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So there's the trivial answer, which is that the program "run every program of length 1 for 1 step, then every program of length 2 for 1 step, then every program of length 1 again, and so on [1,2,1,3,1,2,1,4,1,2,...] style" will, given an infinite number of steps, run every program of finite length for an infinite number of steps. And my understanding is that the Kolmogorov complexity of that program is pretty low, as these things go.
But even if we assume that our universe is computable, you're not going to have a lot of luck locating our universe in that system.
Out of curiosity, why do you want to know? Kolmogorov complexity is a fun idea, but my general train of thought is that it's not avtually useful for almost anything practical, because when it comes to reasoning about behaviors that generalize to all turing machines, you're going to find that your approaches fail once the TMs you're dealing with have a large number (like 7 for example, and even 6 is pushing it) of states.
We're debating epistemology, and @self_made_human is arguing that some unfalsifiable theories about the origin of the universe are superior to others because they are "lower complexity" in the information-theory sense, which he proposed measuring through Kolmogorov complexity. My position is that there is no way to rigorously measure the Kolmogorov complexity of the Christian God, or of the Karmic Wheel, or of a universe that loops infinitely via unknown physics even in principle; you cannot measure things you cannot adequately describe, and mechanisms that are unobservable and unfalsifiable cannot be adequately described by definition.
There are a few things I imagine you could be saying here.
I am guessing it's either 2 or 5, but my response to you will vary a lot based on which it is and the details of your viewpoint.
Take two theories about our actual universe:
A) The universe loops infinitely based on physical principles we have no access to.
B) The universe is a simulation, running in a universe we have no access to.
My argument is that none of us can break out paper and pencil and meaningfully convert the ideas behind these two statements into a formula, and then use mathematics to objectively prove that one theory is more likely to be true than the other, whether by Kolmogorov complexity, or minimum message length, or Shannon entropy, or Bayesian Occam's Razor, or any other method one might name. It seems obvious to me that no amount of analysis can extract signal from no signal.
In short, I'm arguing that when there is no evidence, there is no meaningful distinction between priors.
I assume you have some reason you think it matters that we can't use mathematics to come up with a specific objective prior probability that each model is accurate?
Edit: also, I note that I am doing a lot of internal translation of stuff like "the theory is true" into "the model makes accurate predictions of future observations" to fit into my ontology. Is this a valid translation, or is there some situation where someone might believe a true theory that would nevertheless lead them to make less accurate predictions about their future observations?
I don't think reasoned beliefs are forced by evidence; I think they're chosen. He's arguing that specific beliefs aren't a choice, any more than believing 1+1 = 2 is a choice. To support that thesis, he's claiming that the math determines that one of those is less complex than the other, and therefore the math determines that the less complex one is more likely, and therefore he did not choose to adopt it, but rather was compelled to adopt it by deterministic rules. If in fact he's mistaken about the rules, then they can't be the source of his certainty, which means it has to come from somewhere else. I think it can be demonstrated that it's derived from an axiom, not a conclusion forced by evidence.
Close enough, I think? The larger point I'm hoping to get back to is that the deterministic model of reason that seems to be generally assumed is a fiction, and that one can directly observe the holes in this fiction by closely examining how they themselves reason. You drew a distinction between "beliefs as expected consequences", and "beliefs as models determining action". I would argue that our expectation of consequences are quite malleable, and that the we choose decisively shape both the experiences we have and how we experience them.
[EDIT] - Sorry if these responses seem a bit perfunctory. I always feel a bit weird about pulling people into the middle of one of these back-and-forths, and it feels discourteous to immediately unload on them, so I try to keep answers short to give them an easy out.
The choice of term "reasoned belief" instead of simply "belief" sounds like you mean something specific and important by that term. I'm not aware of that term having any particular meaning in any philosophical tradition I know about, but I also don't know much about philosophy.
That sounds like the "anticipated experiences" meaning of "belief". I also cannot change those by sheer force of will. Can you? Is this another one of those less-than-universal human experiences similar to how some people just don't have mental imagery?
I don't think I would classify probabilistic approaches like that as "deterministic models of reason".
But yeah I'm starting to lean towards "there's literally some bit of mental machinery for intentionally believing something that some people have".
