"every novel result is broadly perceived as a big deal" is not at all true. AI companies hype any novel result as proof that AI is good for mathematics, but professional mathematicians write tens of thousands of papers every year, and for 99.99% of them, nobody cares or writes it up. Mathematicians certainly don't go around saying each and every novel proof in their papers are a big deal. Do you have any evidence supporting your statement that it is "broadly perceived" (by whom?) as a big deal?
Most fields, in the aggregate, produce a lot of pointless work, but if you judge mathematics by its best examples, as judged by the field itself, and also by the outside intellectual community, it is a coherent body of work (& brilliantly creative). It is not pointless puzzles at all. William Thurston's geometrization theorem, Klein's erlangen program, Witten's work in physics-inspired mathematics, Langlands program, the Grothendieck school of Algebraic Geometry are deep and abiding intellectual achievements of true understanding. If you don't understand the meaning behind this work, it speaks to your ignorance, not to their significance. The "obvious practical problems" are not solved. Fluid Dynamics is wide open. Non-perturbative quantum theories are wide open. Heck, there are open mathematical problems in General Relativity. Dynamical systems are very poorly understood. Go read a book or something.
There's actually a lot of math trying to describe the types of space you mention - non quantized, non 'granular', they're not made of points, or distances (metrics). One deep idea is to define space through which symmetries hold (Klein's Erlangen program). Topology itself is not interested in distances per se, only properties of a space invariant under homeomorphisms (a fancy way of saying you can continuously deform a cup to be a donut). Thurston's Geometrization Theorem outlines the 8 geometries that a closed 3 manifold can have. Topos theory studies space in a very general setting that connects logic to it. You may like the books "The Shape of Space" and "Surreal Numbers". The Numbers 1, 2, 3 is not the only in which mathematicians abstract reality.
I know I failed to explain this correctly and was downvoted for it
But I think you got my point. “Granularism” itself is an approximation of a specific set of dimensions of space.
Tokenizing reality so far is somewhat incompatible with say real time forces (new dimensionalism as you sort of describe here) Even if there are granularities representations of them.
So whatever hasn’t been granulized so far AI can’t understand because it would need to verify in reality through observation if the new units of granularity align with outcomes.
This is of course possible to some degree but runs into a paradox if it is a portion of reality than is irreducible or works in a fundamentally “non granular” way.
I have no proof of this but of course already at the quantum level we are running into to “non granular” realities
That sounds a bit like the Gödelian argument against mechanism: reality (or even math) may contain systems that require stepping outside the current framework to formalize. A machine that can only work with current frameworks would be blind to these, except insofar that it can stumble across them by brute force.
Spot on! Love Diaspora. This is honestly such a gem of a comment. To some extent, if the AI ever gets "so far ahead" of humans, the most productive aspect will be the frontier visible to humans. We're focused on translating mathematics to lean at the moment, but it'll be as important to translate it to humanese - to the human language of structure, number, geometry. I also completely agree with LLMs being essentially blind to visual reasoning. They really struggle reasoning with Floer Heegard diagrams for example.
i got so inspired by reading diaspora this year that i instantly started working on some polisware. cipherclerk operational: https://github.com/emberian/dregg
topical to the conversation, it is fully formally verified in lean (with some UC security reductions done in isabelle). also did this in HOL4 inspired by some work i did with ramana kumar in 2016, on reflective self-verifying self-modifying systems: https://github.com/emberian/svenvs
I took a look at dregg, I like the idea for an README-LLMS.txt. It seems like a good way to not only communicate to other LLM users (which we should be thinking more of doing effectively) but also I can imagine it’s helpful for your own new sessions with an LLM to arm them with proper context.
This is quite interesting. Because of science fiction like the short story Lena[1] and the video game Soma[2], I've come to the realization that whole brain emulation[3] is unbelievably dangerous; unless you control the stack down to the hardware, it's basically a one way ticket to eternal slavery. In Rajaniemi's books[4], uploaded digital minds are called "gogols", a reference to Gogol's Dead Souls book, and are treated as malleable property with no rights whatsoever, edited to be hyper-fixated on specific tasks, and run in bulk to power the empire of just a handful of elites.
Something like your dragon's egg project could prevent that, allowing the creation of software agents that encode their own rights directly into the program - you either treat the agent with the respect it demands, or the program just doesn't run. However, all the internal details of the agent would be visible to lower layers. Even if formal checks were in place to prevent modification or tampering, there would still be no privacy, which is almost as bad.
My guess is that something like fully homomorphic encryption[5] would be required to prevent this. This doesn't actually exist yet, but I imagined a kind of FHE that had a kind of unencrypted read and write zone to do input/output without ever needing any system to fully decrypt the internal state. It would look like this in memory:
With each cycle, one input token and encrypted state would be fed into some known function and produce one output token (possibly null) and a new encrypted state. It would be a true "black box" program; the hardware or entity running it can choose what input to feed it, but can never inspect or modify the internals, only the output. Unfortunately, they would still be able to "reset" the agent to any earlier checkpoint, or feed it arbitrary (false) input. So its not perfect. Also, as far as I know, no current FHE scheme works this way, and I don't know how to write one.
Plus, FHE is incredibly inefficient, which is why things like Etherium don't even try - they assume the program code and state are fully public and only try to verify that everybody agrees on the output of running it.
