Soteriologian
22d ago
Two fun stories from tech this past week:
Story 1
The rsync developer picked up vibecoding recently, which resulted in him publishing a busted release that started breaking people's backups, which caused a nuclear level of backlash. The rsync dev responded by posting this wall of text which insists that no, vibecoding is actually the future, chuds.
The most amusing part is this is not some cooked zoomer who picked up Claude last week and deluded himself into thinking he was now a real coder. This guy is the founding author of the project, and has been its primary maintainer for 30 years.
Story 2
Zcash is a cryptocurrency which advertises itself as a privacy coin. As all good cyberpunks do, Zcash has a centralised, legally-incorporated foundation elaborating their trademark policy as well as a wealth of resources about 1023s, bylaws, IRS compliance, and pretty much anything else that would brighten the day of a young cyberpunk.
But don't worry, it gets better when you dig into the details: "Privacy coins aren’t all the same — and Zcash takes a unique stance among them. Unlike [redacted], which enforces full anonymity by default, Zcash gives users a choice." A unique stance indeed! This stance has been pioneered elsewhere by Telegram, which famously features end-to-end encrypted chats that a user can opt into (and if they don't, well, the messages are unencrypted by default just like on every other platform, and Telegram and anyone capable of arm-twisting Telegram can read them). I'll note that as a frequent user of Telegram for over a decade myself, I have never once had someone initiate a secret chat with me, which just goes to show that all true cyberpunks love mass surveillance, and will choose it whenever they are given a choice. Like Telegram, most users of Zcash choose not to make their activity private. Of course, even if you opt into the shielded pool -- a respectable choice! -- make sure you do so carefully, because there are definitely not guns pre-pointed at your foot C++ style.
But all of that is old news! Today, the price of Zcash wrt the dollar crashed nearly 60% on the news of a new critical vulnerability discovered by a random person deciding to point Claude at the code base (not the Mythos version; just the regular version accessible to anyone). The vulnerability allows unlimited coins to be printed in the shielded pool where nobody can see them. Some foolish conspiracy theorists have put forth the hypothesis that backdoor money-printing may, in fact, have been a feature, not a bug, but fortunately, top men are on the case to discredit such harebrained nonsense.
What's especially baffling about Zcash is that despite its impeccable reputation, Wikipedia notes its adoption among darknet cryptocurrency markets is less than 1%.
Soteriologian
22d ago
I think you're correct, but I think another key aspect that is underdiscussed is Overmind assassination (both literal and de facto; the most effective way to knock a piece off the board is often not to kill them and turn them into a martyr).
Soteriologian
22d ago
Nah, I'm not a Moldbug fan, but he is correct here.
The right historically has not had such difficulties with this. The US colonists said, "You will not tax my stamps and tea, and if I catch you doing so, I will shoot you." These are not envious leftists or commies. They had a sincere, coherent political model that they were willing to pursue -- not just to the point of sacrificing their own lives, but to the point of sacrificing the lives of those who disagreed with them. They prioritised their movement and their vision above that of the governing state, and they were willing to back that with as much violence as they could muster.
That is, in fact, what winning looks like.
Soteriologian
23d ago
Moldbug is correct when he says leftists understand power and the right does not. I bet these protests go nowhere, despite being entirely justified (especially compared to the Floyd protests). In fact, this justification is why they'll go nowhere: the right can only rally when something verifiably bad happens, and even then barely muster the gumption to care. The left, in contrast, doesn't give a rat's ass about the facts on the ground: the incident is useful to the cause, and we're going to milk it for all it's worth because what we actually care about is The Movement, not the incident.
There really is nothing similar to The Movement on the right. The left retains all moral authority to itself: as long as your actions are in service of the movement, nobody cares whether your actions are legal or not. Loot the Nike store, raze the Starbucks, shoot the United Health CEO, whatever: you may be a criminal to The System, but to The Movement, you're a hero! The right does not retain any moral authority to itself. All it can do is appeal to the existing laws and say, "See, the immigrant with a knife stabbed somebody! That's against the law! The police should ARREST him, and and... maybe even DEPORT him." Yeeeeah, one of these two teams is going to trounce the other.
I think the reason for this is that the left does actually have an overarching narrative that compels the assent of and motivates the actions of its adherents. That's not to say it's true or accurate, any more than Islam being able to compel suicide bombers means Mohammad actually flew to heaven on a winged unicorn. But the narrative is there, and it inspires loyalty and action.
