Computation as a universal and fundamental concept

https://ergo.org/courses/computation-as-a-universal-and-fundamental-concept

by simonpure • 12 days ago

177 176 12 days ago

sgt1013• 12 days ago

Computation has turned out to be a far more general concept than I think was imagined, up to the point that many computer scientists now seem to equate computation with the functioning of the universe. Recently it's been shown that there are real, physical processes which are undecidable (we cannot know if a latice of atoms has a spectral gap or not, we cannot determine if a specific particle in a fluid flow will reach a specific place or not, we cannot determine if a ray of light will reach a specific target in certain configurations of reflection).

Our world appeared computable, but it isn't, even if P=NP.

gradys• 12 days ago

It can be the case that both:

- The physics of the universe can be completely modeled as computation, and

- It's possible to pose undecidable problems about the way the universe unfolds

This is intrinsic to the idea of undecidability even for Turing machines, e.g. "we equate computation with the functioning of Turing machines, but there are real processes executable in Turing machines that are undecidable".

sgt1013• 12 days ago

Of course, if our universe is undecidable it must be the case that computable processes can be executed within it, and it might be the case that all of the processes that are ever executed within it are computable... but it might be that some of the processes that are executed are not computable... because the machine may.. or may not?

woopsn2• 12 days ago

A key thing about the undecidability problem wrt physics is preparation of the initial state. In math and computer science it is relatively straightforward to prepare such problems now (though this represented an enormous leap conceptually), but the "undecidability" of all physical problems relies on construction of materials that are clearly unconstructable - systems of infinite negentropy (eg Turing machines), infinite mass (the lattice), bespoke local interactions etc. Problems standing in the way of physics decidability are typically chaos, far from equilibrium mechanics, elementary SNR considerations and so forth, not problems of logic.

Maxatar2• 12 days ago

Recently it's been shown that there are real, physical processes which are undecidable

I want to push back a bit on this claim along two dimensions.

Imagine a physical Turing machine built out of atoms, gears, levers, and an electron parked on the read/write head and ask whether that electron ever crosses some fixed plane in space, which it does only when the machine enters its halt configuration. That's now a purely physical question about a trajectory (does this electron ever reach a certain target), yet answering it for the whole family of such machines is literally the halting problem, so there's a physical process that's undecidable.

Your examples about physical processes being undecidable are all basically just this... there examples of using reflections of light, or the flow of liquid, etc... and demonstrating that these physical processes in principle are sufficient to model a universal Turing machine.

And while it's fascinating that certain things you may not have expected can be used to model computation, it's misleading, or rather it's too strong of a claim to believe that there exist actual/real physical processes whose outcomes are undecidable. That's a subtle but very common misinterpretation of what undecidability is.

Undecidability, whether in physics or computer science, only applies to the infinitely broad class of a problem as a whole, it never applies to a specific instance of a problem. So it can never be the case that there's a certain configuration of reflections for which it's undecidable whether a ray of light reaches a target. Nor can it be the case that for a specific lattice of atoms, it's undecidable whether it has a spectral gap or not. It can only be the case that for the problem as a whole where the parameter space is entirely unbounded, there is no single algorithm that can decide if a ray of light reaches a specific target for all possible arbitrary (and infinitely many) configurations. Once you fix a specific system, then the undecidability goes away.

Not claiming that you are necessarily making this misconception, but I often see people misinterpret undecidability to mean that there exists a specific problem, like with specific inputs, where it's somehow impossible to know what the answer will be. Undecidability always requires an infinite family of instances, and it's a statement about the nonexistence of a single algorithm that correctly answers every instance in that family. It says nothing about any particular instance being unknowable/undecidable.

eth0up3• 12 days ago

If I am wrong, please pardon. I suspect I am. But was this comment edited by Claude? I ask specifically because it is well written, substantive, all which is expected here, but the "push back" part, to me, must be a) an artifact of Claude, either by osmotic assimilation (Which is happening to many innocent users) or b) Claude itself.

Feel free to flag this comment if I get an answer. I do want to know.

sgt1013• 12 days ago

I may have been making this claim, I need to think about this for a while and re read what you have written.

