Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be.
Tech companies are as much the topic of this post as AI, I think that's the immediacy.
To a significant extent, the pursuit of mathematics research is a pursuit of human understanding of mathematics, without knowing where it might lead, or whether it might lead anywhere at all. I don't see how the motivation for that goes away on its own, but the institution supporting it is certainly threatened by the potential loss of grant money and graduate student applications.
> Does mathematics still have a practical impact without humans in the loop?
There's a single answer to that question: yes, math very much has an impact without humans in the loop.
Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.
We're way into diminishing returns in matrix multiplication, and being clever about ALUs and cache layout is likely to dwarf any asymptotic improvements you're going to find. Any better examples of improvements in the last decade?
The main situation I can think of where better calculations have a really visible effect is video and image compression, and that stuff is very far away from mathematical proof territory.
Wow that's a terrible paraphrase! I asked about algorithms where recent/ongoing improvements were important and they already replied with a list.
If you tell someone they can't use a matrix multiplication with better asymptotic performance than n^2.3755 from 1990 they're going to shrug and not care.
As the US has offshored manufacturing, the number of patents issued for those processes has fallen. Innovation occurs where the foundational understanding is applied; they arise from a desire to do the required work more efficiently.
Similarly in math, attempting to solve a problem leads to new questions. IF you actually do the work.
You need to have done enough of the work to know what the correct next question are, or you need to rely on AI for everything.
so you're 100% sure that AI will solve every intellectual problem in the future, since as long as that's not the case, it's us who need to ask the questions. I don't know man, I wouldn't bet on that. What if we end up being wrong and then there is not research community?
I don't understand what you're proposing then. We can ask AI to solve practical problems of interest (making a computer faster for instance), but I'd say no one really believes that this is an unlimited resource. At some point we'll reach a plateau, and then AI will be an important tool but to continue advancing we'll need someone to ask the right questions.
Isn’t the implication that the vulnerability had already been found and exploited instead of reported to Google, because its value to Google was so low? Whoever found it originally had more incentive to sell it on the grey/black market. Or is the incentive structure truly different for vulnerabilities discovered to be already in the wild?
Some exploit hunters sell strictly to the grey/black market to avoid opsec issues. If you're selling on both, you're more likely to be identified by both.
It’s Foucault’s interpretation of the panopticon. If we know that we may be watched — and punished — we self-police into following the norm, even if we do not know when we are being watched or that someone is necessarily monitoring us individually.
When I was a kid in the 80s none of this was an issue and I was free to roam. Starting in the 90s this became an issue and not only will parents not let their kids roam but the kids themselves have less interest because the norm is to stay in or only go out when supervised. You know you are doing something slightly wrong. It only takes occasional reminders like this to reinforce the rule, once established.
Same, this is like blogspam in the days of old that doesn't add anything to the original content and is just there to generate revenue for this site. The linked posts are better and per HN guidelines the toplink should probably be changed to one of those.
This line of thinking diminishes the real struggles autistic people face. Not everyone is autistic, and it's not just a quirky set of traits. I do believe society could be better arranged for people who for whatever reason don't conform to the overculture norms, so we could talk about disability along the axis of how society privileges or disadvantages certain individuals.
The concern is that autism as a rigorous category may be useless, but that doesn't mean that autistic people are suddenly neurotypical -- a term that is more politically than scientifically oriented. People who are not autistic broadly are allistic, to be precise with language. They may be neurodivergent in other ways.
I'm reminded of an anecdote I heard once from a psych(ologist/iatrist?) that goes something like: if you think you hear voices in your head, but the voices tell you to go to bed on time and drink plenty of water, you don't need a diagnosis/treatment.
The point is that a lot of things, when it comes to humans and their brains, is judged first based as to whether or not it negatively affects your life. Think of how we define addiction.
General doesn’t mean it applies to literally everyone. If autism turns out to be a specific condition that is e.g. the result of abnormal neuron pruning during early development, it could have a wide array of symptoms, but that understanding may someday lead to genetic treatments for sever cases, better early childhood interventions, etc.
I do think that the current ASD umbrella as written in the DSM is so broad as to seem nearly meaningless when take in isolation. It’s not meant to be in isolation however, it’s defined first and foremost as a disorder, so the symptoms need to cross some threshold of tolerable. It’s also associated with a growing body of research as to how nervous system development can cause related clusters of symptoms.
