The Church-Turing thesis is a statement about symoblic processes, and symbolism is simply not fundamental to the universe. It is fundamental to how humans understand the universe. That's the distinction.
714 karma · joined June 26, 2026
I don't think your claim is possible to prove statistically - what does "pure reason" mean? And of course it's "pure reason + empirical observations": even if they're not running reproducible experiments they still see natural phenomena.
Overall, they are making algorithmic progress 50% faster than they would without AI assistants
And ironically they didn't predict the actual 2026 reality that Mythos sucks as an agent but commanded global attention as a cybersecurity tool.
Also this just seems childish and clearly hasn't really panned out:
But China is falling behind on AI algorithms due to their weaker models. The Chinese intelligence agencies—among the best in the world—double down on their plans to steal OpenBrain’s weights.
The article hinges on AI automating R&D and finding something fundamentally more powerful and reliable than the current transformer LLMs. But that hasn't panned out at all. What has panned out is better scaffolding around running the LLMs in an iterative loop.
It actually seems to me AI 2027 holds up badly, unless your only takeaway is "AI gets better."
Assuming you have the background, the boring answer is "patience and practice." For years I had to practically rewrite math papers word for word in order to get anything to stick. These days I am better at reading "mentally," but still sloppy and prone to misreading (just yesterday I misread GPT's proof because I was lazy and on my phone). More so than the empirical sciences, mathematics demands you understand every sentence before moving on to the next. Skimming does you no good. It really does just take patience and perseverance.
The nice thing about this paper is that the math isn't especially advanced, and it's broken up with qualitative historical discussions. If you know a decent bit of linear algebra (enough to understand artificial neural networks), I think you can muddle through this.
"Visual complexity" is just wrong: simple black / hot pink stripes are visually exhausting upon immediate perception, whereas the monochromatically brown detail of a tree trunk is only visually exhausting on close inspection.
God, what a useless website. I hate LLMs. The actual paper is here: https://www.mdpi.com/2411-5150/10/2/34
The paper itself is open access: https://www.mdpi.com/2411-5150/10/2/34
“This idea that relativity is important in heavy elements has been around since the 1970s,” said Lai-Sheng Wang, a professor of chemistry at Brown and the study’s corresponding author. “But we show direct spectroscopic evidence that what we learned in high school about chemical bonding isn’t true in heavy elements."That said, you are still making the same mistake I pointed out, elevating human symbolic information to a higher plateau than it deserves. I think it's because you're being too vague about the connection, when it's fairly mundane. The "fundamental connection" is that physical quantities are information, and on the other hand information is always a large collection of semi-independent semi-stochastic physical objects and can be profitably modelled by some sort of statistical mechanics. Information theory is relevant all over physics because human agents collect all sorts of physical information. The universe "doesn't care" about information in and of itself. Shannon entropy and Boltzmann entropy have similar formulas because they measure precisely the same thing; put another way, a goofy but formally equivalent way to model a gas would be a noisy radio channel communicating each molecule's kinetic energy.
The problem with the black hole information paradox isn't that information is destroyed per se, but that it appears to be destroyed in a way that violates quantum mechanics (destroying quantum state without a measurement). The theoretically predicted destruction of information points to a more general problem.
The Laundauer limit is no more fundamental to the universe than "a mechanical crane cannot violate the laws of pulleys." It says that no matter how you design your binary (or whatever) computer, it must involve an ensemble of binary states, and statistical mechanics puts an absolute floor on how little heat is required to alter such states. Whether these states are gas molecules or the written symbols "0" and "1" is immaterial.
Computation is a metaphysically universal and fundamental concept, since metaphysics is (tautologically) the domain of humans and we use symbolic communication. So of course very general theories of symbolic processes (e.g. Turing machines) are pertinent to the symbolic methodology we use to understand scientific processes.
But it is a fundamental mistake to jump from that to saying computation extends to a law of the universe. Computation reflects laws of the universe, but only in the exact same way that scientific and mathematical human speech do. The mystery (still totally unsolved) is how humans are able to intuitively understand space / time / causality / etc in order to define coherent symbolic rules that reflect real processes. That computers can seemingly always implement these rules having been given the symbols is of philosophical/scientific interest, but it's solipsistic to say it's a fundamental concept of the universe.
The job performed by the humans was broader than what was requested of the model in this benchmark: humans also had to find the relevant invoices (searching through mailboxes, or requesting them from providers) and reason through any circumstances which cannot be inferred from the bank feed and invoices/receipts on their own. In the benchmark these circumstances are presented to the model as “user notes."
And I would be pretty nervous about asking any of the frontier LLMs to retrieve invoices: "cool, Claude logged that it found the May 6th bill from the paper supplier, I am sure it didn't just make something up arbitrary, then compound on the error by agentically iterating over the made-up invoice lurking in its reasoning traces. I checked the first 30 times and there were no problems!"
The European Dark Ages after the fall of Western Rome was a real thing. Many people regressed to the Stone Age for hundreds of years, and we lost almost every written work from ancient Greece and Rome. That can absolutely happen with the US and EU by 2200, especially considering digital information is far more fragile over centuries than papyrus and parchment.
> The density of useful information I gather from places like Wikipedia, even long form articles is substantially higher than I got reading non-fiction.
You're in good company. Sam Bankman-Freid:
I would never read a book. I’m very skeptical of books. I don’t want to say no book is ever worth reading, but I actually do believe something pretty close to that. I think, if you wrote a book, you fucked up, and it should have been a six-paragraph blog post.
