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Imagine a box of balls. They have size, weight, colour, density… etc. These properties, each a measure, are dimensions and they are orthogonal to each other. Taken together are multi-dimensional.
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Now take a set of words. They have "sizeness", "weightness", "colorness" and "densityness"...and "pythonness" and "haskellness" and even "adjectiveness" and "verbness" and so on and so forth...You can readily see that this can encode arbitrary patters (like language grammer or program syntax)

Training identifies these dimensions in the training data and links it with each word/token. Then given a stream of such tokens, each with its own set of dimensions (which can be huge), and LLM predicts the dimensions that the next token is most likely to have...

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my take from all these is that is perhaps possible to teach similarity search to 5th graders. not an elementary teacher myself, but many math concepts are much easier to explain with allegories (visual and other) than with formalism. a good example perhaps is what Mamikon does in his visual explanations of calculus (https://calteches.library.caltech.edu/4007/1/Calculus.pdf)

formalisms come only after there is understanding of the phenomena and a specific need to communicate concepts across members of community - in a concise and commonly comprehensive way. my understanding is that education often fails to train understanding and jumps directly to formalisms. and this is right also for STEM schools, where it is presumed everyone has some innate inclination to the matter. but this presumption, in my experience as university teacher, is not entirely correct, and students are not universally prepared to express lack of understanding, and particularly when it is expected from them to rather indicate understanding.

it seems very weird, the concept, to reward the correct answer, while suppressing and discouraging the expression of misunderstanding or confusion. why is weird? because learning comes trough trial and error, and the error part is half of it. so we need to encourage people to express their errors or lack of understanding, so that we can then fill in the gaps and eventually stand on a common ground. sadly, many forums, HN included, does not cherish misunderstanding. our posts here mostly get upvoted whenever they cross a sort of threshold about the amount of truth in our writing, and not because of daring expressions of confusion.

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This is nonsense. The human mind cannot visualize more than 3 dimensions. It can perfectly comprehend any number of dimensions as long as they are represented in a vector space. In fact, that's what linear algebra does.
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I think you accidentally a word, there. GP is talking about comprehending the capacity of massively multi-dimensional space.
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Correct. I implied nothing about visualizing. I was talking about (information) capacity.
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I think the human mind can visualize anything, eg here are some visual descriptions of higher dimensional objects: https://gfody.substack.com/p/mini-hyper-golf
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My aphantasia says your milage may vary on that.

On the other hand I deal with higher dimensions better than most, possibly because of my aphantasia.

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I think it would be fair to say that at least a few people can do a small amount of 4d visualisation.

Agreed, I don't think anyone has a good grasp on, say, 64K D, but we can do a bit better than just 3.

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I’ve heard people claiming that they can but I’ve never heard compelling evidence that they’re directly visualising 4D objects rather than 3D projections of them, or some symbolic representation (arrays of numbers etc.)
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What would you regard a trusted demonstration that someone can?

I mean, there are people with aphasia and hyperplasia - how do you prove actual 3D visualisation.

There are games that people play that need 4D visualisation to be able to do well and they perform at that.

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All I’ve been able to do is mentally tag parts of a shape as being at different “depths” (possibly with two parts at the same 3D location but tagged as having different “depths”). Which, yeah, I agree isn’t really visualizing a 4D shape. I think someone better at it than me might be able to use this to leverage one’s visual spatial intuition in a way that is a bit closer to what 4D visualization might be like if it were possible.

But I don’t think it is possible for us. At least, for strict senses of visualization. I suspect that the architecture of our brains doesn’t support it. This is rather speculative because I don’t know basically any neuroscience, but I wonder if the whole “the brain is largely a very wrinkled surface (though with several layers to this surface), and the retinas are also surfaces” may have something to do with this. A retina in a eye-4-ball would have a 3D boundary (I.e. hypersurface), and I imagine that the amount of information that it would take in if it had an at all similar angular resolution, would be too great for our visual cortex to be able to represent all of it.

Of course, our vision only really has the high resolution it seems to everywhere in the narrow region we’re directly looking at, but still.

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So it is like 3D because you do not visualize the complete 3D models but only 2D projections of them. Or do you really visualize the back and inside of a vase at the same time?
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If I visualise a 3D object then it’s in at least pseudo-3D (as in front surface with depth) but I can switch it to a kinda volumetric view. This might be thanks to years worth of 3D modeling and CAD which helped me map between first person and third person cameras and between solid and transparent, though. 4D doesn’t even make sense though, like I can do an animated 3D volume?
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Yes. It's worth pointing out that anything with n distinct parameters is just a point in n-dimensional space. We're so used to handling so many dimensions that nobody ever bats an eye until someone brings up the magic word "dimensions". It's quite intuitive actually.