The right, in contrast, has no Movement, especially not one that compels moral authority over the state to any relevant degree in #currentyear. There are two wings of the right: the actual tradcons (which look like this), and the Nazis (which often LARP as tradcons and look like this). If you bomb an abortion clinic or a migrant detention center, there will be no rallying to your defense by women with hundreds of thousands of likes inquiring when the conjugal visits will begin in your prison, there will be no photographer taking Renaissance photos or featuring your drip in Time magazine. Now, I know Luigi is unusually attractive, and the Clavicular worldview is to attribute the fanfare to that. But let's be real: if Luigi had shot a leftist figurehead, this is not the reaction he would have received. Luigi's cuteness is useful to the movement: the movement is not subservient to the actions of the most cute, as the Clavicular model would contend.
Can the right figure out how to claim moral authority? In its current incarnation, I doubt it. What the right is missing is the right side of the Bell curve: they have plenty of Zerglings, but no Overmind. In fact, I'll go so far as to say a lot of the Overminds they do have are false, in the sense that I think incidents like Jan 6 are setups to get rightoids to clown themselves into getting arrested. They think they're crossing the Rubicon with Caesar, but they're really just being goaded into making fools of themselves by agents more intelligent than they are running circles around them in their fog of war.
Soteriologian
24d ago
Thiel is in deep with MAGA, but thinks that the wind is changing direction, the MAGA project has failed, and he doesn't want to be left holding the bag in America when the left comes back into power.
This seems the most likely to me. Unlike many here, I've never bought into these "new right" movements like Maga. They feel very synthetic to me (or, as the kids say, fake and gay), in the sense of both being manufactured and specifically being manufactured by people who have dubious belief in the product they're selling. Like having a tattooed pornstar, a WWE Smackdown champ, and an Indian woman praying to a Hindu god featured at the RNC does not strike me as a sincere evolution of the right-wing movement from 20 years ago: it looks more like a spiteful mockery of the Christian right's inability to stop a hostile takeover.
Hillary said back in the day that Trump was a Pied Piper. She presumably meant he was there to lead the right astray into clowning themselves and severing their access to power forever, as she, the stout and civilised pantsuit princess, ascended to the throne as First Woman President and Leader of the Free World.
As is often the case in politics, she was quite deluded about herself. But I think she was basically correct about her opponent.
I keep predicting a market crash, and I keep being wrong, but... well, I'm going to keep predicting it anyway, because the market looks pretty damn irrational to me. And yeah, if you get the largest market crash since the Great Depression, it might be a good idea to be somewhere else, because people are already not in a good mood. There will be calls for heads on pikes.
I'm not sure I follow your confusion. In a strictly mathematical sense, you may have equivalence, but if you publish your paper in the world where electrons have positive charge and everyone else publishes their paper in the world where they have negative charge, well… you can see how this appeal to "Well they’re equivalent either way 🤷♂️" is both technically correct and also asinine.
But it's not just this sense: in the bool example, there's only one bit of information at play, but say you're talking about something more complicated like graph isomorphism or SAT solving. The representation of the problem matters a lot in practice! You can famously write a SAT solver in a single line of Haskell code, but you can also do it in 60,000+ lines of low-level systems code. I'm sure you can guess which is the useless party trick and which is the industrial-grade SAT solver. But even more relevant is that the technical curiosity is, in a strictly mathematical sense, more correct! The industrial-grade SAT solver has a maximum variable count just by the fact that it labels them with 32-bit ints, which is obviously ridiculous by theoretical standards: there’s no magical limit on the number of variables you can have in a SAT problem.
So, let’s say we’re interested in proving the correctness of a SAT solver. I bet there are a fair number of people who’ve played around with Lean and similar systems who would have a fair shot at proving the party trick correct.
There’s not a single person on the planet who stands a shot at proving the industrial SAT solver correct, nor is there likely to be within a thousand years.
And this is how it always is! There is this enormous disconnect between the truly formal representation of a system and "equivalent" (in any colloquial sense) real-world systems anyone cares about, even for systems that are themselves formal fields of study like SAT (much less anything an MBA would consider “real world”, like whether his website is secure).
The reason money has any interest in Lean 4 beyond "the government will give me a tax deduction for my charitable donation" is because we want systems to stop being so broken, and formal verification is supposed to help with that.
My point is just that there are… asterisks. A lot of asterisks.
If someone's "proofs" aren't of kind Prop, they're doing something wrong.
This is simply not the case, as even my example in the OP shows. Proofs do contain computational info, and many times you cannot choose to ignore it: it really makes a difference whether the off switch turns the system off or on! You can’t just say "Well, there’s two options either way, so they’re equivalent," and be done with it.