Is autism as we understand it scientifically accurate? Probably about as much as anything hovering in the intersection of social sciences and medicine. It does have some predictive power. If you meet the diagnostic criteria for autism you are likely to have certain comorbidities for example. Having certain autistic traits are good predictors of certain outcomes later in life. And we do have better therapies especially for young people than we have in the past.
The fact that people can have non-overlapping clusters of traits and still be autistic does seem problematic. It may not be the right model. Just my $.02, I’m not the autism researcher in this convo, but I am autistic :)
> But different autistic people struggle with different things, in different ways.
Different asthmatic people struggle with different things, in different ways too, but it's useful to have a general diagnosis umbrella to cover those who have asthma even though symptoms and effective treatments may vary.
Work is ongoing to get better defined categories for autistic people, but for now at least we've got a category for people that match a broad set of traits/symptoms/challenges to work from.
The problem is that the set of problems is very broadly defined, changes over time, varies from person to person, it's often impossible to obiectively test.
Can't it be that a neurotypical person is bothered by some autistic triggers? Would that make them neurodivergent? How many of those triggers do you need to have to be under that umbrella? 1? 5? 20?
It is indeed called a spectrum, and I think it gets so fuzzy at the edges that the only way to define where it starts or ends is purely arbitrarly chosen.
It's a bimodal distribution. There are people with few of these traits lightly, and people with many or with a few severe ones. Not so many in between. This already makes it an interesting line to draw.
No so different things, and not so different ways. The "if you met one, you met one" is overplayed. Yeah, they have different interests and might have different comorbidities, doesn't mean they don't just have different core issues that are merely expressed differently (e.g. hates jeans vs hates wool sweaters or hates noises, but underlying both is sensory sensitivity).
The fact that they don't is why diagnostic tests exist and work.
That's a good example: they hate certain things, and are ok with others.
Depending on what you "hate" your life and disability can vastly drastically. Be it eye contact, clothing, certain foods, or the inability to change your routine or environment at all, or to even leave the house alone.
>The concern is that autism as a rigorous category may be useless, but that doesn't mean that autistic people are suddenly neurotypical
IDK. I'm diagnosed as autistic, but I've become a bit less attached to that label in recent years. Like, I do struggle with eye contact, excessive noise, and social situations. I'm not going to say that I'm just a normal guy, but I do think that there's a wide spectrum here that encompasses everybody. I don't buy the idea that autism is some special category of people that are totally unlike neurotypicals. Instead, it's just one side of the spectrum, with neurotypicals on the other end, and an ambiguous group in the middle[0]. I think that once society becomes more accepting of neurodiversity, we're going to stop getting so hung up on labels like "autistic" and "neurotypical" and accept that there's a lot of nuance in the human condition.
[0] In reality, this spectrum would be multi-dimensional, but I'm choosing to describe it as a 1D line for illustrative purposes.
When I first considered my condition, I was looking around and was trying to mentally label people as neurotypical/neurodivergent.
After a few years, I started labeling more and more people as neurodivergent, because I could notice more subtle hints. Now, I instead just try to figure out how far on the spectrum everyone is, to know how the relationship dynamic will be like.
But that's the thing, sight and blind can be easily defined.
"Autism" can't, most of the people live undiagnosed, many mask the symptoms unknowingly, specialists can't even tell exactly if someone is autistic or not, many people are misdiagnosed, or diagnosed as neurotypical by some specialists and neurodivergent by others.
I don't think the ratio is that far towards neurotypicals as it was previously believed. I think that, as most things in life, it's a gaussian distribution.
I’m not sure why you were downvoted. I have to use Windows for work. The barrier to entry is simply lower for many system administrators and users alike. The homogeneity of a Windows rollout is extremely attractive. You are going to have a hard sell getting your accounting team and receptionist onto Linux. Your developers will complain and make do. I love complaining about Windows!
Their sandbox just sucked, the agent found a route through artifactory which was also connected to the internet. After the agent breached it, they put it back in the patched sandbox and it found its way out with another artifactory exploit — which was still connected to the internet.
No attempt was made at an actual air gap as far as I can tell. OpenAI is dangerous and irresponsible and doing a lot of pearl clutching over how their cybersecurity agent is doing cybersecurity things.
They cannot scan the books then resell them or donate them under current US copyright law. It’s not clear to me that they could warehouse them if they wanted. In the recent Bartz v Anthropic case the judge ruled this destruction as legal, saying
> The print original was destroyed. One replaced the other.
