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Just as a hypothetical thought experiment, suppose the entire description of our universe laws of physics and initial conditions can be described with a bits st

Just as a hypothetical thought experiment, suppose the entire description of our universe laws of physics and initial conditions can be described with a bits string of size X. Add a few more bits to describe a specific location and time, and a few more bits to decode whatever it is that humans wrote at some time. Then everything humanity will ever reach or know has Kolmogorov complexity no larger than this X. My intuition is that if you take X to be too small, the general "nothing's special about the universe and it's all extremely typical" argument and you must surely reach a contradiction. Surely not everything is so incredibly compressible, is it? Physicists keep crying about fine tuning and what not, but honestly, I would be even more surprised if the initial conditions and the laws of physics were extremely small. Because we already know the laws of physics are relatively simple, I would put my bets on the initial conditions having most of the entropy.

jakeinspace 4y ago
Either that, or reality is inherently quantum and the entropy of an evolving unitary wave function (well, the entropy of any given amplitude) basically goes to infinity.
voxl 4y ago
There is an easy counter model. The universe is _literally_ a real number machine, i.e. even a particular point is only describable to us in the approximate. The laws of physics get to be finite, but you can't talk about a particular location or place in time without infinite information, or you talk about it in the approximate.
- Mtinie 4y ago
  Am I correctly summarizing this statement, for my own understanding? “All values in the cosmos are integers. Decimals exist to help humans make comparisons between objects.”
  - empyrrhicist 4y ago
    I mean, they seem to be saying the exact opposite of that based on the usual way people talk about the "reals".
  - Blackthorn 4y ago
    No. They're talking about real numbers; even decimal numbers (rationals) are isomorphic to integers. The reals are different.
- visarga 4y ago
  You could put all the human knowledge in a single real number and still have infinite room left.
  - vlovich123 4y ago
    There exists an abstract mathematical mapping, sure. However, finding the spot in the real number where that's the case may require infinite storage (you need to store the pointer) or infinite time (you start searching through the number to find what you want). It also has a halting problem where you don't actually know how you'll know when you find that data.
- civilized 4y ago
  > The universe is _literally_ a real number machine I am wary of this. Just because you have a good predictive model based on math, and the math can be made rigorous using ZFC / Cauchy sequences / infinite decimals / etc., doesn't mean that any of those rigorous mathematical concepts are literally running the real universe. Personally I don't think there's any reason to believe that any numbers, even zero and one, have any existence outside of being concepts in our heads.
  - oezi 4y ago
    I don't get what you say in the last paragraph. Isn't the mapping of zero and one to nothing and something kind of the easiest thing (e.g. one photon or no photon)? For the first paragraph it is my understanding that the universe is discrete/quantizied and it is not running on 'real numbers'.
    - civilized 4y ago
      > I don't get what you say in the last paragraph. Isn't the mapping of zero and one to nothing and something kind of the easiest thing (e.g. one photon or no photon)? You can map and mapping is useful, but the map lives in your head and isn't the territory. > For the first paragraph it is my understanding that the universe is discrete/quantizied and it is not running on 'real numbers'. This is a widely believed folk myth among software engineers, but it isn't supported by evidence. There are some speculative theories that try to solve some problems in physics by quantizing space, but right now they are no more empirically supported than other speculations.
      - lo_zamoyski 4y ago
        Worth a read: 1. "Russell’s No Man’s Land" [0] 2. "The hollow universe of modern physics" [1] [0] https://edwardfeser.blogspot.com/2020/08/russells-no-mans-land.html https://edwardfeser.blogspot.com/2020/08/russells-no-mans-la... [1] https://edwardfeser.blogspot.com/2022/05/the-hollow-universe-of-modern-physics.html https://edwardfeser.blogspot.com/2022/05/the-hollow-universe...
      - 4y ago
- Enginerrrd 4y ago
  >There is an easy counter model. The universe is _literally_ a real number machine, i.e. even a particular point is only describable to us in the approximate. There is actually some debate about that, and for good reason. There are even a couple of practicing physicists looking at how predictions would differ assuming the universe has finite precision, and if I recall correctly the results from that investigation are non-trivial.
ninkendo 4y ago
The universe appears chaotic, in that outcomes have sensitive dependence on its initial conditions. Even if all laws of physics are deterministic. So for there to be a wide range of possible things happening from the initial starting point (including you and I having this conversation right now), IMO it follows that a complete description of the initial conditions would have to be absurdly (infinitely?) large to cause the universe to replay to this exact moment if you started it all over again. In other words, the size of X would have to be extremely large… so I think I agree with you. (Edited once I realized that myself and OP are likely in agreement.)