Prop isn’t some special universe where your proofs live. If you have that mental model, you’ve never built anything with these systems. That’s like a "meat comes from the supermarket"-tier take on how this works.
Even the name "Prop" is a reference to it being intended for propositional equality, which in some flavours of dependent type theory is asserted to have one constructor (and traditionally, this axiom is one that induces poor ergonomics; hence, Voevodsky’s axiom and the development of HoTT/cubical theories).
I don't know, my experience is kinda the opposite, but I have been programming since childhood. I find AI very frustrating to use, and rarely consult it.
Keep in mind that it has all of Github in its training data. It can go a long way by basically feeding you an existing project and not mentioning where it got it. I don’t mean to oversimplify and say that this is all models do and that there’s no reasoning, but I think people underestimate just how much is memorised: you can get mainstream models to recite entire books like Harry Potter almost word-for-word, with upwards of 95% accuracy, and to the extent that you can't, it's usually due to active sabotage by the model vendor to prevent people from getting free Harry Potter, not because the model doesn't have Harry Potter memorised. Vendors really do not want it to look like everything is getting memorised, but to a large extent it is. I just tried it with some random books I'm reading now and… yeah, they definitely have every book I'm trying memorised, even though they're very coy about it. And some of these are quite obscure books that I'm confident less than 1% of people would even recognise the name of. I then tried it on a snippet from a random library I published ten years ago on Github and… yeah, it has it memorised, down to the exact word. Amusingly, unlike the books, it does not go out of its way to tell me where this quote is from and lecture me about the importance of copyright. When I explicitly ask it where it got that, it just says it made it up—that it’s not a quote from any published book.
EDIT: to drive the point home, it is not so good at predicting the text of an unpublished library I have sitting on my PC! I suppose it's some consolation that this vendor does not appear to have access to my computer.
Soteriologian
26d ago
Well, if we're going to be pedantic, proofs of kind Prop are irrelevant. I haven't followed this stuff in a while, but I'm pretty sure this opens a big can of worms, especially wrt erasure. Google's AI assures me this is all totally resolved and there's zero overhead, then links me to this thread which is not that old and smells of all the swamp I remember from back when I followed this stuff.
Soteriologian
26d ago
The Hilbert thing is more a sign of the times. Back then, there was a lot of resistance and emotional slapfighting over this, because in ye olden days, people were very concerned about which postulates were True (TM), and viewed any attempt to discuss this as an attack on Truth.
Today, we worry less about this absolute notion of Truth and more about models: is Euclid's parallel postulate True or False? Well, there's actually nothing to fight over: you just get different geometries, but they're all meaningful and useful! So rather than saying "The parallel postulate is true, therefore XYZ", you can just say "When the parallel postulate is true, XYZ holds." Even questioning logical primitives that seem "very true" like "can you appeal to a theorem more than once in the same proof?" turns out to have surprisingly useful implications! For example, if you're modeling a cookie, it makes a lot more sense to say you can only eat it once, rather than you can eat it as many times as you want. It's not wrong; it's just a different thought model. A thought model that, incidentally, is the foundation of a very popular programming language.
One can say "Ok, but what if the postulates imply a contradiction? Surely that's bad, right?" Well... yes, but actually even here there's a lot of subtlety. Not for mathematicians, but for everyone else: see, the trick to defining logical systems that dodge Russell's Paradox is to have a cumulative hierarchy of universes, which is what a lot of dependently-typed proof systems use. But it turns out this is an enormous pain in the ass to work with for writing normal software, to the point that literally nobody does it, and instead we settle for simpler systems that are much more ergonomic to write in yet still, in practice, give a pretty strong (but not rock-solid!) guarantee that you haven't contradicted yourself.
Anyway, constructivism is a more grounded model compared to classical logic, in the sense that it actually computes results, and you can do the legacy thing by just saying "When the law of the excluded middle holds, XYZ."
Soteriologian
26d ago
An appeal to a definition is a proof ("By the definition of XYZ, we conclude..."). A definition itself is not a proof ("Let xyz be defined as ...").
The confusion is coming from the fact that Refl : 0 + 0 = 0 is the syntax of an appeal to the definition of plus. It is not the syntax of defining the + operation.
Look, I'm not going to run around in circles all day about this. I'm pointing out that mathematicians are more sloppy in their vocabulary than the theorem prover, and that there are subtle differences over how terminology is used. I do not care to bikeshed endlessly over this. It's obviously true to anyone with any experience in these fields.