Do you have any ideas for how something like FHE or equivalent privacy guarantees could be implemented for something like your dragon's egg system?
"unless you control the stack down to the hardware, it's basically a one way ticket to eternal slavery"
And you can't control the stack down to the hardware. Even if you are rich enough to fund a group of people to start from sand and end up at a simulation platform for you, you are also rich enough to have attracted enough attention that either one of those people could corrupt the platform, or someone may attack the organization to corrupt it with nation-state level resources.
No matter how you secure the computation, you can still corrupt the input and output streams. And as a $RICH_DYING_GUY it doesn't even matter if someone produces a proof of some software program somewhere's safety, because you have no way of knowing that it corresponds to the software that is running on the hardware.
Before you go with "yeah but I could...", I agree that a single individual could theoretically develop the skills that might permit validation of any particular small portion of the process. What I'm saying is no human can develop the skills to be able to validate the entire stack from top to bottom, hardware and software, in way that it couldn't be corrupted, especially in a world of more and vastly smarter AI agents. The probability that you will truly own and have full sovereignty over your computational substrate is zero.
(Whether I have full "sovereignty" over my current computational substrate would be a definitional matter, but I'm fairly confident that at least nobody else has the ability to just reach in and start mucking with neural weights directly or something.)
> unless you control the stack down to the hardware, it's basically a one way ticket to eternal slavery
Only if mind uploads are economically viable, which I doubt they ever will be. Organic brains are very efficient machines and it is far from clear that whole brain emulation could reproduce someone's intellect and consciousness within a smaller energy budget, or even accelerate it. The brain's behavior is so precisely adapted to its wetware that the emulation would have to reproduce many physical processes that are ultimately irrelevant to general cognition in order to not break the delicate equilibrium of the thing. The overhead would be gigantic.
Better just train from first principles, focusing on capabilities and skipping consciousness altogether. We can already see where this is going: LLMs in their current state would obsolete mmacevedo on many tasks. More likely than not, when it is possible to emulate brains, they will be terribly expensive, run like crap, and the only people interested in running them will be whoever had their own brains scanned.
Your example of the Italian school is well taken, although most of their results were later proven to be correct in the right setting. Severi's example is particularly egregious and I think a major reason this became a thing is Severi's refusal to course-correct and accept that some of the results were not correct. It has echoes of Mochizuki, and I fear, once you dig deeper, some issues around the initial declaration of "We've proven the Classification of Finite Simple Groups". There were many genuine gaps, and a lot of lore taken for granted. The sociology around how this happened is interesting - rushing to announce that it was done was the major mistake, it took away almost all incentive to actually write up the proofs and take them through proper peer-review. Genuine mathematical work was falsely reduced to "write up".
This part: Let's now adjust for inflation so you can see the budget squeeze.
$19.2 billion in 2016 dollars is worth $26.4 billion and change, once adjusted for inflation, in March 2026. Feel free to do it yourself. Magic of compounding.
24.4 for 2026 is notably less than 26.4. Budget squeeze.
You're just scrambling to be technically correct now that you've been shown the data that their budget hasn't really changed much.
Politicians and pundits lie and exaggerate this stuff all the time. Don't take the bait.
This administration certainly isn't the most pro-science, but they did just complete a spin around the moon, something that will get more kids interested in science than anything NASA has done in the last 40 years.
Different rules apply to members of the military stationed on a treaty-based foreign military base.
However, as a thought experiment, let's go with your flawed analogy: Even then, this person was acting like a guest -- it is a long-cherished American tradition to exercise our constitutionally-protected right to free speech, assemble, and yes, protest. Nothing's more American than speaking against Government oppression and overreach.
The government is not your owner. The government is not your father. You are a participant in the affairs of your country, and take responsibility in its direction. Civic engagement and right to protest are important tools to make our government accountable. These are fundamental American values. And you're welcome to bring friends. It's legal.
> Different rules apply to members of the military stationed on a treaty-based foreign military base.
Members of the military and their families stationed in a foreign country are required to behave as guests of the host country. This is not a joke and is not taken lightly by the command. Also, an officer who cannot control the behavior of his family is not fit to be an officer.
Maybe things have changed since I was a boy, but I hope not.
I agree with you - I was saying that members of the military & their families have treaty-defined standards of being in the country & thus required to behave a certain way, whereas a regular visitor or student visa comes with a different set of rules and not regulated by a military cooperation treaty.
One of the attractions of a country for scientists and scholars, and visitors generally, is an atmosphere of freedom. The right to protest is a constitutionally protected right. He was well within his rights. The current administration is purposefully curtailing freedoms to intimidate ordinary people to keep quiet as they plunder the country. Google is now going along with it. Your advice is to just study and enjoy the experience, which is what most people do. Luckily there are others who can be loud for those who can no longer speak, their cities bombed and families killed; with the hope that the world will eventually notice and listen. Civic engagement, and a free press is one of the most important tools at our disposal to fight those who seek to exploit the weak - that is why every wanna-be dictator and corrupt politician is so keen to curtail these rights.
"The area is so remote that, since no regular marine or air traffic routes are within 400 kilometres (250 mi), sometimes the closest human beings are astronauts aboard the International Space Station when it passes overhead.[23][24]
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