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Culture War Roundup for the week of December 11, 2023

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The Kolmogorov complexity of a concept can be much less than the exhaustive description of the concept itself. Pi has infinite digits, a compact program that can produce it to arbitrary precision doesn't, and the latter is what is being measured with KC. I believe @faul_sname can correct me if I've misrepresented the field.

Sounds right to me.

there's no argument that can convince a rock

You're just not determined enough. I think you'll find the most effective way to convince a rock of your point is to crush it, mix it with carbon, heat it to 1800C in an inert environment, cool it, dump it in hydrochloric acid, add hydrogen, heat it to 1400C, touch a crystal of silicon to it and very slowly retract it to form a block, slice that block into thin sheets, polish the sheets, paint very particular pretty patterns the sheets, shine UV light at the sheets, dip the sheets in potassium hydroxide, spray them with boron, heat them back up to 1000C, cool them back off, put them in a vacuum chamber, heat them back up to 800C, pump a little bit of dichlorosilane into the chamber, cool them back down, let the air back in, paint more pretty patterns on, spray copper at them really hard, dip them in a solution containing more copper and run electricity through, polish them again, chop them into chips, hook those chips up to a constant voltage source and a variable voltage source, use the variable voltage source to encode data that itself encodes instructions for running code that fits a predictive model to some inputs, pretrain that model on the sum total of human knowledge, fine tune it for sycophancy, and then make your argument to it. If you find that doesn't work you're probably doing it wrong.

Sounds right to me.

Do you think we can rigorously define the Kolmogorov complexity of the Christian God, and/or infinite looping universes based on unknown physics?

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.

  1. Determining what you expect your future experiences to be by taking your past distribution over world models (the "prior") and your observations and using something like Bayes to integrate them is basically the correct approach. However, Kolmogorov complexity is not a practical measure to use for your prior. You should use some other prior instead.
  2. Bayesian logic is very pretty math, but it is not practical even if you have a good prior. You would get better results by using some other statistical method to refine your world model.
  3. Statistics flavored approaches are overrated and you should use [pure reason / intuition / astrology / copying the world model of successful people / something else] to build your world model
  4. World models aren't useful. You should instead learn rules for what to do in various situations that don't necessarily have anything to do with what you expect the results of your actions to be.
  5. All of these alternatives are missing all the things you find salient and focusing on weird pedantic nerd shit. The actual thing you find salient is X and you wish I and people like me would engage with it. (also, what is X? I find that this dynamic tends to lead to the most fascinating conversations once both people notice it's happening but they'll talk past each other until they do notice).

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 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?

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.

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.

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.

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.

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.

He's arguing that specific beliefs aren't a choice, any more than believing 1+1 = 2 is a choice.

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?

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

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".

More comments

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

Abstract

Occam’s razor—the idea that all else being equal, we should pick the simpler hypothesis— plays a prominent role in ordinary and scientific inference. But why are simpler hypotheses better? One attractive hypothesis known as Bayesian Occam’s razor (BOR) is that more complex hypotheses tend to be more flexible—they can accommodate a wider range of possible data—and that flexibility is automatically penalized by Bayesian inference. In two experiments, we provide evidence that people’s intuitive probabilistic and explanatory judgments follow the prescriptions of BOR. In particular, people’s judgments are consistent with the two most distinctive characteristics of BOR: They penalize hypotheses as a function not only of their numbers of free parameters but also as a function of the size of the parameter space, and they penalize those hypotheses even when their parameters can be “tuned” to fit the data better than comparatively simpler hypotheses.

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.

It is not just that they are lower complexity, it's that for a given amount of evidence, Bayesian reasoning privileges simpler answers.

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, the Standard Model etc all claim to explain the world as we observe it. The former is absolutely rubbish at predicting future events,

Abrahamic God and the Standard Model are not necessarily competing explanations for the world we observe.

...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.

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.

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.

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 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.

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.

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.

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

Minimum message length (MML) is a Bayesian information-theoretic method for statistical model comparison and selection.[1] It provides a formal information theory restatement of Occam's Razor: even when models are equal in their measure of fit-accuracy to the observed data, the one generating the most concise explanation of data is more likely to be correct (where the explanation consists of the statement of the model, followed by the lossless encoding of the data using the stated model). MML was invented by Chris Wallace, first appearing in the seminal paper "An information measure for classification".[2] MML is intended not just as a theoretical construct, but as a technique that may be deployed in practice. [3] It differs from the related concept of Kolmogorov complexity in that it does not require use of a Turing-complete language to model data.[4]

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.

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.

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.

You called for an expert, and it seems to me that the expert agreed with me that KC can't do what you claimed it did. Does the reversal of expected evidence change your position any? If not, what evidence does your conviction derive from?

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.

BOR does have implications for when we have zero evidence. And that would be to choose the most minimal potential hypothesis...

...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.

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?

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.

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.

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.

It may be more complex. It is not necessarily so.

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.

Besides, it's not just the Big Bang we're considering, it's the Big Bang and everything else.

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"?

Minimum message length (MML) is a Bayesian information-theoretic method for statistical model comparison and selection.

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 provides a formal information theory restatement of Occam's Razor: even when models are equal in their measure of fit-accuracy to the observed data, the one generating the most concise explanation of data is more likely to be correct.

"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?

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.

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.

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.

I might be wrong though. It is conceivable to me that some people can change their beliefs(1) by sheer force of will.

@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.

More comments

You're just not determined enough. I think you'll find the most effective way to convince a rock of your point is to crush it, mix it with carbon, heat it to 1800C in an inert environment, cool it, dump it in hydrochloric acid, add hydrogen, heat it to 1400C...

My, that sounds like an exceptionally involved and complex procedure, surely it can't be economically viable? I'll continue trusting in my trusty hammer, that rock will come around if it knows what's good for it! Science fiction fans these days, coming up with the darnedest ideas..