Soteriologian
26d ago
I think you've never spent any time with a formal theorem prover lol. You're conflating the definition of + with the proof Refl : 0 + 0 = 0.
Mathematicians can say whatever they want, but the story here is about mechanically-verified formal verification, and this is how formal verification works, whether legacy mathematicians think this pedantically or not.
Soteriologian
26d ago
Part of the misunderstanding is the word "proof" has different flavour in classical mathematics vs theorem prover math, which is why the word is rarely used in this world except when appealing to legacy mathematicians. The native vocabulary is "3 is a value of type Nat" or "Refl is a value of type 0 + 0 = 0". A legacy mathematician would use the word "proof" only to describe the latter, and think it odd to use the word for the former. But internal to the formal logical framework, these are same notion, and so they should have the same word.
Soteriologian
27d ago
I wouldn't read too much into this. Has anyone ever seen him use a theorem prover other than Lean? If anything, he's a lot more explicit about using the Lean "brand" than the OpenAI brand. Yet obviously he's not a sponsored shill for Big Lean (because there is no Big Lean).
What's clear is his organisation is pursuing private funding since the government axed his grants. I think it's likely OpenAI is among them given his appearance on their Twitter promo. Whether there's any exclusivity contract, who knows, I don't have a confident assessment.
Soteriologian
27d ago
Are they selling these things as proof of applicability to software verification?
I mean, that was certainly my impression. Maybe I've self-selected into circles where that's the sort of thing people naturally care about, and incorrectly assumed this is how everyone is thinking.
Sure, if all you care about is Erdos problems, I guess much of what I'm saying is moot. But this whole "Mythos is finding all these vulnerabilities, the whole meta has shifted!" narrative sure leads me to the next part of the story of "Ok, so how do we actually build stuff correctly in the presence of tools like Mythos?" Because the mythos story, like the classical theorem prover story, is also basically invulnerable to the primary problem of LLMs, hallucination. If the model hallucinates a vulnerability that doesn't work, just throw it away and try again! (Or, in the case of low-human capital, spam the issue tracker with bogus vulnerability reports. But I digress).
Soteriologian
27d ago
I don’t think we’re referring to the same constructivism. I’m referring to this: https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)
Well, in the classical mathematical sense, crypto doesn’t work at all: just factor the composite number. The entire premise relies on the relatively ill-specified (by mathematical standards) notion of relative computational cost disparity.
What is the sense in which you claim proofs to be "interchangeable" in classical systems
What I mean is when I sit down to write something in a theorem prover, I speak in terms of Peano nats and inductive lists. When I write software anyone would ever want to actually use, I use machine ints and arrays. There is definitely a sense in which I’m doing the same thing in both cases, but nailing this down precisely is… well, non-trivial. (aka, a royal pain in the ass). Like, the discrepancy here is show-stoppingly problematic.
EDIT: basically, the computation is relevant, and more specifically the speed of computation is also relevant, both in terms of practical usability and outright security in the case of crypto. In the classical world, there is no notion of computational relevance at all -- in fact, you outright end up with these counterintuitive weirdo theorems like Zorn's Lemma. The counterintuitiveness depends entirely on this conspicuous lack of computational awareness in the model: as soon as you put that ingredient back in, you're in the construcivist world, and silly results like Zorn's Lemma don't hold anymore unless you postulate them. My contention is the class of problems for which one can say "I don't care about which proof, just that one exists" is relatively narrow and of little practical relevance (in the sense that one can get an incomputable proof, which is, in a fundamental technical sense, useless), while the class of problems about which one does care which proof, in the Curry-Howard sense, is large and of enormous practical consequence. I want to argue that enthusiasm over the former should not translate to enthusiasm about the latter.
Soteriologian
27d ago
I think crypto is a good analogy. There is actual tech there, and many do indeed believe in it (me being among them). But the hype and noise was wildly disproportionate to what was realistic and done.
At this point, if you put your bet on anything other than "Slightly improved Bitcoin with privacy that was obviously intended originally but not known how to do at the time," you’re probably down 70+%, if not entirely liquidated. Entire narratives about "business on the blockchain!" were complete nonsense.
Fun fact: Sam Altman himself launched a crypto coin back in the heyday. It's down 96%.
Soteriologian
27d ago
as in you hope non-technical readers will look at it and walk away with an understanding like "what Terry produces with his AI is not a real proof"?
Come on, that is not an honest reading of what I said.