This is very helpful though, thank you.

joelshep• 12 days ago

I may be misremembering Godel's proof or misunderstanding your last paragraph, but I thought Godel's proof actually presented a specific undecidable statement. The hope then was that somehow undecidable statements could be cordoned off from decidable statements, and Turing's result showed that that wasn't possible. Perhaps that's what you mean by "the nonexistence of a single algorithm that correctly answers every instance in that family"?

jesuslop2• 12 days ago

I think Gödel undecidable sentence is always relative to a formal system (the title of the paper spoke about systems in the expressive power rank of Russell's Principia, of which he gives one particular example assuming it shows how his methods apply to the whole family of systems), but now Hilbert problem #6 still stands for the lack of a comprehensive axiomatization of Physics, as its modern heir the mass-gap millennium problem, that still also lingers, so we don't have a controllable notion of naked/absolute undecidability for physical phenomena or for arbitrary assertions unbound by explicit logic rules in general.

wasabi991011• 12 days ago

Agreed, and I'll add: the universe is sufficiently messy and complex that some of the claimed undecidability results may never occur in practice.

For your Turing machine example: even if we built such a machine, it would never truly be giving an answer to the halting problem, because any stray cosmic particle could excite the electron and cause it to cross whatever plane.

For a more realistic example: the ground state of an molecule is a physically relevant quantity, and in theory any molecule alone should lose energy and attain it's ground state, even if finding the ground state electronic configuration is undecidable. But in reality, no molecule is ever truly isolated and so would never actually be guaranteed to enter it's ground state (or if it were truly isolated, it would not be observed at all rendering the question moot)

SideQuark• 12 days ago

… so there's a physical process that's undecidable.

No, since you cannot physically build a Turing Machine. A Turing machine requires infinite tape. Any physically realizable machine doesn’t have that, so has finite states, so is decidable: enumerate the states in finite time - it halts or repeats, so all programs on a finite state machine are decidable.

Your example is not an undecudable physical process.

Godel things also don’t apply: Godel theorems are about proof of this or that from within the same system. In logic one can prove such things from an outside system, then construct towers, avoiding Godel theorems. Godel theorems also require a model of integers including multiplication (without multiplication, such systems were proven complete and decidable). However the universe does not contain a model of integers, as the physical universe is not unbounded: relativity places a finite limit in spacetime on what can interact.

Mixing math as reality fails at these requirements.

RandomLensman7• 12 days ago

How to build a Turing machine to tell which one of ten atoms of a radioactive element decays next?

plastic-enjoyer• 12 days ago

up to the point that many computer scientists now seem to equate computation with the functioning of the universe.

Do you think that's a kind of tunnel vision? If the only thing you focus on is computation, you'll probably end up seeing computation everywhere - it became a way of seeing the world.

jerf4• 12 days ago

It is a common accusation. There's a somewhat famous quote I've seen a few times:

"It's interesting to look back through history on this one. Each age has its pinnacle of technology, and each age uses that technology as a metaphor for nature, for the universe. In ancient Greece, the technological marvels were musical instruments and the ruler and compass. The Greek philosophers tried to build an entire cosmology from number, harmony, proportion, form, and so on — from mathematics, basically. Remember the music of the spheres? The Pythagoreans believed that nature was a manifestation of rational mathematics. Later on the pinnacle of technology was the clockwork. Newton wanted a clockwork universe, the entire universe as a gigantic clockwork mechanism, with all the parts interlocking and ticking over with infinite precision. Then in the 19th century along came steam power, and the universe was then depicted as an enormous heat engine, or thermodynamic machine, running down toward its heat death. Today the computer is the pinnacle of technology, so it's now fashionable to talk about nature as a computational process."

Which seems to source from https://www.edge.org/conversation/paul_davies-time-loops .

While "computer" may give us impressions of something with "a CPU" and "RAM" and "a disk drive", it does at least seem plausible that the universe as computation is a plausible base level, though. Unlike "the music of the spheres", which to the extent that it made predictions of the world, it got them wrong in the most basic way, viewing it through a lens of computation allows us to put some quite subtle and interesting limits on things. "Computation" is a pretty flexible substrate; it is difficult to imagine how the proposition "the universe is a computation and subject to the limitations thereto" could be falsified, and if it could, it is difficult to imagine how we would be able to know it was so falsified. Nevertheless the math of computation allows us to say non-trivial things about the universe as a result; it is not a vacuous generalization, though it is certainly a loose one... being able to say yet more concrete things about the nature of the computation, such as "this is exactly how gravity works", has quite a bit more utility.

mondrian• 12 days ago

Undecidability is a problem of answer-extraction from a process, it doesn’t preclude the process from executing deterministically. The universe could well be the live execution of a deterministic, even basic algorithm, with all kinds of questions about its execution being undecidable.

__rito__2• 12 days ago

One sentence I heard somewhere wraps up the totality of computing:

"If Mathematics is the 'what', Computer Science is the 'how'".

