It's like 2.5D, maybe like 2.75D or so. Technically, every map in vanilla Doom is a 2D map, with various "sectors" in the map having height; they're rendered in a sort of pseudo 3D, but crucially the map will never have one floor about another¹. I don't think I'd argue the 2D maps technically make it "not 3D", though.
However, Doom also renders textures using an algorithm that sort of paints walls as like vertical lines of sorts. The exact algorithm it uses makes it hard to look up (to pitch), and I think impossible to roll the camera. See <https://en.wikipedia.org/wiki/Doom_engine#Rendering> — it has a good animated graphic of what happens if you do look up, and the differences between the output of Doom's software renderer's algorithm and something actually rendering 3D.
¹modern ports have ways to accomplish this, and even before there were direct ways of doing it, clever map layout and instantaneous teleporting can get pretty close.
Raycasting (in gaming, some graphics folks just use it as another term for raytracing) means to fire a ray for each column of the screen, identify where it collides with a wall, and use that to determine what to render for that column - it's basically per-column raytracing.
DOOM's engine instead uses a BSP tree so that, from any position, you can determine which walls are on-screen instantly just by walking the tree - the nearer walls appear earlier in the traversal than farther walls. It's still column-based (it tracks whether each column has been drawn and won't draw further walls behind an already drawn column, and stops drawing once all columns are filled), but there's no rays cast.
A few years ago I seriously contemplated making a game using software rendering, in part because the only target was SDL. I actually got a 3D engine running 2K@60Hz with HL2-level scenes, with the CPU basically idle, so it's not a terrible idea.
(Then LLMs started taking off and I decided I needed to reskill out of the industry, just in case)
When you're calling a function, you're putting some things into the function... You have to get the things first before you can put them in...
Why didn't it evolve like that in the first place? Is it a byproduct of mathematical notation? If so, I wonder why mathematical notation evolved that way in the first place...
Forth (or Postscript by the way) works exactly like that, but writing the function first also makes sense in functional programming, specifically when you care about currying functions: writing "f(g(h(x)))" (or "f g h x" or whetever) makes more sense, since you are not supposed to put all expected arguments at once.
Do you have to write a function first before it is referenced in PostScript? (I did a lot of PostScript programming in NeWS once - but it was ~35 years ago...)
They wrote which things they're concerned about in the article. They included things like "Capitalists say it will replace workers", which, if you're a magazine intending to provide your own perspective, repeating the capitalist narrative but then inverting it and saying it's bad does, I think, suck as a narrative.
I'd agree with you if that was in fact the only thing they mentioned... but there was much more nuance and content than that in the article if you read the full thing.
For example, this raises the issue of a drop in quality and a change in publishing model - which is obviously quite different than parroting back an existing argument and saying its bad like you are suggesting.
> Even if you lost 60 percent of your readership, you might still make a lot more per story, because you can pump them out in seconds.
It looks like the spent $20 on writing the actual papers.
If they actually wanted to do good for the world, they wouldn't have released these as the slop grenades they are.
In their current state, they are actively damaging the mathematics community.
It shows a lack of respect and care for the impact that their technology has.
It shows that they cannot be trusted for things like private data, AI safety, and company partnerships.
In math/science, repeatability and review are critical to the process.
The right way to handle this would have been to work with the mathematics community to co-develop and create meaningful proofs rather than slop grenades.
If they proceed in the current state, we'll just get a bunch of spaghetti math that won't do anything for helping people build an understanding.
Maybe some day, we won't need people to understand things, but that's certainly not the case at the moment, and likely won't be for several more years.
Perhaps this is projection, and the staff at OpenAI doesn't understand their work anymore? Not a great sign regardless.
> The right way to handle this would have been to work with the mathematics community to co-develop and create meaningful proofs rather than slop grenades.
The mathematics community can finish the job OpenAI started. Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
They didn't just "start" it though - they released slop papers.
That's finishing it - not starting it as far as scientific publishing is concerned.
> Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
Not exactly - but that is part of it.