The trivial example that comes to mind is the character customization sliders in many video games.

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>The human mind cannot comprehend the capacity of massively multidimensional space.

That is why the scam works, because investors are humans...

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Which scam sorry?
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The scam that is based on the implicit claim that LLM is a path to AGI.

Seeing LLMs for what they really are will also make it clear they are fundamentally unfit for a lot of tasks they are currently marketed for...

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Too broad a statement, and without substantiation, to be taken serious, sorry.
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Is it?

They're borderline useless and certainly potentially inadvertently malicious for writing, customer service, speech to text, writing large amounts of complex code, therapy, medical diagnostics... the list goes on

Sounds like you're part of the problem?

It's really a serious problem just eroding the fabric of society in real-time. Being complacent in it or believing in the promise is just wholly foolish and bad for everyone.

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Too shallow of a dismissal, and you don't determine what everyone else takes seriously.

It's been several years now of LLMs only appeasing those with low expectations and inexperience. Unless the only goal was generating boilerplate or really sloppy proofs of concept, LLMs are a waste time for everyone else. This argument is so over already. We're all just hoping for a soft landing when the hangover really kicks in.

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I have 40+ years experience and extremely high standards. What you say is entirely wrong.
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>I have 40+ years experience

What domain?

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Why is it always the ones with the highest karma giving the most hollow defense? How's retirement treating you?
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You are disconnected from reality. The whole industry is already completely dominated by LLMs generating code. Bury your head in the sand all you want. This is not about low expectations or inexperience at all. Your condescending tone doesn't make you look smarter, it makes you look like an Amish who expects the industrial revolution is temporary and soon people will come to their senses and stop using all this nonsense industrial technology.
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A sidenote, but that is not a typical Amish opinion of technology:

"Amish do not view technology as evil, and individuals may petition for acceptance of a particular technology in the local community" - https://en.wikipedia.org/wiki/Amish_way_of_life#Use_of_moder...

See also https://thereader.mitpress.mit.edu/how-the-amish-let-technol... about some Amish use of cell phones with adapters to be more payphone/landline-like and https://news.ycombinator.com/item?id=21349989 was a discussion about the use of pneumatic machinery by the Amish.

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Yup and the industry is worse than ever.

Maybe you forgot that important tidbit?

People are using them because they're being shoved down their throats and they're complacent.

Software quality, maintainability, exploitability, morale, competency are all at all-time lows and just worsening.

It's really bad to defend this.

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I spent the last 6 months reviewing all of the AI generated code primarily with gpt 5.3 codex but after I bought the subscription I also used gpt 5.5 and although I was constantly rejecting the bad code and I was mostly happy with the end result.

Then they removed the approve everything manually mode and I thought, maybe I'm the one out of touch, I should try vibe coding. I gave it a big spec of things to implement and I was pretty vague on the details, but I was kind of hoping that the AI would get it right anyway.

I noticed that when you let the AI just do its thing, you spend a lot of time staring at the screen waiting for it to finish. No wonder all these people are obsessed with parallel agents.

Anyway, after a while it produced the end result and it was pretty bad and I don't even mean the code. This was with gpt 5.6 Terra. Definitively not the type of "did a week's worth of work in one hour" type of deal.

Meanwhile if you guide it with your own technical skills the end result is a tireless code generator that operates at 80% of the quality of your own code but is only roughly 1.5x to 2x faster than doing it yourself. The biggest multipliers come from making the AI do things humans don't want to do, like writing a bunch of thorough tests but those don't translate into increased productivity, the opposite in fact. They translate into higher software quality but if you vibe the tests and don't review them, even that disappears.

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to avoid lot os problems i use kaplira to help maintain de code in boundaries and not let the agent do everything they want.
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yes i have written a jillion lines with AI as well

i'm a worse programmer now because of it

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What about the mathematical advancements?
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Doesn't that say more about the massive crumb tray nobody ever bothered to empty at the bottom of mathematics?

I'm sure someone will point out something like the 4-color theorem as a counterargument. Where is that kind of theorem proving in this generation of AI? We seem to have hit a dead end rather quickly.

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Lol, are you saying the Erdos problems are a "crumb" that nobody bothered to empty? Are you doing a comedy routine?
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Explain to the rest of us how far along those problems were before AI.
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Are they crumbs? Why aren’t you answering?
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