What is computation? Does computation = causation

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What is computation?

This is a surprisingly hard question to get a straight answer on. The Stanford Encyclopedia of Philosophy article on physical computation offers nine competing theories on how computation is instantiated in the world.

Things do not get better if you want to look at computation abstractly, from the perspective of pure mathematics. SEP has no article on computation sans physical instantiation. Nor is it easy to find articles on "what computation is" in any sort of philosophical sense. This excellent free textbook titled "Mathematics and Computation" is no exception. The introduction briefly addresses the issue, and then moves right along to Turing Machines, computational complexity, definability, incomputability, etc.

I'm wondering if anyone knows any good resources on this topic?

I'm going to propose a few radical positions. I will back them up later in this thread, but this post would be too long if I went into all of them.

• Computation is what defines mathematical/abstract objects rather than it being some activity that you do with them. In some ways, this is not far off the position of formalism in mathematics ("a number is what it does"). However, a major implication of this position that has generally been missed is that you cannot ignore the stepwise nature of computation. Equivalent functions are not equivalent until computation makes them so. Or, for a less strong view, "computation is as essential as abstract objects and its stepwise nature is essential even when considering equivalences in abstraction."
• In many respects, it is impossible to distinguish communication from computation in contemporary theories. I think they are different and that this shows a weakness in the theories.
• For all intents and purposes, "computation" in physical systems is identical with what we generally mean by "causation." Replacing "conserved quantities" with "conserved information" in causal theories has been successful, but they would be more intuitive if you took this extra step.
• Conservation of information was just sloppily imported from other conservation laws in physics. This is a larger problem with digital ontology in general, which attempts to just replace "fundamental particles" or fields with bits. This doesn't work, since information, a measure of contextual difference, doesn't work with reductionism. If information is fundamental, reduction doesn't work in many respects. (I should note that some measures of information DO appear to be conserved in some interpretations of QM)

Computation is what defines mathematical/abstract objects

If we throw a Hamiltonian Path problem with a sufficient number of nodes at a supercomputer we will be waiting until the heat death of the universe for it to compute our answer. However, it is possible to write an algorithm that specifies the answer we wish to calculate using a tiny fraction of the resources it takes to calculate the answer.

The key point is that in the real world it takes time and energy to transform one representation of an abstract object (e.g., a number) into another. If we agree that numbers and other abstract objects only exist inasmuch as they are instantiated in the universe (be that in the external world or in our minds) then it seems like we should take computation as essential to these objects' nature.

You cannot feed 10 + 10 into a computer and get it to return 20 without having it preform computations. Presumably, the same is true for our minds. Take P1 - "The total spent on popcorn and vitamins in the United States from June, 1989 to October 1990." P1 defines a real number, but it is in important respects not equivalent to that number. The key difference, aside from the fact that capturing data on all those sales would require a lot of energy expenditure and information storage, is that P cannot be used in many computations. For example, P1 > P2, where P2 is some other equally frivolous description of a real number, is not computable.

However, for the most part, it seems that the ghosts of Plato and Pythagoras still have a lot of influence on how we conceptualize abstract objects. Abstract objects seem to exist in some eternal realm, at least as far as computation is concerned. If two functions are equal to the same number then they are "describing the same thing", they are just "different names." That is, 8 + 8 and 10 + 6 share an identity. This is seemingly unproblematic with simple algorithms, but is a serious issue when the resources of the visible universe wouldn't be enough to turn X into Y.

Even if relationships between objects or transformations of them must occur stepwise, both conceptually in our minds and observably in nature, it is assumed that this "step-wise-nature" is an artifact of our limitations, that these objects' relations are in fact eternal and direct. This is one place where it seems even very committed nominalists appear to let the eternal slip into their metaphysics.

Existence proofs are a challenge to this view, but I don't think they are a big one. Sure, there are ways to show that an object exists without computing it in total, but proofs themselves are computation, logical operations. They can be seen as simply ambiguous descriptors, the same as P1 up above or "the first number that violates the Golbach Conjecture," if such a number exists.

I find this view promising because it resolves the scandal of deduction/paradox of analysis (the problem that logical truths and computation should give us no new information). It also jives with P ≠ NP. It would also get past some of the main barriers facing "physics as computation" models. I like those models because there, computation becomes pretty much synonymous with causation, and the former is understood much better than the latter.

There is obviously more to be said here. I still haven't answered "what is computation?" I think a metaphysics where computation emerges from fundamental ontic difference and logic could ground the system, but obviously huge holes will remain because there are huge holes in mathematical foundations in general.
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As to the conservation of information:

If I have perfect information about a billiard table and can predict an upcoming shot, it does not follow that state S1 before the shot and state S2 after the shot are the same thing or indistinguishable for me. If earlier states of the table, or the universe, are such that perfect information about S1 would allow you to perfectly predict S2, it still seems that recording all the information in the universe at one instant (S1) is not the same thing as recording all the states of the universe (S1 to S max).