My opposite above pointed out that some people have beliefs induced by severe mental illness, and that these beliefs are not chosen. It's a fair point, and those certainly aren't the type of belief I'm talking about. Likewise, 1+1=2 or a belief in gravity are self-reinforcing to a degree that it's probably not practical to shift them, and may not be possible at all. Most beliefs are not caused by mental illness, though, and are not as simple as 1+1=2. We have to reason about them to arrive at an answer, so "reasoned beliefs" seems like a more precise term for them.
in terms of 1+1=2 or gravity, no. I think this might be because they're too self-reinforcing, or because there's no incentive to doubt them, or both, but they seem pretty stable.
People talk about reasoning as though it's a deterministic process. They say that evidence has weight, that evidence can force conclusions. They often talk about how their beliefs aren't chosen, they just followed where the evidence led. They expect evidence to work on other people deterministically as well: when they present what they think is a weighty piece of evidence, and the other person weighs it lightly, they often assume the other person is acting in bad faith. People often expect a well-crafted argument to force someone on the other side to agree with them.
I used to believe all these things. I saw logic and argumentation as something approximating math, as 1+1=2. I thought if I could craft a good enough argument, summon good enough evidence, people on the other side would be forced to agree with me. And likewise, I thought I believed things because the evidence had broken that way.
Having spent a couple decades debating with people, I think that model is fatally flawed, and I think believing it makes people less rational, not more. Worse, I think it interferes with peoples' ability to communicate effectively with each other, especially across a large values divide. Further, I think it's pretty busted even from its own frame of reference; while evidence cannot compel agreement, it can encourage it, and there is a lot of very strong, immediately available evidence people do not actually reason the way the common narrative says they should.
I think that's a very pragmatic and reasonable position, at least in the abstract. You're in great intellectual company, holding that set of beliefs. Just look at all of the sayings that agree!
And yet! Some people do change their mind in response to evidence. It's not everyone, it might not even be most people, but it is a thing that happens. Clearly something is going on there.
We are in the culture war thread, so let's wage some culture war. Very early in this thread, you made the argument
What does replacing the Big Bang with God lose out on? I think the answer is "the entire idea that you can have a comprehensible, gears-level model of how the universe works". A "gears-level" model should at least look like
So I think the standard model of physics mostly satisfies the above. Working through:
Side note: the Big Bang does not really occupy a God-shaped space in the materialist ontology. I can see where there would be a temptation to view it that way - the Big Bang was the earliest observable event in our universe, and therefore can be viewed as the cause of everything else, just like God - but the Big Bang is a prediction (retrodiction?) that is generated by using the standard model to make sense of our observations (e.g. the redshifting of standard candles, the cosmic microwave background). The question isn't "what if we replace the Big Bang with God", but rather "what if we replace the entire materialist edifice with God".
In any case, let's apply the above tests to the "God" hypothesis.
My point here isn't really "religion bad" so much as "you genuinely do lose something valuable if you try to use God as an explanation".
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It is not just that they are lower complexity, it's that for a given amount of evidence, Bayesian reasoning privileges simpler answers. If additional complexity helps predict the behavior of system better, then we accept it. F=ma is far simpler than General Relativity or QM, but the latter generalize to situations where Classical Mechanics fails.
PDF warning:
Bayesian Occam’s Razor Is a Razor of the People
Abrahamic God, the Standard Model etc all claim to explain the world as we observe it.
The former is absolutely rubbish at predicting future events, and to the extent that you are under the impression that God is responsible for ensuring the operation of the Standard Model (or a complete description of physics), it is necessarily more complex.
Since belief in God does nothing to constrain future expectations be it for novel evidence or even developing practical models for simulating things, it is largely worthless, and unless you start from the assumption, no rational agent will reach it.
In this context, Kolmogorov complexity is one way of representing the notion that certain ideas or hypotheses that seem intuitively "simple" are not actually so in any more rigorous sense.
Yes. But when the "given" amount of evidence is "Zero" for multiple answers, BOR has no method to distinguish between them.
Is [unknown number of digits excluded]12084038 bigger or smaller than [unknown number of digits excluded]0? The answer is mu, because we don't have the necessary data to do the math. You have claimed that we can do math with no data whatsoever. In the first place, this claim seems clearly wrong, but in the second place, it seems very interesting that someone as intelligent as you would make it.