Not reading books because of "information denisty" is a lazy rationalization for dumbing yourself down. Wikipedia is good as a quick reference if you already understand something, but a disaster for learning.
They are making little web applets demonstrating the physics concepts. You obviously can't do this in pure R6RS/etc., you need to pick some implementation that either has JS/WASM FFI or something built in. Likewise if they were doing this as a desktop application, etc. Pure Scheme can model the physics and return the correct numbers, but you need something more for graphics and interactivity.
I will change my mind if someone demonstrates such a robot. Absent this demonstration, cockroach-level AI is still an unsolved problem. Given how ignorant and arrogant and wealthy AI researchers are, it will remain unsolved. I don't think anyone alive today will live to see a robot smarter than an ant.
Did I not, then, as I grew out of infancy, come next to boyhood, or rather did it not come to me and succeed my infancy? My infancy did not go away (for where would it go?). It was simply no longer present; and I was no longer an infant who could not speak, but now a chattering boy. I remember this, and I have since observed how I learned to speak. My elders did not teach me words by rote, as they taught me my letters afterward. But I myself, when I was unable to communicate all I wished to say to whomever I wished by means of whimperings and grunts and various gestures of my limbs (which I used to reinforce my demands), I myself repeated the sounds already stored in my memory by the mind which thou, O my God, hadst given me. When they called some thing by name and pointed it out while they spoke, I saw it and realized that the thing they wished to indicate was called by the name they then uttered. And what they meant was made plain by the gestures of their bodies, by a kind of natural language, common to all nations, which expresses itself through changes of countenance, glances of the eye, gestures and intonations which indicate a disposition and attitude--either to seek or to possess, to reject or to avoid. So it was that by frequently hearing words, in different phrases, I gradually identified the objects which the words stood for and, having formed my mouth to repeat these signs, I was thereby able to express my will. Thus I exchanged with those about me the verbal signs by which we express our wishes and advanced deeper into the stormy fellowship of human life, depending all the while upon the authority of my parents and the behest of my elders.
Humans learn language opportunistically. Toddlers start with a powerful "superchimpanzee" understanding of the real world, and use that to learn words in order to satisfy their needs and desires. Statistical frequency is incidental to what words a toddler learns: what matters is the real-world context. Also note how important it is that infants instinctively understand nonverbal communication.
The most depressing thing about the 2020s AI summer is watching ignorant tech workers use the success of LLMs to launder their own ignorant misanthropy. Your views are many many centuries out of date.
Did I not, then, as I grew out of infancy, come next to boyhood, or rather did it not come to me and succeed my infancy? My infancy did not go away (for where would it go?). It was simply no longer present; and I was no longer an infant who could not speak, but now a chattering boy. I remember this, and I have since observed how I learned to speak. My elders did not teach me words by rote, as they taught me my letters afterward. But I myself, when I was unable to communicate all I wished to say to whomever I wished by means of whimperings and grunts and various gestures of my limbs (which I used to reinforce my demands), I myself repeated the sounds already stored in my memory by the mind which thou, O my God, hadst given me. When they called some thing by name and pointed it out while they spoke, I saw it and realized that the thing they wished to indicate was called by the name they then uttered. And what they meant was made plain by the gestures of their bodies, by a kind of natural language, common to all nations, which expresses itself through changes of countenance, glances of the eye, gestures and intonations which indicate a disposition and attitude--either to seek or to possess, to reject or to avoid. So it was that by frequently hearing words, in different phrases, I gradually identified the objects which the words stood for and, having formed my mouth to repeat these signs, I was thereby able to express my will. Thus I exchanged with those about me the verbal signs by which we express our wishes and advanced deeper into the stormy fellowship of human life, depending all the while upon the authority of my parents and the behest of my elders.
In the modern academic practice, the question of where a particular idea came from, or whether an axiom is ontologically correct, is considered vacuous and out of scope. For the most part, you’re just handed a rulebook to play someone else’s game.
To be clear I think the standard intuitive semi-naive set theory is the correct approach for most math students. But it didn't work for me. I needed to see the axioms and formal language.
>> Wait, looking at the prompt history, the model had a strange quirk.
Throughout every prior thinking trace in the conversations (and, honestly, every other thinking trace across all other conversations I've had with it), the frame is always in first-person, including the moment in this one where it "noticed" the corruption: "I noticed," "I had some weird typos," "did I do that on purpose?" And then the moment the anomaly couldn't be reconciled with the self-model, the language shifted to third person: "The model had a strange quirk." Effectively, the thing doing the thinking dissociated from the thing that produced the anomalous output, as if they were two entirely different layers of the process, much in the same way a person might fumble an easy sentence and then go for something like "my brain just did something weird." Except, of course, that "me" vs "my brain" is a distinction without a difference in much the same way Gemma's "I" vs "the model" is. Gemma is the model, just as much as we are our brains.
Likewise with Claude referring to "the model" - that quote sounds like something an Anthropic worker would say. Seems like a pithy little line Claude could have learned "on the job."
a) I got bullied into sharing my math homework so people could copy it, just like high school and college... but this was math grad school!
b) In 2011 I TAed a 4000-level course where the instructor left the solutions to the homework online (he wrote the book). I estimate 95% of students copied the solutions. It was only 5% of the grade and they paid for it on the exams. Still. Kind of stunning to see at U Waterloo - it was a continuous optimization course and most of them wanted to work in finance, yikes.