So that there was still only one “copy” of the book. This is in compliance with the DMCA. You can make a personal digital copy of a work but then you cannot resell the hard copy and keep the digital one. Same principle applies here.
Nowhere in this description did it require destruction of the physical book. This is being done because it's easier to scan a shucked book, and this explanation is circulating because it's easier to blame it on the law and that pesky meddling government.
"Here, every purchased print copy was copied in order to save storage space and to enable searchability as a digital copy. The print original was destroyed. One replaced the other. And, there is no evidence that the new, digital copy was shown, shared, or sold outside the company. This use was even more clearly transformative than those in Texaco, Google, and Sony
Betamax (where the number of copies went up by at least one), and, of course, more transformative than those uses rejected in Napster (where the number went up by “millions” of copies shared for free with others)."
"For the print library copies that Anthropic purchased and then converted into digital library copies, Anthropic already enjoyed entitlement to keep the copies in its library. The purpose of the copying was to keep them in its library but with more favorable storage and searchability properties. Copying the entire work was exactly what this purpose required. There was no surplus copying. The source copy was destroyed.
The third fair use factor favors fair use for the purchased library copies converted from print to digital."
Why would a company keep the hard-copy around at the risk of it being inadvertently given away, resold, etc.? It's a huge outstanding liability given that the illegal copying of works -- the other part of that case -- is what they settled out of court for some huge amount of money. Destruction is the only thing that makes sense.
I'm old enough to have been around when DCMA legislation was under discussion. Many people were dead-set against it and raised concerns over matters exactly like this. In Rainbows End (2006), Vernor Vinge wrote about a similar scenario where a robot went through the university library shredding books, and scanned the shredded pieces to recombined them into a digital archive.
Anthropic may be doing shady things and may have even done this on their own recognizance, we just don't know. As it stand, this is 100% a consequence of US copyright law, much of which was written by large corporations to protect their own assets.
I agree fully that it makes logistical sense. But it is not a legal requirement, and they should not be permitted to use that as an excuse to wash their hands of their own decisions.
I think I agree with you in spirit. I don’t like what these companies are doing, and Anthropic’s actions can for the most part stand on their own. Copyright law is just a special interest of mine, and I do think it’s important to recognize what external incentives exist and what they prioritize. Because other companies will act in similar manners under the same incentive structure, and the problem is going to cascade and magnify if it hasn’t already. There are active court rulings setting precedence for this behavior - take note!
The ruling was that what they did was within the law, not required by law in every detail. They cannot resell the copies. I saw nothing in that ruling that required their destruction, because it is not required.
A person can digitize their own books without destroying the original. So can Anthropic. They are choosing to destroy the books for easier scanning and trying to palm off the blame for it.
The ruling was that training is fair use but still they can't make unauthorised copies to enable training. They had to pay a huge fine for each unauthorised copy. So now they aren't making unauthorised copies.
1 point by jonhohle 0 minutes ago | edit | delete [–]
You’re missing the point. It doesn’t require that they destroy the book, but it precludes them from giving it away. It’s their property, so they can choose to store it, but that has real, ongoing cost and may eventually leave unusable books anyway due to fire, pests, water damage, etc. if they’re not maintained properly.
This is why we have hierarchies of abstraction. Pretty much every field of mathematics relies on constructing notations, models, and other tools to simplify things in a way that is verifiable. LLMs rely on the same basic technique, they can just pull from a wide variety of these abstractions at once. So far we've been able to understand their proofs just fine. Computer-assisted proofs in the past that relied on brute-force is where we have run into trouble. We cannot reason about millions of possibilities at once, and we had to trust that the computer program that analyzed them was correct, which is a really hard problem and leaves humans fairly unsatisfied. I think we are actually progressing in terms of understandability in computerized proofs.
You deploy an application that ostensibly has the desired capabilities but it fails at scale, or the architecture is not extensible to add new capabilities or fix bugs. Those are expensive mistakes and in safety-critical domains could be deadly.
The thing is I've worked on plenty of code like this written by humans. AI just accelerates the process and puts this type of code within reach of more people. It could be seen as a step backwards in good software engineering practices we've painfully learned over the last two decades. I see it as a cycle repeating itself in a new iteration, with the hope that we'll end up with still better tools and processes in another few years. But I agree it can and will result in real harm in the meantime.
Tech companies are as much the topic of this post as AI, I think that's the immediacy.
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