This applies to each and everything.

athrowaway3z• 12 days ago

If two people agreed on that statement, its entirely unclear if they agree with each other and if they found something profound in the first place.

The imo much more foundational relationship not everybody is aware of is https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...

not-a-llm• 12 days ago

Recently it's been shown that there are real, physical processes which are undecidable

According to the currently known laws of physics. Which we know are incomplete/incorrect in several places.

woopsn2• 12 days ago

The infinite lattice doesn't represent a "real" physical processes, it's just mathematical technique for closing a (fundamentally) quantized combinatorial sum over millions of interacting elements. The gap problem exists in the limit. For real systems the spectrum can be measured (in principle) by probing the ground state. The computational paradigm is incredibly general but only within what's apparently a pretty atypical thermodynamic regime (the ordered universe).

peter_m118• 11 days ago

In this case quantum thermo.

nl• 12 days ago

Undecidable isn't uncomputable.

"Computable" can mean probabilistic, and classical computers can function over probability distributions just fine.

salutis• 11 days ago

This is incorrect. An undecidable problem is one for which no algorithm can compute the correct result for every given instance. Probabilistic classical computation is irrelevant here.

spragl2• 12 days ago

Both P and NP are computable. That is, a Turing machine can compute both of them.

Those quantum processes are interesting. Take the random numbers generated from radioactive decay. They are (after some cleanup) truly random. That is what we think. But how could we tell the difference from pseudorandom numbers, generated by a sufficiently advanced algorithm? We couldnt. So particles could simply be Turing Machines running sufficiently advanced algorithms that we cant reverse engineer. If so, quantum mechanics is computable even if we cant compute it.

(Particles being TMs doesnt mean they are FAs with an infinite tape, but that they are computationally equivalent to TMs.)

peter_m118• 11 days ago

There is such thing as a quantum Turing machine you know (Deutsch 1985).

summarybot• 12 days ago

What even is computation? State-based inference. But intelligence itself does not rely on computation, only its biological counterweight seems to and only in certain situations. If Computation is a "Universal Concept" then there are at least 4 or 5 more "Universal Concepts" analogous to intuition and spontaneity.

jojogeo10• 12 days ago

Something has always nagged me about the halting problem, might be my mis-understanding of the problem space but;

- You have a piece of software

- That software does in memory compute only

- The software does not touch any peripherals, networking, or any other external source which introduce unpredictability (x)

I'm convinced that somehow this can be solved/proven whether the execution will halt or not.

(x) The second you touch any external peripherals or networking, you're effectively asking the question of "If I phone my friend, will they pick up the phone?" -> to which the only answer is, "They'll pick it up, only if they pick it up/are there". You can't answer that question without trying it.

Am I missing the point? I'm sure you can introduce other edges even in the limited model above, e.g. where a memory stick stops responding or something; but all in if you have reliable kit and don't touch anything external, why can't this be solved?

makerofthings• 12 days ago

Imagine a program that generates the digits of pi, one after the other and stops when it is finished. A general purpose program analysing this program to decide if it stops or not would have to know about pi. And about every other possible algorithm.

jojogeo10• 12 days ago

This is a brilliant explanation thank you.

tromp• 12 days ago

It can be solved if the memory is bounded. But unbounded memory comes with undecidable problems.

jojogeo10• 12 days ago

This truly leads into "computation"; when we're dealing with known quantities, yes, we can "solve" the halting problem. The second you move into "we don't know the answer yet", the can of worms opens. Thank you.

docfort• 12 days ago

Related: the Busy Beaver problem https://news.ycombinator.com/item?id=40857041

jojogeo10• 12 days ago

Thank you internet stranger, for introducing me to hard-maths drugs; am hooked!! \o/

I love the idea of this. So the BB problems are individual iterations of the halting problem right? To truly solve the problem one would have to come up with a program which would operate on all possible BB numbers?

anon2912• 12 days ago

If the memory is bounded then your software is a simple finite automaton, and can be decided in finite time. The issue is with unbounded memory. The issue with the halting problem is a simple characteristic of infinity. This is actually what people are noticing when they say that computation is a fundamental part of the universe. They are correct! The universe deals with infinitisemals all the time. As humans, we have only discovered ways of dealing with certain classes of infinitesemals (calculus). The others remain beyond our ability to characterize. Indeed, some have been proven to be uncharacterizable.

jojogeo10• 12 days ago

Ahhh thank you it's effectively the known-vs-unknown space;

- How long does it take to get from A to B? => Easy if you know where A and B are, and what mode of transport you're taking to get there.

