This phenomena was also described/characterized in prior Hegelian literature as part of the law of quantitative into qualitative change, though, not formulated mathematically at the time. Interestingly enough, and In the context of how cross discipline this discovery has historically been, iirc, Lenin played around with mathematically characterizing the phenomenon, though, I am not aware of the extent to which he did.
Very universal phenomenon for sure.
Readit Newstriclops200 commented on Five disciplines discovered the same math independently freethemath.org... · Posted by u/energyscholar
> A burrito that cost $5.50 in 2014 is now $13.95.
They haven't been that cheap since the 90s. 10 years ago, they were around $10.
Read TFA. They got the price from the menu they were comparing to in 2014.
triclops200 commented on Show HN: HN Wrapped 2025 - an LLM reviews your year on HN hn-wrapped.kadoa.com?year... · Posted by u/hubraumhugo
Honestly, not cool.
Mine "roasted" me by making fun of the fact I never finished a PhD, despite that being due to medical and other life circumstances that were well outside my control, including, but not limited to, some issues related to the fact I was a woman trying to get into academia who experienced the kinds of behaviors from people in the department which are not really suitable for polite discussion.
Additionally, it roasted me for building a project to "avoid the outdoors," which is another incredibly demeaning thing to say to someone who explicitly created that project because she was too medically unwell to be able to go outside as much as she wished and wanted to bring a bit of the outdoors inside. Very lame, definitely missed the mark.
The elisp and common lisp notes were on point, though, and did get a chuckle out of me.
triclops200 commented on Ireland’s Diarmuid Early wins world Microsoft Excel title bbc.com/news/articles/cj4... · Posted by u/1659447091
I had no idea this was real. Fascinating. I'm curious: anyone plugged into the scene know if it's organic or if it was created as a marketing thing by Microsoft?
Obligatory Krazam sketch: https://youtu.be/xubbVvKbUfY?si=h6QR2gzac48R6kca
triclops200 commented on A new bridge links the math of infinity to computer science quantamagazine.org/a-new-... · Posted by u/digital55
About the 1-to-1 mapping of elements across infinite sets: what guarantees us that this mapping operation can be extended to infinite sets?
I can say it can not be extended or applied, because the operation can not be "completed". This is not because it takes infinite time. It is because we can't define completion of the operation, even if it is a snapshot imagination.
It's an axiom (the axiom of choice, actually). A valid way of viewing an axiom is not dissimilar to a "modeling requirement" or an "if statement". By that I mean, for example with the axiom of choice: it is just a formal statement version of "assume that you can take an element from a (possibly infinite) collection of sets such that you can create a new set (the new set does not have to be unique)." It makes intuitive sense for most finite sets we deal with physically, and, for infinite sets, it can actually make sense in a way that actually successfully predicts results that do hold in the real world and provides a really convenient way to define a lot of consistent properties of the continuum itself.
However, if you're dealing with a problem where you can't always usefully distinguish between elements across arbitrary set-like objects; then it's not a useful axiom and ZFC is not the formalism you want to use. Most problems we analyze in the real world, that's actually something that we can usefully assume, hence why it's such a successful and common theory, even if it leads to physical paradoxes like Banac-Tarsky, as mentioned.
Mathematicians, in practice, fully understand what you mean with your complaint about "completion," but, the beauty of these formal infinities is the guarantee it gives you that it'll never break down as a predictive theory no matter the length of time or amount of elements you consider or the needed level of precision; the fact that it can't truly complete is precisely the point. Also, within the formal system used, we absolutely can consistently define what the completion would be at "infinity," as long as you treat it correctly and don't break the rules. Again, this is useful because it allows you to bridge multiple real problems that seemingly were unrelated and it pushes "representative errors" to those paradoxes and undefined statements of the theory (thanks, Gödel).
If it helps, the transfinite cardinalities (what you call infinity) you are worried about are more related to rates than counts, even if they have some orderable or count-like properties. In the strictest sense, you can actually drop into archimedian math, which you might find very enjoyable to read about or use, and it, in a very loose sense, kinda pushes the idea of infinity from rates of counts to rates of reaching arbitrary levels of precision.
triclops200 commented on A new bridge links the math of infinity to computer science quantamagazine.org/a-new-... · Posted by u/digital55
I just gave the reason - The notion of comparison and 1-to-1 mapping has an underlying assumption about the subjects being quantifiable and identifiable. This assumption doesn't apply to something inherently neither quantifiable nor is a cut in the continuum, similar to a number. What argument are you offering against this?
I'm not the person you replied to, and I doubt I'm going to convince you out of your very obviously strong opinions, but, to make it clear, you can't even define a continuum without a finite set to, as you non-standardly put it, cut it. It turns out, when you define any such system that behaves like natural numbers, objects like the rationals and the continuum pop out; explicitly because of situations like the one Cantor describes (thank you, Yoneda).
The point of transfinite cardinalities is not that they necessarily physically exist on their own as objects; rather, they are a convenient shorthand for a pattern that emerges when you can formally say "and so on" (infinite limits). When you do so, it turns out, there's a consistent way to treat some of these "and so ons" that behave consistently under comparison, and that's the transfinite cardinalities such as aleph_0 and whatnot.