A lot of arguments against the passage of time and existence of change rely on/are motivated by the unwillingness to see computation as anything but something we experience due to being limited beings.

I have a thought experiment that makes this clearer I will try to dig up.

Additionally, even if you don't buy that argument, while the universe is in a low entropy state, it seems like it should certainly have a lower Kolmogorov Complexity because, given fewer possible microstates, the description does not need to be as long to describe which microstate the universe is actually in.
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What is computation?
Here's the first in a series of lectures by one of the founders of 'quantum computational theory' David Deutsch which explains in summary the fundamental nature of computation as a quantum process underlying all classical processes like e.g. the 'Universal Turing Machine'.
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I am a fan of Deutsch but I have never understood how his theory of quantum computation works with MWI. I get that MWI is observably indistinguishable from other interpretations of QM, and so his explanation is fine in that sense. However, conceptually, the idea that copies of a quantum computer in other universe's can help increase our information about the results of an algorithm in our universe seems off. This implies that information is crossing between universes and that one has a causal relationship with the other. This seems to conflict with a core tenant of MWI, that observers, because they are also entangled, only observe one part of the wave function.

But perhaps it is the other possibilities that matter in the same way that possible states drive thermodynamics. I have to think about that more.

I believe I have heard Deutsch use the common explanation of particles "storing information." I know I have heard this from Vlatko Vedral, Max Tegmark, Ben Schumacher and Paul Davies. This appears to be somewhat mainstream and I think it fundamentally misunderstands the logic and mathematics of information.

A particle can only carry information inasmuch as it varies from other particles and measurements of the "void." If this was not the case, they wouldn't hold information, e.g., an electron can't store/instantiate information in universe where every measurement shows charge identical to an electron, at least not in terms of EM charge.

You can transfer information via the quantum afterglow of photons without transferring energy. The void appears to be seething with observables. The general push in ontic quantum computation models unfortunately seems to have fallen back into problems with prior models by just replacing the old fundamentals with "information."

The much less common assertion that virtual particles and QCD condensates don't have information is even more obviously off. If they didn't produce observable differences, information, then how could we know about them and how could their existence spawn books and papers on them. I only see this position in older papers though.
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Great OP, and I am still grappling with it. I think where you lose me is the notion that computation and causation are somehow equivalent. There seem to be too many key differences:

• There is no such thing as causation that goes wrong. It does what it does, it is infallible by its nature. Whereas at every step, the possibility of error hovers over computation.
• Causal processes don't inherently require continuous energy input. Strike the cue ball, and the billiards will take care of themselves. Whereas in a computational process, to proceed requires energy at every step. Cut the power, occlude the cerebral artery, and the computation comes to a screeching halt.
• There is no notion of accuracy of causal systems. They are in themselves infinitely accurate. Whereas for many computations, to achieve perfect accuracy requires infinite time and energy.
• Causation is something that stuff does. Whereas computation, however sophisticated, can never achieve stuffhood. You can computationally simulate every feature of a waterfall, down to the most minute detail. But no matter how sophisticated, you can never touch a waterfall simulator and get your fingers wet.

Something like "Computation is to information as causation is to matter" seems more accurate, but even then I am not sure.

In many respects, it is impossible to distinguish communication from computation in contemporary theories. I think they are different and that this shows a weakness in the theories.

Communication would seem to require encoding, transmission, and decoding. A causal process sandwiched between two computational ones?
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I'm wondering if anyone knows any good resources on this topic?

You might enjoy ‘Consciousness and the Computational Mind’ by Ray Jackendoff, a critique of computational approaches in psychology. Other critiques of computationism in cognitive science can be found dani. the work of Francisco Varela, Evan Thompson and Shaun
Gallagher.
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There is no such thing as causation that goes wrong. It does what it does, it is infallible by its nature. Whereas at every step, the possibility of error hovers over computation.

True, but is there such thing as computation that goes wrong in the abstract sense? Can the square root of 75 ever not be 8 2/3rds + a set of trailing decimals? The very fact that we can tell definitively when computation has gone wrong is telling us something. If we think causation follows a certain logic, e.g., "causes precede their effects," we are putting logic posterior to to cause. But just because we can have flawed reasoning and be fooled by invalid arguments, it does not follow that logical entailment "can go wrong."

When computation goes wrong in the "real world," it's generally the case that we want a physical system to act in a certain way such that it computes X but we have actually not set it up such that the system actually does this.