- How long does it take to get from A to _somewhere_ => As long as it takes!!

jerf4• 12 days ago

For the finite case, the more relevant question is, can you predict whether or not the computation will halt in less time than 1. executing the algorithm and 2. checking whether or not the algorithm ever loops?

Bear in mind checking whether or not the algorithm ever loops means taking the full state of the system and checking against a database of all previous states of the system. Bear in mind that the Atari 2600, and its whopping 128 bytes of RAM, has with that amount of RAM more states than there are planck volumes * planck time intervals in the known universe... by over sixty orders of magnitude. And every three additional bits you add to the RAM of the system your are looking at adds an order of magnitude (minus a bit) to that, so, nearly 3 orders of magnitude more states per byte... not per megabyte or gigabyte, per byte. Call it 2 orders of magnitude per byte if you want to be conservative.

It can be solved, if by nothing else simply by running it, in the mathematical sense. In the practical sense it's not even close. That's why we use the Turing machine analysis... technically it's an approximation because we don't actually have real Turing machines. However the size of the finite state machines we have is such that it is far more productive to simply say "the halting problem is unsolvable" than to argue about how many orders of magnitude of orders of magnitude of resources it takes to solve the question of whether or a given program terminates.

jojogeo10• 12 days ago

Thank you for your insightful answer, in reduction; "Don't fight a god, you won't win, and you'll definitely die in the process!"

The approach you describe though is brute force. I don't think (if there even is an answer to this problem) that it can be brute forced; that's where you run into the limits of hardware/computation/energy and start talking about timeframes which exceed the life of the universe.

I think brute force might be a useful tool in places to validate results, but if there _is_ an answer to this problem it's purely mathematical.

Apologies for sounding both excited and naive; these sorts of challenges make me happy in strange ways that no other thing does!

jeffrallen2• 12 days ago

You might enjoy the book Escher Gödel Bach, the Eternal Golden Braid by Douglas Hofstadter, which will open up the world, power, and "danger" of proofs using contradiction to you.

Bonne lecture !

jojogeo10• 12 days ago

Thank you for the suggestions, I look forward to reading!

jstanley• 12 days ago

The standard argument is:

Assume H(P,i) to be a program that tells you whether the program P will halt on input i. Returns true if it halts and false if it doesn't.

Define a new program G(x) that halts if x does not halt on itself as input and loops forever if x halts on itself as input:

  def G(x):
    if H(x,x):
      while True:
        pass
    else:
      return

Does G(G) halt?

If G(G) halts then H(G,G) is true so we end up in the infinite loop, a contradiction. If G(G) does not halt then it returns without looping, also a contradiction.

So our halting oracle H does not exist, so there can not be a function that tells you whether another function will halt on itself as input, so there can not be a function that tells you in the general case whether some other computation will halt, QED.

quux0r• 12 days ago

For those that are unfamiliar, Tim Roughgarden is a phenomenal instructor, and has made significant contributions to the field of algorithmic game theory, which has strong connections to a lot of the work he appears to be doing here. I highly recommend his excellent introductory lectures on the subject, especially if you're interested in pursuing his ideas here more rigorously: https://www.youtube.com/watch?v=TM_QFmQU_VA&list=PLEGCF-WLh2...

His website also hosts a bunch more work as well as various lecture notes and exercises: https://timroughgarden.org/

Tim's lectures helped me a lot during my PhD when I was getting up to speed on this subject, and some of the more nuanced ways that computer scientists have worked with these broad algorithmic problems.

willtemperley• 12 days ago

I loved his Algorithms course on Coursera which I did during the brief moment Stanford MOOCs were all free. So useful for a non-CS grad doing any kind of algorithmic programming.

Those were good days.

ChrisArchitect• 12 days ago

Ergo: Long Form Philosophy Lectures

https://news.ycombinator.com/item?id=48840497

sim04ful• 12 days ago

I really do think matter wants to be sentient, being sentient is natural. Why i think that exactly, i'm not sure why, it just seems intuitive.

peter_m118• 11 days ago

Your intuition could also be dead wrong.

jdw642• 12 days ago

Is 'computation' really universal and fundamental? Turing machines, lambda calculus, algorithmic notations, they're all human-made formalisms. Are the halting problem and the limits of computability actually constraints that exist only within these human-made formal systems?

