May 17, 2023 at 14:59
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Well, no, it's not really a computation and I'm going to give here, a simpler form of the same thing you're suggesting.

So let's say you have a coin, and you flip it 48 times. Assume heads to be 1, and tails to be 0. Now, this set of 1s and 0s, let's say it's binary for ENIGMA. Have we created a Binary Encoding Computation of sorts? (In context of theoretical coin flips) No. Have we created a random binary generator? Absolutely! You could argue that there are random generators that work on algorithms, however, those are pseudorandom, and are highly, highly chaotic, but never truly random, as purity, is only possible in theory. You can read about the functioning of the random generators here.

This however, (again in context to theoretical coin flips), is truly random, and the code being equal to ENIGMA is a coincidence. Same with your own example, the result being the perfect move is a mere coincidence.

However, here is one thing I did think of you might find interesting. While, this may or may not apply to my own model here, but should certainly apply to yours. Let's assume the rock chips away the hill bit by bit every time you roll it, in such a way that it gives more and more accurate chess moves. What you're doing here, is training an algorithm, similar to how AlphaZero was trained. So I do think that's something to think about, and after enough training it would become a computation, because what you're doing is controlling and restricting the computations to give the result you want. Again, just something to think about.

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  • +1 for RNG analogy
    – J D
    May 18, 2023 at 15:45
  • @JD Thank you so much! May 18, 2023 at 15:47
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There's a variant of this thought experiment in the literature: in Sec. 6 here, Aaronson mentions Putnam and Searle as advocates of it. Suppose a physical system (Aaronson chooses a waterfall, Putnam a clock, Searle the paint on a wall), obeying time-reversible deterministic physical laws, evolves from one of finitely many possible initial states over some time period to one of finitely many possible final states, thereby "computing" some bijection between the two sets of states. In particular, numbering the states in each set allows us to describe this in terms of any permutation of 1 to N, N being the number of possible states at each end. However, their conclusion, rather than being that a computation has occurred, is that computations are syntactic rather than semantic: they don't mean anything, because they can be just as much about a waterfall as anything computable by reduction to finding a permutation with it. In particular, the intent is to critique a computational characterization of consciousness.

Aaronson, who links to criticisms from Block, Chalmers and Haugeland, makes an interesting point of his own. Anyone who wanted to compute something with the waterfall would need an algorithm that reduces a problem of interest to that of thereby obtaining a permutation. Aaronson plausibly conjectures this is an unnecessarily roundabout computation:

I conjecture that, given any chess-playing algorithm $A$ that accesses a “waterfall oracle” $W$, there is an equally-good chess-playing algorithm $A^\prime$, with similar time and space requirements, that does not access $W$. If this conjecture holds, then it gives us a perfectly observer-independent way to formalize our intuition that the “semantics” of waterfalls have nothing to do with chess.

As for the other critics:

  • Block argues no computer is present because alternative computations aren't in general thereby achievable (they may need to use different bijections, which are only available if we suitably relabel the states, which gets us back to Aaronson's point).

  • Chalmers notes a syntactic process's physical implementation may provide additional meaning (his example is a recipe for a crumbly cake).

  • Haugeland's contention is one on which, even if Putnam and Searle's argument against computationalism fails, your thought experiment may qualify as a computation:

The only way that we can make sense of a computer as executing a program is by understanding its processor as responding to the program prescriptions as meaningful.

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Underlying all electronic calculators is a designed arrangement through which countless electrons fall down potential gradients. Does each electron perform a calculation? No.

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    I would argue that each electron actually does perform a computation, which accumulates a less precise probabilistic process into a more precise, more predictable and thus accurate - 'discrete' process. And thus with reduction of electrons passing, the chance of errors should increase, which is something that does happen. The computation each electron does may be extremely trivial (accumulation), but so are of every of the individual logic gates.
    – user369070
    May 17, 2023 at 7:55
  • But on the other hand, in a quantum computer, one sets up a set of coherent qbits and then operates on them without de-cohering them. When one collapses the state function, the set of actual bits represents a number which, for example, must be a prime factor of the number one was trying to factorize. Which prime factor one gets is random, but it's easy to verify that it is and to compute the other with a conventional computer. (Also you would expect to get both with similar probablities if you repeat the quantum computation many times)
    – nigel222
    May 17, 2023 at 9:23
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If the simulation hypothesis is true then everything that happens is (at least in a trivial version of that hypothesis) running code, which is, computations.

Even if we disagree with that hypothesis it may inform how we think about the universe, under which paradigm (much in the Thomas Kuhn sense) we interpret it. The rules under which the universe "runs" — the physical laws — seem well suited to understanding natural processes as a sort of computation. For example, that all interaction is local, that there is an absolute speed of information flow that cannot be exceeded, and that there is a built-in limit to the accuracy of measurements (or, in other words, a finite information density) seem to lend themselves very nicely to the concept of the universe as a computational engine, a cellular automaton.

Your example, by the way, does not fit very well in this modern concept of computation because the information limit results in a randomness which prevents replicable experiments like the one you describe. Your example would fit better with the clockwork paradigm applied to nature (and humans) by baroque thinkers and their successors like Laplace who drove it to the extreme with his demon.

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Generally, computation consumes inputs and produces outputs. The inputs represent the problem, the outputs represent the solution.

Most computers do not use human language, so users must translate their problem statement into the input language of the computer. They must then translate the computation result from the output language to their own, so they can interpret and understand it.

This also means that computation is subjective in that it depends on your understanding of the I/O language.

In your example with the chess moves, you have defined an input in the form of the hill's shape and an output in the form of the landing area. So you can say it's performing the computation on that basis. If you had never seen a chess board and were unaware that the hill is special, it would not be performing a computation from your perspective.

Another important point is the usefulness of the computation. You can retrospectively invent a contrived I/O language to claim that any phenomena is computation. However, the laws of nature are such that it's unlikely these will produce high quality results. For example, in the case of your rock, the odds are very low that its chess moves will actually be strong ones. There are many, many ways in which the shape of the hill and trajectory of the rock can lead to effectively wrong chess moves, and there's very few ways which must be just right for it to actually produce correct moves. Chances are, the person who shaped the hill (or probability, if the hill is naturally formed) will have failed to do a good enough job and the rock will not follow optimal paths consistently. So it will perform some computation, but a low quality one with useless results.

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What if nobody was there to witness the possible computation? Then did the possible computation really happen in that case? That's like asking, if a tree fell in the forest, and nobody was there to hear it hit the ground, did it make a noise when it fell down? The difference is, a computation isn't necessarily random. It's possible that a random set of events might create a very specific outcome, but not necessarily so.

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