There is no available evidence about what caused the Big Bang at all, and there is no rigorous definition of "simpler" by which any speculations we may have might be measured.
We agree that effects have causes within our system. We agree (I think) that there is an effect whose causes are unobservable from within our system, at least given our current understanding. Since effects have causes, and since we cannot observe a cause for this effect from within our system, the cause must come from outside our system. Since we cannot see outside our system, we have zero evidence about the nature of that cause. Since we have zero evidence, tools like BOR and Kolmogorov Complexity cannot be used to select theories in a rigorous fashion.
Abrahamic God and the Standard Model are not necessarily competing explanations for the world we observe.
It is indeed necessarily more complex than the Standard Model. In exactly the same way, "True Physics" being responsible for ensuring the operation of the Standard Model is necessarily more complex than the standard model.
Given that we have to add something, and given that we have zero data from the hard sciences on what that something is, we likewise have no concrete evidence of which explanation is more or less complex than another.
Certainly. But you are the one claiming that some unobservable hypotheses or ideas are simpler than others, and it seems you cannot actually use Kolmogorov Complexity to prove it in the way you claimed you could.
I reiterate that I am not attempting to convince you to believe in the Christian God. I am trying to demonstrate an observable, verifiable, testable fact: that all beliefs are chosen. It seems to me that you are appealing to Kolmogorov Complexity and Bayesian Occam's Razor because you want to claim that your commitment to materialism is not a choice, but rather a deterministic outcome of accumulated evidence. But it seems obvious to me that neither KC nor BOR can possibly work the way you are trying to use them, and in fact neither is the source of your conviction.
You called for an expert, and it seems to me that the expert flatly contradicted your claims. Does the reversal of expected evidence change your position any? If not, what evidence does your conviction derive from?
BOR does have implications for when we have zero evidence.
And that would be to choose the most minimal potential hypothesis, though I am unsure what that could possibly mean. What hypothesis explains a coin flip that never happened?
It is, however not true that we have "zero" evidence about what caused the Big Bang. After all, I presume you admit that there could be evidence along the lines of say, the cosmic microwave background radiation spelling out "God here. Glad you're reading this, good to see you're advancing up the tech tree" in English, and you (and I) would have no qualms about ascribing that as evidence for God causing the Big Bang? I don't think either of us would claim that it has no relevance, that it cannot be the case that observations made within a universe could inform our understanding of what lies outside it.
In a similar vein, to the extent that you expect a universe designed by the Judeo Christian deity to differ in any way from one that's purely mechanistic, the absence of such evidence is Bayesian evidence of absence.
It may be more complex. It is not necessarily so. Much of the charm of the Standard Model is that by establishing symmetries, it simplifies and explains whole bunch of seemingly disparate observations. You can imagine someone who studiously makes a table showing the rates of deceleration for a whole range of different masses under gravity, which is actually useful in real life, but more complex when compared to just applying Newtonian gravity and air resistance when supplied with a given value for m. I am mostly agnostic on whether the GUT will be "simpler" than the Standard Model, even if I'm mildly expecting that to be the case. Physicists certainly consider it desirable, but the only true necessity is that it explains things better, especially for situations not in the data used to derive it.
Kolmogorov complexity is a beast, but if you really cared to, you could easily substitute minimum message length or Shannon entropy and get the same result.
In fact, it was an error (or at least suboptimal) for me to even bring up KC, when MML exists:
https://en.wikipedia.org/wiki/Minimum_message_length
Besides, it's not just the Big Bang we're considering, it's the Big Bang and everything else. Here, once again, BOR implies that God is a terrible answer.
I apologize for the digression into KC, even if that's an interesting topic.
All beliefs are not a choice, assuming you're using "choice" in the standard sense.
A person suffering from Capgras delusion, who believes that his kin have been replaced by body snatchers, is not choosing to think so. You can argue with him, shake him about, shock him with a cattle prod, and he will never relent. The disease has stolen away even the option for him to think otherwise. A schizophrenic does not "choose" to think he's the reincarnation of Jesus or Napoleon.
I am pretty sure that @faul_sname agrees with my statements regarding the "objective" Kolmogorov complexity of different hypothesis. I know, and he knows I know that it's incomputable, because that came up as the subject of conversation not that long ago. But while Kolmogorov complexity might not be an ideal use case for anything except theoretical discussions, MML is, and I should have substituted it at the start if I remembered that the latter is a practical metric.