When we constrain a formalism to reduce complexity, it feels like necessity emerges from within those constraints. For example, when we say 'CRUD app,' we immediately think of a specific pattern. In the same way, once you adopt a 'form,' the constraints that come with that form progressively expand the state space. In that sense, it feels like both discovery and invention.

Famous mathematicians and scientists often distinguish between model and reality, yet we tend to mistake the model's shape for reality itself. People like John Wheeler and Stephen Wolfram argue that computation is a fundamental property of the universe. But can we really say that when we downcast reality to fit human cognition, losing information in the process, and then upcast it back, the information is fully restored? I always find this point difficult.

Landauer's principle says that abstract logical operations, information erasure, necessarily increase physical entropy. That shows there's a thermodynamic cost to physically implemented information processing. But I don't think that proves computation is fundamental.

Whether it's computation or geometry, they're all abstract formalisms created by humans. But when we actually measure things, they're subject to physical laws. Still, whether that makes them fundamental is a difficult question. I think these are just results of the process where humans name phenomena and constrain them. I don't think they're the cause.

You can define computation broadly enough, as 'a process where a state changes to another state according to rules,' to make almost everything look like computation. But being able to explain something with computation and claiming that computation is fundamental are different things, aren't they?

Meaning exists within the structures and constraints of human-made formalisms. We artificially lower cognitive complexity and translate things into human language. Whether that's fundamental, I'm not sure.

Maybe I'm a reductionist. Plenty of intellectually brilliant scholars make those claims, but people like me, with slower minds, end up thinking these kinds of stupid thoughts. I wish I could organize my own thoughts bette

jojogeo10• 12 days ago

Ahhh this is fantastic thank you; it _is_ hard to reconcile whether problems come with the original topic or whether they are introduced by the abstraction that we _need_ to make in order to quantify a thing/explain it to ourselves and others.

Regarding the downcast/upcast; I think it _can_ be possible to do this successfully;

I have a glass, I throw it at a hard surface. What will happen? Well (duh) the glass will (most likely) break.

This hypothesis completely ignores nearly 100% of all relevant physics and the laws surrounding the problem; the arrangement of air molecules, the arrangement of the molecules in the glass, the physical forces governing me, it reduces the entire equation down to some really basic napkin physics.

But; does the outcome work? Has my interpretation of the universe and its physics actually predicted what will happen?

Probably a stupid example, but I think that a lossy picture of the universe can still yield a correct answer.

I can't physically run a simulation of the entire universe in my brain, as my brain is part of that same universe. Lossy representations/models are a necessity in the thinking-ham bound world in which we exist.

jdw642• 12 days ago

You're right. But consider this: the geocentric model perfectly predicted planetary positions for centuries, and it was certainly useful. But could we say it was the essence of the universe? In the end, it's a useful model within limited cognition, but whether it's 'fundamental' is a separate question.

I think the key is that different phenomena require different approaches, and even if you interpret a single phenomenon through multiple mental models, none of them necessarily captures its essence. Ultimately, it's about which mental model is shared by a 'group'—not about what's fundamentally true.

We currently share the model of computation, but whether that makes it fundamental is a different story.

As a programmer, I'd put it this way: no matter how well an API describes the backend, the backend itself is not the API.

Here, the API is human knowledge, and the backend is the world

amavect• 12 days ago

You sound like you believe in philosophical skepticism. Tell me: can a map ever properly describe the territory? When would a map properly describe the territory? (Can a theory ever properly describe reality? What does a theory need to properly describe reality?)

We know that universal Turing machines can emulate other Turing machines. Weirdos like Wolfram believe that a universal Turing machine can emulate reality. In a quick skim of this lecture series, the presenter doesn't talk about that, rather he just calls computation a scientific principal (universal and fundamental in the sense of physical laws, not fundamental in the sense of emulating reality on a computer).

peter_m118• 11 days ago

We can still test the theory that computation describes physical reality with experiment (presumably it makes predictions). The scientific method still holds.

jeffrallen2• 12 days ago

Discrete math and Algorithms were two of my favorite college classes. They were really the only part of computer science that was mind blowing. The rest was software engineering, which was transparently "possible". Like, yes, big programs and OSs and numerical models exist, and yes I will graduate and work with them and add to them, someday, yeah sure.

But decidabilty, Godel's theorm, busy beaver numbers, etc... those were unexpected and worth the price of admission.

Thanks Prof Hadas, you made it fun to have my mind blown.

peter_m118• 11 days ago

Theoretical computer science is where it's at.