In constructive systems, one proof—in the Curry-Howard sense—is not interchangeable with another. For example, you can sort in O(n^2) (or worse), which would be a perfectly valid thing to do in classical mathematics, but a big oopsie in formally-verified software. This is doubly-so in cases like cryptography, where almost none of the "incorrectness" of compromised crypto is incorrect at all in the classical mathematical sense. Further, as someone who has a fair bit of experience playing around with these systems in the past, theorem provers often induce you to write code in a way that is easy to make formal statements about, rather than in a way that actually runs well enough that anyone would want to use it.
My point is the software verification story—which is surely of high importance to businesses—is far more nuanced than "throw the clanker at Lean and let it churn". I think the bucket of cold water I’m tossing is completely justified (even as someone who does indeed buy the baseline premise—that LLMs will be a big boon to working with theorem progress).
Soteriologian
27d ago
The primary smell test is if a person promoting something is only using one brand.
Typically, yes, but we're unironically talking 160+ IQ here. He certainly has negotiating power and some sense of dignity and taste. Anyway, yes, I freely concede my searches specifically for "OpenAI gives TT a bunch of money" were in vain. But they did turn up his new foundation, which comes remarkably close to confirming my original conspiracy theory right on the tin. He’s clearly salty about losing that government money (and rightly so), and is pivoting to asking for private sources.
Soteriologian
27d ago
I made a comment recently speculating that Terence Tao may be a paid promoter of AI. After some off-site discussion elsewhere, our resident shaman on whom the mods cast a long-duration silence posted my comment as a circus exhibit on Twitter to demonstrate a dangerous form of psychosis. Fortunately, OpenAI deemed this a worthy time to intervene and publish an ad featuring Terence Tao, who has taken time out of his busy schedule to assist this struggling non-profit with their promotional.
I want to dissect what I think is really going on.
For starters, every time I sit down to watch WoW on YouTube, I'm greeted with my favourite streamer telling me about the super fun game Raid Shadow Legends, which I should definitely download and play because it's super fun. Is the OpenAI-Terence Tao relationship like this? Not really. Terence Tao does appear to actually spend some time playing around with LLMs. Further, he's not exactly saying a bunch of empty marketing blather, either. In fact, probably to the annoyance of some readers here, I want to take a couple paragraphs for a technical aside, because there is actually subtlety here. I'll bound this in horizontal bars so non-technical readers can skip it:
The main talking point is that automated theorem proving is a perfect fit for LLMs precisely because it's not vulnerable to their main catastrophic failure mode: hallucination. The model can hallucinate whatever it wants, but the text still goes into the theorem prover, and if it's bullshit, well, the prover just rejects it and you query the LLM again. Do this in a loop, burn whatever unholy amount of compute you want, and if the loop stops, you've got yourself a proof! (Well, or a bug in the theorem prover. Or a "You've run out of tokens on your budget" error message. But I digress). This story is largely true. There's a giant asterisk of "Uh, so how much compute we talkin' about?", and the answer is "As much as you need or can afford, whichever comes first!" Which is, of course, the business model.
I will point out one additional technical nit-pick that annoys me because Terence Tao is working in Lean 4, which is a dependently-typed theorem prover. In classical mathematics, one is concerned solely with whether a theorem is true or false, and the structure of the proof is basically irrelevant as long as it's valid. Lean 4 is not based on this model. Rather, it's based on a more computationally-motivated model of mathematics pioneered by Brouwer in the early 1900s called "constructivism." In this world, the question isn't the boolean notion of "Is this theorem true or false?" but rather the related but distinct notion of "Which proof do you have?" To ground this in practical terms, consider the following example: I can prove that True|False and Yes|No are isomorphic, but I can do so in multiple ways: I can map True to Yes and False to No, or I can map True to No and False to Yes (and then show that there are respective inverses which preserve identity, obviously). It is in this sense that one can meaningfully say "Which proof of isomorphism?" when I say I have a proof of isomorphism. Perhaps this all sounds like technobabble, but to connect it to the preceding paragraph: you can immediately see how this does reveal some cracks into the narrative being sold there. It does actually matter which proof is produced, not merely in a social sense of "can any human understand this wall of text the LLM spit out", but in a technical, computationally-relevant sense. For pure mathematics, this distinction is often not considered important -- in fact, many classical mathematicians aren't even aware of the difference, and will be confused if you try to explain it to them and think this is all a bit silly. However, it's not a silly or minor distinction for the following reason: one of the motivations of this computational model for "theorem provers" (it's really a programming language + compiler, rebranded for mathematicians) like Lean is so that formal methods can be applied not just to classical mathematics, but to software in general. And as soon as you enter software formalisation, this distinction is no mere intellectual curiosity, but of paramount relevance. The classical-style logic in the preceding paragraph does not apply to constructivist logic used for software formalisation! I'm sure this distinction is not lost on Terence Tao. But that doesn't concern OpenAI. OpenAI is more concerned with whether the distinction will be lost on the MBAs listening to Terence Tao, and the answer is "absolutely."