Causal processes don't inherently require continuous energy input. Strike the cue ball, and the billiards will take care of themselves. Whereas in a computational process, to proceed requires energy at every step. Cut the power, occlude the cerebral artery, and the computation comes to a screeching halt.

I was coming from the suprisingly mainstream understanding in physics that all physical systems compute. It is actually incredibly difficult to define "computer" in such a way that just our digital and mechanical computers, or things like brains, are computers, but the Earth's atmosphere or a quasar is not,without appealing to subjective semantic meaning or arbitrary criteria not grounded in the physics of those systems. The same problem shows up even clearer with "information." Example: a dry riverbed is the soil encoding information about the passage of water in the past.

The SEP article referenced in the OP has a good coverage of this problem; to date no definition of computation based in physics has successfully avoided the possibility of pancomputationalism. After all, pipes filled with steam and precise pressure valves can be set up to do anything a microprocessor can. There are innumerable ways to instantiate our digital computers, some ways are just not efficient.

In this sense, all computation does require energy. Energy is still being exchanged between the balls on a billiard table just like a mechanical computer will keep having its gears turn and produce an output, even without more energy entering the system.

I do have a thought experiment that I think helps explain why digital computers or brains seem so different from say, rocks, but I will put that in another thread because that conversation is more: "what is special about the things we naively want to call computers."

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As to the other points, look at it this way. If you accept that there are laws of physics that all physical entities obey, without variance, then any given set of physical interactions is entailed by those laws. That is, if I give you a set of initial conditions, you can evolve the system forward with perfect accuracy because later states of the system are entailed by previous ones.

All a digital computers does is follow these physical laws. We set it up in such a way that given X inputs it produces Y outputs. Hardware faliure isn't a problem for this view in that if hardware fails, that was entailed by prior physical states of the system.

If the state of a computer C2 follows from a prior state C1, what do we call the process by which C1 becomes C2? Computation. Abstractly, this is also what we call the process of turning something like 10 ÷ 2 into 5.

What do we call the phenomena where by a physical system in state S1 becomes S2 due to physical interactions defined by the laws of physics and their entailments? Causation.

The mistake I mean to point out is that we generally take 10÷2 to be the same thing as 5. Even adamant mathematical Platonists seem to be nominalists about computation. An algorithm that specifies a given object, say a number, "is just a name for that number." My point is that this obviously is not the case in reality. Put very simply, dividing a pile of rocks into two piles of five requires something . To be sure, our groups of physical items into discrete systems is arbitrary, but this doesn't change the fact that even if you reduce computation down to its barest bones, pure binary, 1 or 0, i.e., the minimal discernable difference, even simple arithmetic MUST proceed stepwise.

Communication would seem to require encoding, transmission, and decoding. A causal process sandwiched between two computational ones?

Sure, but doesn't computation require all of that. Computer memory is just a way for a past state of a system to communicate with a future state. When you use a pencil for arithmetic, you are writing down transformations to refer to later.

We might be the recipient of a message transmitted onto a screen, but an important sense our eyes send signals, communications, the the visual cortex for computational processing. A group of neurons firing in a given pattern can act as part of a signal/message to another part of the brain, but also be involved in computation themselves.

This is what I call the semiotic circle problem. In describing something as simple as seeing a short text message, it seems like components of a system, in this case a human brain, must act as interpretant, sign, and object to other components, depending on what level of analysis one is using. What's more, obviously at the level of a handful of neurons, the ability to trace the message breaks down, as no one neuron or logic gate contains a full description of any element of a message.

Even in systems modeled as Markov chains, prior system states can be seen as sending messages to future ones. The two concepts are discernible, but often not very. I will look for the paper I saw that spells this out formally.
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Is there computation in a mindless universe?
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What is computation?

As a non-mathematician, I am curious about the following:

Question one: if I put one pebble on a table and alongside it put another pebble, has a computation been carried out ? Because, whatever has happened has proceeded in a series of steps, within the system there has been a change in information, something has caused the pebbles to move, time and energy have been needed, two has been instantiated in the physical world as two pebbles but also two exists as the abstract object two and two pebbles existing as a single whole is different to two pebbles existing as two separate parts.

Question two: if in the absence of any observer, a pebble moves alongside another pebble
under natural forces, has a computation happened ?
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The original conception of computation was of a "mechanical method" that is synonymous with a deterministic "winning" strategy with respect to a single player game of finite and complete information. To recall the Church Turing Thesis

A method, or procedure, M, for achieving some desired result is called ‘effective’ (or ‘systematic’ or ‘mechanical’) just in case:

1 ) M is set out in terms of a finite number of exact instructions (each instruction being expressed by means of a finite number of symbols);

2) M will, if carried out without error, produce the desired result in a finite number of steps;

3) M can (in practice or in principle) be carried out by a human being unaided by any machinery except paper and pencil;

4) M demands no insight, intuition, or ingenuity, on the part of the human being carrying out the method.