__rito__2• 12 days ago

From the site's "About" section:

"Ergo is a nonprofit that publishes long-form philosophical lecture courses with leading scholars. Everything we publish is freely available, without ads or paywalls."

I know what to do this weekend if it rains!

sdevonoes• 12 days ago

From my naive pov: Related to computation is the concept of state (I know, functional languages can get away without it, sort of). I always wondered how the universe “knows” the mass of the sun. If there are some underlying functions/computations “running” in the background to keep planets moving and so on, and if the mass of planets is a key element in such computations… then either: the mass is calculated “on the fly” every time (seems expensive) or it’s a variable (how is it updated? Where is it “stored”?)

AlotOfReading• 12 days ago

The somewhat abbreviated answer is that the "state" is formalized into the concept of fields. All the physical properties we can observe are from coupling with the relevant fields. The speed at which changes can propagate in fields is C, hence the speed of light being the same value.

dleeftink• 12 days ago

As far as I understand it, the storage is the space, or rather, spacetime emerges from a system's informational capacity and the degrees of freedom along which information can spread. On the balance all information is retained but undergoes various phase transitions (the 'computations').

khalic• 12 days ago

Functional programming very much has states. But you’re describing the transitions instead of the states directly. What it does is removing the hidden states and effects and makes them typed, explicit and contained

amwet2• 12 days ago

I think it’s easier to conceive of it like this: Each point in spacetime IS storage. Storage can be queried by interacting with it (in a variety of ways), though the process of querying affects the value not only of the querier, but also the queried, which may have side-effects as well. The interaction itself is the computation.

A simple example for the computation: It’s like placing boxes next to each other. Yes I could say 1 box + 3 boxes = 4 boxes, via explicit calculation. I could also simply place 1 box next to three boxes, and without having to explicitly calculate, by nature of the interaction, the result (4 boxes) has been produced

There is no background computation or storage. The universe IS computation and storage. Each spacetime quanta IS storage, and each interaction IS computation.

ianburrell• 12 days ago

Spacetime isn't quantized as far as we know. We don't know since we don't have quantum gravity or ability to probe Planck scale. Quantum fields are continuous, it is excitations in the field, particles, that are quantized.

peter_m118• 11 days ago

The theory of general relativity answers this exact question. It has been tested experimentally and has been found to be correct in the classical regime. By correct I mean that the experimental data agrees with theoretical prediction.

Diogenesian7• 12 days ago

There are a lot of long comments basically saying what I am about to say so I will try to keep this brief:

Computation is a metaphysically universal and fundamental concept, since metaphysics is (tautologically) the domain of humans and we use symbolic communication. So of course very general theories of symbolic processes (e.g. Turing machines) are pertinent to the symbolic methodology we use to understand scientific processes.

But it is a fundamental mistake to jump from that to saying computation extends to a law of the universe. Computation reflects laws of the universe, but only in the exact same way that scientific and mathematical human speech do. The mystery (still totally unsolved) is how humans are able to intuitively understand space / time / causality / etc in order to define coherent symbolic rules that reflect real processes. That computers can seemingly always implement these rules having been given the symbols is of philosophical/scientific interest, but it's solipsistic to say it's a fundamental concept of the universe.

Robotbeat5• 12 days ago

This is a misconception. It’s more fundamental than that. There’s a fundamental connection between (Shannon) information theory and thermodynamics. The Landau Limit, whether blackholes can destroy information or not, quantum mechanics, etc.

Information is actually tangible. It’s not just an analogy or a coincidence that the word “entropy” is a word used in both physics and computer science (information theory). Thermodynamics, mind you, is perhaps THE most fundamental elements of physics and how the universe works.

chermi• 12 days ago

Did you mean landauer?

Diogenesian7• 12 days ago

Information and computation are not the same thing. I was very specifically talking about Turing machines and other theoretical models of computation.

That said, you are still making the same mistake I pointed out, elevating human symbolic information to a higher plateau than it deserves. I think it's because you're being too vague about the connection, when it's fairly mundane. The "fundamental connection" is that physical quantities are information, and on the other hand information is always a large collection of semi-independent semi-stochastic physical objects and can be profitably modelled by some sort of statistical mechanics. Information theory is relevant all over physics because human agents collect all sorts of physical information. The universe "doesn't care" about information in and of itself. Shannon entropy and Boltzmann entropy have similar formulas because they measure precisely the same thing; put another way, a goofy but formally equivalent way to model a gas would be a noisy radio channel communicating each molecule's kinetic energy.

