The "top layer" of maths being this is one thing. Now imagine another layer of this. Then another. Then another. Then another.
At one point intuition helps to build out usage of the math itself. See stuff like "oh I can do rotations through matrix multiplication"-style ideas.
It is helpful for us to be able to reach for those tools quickly. The more tools that require advanced prep to use, the less we'll be able to use the results in easier contexts. Everything will be hard
Of course nothing really prevents people from looking for the simpler tools and proofs. Lots of math stuff starts off complicated and gets simpler.
Can people please make something with the tools they are pitching before putting it out in the wild?
Not the stupid useless field tests that no one uses. Make a real thing that gets used by more than 5 people. Then consider whether your thing is actually useful. Then maybe put it out to the world
Perhaps you don't want to waste your time or tokens or whatever REing a thing and instead can use something someone else has distributed to solve the problem in a general way
It's unfortunate because like... in theory if you apply the right kind of debugging philosophy you can use this tooling to help you move through the work a bit more easily.
But just kinda randomly trying at various reasoning efforts reminds me a lot of hearing people just randomly replacing various libraries or code snippets with stuff found on stack overflow. No real theory of the system.
There's not even much of an excuse, cuz you can "just" sit there and type "why?" or "why not?" over and over into an agentic chat session and probably get things working quite quickly. Principled debugging is state space elimination for the most part!
I think the important idea here in Terrence's hypothetical is that in the hypothetical there is no hill-climbing. The AI shows up with a thing and says "we don't need to hill-climb for years and waste time, here's a thing that I know will work".
And maybe it does a single finalized clinical trial.
You end up with this miracle drug (supposedly!), but no understanding of why it works or access to the iteration that would lead to that understanding (and increase in confidence that it doesn't cause people to drop dead anyways).
I think the medical example is a bit obtuse overall because "proof nobody understands for an open problem" isn't "miracle drug we are too scared to use". But understanding things feels useful and good.
> You end up with this miracle drug (supposedly!), but no understanding of why it works or access to the iteration that would lead to that understanding (and increase in confidence that it doesn't cause people to drop dead anyways).
That is literally how all drugs worked for almost all of human history--nature gave us the compound in the form of a plant or other natural product; a brave, stupid, or desperate human consumed it; and then we watched what happened and the survivors learned. It's obviously good to have more understanding (more survivors!), but even now we often don't.
Most human endeavors are empirically grounded--we think an action will succeed not because we understand exactly why, but because it succeeded many times before. Math and CS are the weird exceptions, and the intuition that people with that background have for other fields is often bad.
You interpret that wiki list of 154 items as proof that we know nothing. I interpret that as "oh wow, only 154!" That list feels pretty short, but of course it's just a wiki list.
I do get what you're getting at. I just feel like for every bit of drug that is just dumb luck we have a good amount of iterative processes.
I agree that you often find effects before understanding causes (I think that math also exhibits this! Many endeavors are about finding existing structure that we sense to be there but are unsure of).
Just... well... if you go down the "we don't understand anything anyways" path too much what makes your work different from alternative medicine?
I certainly don't mean to suggest we know nothing, and our current imperfect level of mechanistic understanding gives a much better hit rate than eating random plants. I just mean that when the understanding fails, we're happy to use the drug anyways if the clinical trials pass. The confidence comes from those human trials, and the mechanistic insight is more about probabilistically improving our screening before that.
> Just... well... if you go down the "we don't understand anything anyways" path too much what makes your work different from alternative medicine?
"Alternative medicine" in the pejorative sense is medicine that doesn't work, i.e. that would fail the clinical trial. That seems like a different question from whether we understand why it works.
The idea that we could know that something works but not why is almost inconceivable in computer science ex ML. That's the default state of most applied science though, consistent with your observation that effects are often discovered before causes.
the reason why clinical trial exists, is to prevent reward hacking. either by organizations or LLMs. the reasoning about why a drug works is usually post facto discovery (if that happens at all). the R&D environment around drug discovery is hilariously lacking (my wife works in this space. sometimes my mind just blows hearing some stories.)
if the model comes with a ridiculously shaped drug that no human could understand. you could basically put through the clinical trial process (mouse -> apes -> RCT with humans.) and decide whether we want to continue or not.
Is a basic webcam really able to read text at that angle for the “what is this word” example?
I wasn’t sure if any of this was real and that example looked extremely fake to me because I had a hard time believing the device being able to read text from that distance.
In that demo, the lightbulb sits on the desk, less than a meter away from the page. What feels implausible about this setup? This is kind of thing you can do with your smartphone today.
So is the demo real or is it smoke and mirrors? Could you have pointed at other words and have it work?
(I think I overestimated how much of an angled shot it was the first time I saw it, on top of how easy or hard turning your finger into “actually capture this text”… but you’re totally right that in principle a camera at a non agressive angle can capture that text)
(I like this overall concept a lot! Cooking is the right example, voice interfacing’s 96% use case is basically “my hands are dirty but I must use computing”)
It doesn't feel implausible, it is implausible, because your idea would require either a camera with good optics pointing in a specific direction, which means it's no longer a set-and-forget lightbulb, or some kind of 360 view more-or-less 3D camera to cover all the angles, which probably isn't going to have the resolution to read angled text at that distance.
At the very least it's going to have a range limit on that feature.
And there's a projector in there too.
In something smaller than a smart phone.
It's a great concept, but not a very workable one. Kitchens get steamy, tables can be huge, and management will want to use the cameras for user surveillance.