This original conception of computation in terms of a mechanical method is therefore strongly, if not completely normative, strictly in relation to perspective, and anti-real in being defined entirely in relation to human purposes and human psychology, whist forbidding any empirical contribution from mother nature herself to the computational process. Or as Wittgenstein summed it up : "Turing Machines are what humans do" . Such single player games are incompatible with a realist's conception of causation as a zero player game that is fully determined by the initial state of the game without any subsequent interventions by man, nature or god.

To bring causation and computation into line requires their definitions to be weakened and generalised so as to refer to strategies of two player games involving interaction and dialogue between man and nature. Computer science and mathematics can then be understood as attempting to answer questions of the form "If nature were to act in such-and-such a fashion to my actions, then what are my available winning strategies in relation to my goal?". While physics and it's concept of causality could be understood as asking the complementary dual question "If one were to act in such-and-such a fashion, then how is nature expected to respond?"
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Great OP, and I am still grappling with it. I think where you lose me is the notion that computation and causation are somehow equivalent.
I would say in the other way: if you think that computation and causation are equivalent, then you think that mathematics and physics are equivalent. Not just that physics is accurately modeled using mathematics.

First of all, there do exist mathematical objects that are true, but not computable.
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The easiest way to conceptualize how rocks act as computers is to think of them modeling something simple, like a single logic gate.

In terms of grouping rocks together, it's probably easier to conceptualize how the cognition of "there are two rocks over there," and "there are 12 rocks over there," requires some sort of computational process to produce the thought "there are 14 rocks in total."

Wouldn't physics generally be answering the question of "if nature acts in such-and-such a fashion how will nature respond?" In general, scientific models are supposed to be about "the way the world is," not games. I don't think such interpretations were ever particularly popular with practicing scientists, hence why the Copenhagen interpretation of QM, which is very close to logical positivism, had to be enforced from above by strict censorship and pressure campaigns.

I wouldn't agree that mathematics necessarily has anything to do with goals.

Lambda calculus doesn't come with the thought experiment baggage of Turing Machines but is able to do all the same things vis-á-vis computation. I think it would be a mistake to misconstrue the framing Turing gives to the machine with something essential to it. In any case, classical computing wouldn't be equivalent to causation in the physical world. Something like ZX calculus would be the model.

I would say in the other way: if you think that computation and causation are equivalent, then you think that mathematics and physics are equivalent.

Certainly that's a hypothesis that's been raised from a number of angles (Tegmark, Wheeler, etc.) I don't think that's a necessary implication though. Not all forms of mathematics appear to be instantiated in the physical world. Mathematics is the study of relationships. The physical world observably instantiates some such relationships.

Indeed, most forms of the hypothesis that physics is somehow equivalent with mathematics are explicitly finitist. Infinites and infinitesimals are said not to exist, but clearly they are part of mathematics, so the two aren't fully equivalent.

Saying computation is causation is simply saying that one thing entailing another in the physical world follows the same logic as computation in mathematics. One doesn't reduce to the other, they are just different ways of looking at the same thing, i.e., necessary stepwise relationship where states proceed from one another in an ordered fashion.

In an algorithm you have initial conditions, your inputs. The algorithm then progresses in a logically prescribed manner through various states until is reaches the output of the process. In physical systems, you have initial conditions which progress in a logically prescribed manner until the process ends.

Of course, "systems" and "processes" are arbitrarily defined in physics. Any one process can be an input for another process, one system is merely a part of another system, etc. However, this mirrors mathematics, where inputs are also arbitrarily selected.

These brackets might be artificial, but my argument is that the step wise progression of computation is not. Equivalences of two different functions are not a shared identity. Rather, through a process one can become identical to the other. Such becoming, the continual passing away of one state into another is the hallmark of our world and I think it's been a serious mistake to dismiss it as illusory and that this mistake owes to a seriously calcified view of mathematical objects tracing back to Pythagoras.
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I suppose the arbitrary system boundary problem and semiotic circle problem both are akin to the concept of levels of abstraction in computer science. The problem is that there is no clearly defined level of abstraction like there is in CS.

I don't know if this is simply a lack of knowledge about the way the world works, or a more fundamental problem where an observer within a system cannot clearly delineate its levels of abstraction on principle. I will have to think about that one.
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In terms of grouping rocks together, it's probably easier to conceptualize how the cognition of "there are two rocks over there," and "there are 12 rocks over there," requires some sort of computational process to produce the thought "there are 14 rocks in total."

