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Elon Musk just launched Grokipedia, a kanged version of wikipedia run through a hideous AI sloppification filter. Of course the usual suspects are complaining about political bias and bias about Elon and whatnot, but they totally miss whole point. The entire thing is absolute worthless slop. Now I know that Wikipedia is pozzed by Soros and whatever, but fighting it with worthless gibberish isn't it.
As a way to test it, I wanted to check something that could be easily verifiable with primary sources, without needing actual wikipedia or specialized knowledge, so I figured I could check out the article of a short story. I picked the story "2BR02B" (no endorsement of the story or its themes) because it's extremely short and available online. And just a quick glance at the grokipedia article shows that it hallucinated a massive, enormous dump into the plot summary. Literally every other sentence in there is entirely fabricated, or even totally the opposite of what was written in the story. Now I don't know the exact internal workings of the AI, but it claims to read the references for "fact checking" and it links to the full text of the entire story. Which means that the AI had access to the entire text of the story yet still went full schizo mode anyways.
I chose that article because it was easily verifiable, and I encourage everyone to take a look at the story text and compare it to the AI "summary" to see how bad it is. And I'm no expert but my guess is that most of the articles are similarly schizo crap. And undoubtedly Elon fanboys are going to post screenshots of this shit all over the internet to the detriment of everyone with a brain. No idea what Elon is hoping to accomplish with this but I'm going to call him a huge dum dum for releasing this nonsense.
This reminds me of Vox Day's Encyclopedia Galactica project, or the even more retarded Conservapedia.
Wikipedia and crowd-sourced intelligence in general has its obvious failure modes, yet Wikipedia remains an extremely valuable source for.... most things that aren't heavily politicized. Even the latter will usually have articles that are factually correct if also heavily factually curated.
The problem with AI-generated "slop" is not the "schizo" hallucinations that you see. It's the very reasonable and plausible hallucinations that you don't see. It's the "deceptive fluency" of an LLM that is usually right but, when it's wrong, will be confidently and convincingly wrong in a way that someone who doesn't know better can't obviously spot.
With Wikipedia, if I read an article on Abraham Lincoln, I am pretty confident the dates will be correct and the life and political events will be real and sourced. Sure, sometimes there are errors and there are occasional trolls and saboteurs (I once found an article on a species of water snake that said their chief diet was mermaids), and if you are a Confederate apologist you will probably be annoyed at the glazing, but you still won't find anything that would be contradicted by an actual biography.
Whereas with an AI-generated bio of Lincoln, I would expect that it's 90% real and accurate but randomly contaminated with mermaids.
So, yes, I'm sure most of us are aware that Wikipedia political articles are going to be as misleading as they can get away with, but let me just say that there are some completely non-political articles that are factually wrong, too. If you look up the Sleeping Beauty problem, the article states that there is "ongoing debate", which is ridiculous. For actual mathematicians, there's no debate; the answer is simple. The only reason there's a "debate" is because some people don't quite understand what probability measures. Imagine if the Flat Earth page said that there was "ongoing debate" on the validity of the theory...
And don't even get me started on the Doomsday argument, which is just as badly formed but has a bunch of advocates who are happy to maintain a 20-page article full of philosobabble to make it sound worthy of consideration.
I'm sure there are many other examples from fields where I'm not informed enough to smell the bullshit. Crowdsourcing knowledge has more failure modes than just the well-known political one.
I hope you knew what you were getting into bringing up Sleeping Beauty, haha. I have a degree in statistics (which doesn't necessarily grant me as much insight into probability theory as you might imagine) but I usually avoid getting into the weeds by simply stating that the question: "What does probability mean in real life?" is NOT a settled question, at all. You cannot escape bringing in philosophy. I recommend this Stanford encyclopedic entry for a pretty nice and thorough treatment/overview of some of the difficulties involved in what initially seems to be a simple word.
Put more simply, it's not fair to imply that there is a mathematically "correct" interpretation of probability. This is wrong. In fact you can axiomatize something mathematically in several different ways while still retaining most if not all desirable math traits we want out of "probability" (see link), even if many end up being fairly similar... with that said, however, you are correct as far as I'm aware that Sleeping Beauty is better seen as a semantic or definitional disagreement than a mathematical one per se. Even there, though, you go too far. You can make the math satisfy your basic probability axioms of your choice, whether you're a halfer or thirder alike, once you've defined a sample space (and thus what counts as a "trial") and any other relevant definitions have been clarified (especially clarifying what, precisely, is being conditioned on!!). In short, no experts consulted are making math mistakes, they merely are speaking in scissor statements, as we might say around here.
Somewhat. I've gotten into arguments about this on astralcodexten before, and it honestly wasn't too bad. The way I try to sleep easy at night is by telling myself that 99% of people here are probably sensible, and it's only the 1% I end up having to argue with, who think that weird philosophical arguments can let you ignore the results of an easy-to-replicate experiment. (I'm not including you in this, to be clear.)
Well, I understand what you're trying to say, but there IS a mathematically correct theory of probability, if you just stick with axioms and theorems. (Uh, without getting into the weeds of the Axiom of Choice, which shows up pretty quickly because probability is intricately tied with measure theory.) As your link says, there's a "standard" set of axioms that are pretty uncontroversial. However, you're right that there can be some tricky philosophical questions about how the real world maps to it. For instance, while the Doomsday Argument is wrong (you can't tell the future with anthropic arguments), there are other anthropic arguments that DO seem like they work and have some rather weird implications. I'd love to have a real discussion about those sometime instead of this minutia.