In this case, the relevant update for me is to do a better job of representing theories I only understand at a superficial level, not a knock against the generalized claim I'm making.
...Which presumes you can rank the hypotheses from minimal to less so. By what measure are you ranking them? What are you measuring? If you were measuring something, the thing you were measuring would be evidence, no? If you don't have that, you have nothing to measure, and the measurement is indeterminate.
Suppose we have two integers, each of them incomplete.
[unknown digits excluded]193692 [unknown digits excluded]923013
From that dataset, I do not think there is a way to say which of those numbers is larger. I don't think you can do it with Kolmogorov Complexity. I don't think you can do it with Bayesian Occam's Razor. I don't think you can do it with minimum message length. I don't think you can do it with Shannon entropy. I don't think you can do it at all, in any rigorous, meaningful way. The only correct answer is mu, because there is insufficient data to calculate or reason from.
If I argued that we should presume that the second number is bigger, because of all the numbers we've run into, the ones with a 9 in the leftmost place tend to be larger than numbers with a 1 in the leftmost place, that would not be a rigorous proof that the second number was actually bigger. On the other hand, if we take those two integers and multiply them by zero, we know that the result is precisely zero.
It would be evidence of something, sure. Likewise, I have already agreed that if the Standard model had demonstrated a closed-loop cosmology from within its own logic, that likewise would be evidence that materialistic explanations were simpler. If a physics breakthrough is made that allows the loop to be closed without appealing to unobservables/unfalsifiables, that too would be evidence. None of those have actually happened, though, so none of that evidence is available to influence our decisions here and now.
I don't currently have such expectations, and am not sure why I should. If datapoints contradict my understanding of God, why should I not modify my understanding of God to account for them? In any case, my belief that a God exists to be reasoned about is axiomatic, not conclusive.
Then it seems to me that God may be more complex, but is not necessarily so. If you think it plausible that complexity might be removed by mechanisms you can neither define or demonstrate in any concrete fashion, why should I not do the same? If we could rigorously define and demonstrate such mechanisms, the matter would of course be different. But you can't in the case of "better physics". Likewise, I could submit various ontological arguments, but cannot define or demonstrate their validity either, and so do not count them.
What data does "everything else" provide about what's behind the Big Bang? How does this data allow you to rank the complexity of "physics loop" versus "simulation"?
It seems to me that this fails for the same reason that KC and BOR fail. We don't have a statistical model to compare, so tools for comparing statistical models don't help. Likewise for Bayes: you have no meaningful prior for "thing that exists outside anything we have observed or experienced.", whether that is a basement simulation or a true physics loop. All the evidence tells us such a thing exists. None of the evidence illuminates its nature.
"it's a sim lol" is shorter that "unknown physics maintain a infinite looping universe". Clearly Simulationism is more likely to be correct.
I kid, I kid. Obviously, neither of those arbitrary sentences are a "model" in the sense your excerpt described. ...Only, it seems exceedingly obvious to me that no "models" exist for either simulationism or true-physics, in the sense MML requires to function. This is the same argument I made against KC and BOR, because it seems generally applicable. Am I wrong? Have you confident about the answer here because you've actually crunched the numbers yourself, or have seen someone else who has?
A fair point. Allow me be more specific: All reasoned beliefs are chosen. I have no experience of capgras delusion, nor schizophrenia, so I take no position on the nature of their beliefs.
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I suspect that "belief", rather than "choice", is the word that you two are using differently. You can't choose your "beliefs(1)" in the sense of "what you anticipate what your future experiences will be contingent on taking some specific course of action", but you can choose your "beliefs(2)" in the sense of "which operating hypothesis you use to determine your actions".
I might be wrong though. It is conceivable to me that some people can change their beliefs(1) by sheer force of will.
English, a language stunningly unsuitable for such discussions, not that I know of one that's better.
@FCfromSSC claims to be able to do this, including intentionally convincing himself that a chair he's sitting on is a fake. I'm capable of no analogous feat, but it's hardly the weirdest thing that human cognition has done, and I'll accept his word for it.
I have not ever convinced myself of the nonexistence of a chair I was sitting on.
I could have sworn you used that specific example with me in the past, but regardless, I do remember you claiming you can change your priors/beliefs at will.
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