If I see two rocks on the left, I know that two objects has the name "two".
If I see twelve rocks on the right, I know that twelve objects has the name "twelve".
If I see fourteen rocks in total, I know that fourteen objects has the name "fourteen".

IE, I know there are fourteen rocks in total not from any computational process but from how objects are named.
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Question two: if in the absence of any observer, a pebble moves alongside another pebble under natural forces, has a computation happened ?

This.
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Wouldn't physics generally be answering the question of "if nature acts in such-and-such a fashion how will nature respond?"

There certainly are many scientists who offhandedly assume in an old-fashioned way that causality must be an "objective" notion. But as Bertrand Russell pointed out, the notion of causality is objectively redundant. e.g, what does the notion of causality add to a description of the Earth orbiting the Sun? The notion of causality adds nothing of descriptive value to any proposition that states an actual state of affairs, while the employed purpose of causality is to model possible outcomes in relation to possible actions. Do you really wish to promote the possibilities that exist in relation to a model to the status of objective reality, given the fact that possibilities aren't scientifically testable or observable?

In general, scientific models are supposed to be about "the way the world is," not games. I don't think such interpretations were ever particularly popular with practicing scientists, hence why the Copenhagen interpretation of QM, which is very close to logical positivism, had to be enforced from above by strict censorship and pressure campaigns.

The Copenhagen interpretation itself isn't generally regarded as constituting a game-semantic interpretation of QM, but it should be noted that the the linear logic behind the ZX calculus has very strong game semantics (e.g see Blass and Abramsky's work on game semantics and linear logic ). The conceptual connection between Logic and games goes all the way back to Aristotle. And of course, logic is used to both state the causal assumptions of a model, and also to define computation. So there are good reasons for interpreting both causation and computation at least semi-normatively in terms of game-semantics, an analysis which if correct, precludes both from constituting or describing observer-independent properties of the universe.

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I am now seeing that was not a good example. The quantities you perceive are irrelevant. I referenced cognition because the most popular models of how the brain works are computational. I only meant to point out that in this view, seeing anything is the result of computation. The computational component of seeing things in the world is most easily traced back to the system that generates the observers' perspective being computational.

Obviously not everyone thinks computational neuroscience is a good way to model the brain, let alone consciousness, but I figured its well known enough to be a good example.

If you want to think of rocks computing, you have to think more abstractly. Computers are such that a given state C1 is going to produce an output C2. Rocks change states all the time, for instance, they get hotter and colder throughout the day. You can take the changing states of the rock to be functioning like logic gates.

In theory, you could compute anything a digital computer can by setting up enough rocks in relation to one another such that heat transfer between them will change their states in such a way that they mimic the behavior of logic gates in microprocessors vis-á-vis their state changes. Rather than electrical current, you'd be using heat. Of course, to make this system compute what you want it to compute, you'll have to be selective in the composition of your rocks as well.

It's probably easier to think of how you can spell out any phrase with small rocks. Just line them up in the shape of the letters. Your rocks are now storing information.

But of course, they were already storing information. The locations of the rocks when you found them tells you something about prior events. For another example, foot prints store information about the path you took to get to these rocks.

Information is isomorphic. You could spell out a message with the rocks, then take a Polaroid of said message. Then you could scan the Polaroid and send it to a friend as an email. Your message, which is represented by some of the information that defined each system, remains in each transition. Information is substrate independent. Computation, the manipulation of information, is the same way.

This brings up the question of why computers and brains seem so different in their ability to compute so many different things so readily in comparison to rocks or systems of pipes with pressure valves. I would like to bracket that conversation though.

I will start a new thread on that because I think discernablity between different inputs in the key concept there, but it isn't relevant to "what computation is."

If pancomputationalism seems nonsensical, the best way to see where the idea is coming from is to try to define what a computer is in physical terms and how it differs from other systems.

Do you really wish to promote the possibilities that exist in relation to a model to the status of objective reality, given the fact that possibilities aren't scientifically testable or observable?

I'm not sure what this is supposed to mean, possibilities already seem fundemental to understanding physics. Possibilities are essential to understanding entropy, the heat carrying capacities of metals, etc. The number of potential states a system can be in given certain macro constraints is at the core of thermodynamics and statistical mechanics. Quantitative theories of information on which a large part of our understanding of genetics rest also are based on a possibilities.

For any one specific message the distribution of signals one receives is always just the very signals that one actually did receive. Every observation for every variable occurs with probability = 1. However, a message can only be informative in how it differs from the possibilities of what could have been received.

But as Bertrand Russell pointed out, the notion of causality is objectively redundant. e.g, what does the notion of causality add to a description of the Earth orbiting the Sun?