Regardless, the issue here is that this isn't a complex real-world problem, it's a simple experiment with clear results. And, like Monty Hall, it's one that you can even do yourself with slight modifications. As the experiment is repeated, 2/3 of the times she's asked, Sleeping Beauty will see tails. If she believes she'll see any other results, she's wrong. You can't philosobabble your way into changing this fact, any more than you could talk a coin into flipping Heads 100 times in a row. I absolutely do not agree that there is a reasonable way of defining a "trial" or "sample space" that somehow makes the halfer case make sense. You can see people in this thread trying, and it takes some real mental gymnastics.
When people bring up the Monty Hall problem, do you go around telling THEM that probability is philosophically complex and gosh, how can they really know they should switch with 2/3 confidence? No? Then why is Sleeping Beauty different?
(I mean mathematically correct in the sense that Kolmogorov isn't technically the only game in town with internal axiomatic consistency, though it's universal enough in use I was probably being overly pedantic there)
Because Monty Hall is inherently grounded, while Sleeping Beauty is a weird contrivance pretty much on purpose. Sleeping Beauty relies on a supposed perfect memory-erasing amnesia drug erasing one entire interview and only that one interview. It further relies on Beauty being unable to distinguish the passage of time at all, and even more confusingly we are including Beauty's answers across multiple days in our sample space! This is unintuitive. Our sample space to get 1/3 is: Beauty on Monday on Heads, Beauty on Monday on Tails, Beauty on Tuesday on Tails, yes? Most probability problems are not so casual about employing asymmetric tree diagrams across temporal positions, because the eminently natural assumption about the passage of time is that you were able to perceive it. The weird, nonexistent mind-altering drug breaks that intuition about the unbroken forward flow of time! An assumption we virtually never question in any other scenario.
So despite my best wishes I guess I'll take the bait. To be clear, I'm not so much trying to explain the halfer position as elucidating why I believe the whole debate to be kind of stupid and misguided, though I am quite sympathetic to your view.
Anyways, time flow. In other words, the halfer position rejects that it even makes sense to ask about Beauty on Tuesday, since "obviously" the sample space is only: Beauty on Monday with two possible coin flip results (i.e. guesses). The halfer position says in effect that it's impossible to consider two super-imposed Tails-guessing Beauties on both Monday and Tuesday at once. Or, phrased a different (and probably better) way, a Monday Beauty guessing tails is functionally indistinguishable from a Tuesday Beauty guessing tails, because the "divergence" in intent has already occurred! The only relevant guess is the coin.
The second illuminating follow-up question: What is our reward scheme? Do we reward Beauty for a correct answer every time she wakes up (and then steal it back when she sleeps and forgets, thus making any gain ephemeral; though optionally we may choose to sum all three of her choices for aggregate statistical reasons), or do we reward Beauty only after it's Wednesday? For the former, we are effectively rewarding each awakening, but for the latter we provoke a philosphical crisis. Is Tuesday Beauty really making a truly independent choice? Halfers might say no, of course not, "reality" already diverged. Thirders would say yes, of course, it's a new day so thus a new choice. Crisis aside, consider a Beauty who goes "screw it, I'm not playing mind games, I'm choosing heads literally every time" - for a one-time Wednesday-only reward, she wins half the time. Can we truly treat a Beauty who goes "screw it, I'm choosing Tails every time" differently? It depends on our reward scheme! In one setup it's clear this Tails-stubborn Beauty gets double winnings every Wednesday (because even though both awakenings gave the same answer, they were rewarded separately thus double dipping), while in the other she is no better off than the Heads-stubborn one (because the coin was, in fact, tails just half the time, and she's only rewarded at the end). Hopefully that teases apart why it matters.
But you see the issue here, previously obscured? Not only is this contrived, but we require some clarification here about definitions to deliver an answer. We could use a computer, but then we're merely revisiting the same problem with our programming as a design choice: when the coin comes up Tails, do Monday-Beauty and Tuesday-Beauty execute their decision-making code twice with independent randomness, or does Tuesday-Beauty simply output the duplicated cached result from Monday? We implicitly make a claim, one of the following:
This whole setup is odd, because typically in a probability problem, identical epistemic states with identical available information should have identical probability outputs/beliefs, right? Yet in one of these cases, we're saying the two events are separate because 'someone said so'. Or maybe more accurately, in one case we're talking about epistemic states of knowledge, and in the other we're talking about specific events. Scope is subtly different. The problem has laundered in a sneaking modeling choice without you realizing it. Your choice of model literally determines if additional randomness is injected into the system or not, and thus influences the long-run probability you will find. This is especially clear when you add simple rewards like I described.
But anyways real life does not contain weird situations like these reminiscent of quantum physics. Monty Hall can be modeled strictly mechanically, and in a loose sense so can Sleeping Beauty... but how you represent said model is not a settled question. Is the experiment truly "reset" when we move from Monday to Tuesday? Again that's really a purely philosophical question, not a mathematical one. The presence of a belief-having chooser like Beauty is required for us to even talk about "beliefs" and "rational bets" and all that stuff. This is the doubly case when it comes to time. It's one of the most frustrating aspects of statistics and probability: we cannot actually run perfectly authentic, true counterfactuals, because time runs in one direction. Just like science fiction can only theorize and imagine what would happen in multiverses or if we perfectly cloned a human mind, probability also struggles to perfectly map to reality and human perception because of the aforementioned triple concept divergence in what we mean when we say "probability".
Maybe I'm being too harsh on this thought experiment, but I have little patience for them when they so obviously diverge from reality. We shouldn't be surprised that setting up an unintuitive situation produces unintuitive answers.
I think I'm Sleeping Beauty'd out, but thanks for your comments. I honestly don't think the problem's all that existentially weird - compared to many thought experiments, this one could at least take place in our physical universe.
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