layer8 4y ago
We don’t know that the universe is discrete, hence a description in a finite number of bits, and Kolmogorov complexity, may be inapplicable.
pfortuny 4y ago
Also keep in mind that everything assumes the equations are Lipschitz in order to guarantee uniqueness of the solution given specific initial conditions. But this is too optimistic. y’=y^(1/3) with y(0) = 0 has an infinite number of solutions.
- constantcrying 4y ago
  It gets far worse if it is not an ODE, but a PDE, there a uniqueness criteria is somewhere between "for this PDE in this extremely special case with these extra assumptions ..." up to "?????".
BurningFrog 4y ago
Does this assume the/a universe is deterministic?
otabdeveloper4 4y ago
> Then everything humanity will ever reach or know has Kolmogorov complexity no larger than this X No. Information complexity does not obey conservation laws. The initial rule for generating the Universe is simple, but as time goes on information complexity only increases exponentially. It's a singularity of information complexity and we are at the center of it. (This is the real reason, by the way, why aliens don't exist and Fermi's "paradox" isn't really.)
- canjobear 4y ago
  What do you mean by "information complexity"? Quantity of information absolutely does follow conservation laws, at least in quantum mechanics.
  - otabdeveloper4 4y ago
    Same thing as the Kolmogorov complexity the original poster mentioned. It corresponds to entropy somehow, so I don't think quantum mechanics is on topic here.
jondeval 4y ago
> Surely not everything is so incredibly compressible, is it? I like your line of thinking and I'm actually quite excited about this recent shift in physics to a more information-theoretic line of inquiry. Is it fair to state a corollary of your question this way? Given a complete description of some hypothesized universe/multiverse generator (essentially the next layer down that we are actively trying to discover), the Kolmogorov complexity (or some variation of K-Complexity) of this description must be greater than the K-complexity of any generated universe. In my view, it would be very weird if this were not true. And (to me) it would be even weirder if this K-complexity was some large number but still less than infinity.
- wongarsu 4y ago
  You could have an incredibly simple universe generator that just produces universes with random laws of physics and random initial conditions. From our human point of view that's indistinguishable from a highly sophisticated universe generator, since we can only observe the successes (or rather only one, that by our definition is a success)
constantcrying 4y ago
>Then everything humanity will ever reach or know has Kolmogorov complexity no larger than this X. Only if it is deterministic, which certainly seems not very plausible. (You could say everything is a probability distribution, but to me it seems to get extremely complex after that, collapse?) >Because we already know the laws of physics are relatively simple, I would put my bets on the initial conditions having most of the entropy. Just because the laws are simply expressible does not imply they are simple. A variational minimization problem can be very easy to state (certainly that seems a good candidate for a "true" law of nature), but it can easily be as hard as a PDE!
- PartiallyTyped 4y ago
  It’s also possible that our __models__ are simple, but the underlying reality is not, so as long as there exists some error after sufficient evaluations it is safe to say that our model’s complexity is less than the universe’s.
  - constantcrying 4y ago
    Yes, I agree. It is definitely possible that the underlying laws are extremely complex and there is absolutely no simple way to state them. But what I think is really interesting that this extreme complexity can only be found in extremely large and small scales. E.g. Newtons laws are phenomenal at predicting the universe at "human scales". The systems which can arise in Newtonian physics can be extremely complex, but their descriptions are usually very simple. Deviations from Newtonian predictions either are very small or arise only at large/small scales.
    - PartiallyTyped 4y ago
      > Newtonian physics can be extremely complex, but their descriptions are usually very simple IIRC Constructor theory builds on this, in a way, it defines some very basic and simple building blocks out of which the rest of the laws that govern our universe. https://en.wikipedia.org/wiki/Constructor_theory https://en.wikipedia.org/wiki/Constructor_theory
robertlagrant 4y ago
> My intuition is that if you take X to be too small, the general "nothing's special about the universe and it's all extremely typical" argument and you must surely reach a contradiction. Surely not everything is so incredibly compressible, is it? This sounds similar to saying, "This photograph can be expressed in this small number of bits, therefore it's not special." Why does one imply the other?
ardel95 4y ago
This line of reasoning assumes that all physical processes are deterministic. If they are not (as is the current mainstream belief) then I don’t think that line of reasoning would stand. Instead, the current state is the result of that initial set of inputs, and countless other nob-deterministic dice rolls.