The problem with the black hole information paradox isn't that information is destroyed per se, but that it appears to be destroyed in a way that violates quantum mechanics (destroying quantum state without a measurement). The theoretically predicted destruction of information points to a more general problem.

The Laundauer limit is no more fundamental to the universe than "a mechanical crane cannot violate the laws of pulleys." It says that no matter how you design your binary (or whatever) computer, it must involve an ensemble of binary states, and statistical mechanics puts an absolute floor on how little heat is required to alter such states. Whether these states are gas molecules or the written symbols "0" and "1" is immaterial.

jibal7• 12 days ago

It’s not just an analogy or a coincidence that the word “entropy” is a word used in both physics and computer science (information theory).

Shannon asked von Neumann what to call it, and von Neumann said "You should call it entropy, for two reasons: In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage."

curiousest• 12 days ago

You can say things like, “In the domain of physics, X,” “Assuming the scientific method, X,” or “Assuming the premises of logic, X.”

But “computation is a fundamental aspect of the universe”, in the way it's being understood in this thread (as opposed to the article) does not remain within any of those frameworks. It makes a claim about reality as a whole.

Once you make that kind of universal claim, all the assumptions built into “computation” - about identity, distinct states, lawful transitions, causation, logic, etc. - become part of the claim. You cannot use those assumptions silently and then present the conclusion as framework-independent.

And those frameworks come with consequences. Using the language of computation, they come with "lossiness" wrt modelling "reality".

(see Aristotle Metaphysics -> Kant CoPR -> later Wittgenstein)

alfiedotwtf• 11 days ago

Thank you. I’ve been thinking about this for a while now and couldn’t express what I was thinking about… but when you linked information theory to thermodynamics, it clicked.

Given the quantum fields were collapsed in the early universe, I’m now wondering how information theory looked like during the different phases on the universe

GoblinSlayer16• 12 days ago

Also Ramanujan summation.

jibal7• 12 days ago

Prove any of this. Or at least provide a cogent argument for it. To me it looks riddled with mistakes, like

metaphysics is (tautologically) the domain of humans

which is frankly incoherent.

andsoitis2• 12 days ago

Metaphysics operates one level up from physics or the sciences, asking what reality has to be like for anything, including the sciences, to be possible or meaningful at all.

hitekker• 12 days ago

Agreed. I’ll also make an observation based on this thread: the idea of computation as a fundamental law is most believable (and desirable) to people who like computers and want to reduce reality to a computer.

The belief is like a cheat code: somehow our tinkering and 9-5 job somehow grants us, the computer nerds, a deep understanding of life, the universe and everything. Deeper than scientists, philosophers, etc. It’s epistemic catnip and pretty tasty at that!

peter_m118• 11 days ago

A related question might be, what's the difference between mathematical (Godel), computational (Turing,) and physical (Yang-Mills) undecideabilty/computability?

vatsachak• 12 days ago

Computation is in the eye of the beholder

lo_zamoyski• 12 days ago

I'd have to look deeper into his views, but I've already come across what seem like similar claims that try to attribute computation to the laws of physics or to matter in general or whatever.

However, these rest on category errors. Consider two characterizations of computation:

1. A mental process constituted by logical and intentional acts.

2. A mathematical model or formalism (or a set of formally equivalent formalisms).

In the case of (1), intentionality rules out computation as an extra-mental phenomenon. Things in the world aren't about something else; they just are what they are. But computation as a mental act is about something else. To claim otherwise would be like claiming deduction is a broad feature of reality, which is effectively some kind of panpsychism.

In the case of (2), if it's a mathematical model, then either by definition it doesn't exist outside the mind as such, or it must be instantiated in some objective manner. The trouble with finding instantiations is that it's not clear what constitutes an instantiation. Can you find correspondences? Sure. In fact, our physical computing machines correspond to these models in some way. But instantiation is more than mere correspondence, and this becomes even more the case when you consider that the lambda calculus corresponds to the Turing machine.

Another problem is that even mathematical models of computation cannot be said to encode mathematical operations as such. Is a Turing machine moving symbols around on an abstract tape actually adding two numbers? I would say that it is merely simulating the addition by producing results that afford that kind of interpretation.

kaashif• 12 days ago

I like how every time a new technology is invented and becomes big, people start to think it explains everything. Like how in the 16th/17th centuries some people thought the universe was a big clock. Or how in the 19th centuries people thought the universe was like a big steam engine. Or now we think the universe is a big computer.

Not saying this is wrong or that I've watched all of the lectures above or anything, but it's just funny to imagine that aliens might look at us the same way we could look at a monkey society saying that the universe is like a big one of those rocks they use to smash nuts open.