It's "objectively redundant," because he is begging the question, assuming what he sets out to prove in his premise. He assumes a full description of a system doesn't involve explaining causation. The fact that "if you've said everything that can be said in terms of describing a system from time T1 to time T2, you've said everything there is to say," is trivial. The argument against cause here comes fully from the implicit premise that cause is properly absent from a description of the physical world.

Certainly an explanation of "why does the Earth rotate around the Sun," adds something here, no? Russell denied the existence of time's passage and in some more flippant remarks on Zeno's arrow, appears to deny that change and motion exist. I don't want to get into unpacking the bad assumptions that get him there, but obviously in such a view cause can't amount to much because what is cause without change?

I don't find it to be an attractive position though.
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Here is a demonstration of the problem I should have led with.

Suppose we have a document 150 pages long. Each page contains either just blank spaces or the same symbol repeated over and over. We have pages for every letter of the alphabet, uppercase and lowercase, plus punctuation marks and mathematical equations.

We also have an algorithm that shuffles these symbols together, working through all possible interations of the pages. Given 2,000 characters per page, and no limits on our algorithm's output, this will produce 2,000^150 pages. Each of the pages is then assembled into all possible 150 page books (simply because books are easier to visualize) made by this process.

This output will include the pages of every novel ever written by a human being, plus many yet to be written. Aside from that, it will produce many near exact replicas of existing works, for example, War and Peace with an alternate ending where Napoleon wins the war. It will include papers that would revolutionize the sciences, a paper explaining a cure for most cancers, correct predictions for the next 5 US Presidential races, etc. The books will also contain an accurate prediction of your future somewhere in their contents. George R. R. Martin's The Winds of Winter will even be somewhere in there (provided it is ever finished).

It will also produce a ton of nonsense. The number of 150 page books produced will outnumber estimates of particles in the visible universe by many orders of magnitude.

If algorithms are just names for specifying abstract objects, then you can create all this with basic programming skills on a desktop computer. The algorithm would just be a highly compressed version of all the items listed above.

But since the output includes mathematical notation, the output also includes all sorts of algorithms. This would include algorithms and proofs specifying every abstract object ever defined by man, plus myriad others. It would also include an algorithm for an even larger random symbol shuffling algorithm, which in turn, if computed, would produce an even larger symbol shuffling algorithm, and so on, like reverse Russian nesting dolls.

If algorithms are just names, a relatively bare bones symbol shuffling algorithm is almost godlike in it's ability to name almost everything.

Two points this brings out to me:

1. Negativity is very important in information. We don't just care about what something is, we care about what it is not. The Kolmogorov Complexity of an object, i.e. the shortest string that can encode said object, is crucially "the shortest string that can define an object and just that object." Otherwise, a random bit generator is the shortest description of all classically encodeable objects.

2. Second, we have to recall that information, and thus computation, is necessarily relational. A paper that tells you how to cure cancer generated by a random symbol shuffler is useless. It would indeed be remarkable to find a coherent page from such a process because there are many more ways to generate incoherent pages than coherent ones (maybe, more of that later). But likewise, there are many more ways to write about incorrect ways to cure cancer than there are actually effective methods, and so such a page is less likely to be useful than one published by a renowned quack.

Leaving aside the physical components of the hypothetical computer and output system here, all the outputs of such an algorithm can tell you is "what is the randomization process being used to mix the symbols." A great example of substrate independence. This , is why I think information has to be defined in terms of underlying probabilities.

The information content of the output can't be measured based on the "meanings" of the symbols. To see why, consider that in this seemingly infinite library would be books explaining step by step ways to decode seemingly random strings of text and symbols (the majority of the output) into coherent messages. Following these methods, incoherent pages might become coherent, while coherent ones become nonsense. Exact replicas of messages on some other page might be decoded from a different page. A string might have very many coherent ways it can be decoded. The only way to make sense of this is through the underlying probability distribution.

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Another thing I always think about when I ponder this example is: "how many characters would need to be on each page in such an algorithm before every discernable human thought has been encoded in the output." Obviously human language can be recursive, which allows for a larger number of discernible messages, but at a certain point levels of recursivity would become indiscernible.

Obviously it's not a very small number, but I'd imagine it's also a far cry from 2,000.
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I referenced cognition because the most popular models of how the brain works are computational

Numbers are computed in language

If asked the question "what is one plus one", as the answer is not contained in either number, I need to carry out a computation in my mind.

If I put one pebble on a table, and then put another pebble next to it, I can see two pebbles.
I don't need any mental computation to know that I see two pebbles, in the same way that I don't need to compute that I see the colour green. Seeing the colour green is the direct effect of the cause of a wavelength of 550nm entering the eye.