I think what would have went over better is:
1. Immediately announce a solution has been found.
2. Do not publish the solution.
3. Put out an open request for anyone with experience in the area who wants to get involved to help collaborate on a construction and human-comprehensible paper. Accept anyone who can demonstrate potentially useful work/experience in the field/problem. Share the solution with them after they sign some kind of NDA that they won't independently publish or share the solution/work.
4. Work with people until a paper is ready (I mean actually ready - not the kind of slop that they released).
5. Publish. Include names of everyone who made meaningful contributions to the paper (not just the proof).
EDIT: Notice the incentive with my proposed second path is that it gives OpenAI an incentive to improve the interpretability of its proofs. This is a good thing! The maths community would be thrilled to actually gain understanding from such releases, and OpenAI would be happy because they could more quickly and independently publish their results. At the moment the "value" of their mathematics research "product" is low because of the lack of this interpretability, and this current approach is simultaneously destroying the opportunity value of the community as well as the incentive for OpenAI to ever improve on what's missing.
OpenAI is doing science the right way. Making the information available as widely as possible so that anyone can check and verify it.
That is the scientific process working exactly as it should.
If that "damages the mathematics community" then all it means is the mathematics community is not doing science and should be ignored.
I cannot stress this enough. If you are complaining about "how they released it" or calling this stuff "slop cannons", you're an unscientific hack that's dragging down humanity.
Engage with the actual claims. Prove them or disprove them. Nothing else matters here.
This is great - I think we're getting close to the core disagreement here because I disagree with almost all of that, and I think its because we have different conceptions of what science is.
To me, science is not a database of facts and data, and the scientific process is not just the process of adding to this database.
It is more than that.
Science is building the database of facts and data, but it is also sharing/disseminating that database so that others can write to it too.
We both agree that "openness" is critical for this, but to me, the scientific process includes things like the actual words that a scientist uses to communicate their ideas/data, the paper they wrote, the collaborations they had, the work that they built upon. Science is not like a database only - its more like a distributed system, and the scientific community is like a living, breathing thing. It is the health of that system which has been damaged in my opinion.
So I have no problem that OpenAI updated the database.
They didn't just make the information available though.
They updated the knowledge database, then released low quality slop papers.
They made it clear that they don't give a damn about sharing/disseminating information.
They are trying to fundamentally say "we can do science without prioritizing sharing.
We don't think its important. We'll release the proof because it makes our stock go up, but we're gonna keep going and building and not spend any time on communication or comprehension because we think that it doesn't matter, and your contributions don't matter, and AI is gonna do all of this independently anyway. We spent $20m on the proof because it made our stock go up $20b, but we'll spend 20 min on the paper. Priorities clear.
I don't disagree that having comprehensible papers is useful. There is undoubtedly value in having well written, easy to understand documents that make it easier for third parties to validate the work presented.
The thing is, that is a "nice to have", not a condition to make science.
If people believe that such things are useful, then the appropriate response is to reproduce, simplify and otherwise make the proofs provided into more easily digestible pieces.
The scientific process is fundamentally indifferent to whatever shibollets and cultural hangups that its presumed participants may have. An alien with fundamentally different norms from us, who experiments to determine the boiling temperature of water is doing science just as much as a human, even if he never submits a paper to a journal.
The issue you're having is that you're under the mistaken belief that the scientific process is the "community" and "norms" that happen to have developed over the past few centuries by this "scientific" priesthood.
It is not. It has never been. It will never be.
This "scientific" priesthood has simply used their power and reputation to enforce their own self-aggrandizing norms, much like the religious priesthood they replaced. They should not be taken seriously, and to go along with these norms when they are unnecessary is frankly ridiculous and shameful for anyone who actually prizes results.
I would urge you to reconsider your stance, and in particular to put deep thought into why you believe these norms are so important.
Those are quite a lot of reactions so i have not read all of them. That said, the sample of 30 or so reactions i did read seems to simply confirm my stance.
Fundamentally the main points being made seem to boil down to this excerpt from Tristan Humbert:
>Open AI claimed a proof of the conjecture in full generality this morning and my first impression was sadness to see my favorite problem get “killed” by AI ; it is definitely easier to ignore a problem when it does not affect you directly. Next, I felt stressed because I am currently applying for postdocs and more of my research plan was now obsolete and I spent the whole morning rewriting everything and sending emails to my advisors in panic. Finally, I felt anger after opening the paper and observing that it was mostly unreadable slop.