jakeinspace 4y ago

Either that, or reality is inherently quantum and the entropy of an evolving unitary wave function (well, the entropy of any given amplitude) basically goes to infinity.

voxl 4y ago

There is an easy counter model. The universe is _literally_ a real number machine, i.e. even a particular point is only describable to us in the approximate. The laws of physics get to be finite, but you can't talk about a particular location or place in time without infinite information, or you talk about it in the approximate.

Mtinie 4y ago
Am I correctly summarizing this statement, for my own understanding? “All values in the cosmos are integers. Decimals exist to help humans make comparisons between objects.”
- empyrrhicist 4y ago
  I mean, they seem to be saying the exact opposite of that based on the usual way people talk about the "reals".
- Blackthorn 4y ago
  No. They're talking about real numbers; even decimal numbers (rationals) are isomorphic to integers. The reals are different.
visarga 4y ago
You could put all the human knowledge in a single real number and still have infinite room left.
- vlovich123 4y ago
  There exists an abstract mathematical mapping, sure. However, finding the spot in the real number where that's the case may require infinite storage (you need to store the pointer) or infinite time (you start searching through the number to find what you want). It also has a halting problem where you don't actually know how you'll know when you find that data.
civilized 4y ago
> The universe is _literally_ a real number machine I am wary of this. Just because you have a good predictive model based on math, and the math can be made rigorous using ZFC / Cauchy sequences / infinite decimals / etc., doesn't mean that any of those rigorous mathematical concepts are literally running the real universe. Personally I don't think there's any reason to believe that any numbers, even zero and one, have any existence outside of being concepts in our heads.
- oezi 4y ago
  I don't get what you say in the last paragraph. Isn't the mapping of zero and one to nothing and something kind of the easiest thing (e.g. one photon or no photon)? For the first paragraph it is my understanding that the universe is discrete/quantizied and it is not running on 'real numbers'.
  - civilized 4y ago
    > I don't get what you say in the last paragraph. Isn't the mapping of zero and one to nothing and something kind of the easiest thing (e.g. one photon or no photon)? You can map and mapping is useful, but the map lives in your head and isn't the territory. > For the first paragraph it is my understanding that the universe is discrete/quantizied and it is not running on 'real numbers'. This is a widely believed folk myth among software engineers, but it isn't supported by evidence. There are some speculative theories that try to solve some problems in physics by quantizing space, but right now they are no more empirically supported than other speculations.
    - lo_zamoyski 4y ago
      Worth a read: 1. "Russell’s No Man’s Land" [0] 2. "The hollow universe of modern physics" [1] [0] https://edwardfeser.blogspot.com/2020/08/russells-no-mans-land.html https://edwardfeser.blogspot.com/2020/08/russells-no-mans-la... [1] https://edwardfeser.blogspot.com/2022/05/the-hollow-universe-of-modern-physics.html https://edwardfeser.blogspot.com/2022/05/the-hollow-universe...
    - 4y ago
Enginerrrd 4y ago
>There is an easy counter model. The universe is _literally_ a real number machine, i.e. even a particular point is only describable to us in the approximate. There is actually some debate about that, and for good reason. There are even a couple of practicing physicists looking at how predictions would differ assuming the universe has finite precision, and if I recall correctly the results from that investigation are non-trivial.

ninkendo 4y ago

The universe appears chaotic, in that outcomes have sensitive dependence on its initial conditions. Even if all laws of physics are deterministic. So for there to be a wide range of possible things happening from the initial starting point (including you and I having this conversation right now), IMO it follows that a complete description of the initial conditions would have to be absurdly (infinitely?) large to cause the universe to replay to this exact moment if you started it all over again. In other words, the size of X would have to be extremely large… so I think I agree with you. (Edited once I realized that myself and OP are likely in agreement.)

layer8 4y ago

We don’t know that the universe is discrete, hence a description in a finite number of bits, and Kolmogorov complexity, may be inapplicable.

pfortuny 4y ago

Also keep in mind that everything assumes the equations are Lipschitz in order to guarantee uniqueness of the solution given specific initial conditions. But this is too optimistic. y’=y^(1/3) with y(0) = 0 has an infinite number of solutions.

constantcrying 4y ago
It gets far worse if it is not an ODE, but a PDE, there a uniqueness criteria is somewhere between "for this PDE in this extremely special case with these extra assumptions ..." up to "?????".

