“All values in the cosmos are integers. Decimals exist to help humans make comparisons between objects.”
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.
For the first paragraph it is my understanding that the universe is discrete/quantizied and it is not running on 'real numbers'.
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.
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-la...
[1] https://edwardfeser.blogspot.com/2022/05/the-hollow-universe...
> Which makes at least intuitive sense that there isn't anything which contains infinite information.
There are no real numbers outside of human beings' minds. The information in a real number is a theoretical mathematical concept from human minds for which there is no evidence in nature.
There is no definitive evidence that nature confirms to either continuous or discrete math at the smallest scales, but for now, if you look at theoretical physics papers, you will see integrals and derivatives, not sums and differences.
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.
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.)
y’=y^(1/3)
with y(0) = 0
has an infinite number of solutions.
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.)
Quantity of information absolutely does follow conservation laws, at least in quantum mechanics.
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.
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!
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.
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.
A collapsing quantum state is so far the only proposed process which would result in a nondeterministic universe. The problem is that absolutely nothing is known about it, and everything around it is fishy.
I personally think that concept of the universal wavefunction makes more sense.
But maybe if you subscribe to multiple worlds interpretation then the hardest part might be specifying which universe you're in, which would require number of bits proportional to the time since the big bang.
A problem: if you consider the contents of the universe (and the precise state of the contents at a given snapshot in time) to be part of "the universe", you have the hard problem of consciousness to tend with (in that humans are a part of the universe, and they rearrange its contents on a regular basis).
> Only if you take some interpretation that there's real physical process of measurement which we don't understand and is indeterministic you can get randomness.
Randomness is not the only means to achieve a non-deterministic universe, there is also the possibility of non-deterministic forces being in play, like human activity.
Of course, one can assert that human cognition is deterministic (no other option may even be available in some cases!), but science strongly suggests that simply asserting something to be true does not necessarily cause it to be true (though it does often cause it to appear to be true to pre-trained instances of human consciousness, a phenomenon which science has well demonstrated).
Abstractly(!), humans seem to be in a very similar cognitive state as they were when they ran on sub-perceptual religious axioms.
https://ell.stackexchange.com/questions/155593/meaning-of-th...
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?
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.