The author doesn't come out and say it, but I don't think there's anything inside that lightbulb in the pictures and videos.
The actual webcam and projector and Mac are not shown.
If you look at the map example, the shadows from the hands go almost straight down. The projector is not in the lightbulb, it is above the table out of frame. Probably the webcam is up there too.
Which of course greatly diminishes the "cool" factor.
I appreciate how you used the light bulb glow as a "prop light" (in stage lighting: a lamp the audience sees but doesn't actually illuminate the scene) to sell the effect in your demo video.
Seems simple, but it really brought it up. Many folks would've stopped after getting the projector working. I should've known, given my experience with projectors, and it fooled me too! :)
"A bad design with good presentation is doomed eventually. A good design with bad presentation is doomed immediately."
This is pretty funny to see, because every financial firm interview process I've seen involves some variant of solving a bunch of stuff with min heaps.
Never before has a set of engineers been more primed to solve a problem
By living off grid they are stress testing things so that when things are tougher (perhaps temporarily!) things have a higher chance of chugging along
And obviously, like, they go to places and talk to people and buy equipment etc.
There’s a whole gamut of failure modes for tech from “total civilizational collapse” down to “cell tower is down”, and time periods from “forever” down to “a couple of days”
People doing this sort of lifestyle but sharing findings and ideas and ultimately maybe pointing out how more can be done with less is part of us building up knowledge together isn’t it?
These people aren’t completely offline even! They blog and post online!
The problem is that one a person writes a 60 page proof in theory that person has spent an inordinate amount of time on the proof and can answer questions, describe some insight, etc etc.
If a random person is given a 60 page proof to digest and not the author, those hidden insights that _aren't_ in the paper might be completely inaccessible. Maybe the AI will "just" be able to provide the insights. Maybe. But pedagogy is tricky work, and despite these AIs being able to do all this fancy math we can't get them to write good cover letters yet, so....
Ultimately we might be left with just a bunch of intellectually unsatisfying proofs. This means way less drive to simplify the proofs or rework them.
End result: we generate a layer of "less efficient" mathematics, that won't get built upon. We will not actually have any shoulders upon which to stand.
But why should process of discovering mathematical insights be any less attainable to AI models?
The concern is being raised without evidence, because the evidence points to the gap simply being frontier models have just started to be able to get a raw proof out. Why, given existing progress, should we expect them to be unable to distill insights from those proofs?
Certainly this even more likely doesn't matter at all for applications: if I can send a radio signal further because my AIs design it a certain way, that's an unambiguous result. Which is really the next step here: turn a proof into a "mechanical" application.
According to Scott Aaronsson, OpenAI set their agents on 8000 different problems, and got 372 final proofs. Even spending twice the original effort on simplifying and reworking those proofs so that they do not "feel like something written by someone who’s on psychedelics" would only increase the compute by less than 10% (assuming all the agents had a similar token budget).
The fact that they did not do so can only mean that either (1) their agents currently lack the capability to do it, or (2) OpenAI are completely indifferent and do not care in the slightest if the proofs are understood or not.
> The fact that they did not do so can only mean that either (1) their agents currently lack the capability to do it, or (2) OpenAI are completely indifferent and do not care in the slightest if the proofs are understood or not.
Come now, this is kind of unreasonable. When you're working on a new technology, you first get the ugly, inconvenient-to-use prototypes functioning with the core new thing you need; then you work on packaging it up into a format useable in production. I'm sure the very first digital camera sensors weren't very useful for photographers either; but it isn't really even possible to build the rest of the technology required to turn raw output of a digital sensor into something a professional photographer can use until you have the raw output itself.
The research is still on going on the raw output; getting things to the next stage, where the results are widely useable by professional mathematicians (and then on to engineers and scientists to whom the results would be practically useful), is a whole new research area.
Seems like you are just subscribing to the first option I gave, "their agents currently lack the capability to do it", but saying you think they will be more capable in the future if they can move away from the inconvenient-to-use prototypes after more research. Thinking it might be possible in the future is not in disagreement with anything I said, so I am not sure what you thought was unreasonable about my description.
Imagine someone looking at digital camera researchers showcasing a ground-breaking new sensor, and reacting by saying "Well obviously they're completely indifferent and do not care in the slightest if their work is used by real photographers or not."
Like, "Orr... maybe they care a lot, but haven't gotten to that part yet?"
You are conflating the two options with each other (lack of capability vs indifference). One of them is true, not necessarily both ("or", not "and"). I did not claim a lack of capability was the same as indifference.
They claim each result used three hours of compute on average. Even spending significantly more on simplifying and reworking would delay the release with a single day at most. If avoiding such a minor delay took precedence over (2), I think "indifference" is the correct term. It has also been a while since the release now, so there is ample opportunity to post follow ups if time pressure was the only concern.
Why do that when they can spend more hours extending QRH to a proof of the full Riemann Hypothesis? The opportunity cost of digging up small potatoes is the whole enchilada.
From launch until 2007, the PSP was capped at 222MHz. After firmware 3.50, the full 333MHz was unlocked. The GoW games were released after this, so I assume they used the full 333MHz.
At one point intuition helps to build out usage of the math itself. See stuff like "oh I can do rotations through matrix multiplication"-style ideas.
It is helpful for us to be able to reach for those tools quickly. The more tools that require advanced prep to use, the less we'll be able to use the results in easier contexts. Everything will be hard
Of course nothing really prevents people from looking for the simpler tools and proofs. Lots of math stuff starts off complicated and gets simpler.
Just important that this is still a goal in mind
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