BurningFrog 4y ago

Does this assume the/a universe is deterministic?

otabdeveloper4 4y ago

> Then everything humanity will ever reach or know has Kolmogorov complexity no larger than this X No. Information complexity does not obey conservation laws. The initial rule for generating the Universe is simple, but as time goes on information complexity only increases exponentially. It's a singularity of information complexity and we are at the center of it. (This is the real reason, by the way, why aliens don't exist and Fermi's "paradox" isn't really.)

canjobear 4y ago
What do you mean by "information complexity"? Quantity of information absolutely does follow conservation laws, at least in quantum mechanics.
- otabdeveloper4 4y ago
  Same thing as the Kolmogorov complexity the original poster mentioned. It corresponds to entropy somehow, so I don't think quantum mechanics is on topic here.

jondeval 4y ago

> Surely not everything is so incredibly compressible, is it? I like your line of thinking and I'm actually quite excited about this recent shift in physics to a more information-theoretic line of inquiry. Is it fair to state a corollary of your question this way? Given a complete description of some hypothesized universe/multiverse generator (essentially the next layer down that we are actively trying to discover), the Kolmogorov complexity (or some variation of K-Complexity) of this description must be greater than the K-complexity of any generated universe. In my view, it would be very weird if this were not true. And (to me) it would be even weirder if this K-complexity was some large number but still less than infinity.

wongarsu 4y ago
You could have an incredibly simple universe generator that just produces universes with random laws of physics and random initial conditions. From our human point of view that's indistinguishable from a highly sophisticated universe generator, since we can only observe the successes (or rather only one, that by our definition is a success)

constantcrying 4y ago

>Then everything humanity will ever reach or know has Kolmogorov complexity no larger than this X. Only if it is deterministic, which certainly seems not very plausible. (You could say everything is a probability distribution, but to me it seems to get extremely complex after that, collapse?) >Because we already know the laws of physics are relatively simple, I would put my bets on the initial conditions having most of the entropy. Just because the laws are simply expressible does not imply they are simple. A variational minimization problem can be very easy to state (certainly that seems a good candidate for a "true" law of nature), but it can easily be as hard as a PDE!

PartiallyTyped 4y ago
It’s also possible that our __models__ are simple, but the underlying reality is not, so as long as there exists some error after sufficient evaluations it is safe to say that our model’s complexity is less than the universe’s.
- constantcrying 4y ago
  Yes, I agree. It is definitely possible that the underlying laws are extremely complex and there is absolutely no simple way to state them. But what I think is really interesting that this extreme complexity can only be found in extremely large and small scales. E.g. Newtons laws are phenomenal at predicting the universe at "human scales". The systems which can arise in Newtonian physics can be extremely complex, but their descriptions are usually very simple. Deviations from Newtonian predictions either are very small or arise only at large/small scales.
  - PartiallyTyped 4y ago
    > Newtonian physics can be extremely complex, but their descriptions are usually very simple IIRC Constructor theory builds on this, in a way, it defines some very basic and simple building blocks out of which the rest of the laws that govern our universe. https://en.wikipedia.org/wiki/Constructor_theory https://en.wikipedia.org/wiki/Constructor_theory

robertlagrant 4y ago

> My intuition is that if you take X to be too small, the general "nothing's special about the universe and it's all extremely typical" argument and you must surely reach a contradiction. Surely not everything is so incredibly compressible, is it? This sounds similar to saying, "This photograph can be expressed in this small number of bits, therefore it's not special." Why does one imply the other?

ardel95 4y ago

This line of reasoning assumes that all physical processes are deterministic. If they are not (as is the current mainstream belief) then I don’t think that line of reasoning would stand. Instead, the current state is the result of that initial set of inputs, and countless other nob-deterministic dice rolls.