9,839 karma · joined March 22, 2011
It's fun to be able to see the 3d effects on passing bridges, etc., and for large baselines on long straight stretches you can see the 3d structure of clouds in a fascinating way.
There's probably a quantification of this in some sense for specific classes of NP-hard problems.
What's interesting is that many algorithms (especially in cryptography) are explicitly designed to create those combinatorial edge cases. A SAT solver looking at normal problems that occur in life and programming will do an amazing job. A SAT solver looking at SHA256, not so much. In fact, arguable the science of developing cryptographic systems is the science of finding these exponential explosions that are resistant to heuristic approximations.
2. The vehicle was correctly identified by Flock as being the one flagged, and verified by the local PD that it was the one that was flagged. That said, they could have verified that the flag was still meaningful before converging on the vehicle.
3. This is a real problem and this is really the core of the oversight.
When the lawsuit over this is filed, it seems like 80% of the liability should attach to #3, and 20% to #2, and essentially none to #1. It's hard for me to see why Flock is even relevant to this discussion except to drum up outrage.
If I bought a book, made a xerox of the whole thing, and then sold the book to another party, I have committed a copyright violation that is in theory actionable. This is basically unenforceable; in theory if it came to light that I had a copy of it and had sold my copy then there is an actionable claim, but nobody is going to do this. But the friction here is high so we know that we can live with this, because nobody could possibly do this at a scale that would make a difference.
With pure digital goods the friction drops to zero. For a while friction kept up with technology; when CDs were first around, making a digital copy of a CD was just not feasible. You maybe had a 1GiB hard drive and could store a single CD on it. With mp3 compression becoming mainstream that math changed, but at least games and things like that, that were not easily compressed, were somewhat safe. CD-R allowed you to break this but was high friction. Same with DVDs when they were first around.
But now storage is no longer a concern, so all of that friction has disappeared.
Streaming and on-demand content gives a possible solution to this, and that's why everything is moving in that direction -- trying to increase the friction of creating durable copies of the media. As soon as you allow backup of the content (as in the GP's post) then everything breaks, so that's the thing that you (as a content creator or distributor) have to fight.
Blockchain does not solve this problem.
*Deleting* data (and its cousin, *moving* data) is a nearly intractable problem. How can you verify that someone no longer has access to data that you gave them?
The best we have is to have some sort of ownership token that is maintained in a shared store, and build a requirement that possession of that token is required to use the data. Even this is practically nearly intractable; you have to have some sort of "trusted" hardware or software that is responsible for validating the current possession of the ownership token before using the data.
Physical media is another way of trying to solve this problem, especially if the physical media can somehow be verified and is exfiltration-proof.
[1] I say "technology" here but really I strongly suspect that this is actually impossible given reasonable theoretical assumptions around what data means.
The question of how LLMs (and "LRM"'s, an unfortunate and by the article's own admission, already outdated term) accomplish what they accomplish is fascinating. The question of whether they reason is meaningless. Most of the article is about the latter, with tiny tiny tiny bits of the former.
I don't know whether you are saying that I have taken it out of context or a more general statement of how other people have interpreted the quote.
To me it is quite clear -- the question of whether machines can reason is just as meaningful as the question as to whether submarines can swim, which is to say not at all meaningful. Can a submarine accomplish by other means what a fish accomplishes by swimming? If so, then what are we talking about?
Can an LLM accomplish by other means what a human accomplishes by "reasoning"? If so, then what are we talking about?
Dijkstra said[1] "... the question whether computers can think. The question is just as relevant and just as meaningful as the question whether submarines can swim."
I don't see a clear demarcation of the things that only "reasoning" can accomplish and can't be approximated or imitated by other methods, and so I think the question is simply not meaningful or relevant.
[1] https://www.cs.utexas.edu/~EWD/transcriptions/EWD08xx/EWD867...
In addition to their use as tools for pure math, they are also used for software verification, where adversarial examples could have real-world applications in verifiable supply chain attacks.
Metamath (and specifically Metamath Zero) is formally verified.