They're essentially angry at "They did before i could", and "Now i don't have a job" and "I dislike how it is written".
It just reinforces the "scientific priesthood" theme.
These are people who had their livelihoods and status derived from this thing which is now fundamentally obsolete, and they are scared and upset that they will no longer have those things.
That's fine, its a normal human reaction. God knows i'm not sure i will have a job in 5 years because of AI!
But we should not be taking it with any more seriousness than we would take a ludite gripping about the mechanization of cloth manufacturing.
The truth is, the value produced by their job just fell off a cliff. They need to find something else that provides value to replace it. That's it. Being upset about it isn't going to be productive.
Perhaps the value they can make is to rewrite the AI proofs to a more understandable format. Perhaps it is to go flip burgers at McDonalds. That's up to them, but i would suspect that calling releasing valuable information as "bad for science" is not very value accretive.
Some of the lean proofs are apparently incomprehensible.
It would be like trying to look at a completed video game's assembly code, being told that it was call of duty, and then being asked questions about the high level code architecture.
AI models are perhaps unsurprisingly good at low level translation (see the progress being made for decomp games)
These models have surpassed human capabilities at math/machine code, but they can't "simplify" yet - in part because they don't have the same need to due to their comparative lack of cognitive constraints. AI Slop code is getting better, but it takes time. At the moment, its embarrassing frankly. It will come eventually, but right now OpenAI is not handling this with the care, respect, or concern that it deserves.
Have you ever wrote some code/algo that seemed "simple/obvious" to you yet to someone else, it seemed incomprehensible?
If you have a 20-40 IQ points gap with another developer, this happens a lot.
The baseline of "simplify" is wildly different based on your IQ points. That's precisely why exceptional students are usually bad in teaching. They try to break things down, simplify, but things still go over the head of normies.
However, we can intervene/train the models. So it should be possible to focus on the simplification, and as you said, it will come eventually.
I've been mostly reading here but created an account to disagree with this statement: The smartest people I know were always amazing at explaining. This was true for me as undergrad and graduate student where the smartest peers and the most renowned professor were always also the best at explaining, and it is true now at research level in a related field.
When I am not sure if I really understood something to the core, I try to find a colleague who knows very little about it; if they understand my explanation well, that's a good sign.
Those who really understand a topic are usually also able (and great at) explaining it in very clear and "simple" terms. This may be part of my personal bias; I see theory builders as those who advance the field the most, and these are usually also amazing at explaining it. On the other hand, those who mostly "grind" through problems (approach them as complicated puzzles) with effort/time were often bad at explaining.
I observed the same for programming: the "architects" usually explain very well, the "debuggers" often don't.
LLMs very much remind of the grind/puzzle approach. It does makes sense that RLVR, which in my understanding enables a lot of these results, would lead to a more mechanical approach.
Of course, I can't make any predictions on whether it will stay that way. But I strongly suspect that we need different ways of training for LLMs to write better text and explain better (I suspect the vagueness of LLM language is the result of RLHF as vague expression is less often incorrect).
I don't disagree with you. However, you are ignoring one key point that I made: the difference of base intelligence.
Let's assume you have an IQ of 135. You are not that far from even the crazy smarts at 150 and as long as they have some social skills, it will work out. I, myself, never had issue with understanding the smart people.
Now let's assume you have an IQ of 110. Unless 140/150 IQ people are spending inordinate amount of time formulating how to simplify things for you, things will fly above your head.
This does not mean just because someone is 150, and someone is 110, the 110 is always the problem.
This also does not mean an 120 explaining something to 140, and failing is 120's fault or the other ones'.
Every combination is possible as we are talking about personalities/ability to articulate oneself.
However, I was talking about a specific scenario, which I have faced myself and saw it happen a lot of times (to other people), where someone's simplification level is still higher than someone's max understanding level simply because the deviation between their caliber is too great. In most cases, this can be worked around by the explainer spending inordinate amount of time.
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