Regarding causation, if Bertrand Russell was correct that the notion of causality is objectively redundant, there would be no work for the National Transportation Safety Board which investigates every civil aviation accident in the United States, for example.

Therefore, I only need to carry out a computation if presented with a problem expressed in language, ie, in the computation of numbers where language and naming cannot be ignored. In language, one object is named "one". When another object is added, the set of objects is named "two". When another object is added, the set of objects is named "three", etc. Therefore, when I see one pebble on the table, I can say "I see one pebble". When I see another pebble added I can say "I see two pebbles". I can then answer the question "what is one plus one" as "two".

Therefore, the computation of numbers within the mind can only occur within language.
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I think the miscommunication here is that you are thinking of conscious computation, thinking about adding figures together.

I was referring to how neurons carry out computations by sending electrical and chemical signals that result in state changes.

Seeing green for example, doesn't occur just because a light wave hits the eye. People with damage to the occipital lobe often lose the ability to experience vision, even if their eyes are completely fine. They neither see nor dream/visualize. Most of the information received at the eye is discarded early in processing, and processing is what creates the world of vision that we experience.

In some sense, they do still see, via the phenomena of blind sight, but they have no conscious experience of color.
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It is actually incredibly difficult to define "computer" in such a way that just our digital and mechanical computers, or things like brains, are computers, but the Earth's atmosphere or a quasar is not,without appealing to subjective semantic meaning or arbitrary criteria not grounded in the physics of those systems.

The question of "what is computation" and "what is a computer" are different. The latter seems straightforward: a computer is a Turing machine, or something that can emulate one. What is wrong with that.

What distinguishes a computer from other physical systems is not that they have states that evolve, but that they can be set up to compute anything computable. You won't find this in any physical systems other than brains and computers.

The mistake I mean to point out is that we generally take 10÷2 to be the same thing as 5. Even adamant mathematical Platonists seem to be nominalists about computation. An algorithm that specifies a given object, say a number, "is just a name for that number."

If not a name, 10/2 is certainly another form of 5. And transforming numbers from one form to another, like the transformation of all information, requires work. This work of transforming information from one form to another is called "computation". Does that sound reasonable?

If the state of a computer C2 follows from a prior state C1, what do we call the process by which C1 becomes C2? Computation. Abstractly, this is also what we call the process of turning something like 10 ÷ 2 into 5.

What do we call the phenomena where by a physical system in state S1 becomes S2 due to physical interactions defined by the laws of physics and their entailments? Causation.

This doesn't seem quite right. In the ordinary sense of the word, a broken computer doesn't "compute" anything. And yet it has C2s that follow from C1s. What is special about computers is not that its states evolve, but that it can be set up to implement ad hoc rules that proceed completely independently of their underlying physical implementation.

This is seen already with assembly language. It doesn't matter how an assembly language is implemented, only that it is implemented faithfully to its specification. A steam computer would work the same as a silicon computer that both implement the same assembly language. And on top of these abstract rules, more rules can be implemented, that don't resemble even the assembly language. This tower of increasing abstraction can be incredibly tall, and culminates in distributed systems like the web and cryptocurrencies.

What makes computers special is that they are not bound by physical, causal reality. It is as if, in them, the informational component of reality broke free of the physical component. Brains are especially impressive, in that they are not just computers, but computers which which managed to create computers.
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And transforming numbers from one form to another, like the transformation of all information, requires work. This work of transforming information from one form to another is called "computation". Does that sound reasonable?

It does. And this is the main problem I have with current abstract conceptions of computation, this work is largely ignored. To be sure, it shows up in the classification of computational complexity and in formalism to some degree, but these are more exceptions.

What makes computers special is that they are not bound by physical, causal reality. It is as if, in them, the informational component of reality broke free of the physical component.

I'm not sure about this. In theory, a computer can compute anything a Turing Machine can, in actuality they need their inputs in a very precise format.

Both digital computers and brains only function in this dynamic fashion within a very narrow band of environmental settings. The brain is particularly fragile.

A human mathematician will not be able to compute algorithms thrown her way if we do something like project the inputs onto a screen with an orange background and use a, for her, shade of orange font that is indistinguishable from the background. All the information is there, but not the computation. The same is true for infrared light, audio signals outside the range of the human ear, etc.

Likewise, a digital computer needs its information to come in through an even narrower band of acceptable signals. Algorithms must be properly coded for the software in use, signals must come in through a very specific physical channel, etc. A digital computer takes in very little information from the enviornment without specialized attachments, cameras, microphones, etc. An unplugged digital computer acts not unlike a rock.