The big Cantorian leap that we make is when we use the diagonal argument to argue that the rationals are countable. All the real construction techniques (Dedekind cuts or Cauchy sequences) effectively only yield the computable numbers, the real numbers outside of the computables are inherited from the diagonal argument rather than being foundational to the construction. I mean, this is trivially true because constructions are constructive.
I disagree that area is tethered to measure theory; I certainly learned about areas in geometry long before I ever heard of anything with measure theory. Measure theory exists to tie up some of the horrifying poorly behaved functions that increasingly wily mathematicians invented to break our notions of area and continuity. But we have better tools now for dealing with those that don't involve measure theory so there's no reason to ever hear the phrase "almost everywhere" or "subadditive" ever again.
To back it up to your closing and my main point -- the constructive numbers are way closer to the way we work with numbers because all numbers we ever deal with, even abstractly, fit this definition much better.
pi and e and sqrt(2) are real numbers and not rational, to be sure. But they are computable! Computable just means that they are arbitrarily approximable. "approximate relative to what" is that whatever criteria defines the number. You can't represent the "true" value of a non-rational number in the rationals, but you can prove that the error of an approximation is (rationally) bounded above and below, and you can have another approximation with a tighter bound.
Rational numbers are already infinitely precise relative to other representations -- finite decimals are another representation that is functionally equivalent to the rationals, but even a simple rational like 1/3 does not have a finite decimal value.
You can prove all the interesting theorems with computable numbers and rational/decimal numbers. You don't need the real numbers because you can't name a real number that exists and is not computable, BY DEFINITION! No mathematical construction can define a real number that is not constructible. These numbers are useless and there's no reason to continue even in abstract mathematics to pretend that they are useful because we have the formalisms to ignore them.
Doing calculus with computable numbers is totally possible and you get all the continuity you need. You need to drop the Lebesgue formulation of the integeral and either use a Reimann integral or the gauge integral (Henstock–Kurzweil) if you need a well-behaved integral in the face of very poorly-behaved functions, but in physical reality these don't exist and in abstract mathematics they are rarely of interest and the gauge integral is as robust as Lebesgue without all the measure theory nonsense.
Intuitionalist analysis and calculus are very well established; the only thing you can't do with them is nonsense like showing that integrating over the characteristic function of the rationals is zero (who cares) or showing that you can break a three dimensional sphere up into three pieces are reassemble them after translations and rotations into a larger sphere (obviously not true).
This isn't fair for what quantization means in reality, but I'm just pointing out that you don't have to introduce the real numbers to get physically meaningless quantities.
But when we say things like "the rationals are discrete" or "the computable numbers are discrete" these are very specific claims in the domain of measure theory, a theory which yields almost nothing of value except endless paradoxes and naval-gazing nonsense. Similarly when people say "the rationals are countable" and "the computable numbers are countable" this is taking for granted the Cantor notion of measuring cardinality by bijective correspondence, once again, a theory that yields nothing of value except endless paradoxes and naval-gazing nonsense.
In the practical sense the rational numbers are quite continuous -- between any two rational numbers there are an infinite (unbounded) number of rational numbers -- there's no notion of a "leap" the way there is with the integers. And any useful number can be approximated arbitrarily closely by rationals.
And for computable numbers there's even less of a gap. With rationals you can only approximate. But you can have a computable number that is exactly equal to the square root of 2, because a computable number is the algorithm by which you form arbitrarily close approximations. The square of that computable number is itself computable and is exactly equal to 2.
What do "real" numbers buy you? That is, what do you get for the trouble of building your formalism around numbers that are not computable? Basically nothing.
And if you're worried that sticking to the rationals and the computable numbers is too much of a concession to "physical reality", rest assured -- the rationals are just as unphysical as the real numbers because they are continuous already, and physics does not give us the power to measure the difference between two sufficiently precise rational numbers just as it barfs when you throw "real" numbers at it.
That is, they can hold such a lunch, but they can't pocket the money personally or even have the money contributed towards their campaign. Pocketing the money personally is just bribery, having it contribute to their campaign would violate the contribution limits (typically ~$10,000 per election max, though less than that in reality because the limit is split between primary and general).