Computation and information really does seem universal though, so this is just a funny thought and not serious commentary.

GoblinSlayer16• 12 days ago

It's just Pythagoreanism.

unknown_user_84• 12 days ago

It strikes me that this is a kind of an escalating pattern though I don't suppose it has to be. Clock -> Steam Engine -> Computer -> AGI -> Skynet -> Throw rocks at robots -> Judgement Day. Also very not serious commentary.

On I suppose a slightly more serious note it also strikes me that there will eventually, probably, maybe be _something_ that fits best; though we are not promised to find it. And it seems wild to say that about a model because all models are fundamentally wrong, but they are usually group-able by less-wrongness, so probably fundamentally feasible.

pilgrim0• 12 days ago

Couldn’t all of them be right, though? In the sense that every technology associated with the functioning of the universe had a systemic, spatiotemporal and evolutive dynamic, which appears to be the sensible facets of the universe’s behavior? In that sense computation is no different, just has more primacy. It gives me some Hofstadter vibes, meaning whatever complex thing we produce within the universe is hopelessly bound to be analogous with it.

peter_m118• 11 days ago

Yes, these are all our attempts at explaining the nature of reality. A kind of reaching into the unknown. A desire to understand the universe and our place in it.

quantum_state• 12 days ago

Would like to think we human are better than what is implied by the course in that we would not mistaken our model of reality as reality itself.

dboreham• 12 days ago

I saw the title and assumed an article by Wolfram. But it's by Tim Roughgarden who I know from algorithmic game theory. Anyway, I'll register my membership in the "it's more fundamental than that" camp.

nullbio• 12 days ago

The universe is a giant transformer.

peter_m118• 11 days ago

Attention is all we need.

voidhorse8• 12 days ago

Computation as realized by computers is a formalism invented by Turing, Church, Kleene and others to make precise the intuitive notion of "algorithm".

An algorithm, at its root, is a procedure rooted in human understanding that human beings can follow.

When Turing and others first introduced this formal notion, not all mathematicians were even fully convinced it was an adequate representation of the informal intuitive notion. For example, some argued it was too broad because traditionally knowing that an algorithm eventually terminates was one of the requirements (to some) for something to be a legitimate algorithm. Why? Because the idea is rooted in human practical concerns and human understanding. Depending on what one cares about, one could actually reject the Turing formalization of algorithm on grounds of the class containing non-convergent (partial) functions.

All this is to say that "computation" is very much a human invention and little more than a formal model of human behaviors (we want to manipulate things algebraically). Elevating it to some objective substance of the universe is just doing 17th/18th century philosophical Idealism wrapped in new clothes.

peter_m118• 11 days ago

The computational view of the universe and the nature of reality has provided us with some new insights.

voidhorse8• 11 days ago

Sure, others would also claim the "financial view" of the universe has also provided insight. That doesn't mean I go around claiming the money is some fundamental universal substance of the real.

peter_m118• 11 days ago

Here is a brief history of computability I wrote as a blog a few months ago, https://deeplp.com/blogs/f/the-birth-of-computability-theory. Hope it's helpful to the conversation.

warumdarum• 11 days ago

Shouldnt physicsifthe universe was a sim, should have an affinity the power of two

MAESTRO19552• 11 days ago

Computation cannot simulate consciousness! https://deepmind.google/research/publications/231971/

Diogenesian7• 10 days ago

Read the title a little more closely :) As far as we know computation actually can simulate consciousness:

- given any system of quantum particles, a sufficiently large Turing machine can solve the matching system of Schrodinger equations

- the human body, including the brain, is certainly a system of quantum particles

- even if you think quantum behavior is directly relevant to consciousness (I don't) certainly there is nothing "beyond" quantum mechanics that would be necessary to explain it, so our system of Schrodinger equations should be able to model human consciousness

- so a Turing machine can simulate a human, including consciousness

The paper argues that this simulation of consciousness is not the same thing as actual consciousness.

MAESTRO19552• 10 days ago

You are right, of course I was in a rush to type, so I misspoke. What I meant to say is that computational simulations of consciousness may make it impossible for anyone to definitively diagnose whether it is a simulation or real consciousness. So, computational simulation of consciousness may render any consciousness detection tools useless. Again, my apologies for my earlier mistake.

GoblinSlayer16• 9 days ago

we do not need a complete, finalized theory of consciousness to assess AI sentience

Erm... this can't possibly work, can it?

Computation as a universal and fundamental concept

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