So I think the unique thing about either is that, given they exist in the narrow band of environments where they will function properly, and given information reaches them in formats they can use effectively, they can do all these wonderful things. How is this? My guess is that it comes down to the ability to discern between small differences. This is also what instruments do for humans and computers, allow for greater discernablity.

With a rock, the way the system responds to most inputs is largely identical. Information exists relationally, defined by the amount of difference one system can discerned about another. Complexity and computational dynamism seem tied to how well a system can discerned between differences in some other system. Zap most physical objects with the signals coming out of an Ethernet cable and the result will be almost identical regardless of what information was coming out of the cable. Not so for our computer. Give humans a bunch of CDs with different information encoded on them and they will be unable to distinguish any difference unless they use specialized instruments.

The key, or at least part of it, is to be able to undergo different state changes based on a much wider array of discernablity for at least some subset of possible medium used as inputs. A rock can have tons of state changes, just hear it up enough, but it can't respond differently to most inputs.
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If pancomputationalism seems nonsensical, the best way to see where the idea is coming from is to try to define what a computer is in physical terms and how it differs from other systems.

A computer is something that computes. My point has been that there are no computers in a mindless universe.
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Is there anything in a mindless universe? Or anything we can say about one? By definition, no one will ever observe such a thing.

Given a mindless universe, could universals/abstract objects exist? I would tend to think not, but that's pretty far afield.

But you're not saying only minded things compute, right?
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Given a mindless universe, could universals/abstract objects exist? I would tend to think not, but that's pretty far afield.

Do they ever exist? Certainly not in the sense that gas clouds and galaxies exist. But wherever sentient beings evolve they will be able to discern them. So they're real as intelligibles, not as phenomena per se.

This output will include the pages of every novel ever written by a human being, plus many yet to be written.

Are you sure about that? I recall reading Simon Conway Morris about the mathematics of the 'protein hyperspace', the number of possible combinations of molecules that could form proteins - and that if these combinations were made by a purely random process, then it would take far longer than the age of the known universe to hit upon the specific combinations that actually comprise working proteins (see his book Life's Solution for details).

Likewise with your imaginary symbol-generation algorithm, whilst one can imagine the possibility of such a computation, it might require vast amounts of time to output all of the actual books, alongside the enormously greater number of 150-page collections of meaningless symbols. Maybe it will produce more 150 page collections than the total mass of the universe. It strikes me as simply a more abstract version of the 'millions monkeys' thought experiment.

Conway Morris' view is that in evolutionary time-scales, some forms are much more likely to emerge than others, because they solve problems (hence, the book's title). Wings and eyes and photosynthesis have evolved numerous times along completely different pathways to solve the same kinds of problems often by drawing on completely different elements and components.
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But you're not saying only minded things compute, right?

No, I'm saying that minds are a necessary condition for computation. IOW, some mind has to observe the computational process in order for computation to occur. Without a mind giving meaning to it all, it's just changes in physical states.
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some mind has to observe the computational process in order for computation to occur.
I think most computation is unobserved though. Is it enough to see the final output of a computational process?

Suppose I run a nightly data job for a dashboard report. It's automated, so on any given night no one observes the job occuring, since it happens on a server in some regional data center through a virtual machine.

Are these just physical changes until someone checks the report in the morning, and then they become computation? Do the physical changes retroactively become computation? Or are they computation because I observed setting them up, or maybe because the aggregate CPU usage for the data center was observed by an employee during the night shift, and my job was a small component of this?
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I'm looking at it more this way: without an observer, how is there anything other than a change in physical states? I don't think you can add on "computation" to the physical state changes without there being observation. Certainly, there needs to be an observer to attach meaning to the outcome of computation, whenever it occurs. What ontological status does a simulation have when no one's observing it? Is it even a simulation?
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Whatever is recorded by instruments remains data until it's interpreted. Data comprises units of information which in themselves do not carry any specific meaning. Information is a set of data units that collectively carries a logical meaning. It also should be recalled that computers are human instruments, extensions of human sensory and intellectual capacities, designed to perform those tasks.
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Whatever is recorded by instruments remains data until it's interpreted. Data comprises units of information which in themselves do not carry any specific meaning. Information is a set of data units that collectively carries a logical meaning. It also should be recalled that computers are human instruments, extensions of human sensory and intellectual capacities, designed to perform those tasks.

Right. A bundle of sticks that looks like this: VIII with no one to observe it is a bundle of sticks. It can't ever be more than that without some mind observing it and attaching additional signifiers. However, when the bundle of sticks is observed by someone who knows Roman Numerals, it's a bundle of sticks AND it picks up a new attribute courtesy of the mind observing it: it's a bundle of sticks and the roman numeral for 8.
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