You're right to be slightly suspicious because these lunches do exist. But they don't go to the campaign or the candidate, they can go to PACs and SuperPACs or to the party. In tern, PACs and SuperPACs cannot give this money to the candidate or the campaign (same limits as above with higher reporting requirements) and cannot coordinate campaign messaging.
This is not to say that corruption doesn't exist -- just that this simplistic form of it does not exist. You'll have to dig deeper than looking at lobbying activities to find the actual corruption, and it's usually masked in revolving door arrangements, speaking fees, and bulk sales of vanity books. But none of that can go through the typical lobbying system because it's too tightly regulated and tracked.
Mostly because those things are directly illegal. Lobbying organizations (and PACs and SuperPACs etc.) are very limited in what they can provide either as direct monetary contributions or in-kind gifts to a candidate. The restrictions here are basically the same as those on an individual, but usually with more strict reporting requirements and lower limits.
The marketing aspect is the only thing that they can legally provide, and that's less a lobbying function than a PAC function, and they are not allowed to coordinate with the campaign or the candidate on this.
The core reality is that cloud infrastructure is becoming commoditized, and substrate-independence is becoming not only possible but the default. So companies looking for things like lower cost or better customer support are looking around and seeing that smaller rising competitors are going to be a better option. Compliance with local regulatory regimes are going to be a factor as the EU continues its efforts to push European companies towards using EU infrastructure.
For the first (cloud vs. non-cloud) it's clear that cloud has some advantages because you don't have to manage hardware.
For the second (AWS vs. other-cloud), at least in my experience, AWS is simply the best experience available. If anything the other cloud providers go out of their way to offer special deals and cozy customer relationships to try to get customers to switch, but AWS is still the gold standard in availability and uptime and ease of use.
The gap is narrowing as the field becomes more commoditized though. And I think that's what we're really seeing here. As things like k8s get more common, solutions are becoming more and more substrate-independent, so companies hunt for smaller, more local, cheaper, ambitious alternatives. Everyone is scared of vendor lock-in so it's getting harder for cloud providers to offer distinguishing features.
But even here, in the Chomsky sense, LLMs clearly exhibit deep structure because they can write at length in an internally consistent manner. Importantly, early generations, GPT-2 and even GPT-3, did not definitively have this property; roughly, an object that was green at the beginning of a paragraph might not still be green at the end of the paragraph. This was strong evidence for lack of a world model.
Current LLMs do not show this behavior. We cannot prove that LLMs have a world model, in fact, their architecture seems to rule it out, but looking at it from a linguistic standpoint, they produce language in a manner as if to reflect a world view. That is, we cannot easily falsify the statement "LLMs somehow represent a world model"; and current examples of "disproving" their world view are so convoluted that even humans do not appear to (observationally) have a world view either.
I'm not making a claim as to LLMs having genuine deep structure or consciousness or anything like that. I'm claiming that we can't rule out current or future capabilities or make structural assumptions. Yes, they generalize from their training data, but unless you can make very specific claims about the kinds of things that they _cannot_ do, I can't take this statement as particularly compelling.
You seem to believe, on a more fundamental level, that LLMs are simply not capable of producing text that has deeper connections to itself or represents abstract thoughts. In my opinion, 99% of text written by humans does not show this, just as 99% of text produced by LLMs does not show this, but both have the capability, and I don't believe that LLMs are constrained in such a way that they can never do this.
Obviously language and the connection to human thought is more subtle than this; I think we all have a rich inner life. Just from an external perspective we can't observe it; all we can see is the token/phoneme stream. I'm just saying that it's a mistake to try to criticize LLMs on this basis because it's hard to see how the same criticism would not apply to any system (like humans) that generate language.
From an external standpoint, talking to another human, it's like the other human says one word and then says the next word. That's just how language works. Humans look like "glorified autocomplete" from this perspective.
I mean, looking at the time evolution of the state of the universe, one could say that all of physics and creation is "glorified autocomplete" to posit a next state of the universe given current and past state.