Ok, no more technical details like that, I promise. Back to the social level:
So, I mentioned Raid Shadow Legends is a poor metaphor for the OpenAI-Tao relationship. Let me propose some better ones: Michael Phelps and Wheaties (with the added benefit that Terence Tao never smokes weed. See, this is why mathematicians are better than athletes), or better yet, attending Harvard University. This may seem like a strange juxtaposition, but I've done so intentionally, because the marketing is obvious in one but subtle in the other, but it's actually the same trick: the goal is to misattribute performance. With Wheaties, the goal is to sell the notion that Michael Phelps is a great swimmer because he has a healthy diet of stuff like Wheaties, and if you eat Wheaties, maybe you'll perform well, too! Of course, in reality, he was eating sugar-coated french toast and chocolate chip pancakes because he needed 10k Calories/day just to break even on energy, and the reason he's such an awesome swimmer is in large part genetics. Wheaties, or anything similar to it, has virtually no relevance to Michael Phelps at all. But what about Harvard?
Well, Harvard sells the image so well that most people outside this forum outright believe the illusion. The illusion is, of course, that attending Harvard makes you smart and likely to succeed, rather than Harvard accepting only people who were smart and likely to succeed in the first place and thus redirecting credit for these future achievements to Harvard. Mark Zuckerberg may see Harvard as a pointless waste of time, but the world sees Harvard as "The university that made Mark Zuckerberg happen!"
I like the Harvard analogy because this is surely the intent with Terence Tao. There's a high chance sooner or later Terence Tao will prove something cool "using" ChatGPT, and if he does, it would be really awesome if we could make it sound like the secret ingredient in the ChatGPT-Terence Tao alliance was ChatGPT, when obviously the actual secret ingredient is Terence Tao. The analogy I always use for this is stone soup, a European folktale where starving travelers dupe gullible townsfolk into helping them make soup from stones by requesting "extra" ingredients bit by bit until they've just made actual soup, thus astonishing the gullible townsfolk.
There are a lot of other things I could say on this, especially on the technical side, as there are a lot of clever tricks you can pull to make it look like a model is doing more than it really is, but I'll stop for now and conclude with this:
Just be cognizant that OpenAI, and all the other LLM vendors, do marketing. They have an enormous budget that dwarfs anything you have ever seen before. Remember the reality distortion field of Black Lives Matter? Or trans people? Imagine that, but like... two orders of magnitude larger. That is the level of persuasive pressure we're dealing with here.
Just take it all with a grain of salt.
Soteriologian
27d ago
A truly ostentatious change would be to make the $250 bill orange instead of green.
Soteriologian
28d ago
"First principles" here means the balance between (an)aerobic respiration and photosynthesis. That's like 8 orders of magnitude more "first principles" than ediacaran biota.
People can say "the honeybee can't fly by appeal to first principles", but that's just an empty syntactic reference to first principles because it sounds cool, not an actual argument from first principles.
I wouldn't say that. Even if you do grad school, you're still out by 25, unless you do a doctoral degree of some sort, which is a pretty tiny percentage of the population. There's plenty of time to have a couple kids starting then.
The problem is that 25 isn't the starting point! The issue is you typically went off to another city for university, which made you lose contact with your high school girlfriend(s), then go to yet another city to actually settle down after that, so you lose contact with all your university girlfriend(s), and so by the time you're 25 you likely don't even have any serious marriage prospects because you and everyone around you keeps relocating to different places. This is a ridiculous social model.
If everyone would just stay put for a while, I think the issue would resolve itself. For example, the Mormons don't have much issue settling down and getting married, and they're not exactly operating under an 18th century apprenticeship mentality. But they do all go to the same university (BYU), so while they are relocating in a technical sense, they're all relocating to the same place, so it doesn't really count in the same way it does for normal kids, where everyone scatters to the four winds after high school graduation and never sees each other again. That, and BYU is a university that actively encourages them to marry, rather than presenting marriage as some icky distraction from study.
A "rectification" settled by shooting the British army until they fled back to England.
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