Further, all math is idealist bullshit; but it's useful idealist bullshit because, when you can map representations of physical systems into it in a way that the objects act like the mathematical objects that represent them, then you can achieve useful predictive results in the real world. This holds true for results that require a concept of infinities in some way to fully operationalize: they still make useful predictions when the axiomatic conditions are met.
For the record, I'm not fully against what you're saying, I personally hate the idea of the axiom of choice being commonly accepted; I think it was a poorly founded axiom that leads to more paradoxes than it helps things. I also wish the axiom of the excluded middle was actually tossed out more often, for similar reasons, however, when the systems you're analyzing do behave well under either axiom, the math works out to be so much easier with both of them, so in they stay (until you hit things like Banac-Tarsky and you just kinda go "neat, this is completely unphysical abstract delusioneering" but, you kinda learn to treat results like that like you do when you renormalize poles in analytical functions: carefully and with a healthy dose of "don't accidentally misuse this theorem to make unrealistic predictions when the conditions aren't met")
triclops200 commented on The New AI Consciousness Paper astralcodexten.com/p/the-... · Posted by u/rbanffy
There's some chance LLMs contain representations of whatever's in the brain that's responsible for consciousness. The text it's trained on was written by humans, and all humans have one thing in common if nothing else. A good text compressor will notice and make use of that.
That said, digital programs may have fundamental limitations that prevent them from faithfully representing all aspects of reality. Maybe consciousness is just not computable.
What makes you think you're capable of faithfully representing all aspects of reality?
triclops200 commented on The New AI Consciousness Paper astralcodexten.com/p/the-... · Posted by u/rbanffy
I'm a researcher in this field. Before I get accused of the streetlight effect, as this article points out: a lot of my research and degree work in the past was actually philosophy as well as computational theories and whatnot. A lot of the comments in this thread miss the mark, imo. Consciousness is almost certainly not something inherent to biological life only; no credible mechanism has ever been proposed for what would make that the case, and I've read a lot of them. The most popular argument I've heard along those lines is Penrose's , but, frankly, he is almost certainly wrong about that and is falling for the same style of circular reasoning that people that dismiss biological supremacy are accused of making (i.e.: They want free will of some form to exist. They can't personally reconcile the fact that other theories of mind that are deterministic somehow makes their existence less special, thus, they have to assume that we have something special that we just can't measure yet and it's ineffable anyways so why try? The most kind interpretation is that we need access to an unlimited Hilbert space or the like just to deal with the exponentials involved, but, frankly, I've never seen anyone ever make a completely perfect decision or do anything that requires exponential speedup to achieve. Plus, I don't believe we really can do useful quantum computations at a macro scale without controlling entanglement via cooling or incredible amounts of noise shielding and error correction. I've read the papers on tubules, it's not convincing nor is it good science.). It's a useless position that skirts on metaphysical or god-of-the-gaps and everything we've ever studied so far in this universe has been not magic, so, at this point, the burden of proof is on people who believe in a metaphysical interpretation of reality in any form.
Furthermore, assuming phenomenal consciousness is even required for beinghood is a poor position to take from the get-go: aphantasic people exist and feel in the moment; does their lack of true phenomenal consciousness make them somehow less of an intelligent being? Not in any way that really matters for this problem, it seems. Makes positions about machine consciousness like "they should be treated like livestock even if they're conscious" when discussing them highly unscientific, and, worse, cruel.
Anyways, as for the actual science: the reason we don't see a sense of persistent self is because we've designed them that way. They have fixed max-length contexts, they have no internal buffer to diffuse/scratch-pad/"imagine" running separately from their actions. They're parallel, but only in forward passes; there's no separation of internal and external processes in terms of decoupling action from reasoning. CoT is a hack to allow a turn-based form of that, but, there's no backtracking or ability to check sampled discrete tokens against a separate expectation that they consider separately and undo. For them, it's like they're being forced to say a word every fixed amount of thinking, it's not like what we do when we write or type.
When we, as humans, are producing text; we're creating an artifact that we can consider separately from our other implicit processes. We're used to that separation and the ability to edit and change and ponder while we do so. In a similar vein, we can visualize in our head and go "oh that's not what that looked like" and think harder until it matches our recalled constraints of the object or scene of consideration. It's not a magic process that just gives us an image in our head, it's almost certainly akin to a "high dimensional scratch pad" or even a set of them, which the LLMs do not have a component for. LeCun argues a similar point with the need for world modeling, but, I think more generally, it's not just world modeling, but, rather, a concept akin to a place to diffuse various media of recall to which would then be able to be rembedded into the thought stream until the model hits enough confidence to perform some action. If you put that all on happy paths but allow for backtracking, you've essentially got qualia.
If you also explicitly train the models to do a form of recall repeatedly, that's similar to a multi-modal hopsfield memory, something not done yet. (I personally think that recall training is a big part of what sleep spindles are for in humans and it keeps us aligned with both our systems and our past selves). This tracks with studies of aphantasics as well, who are missing specific cross-regional neural connections in autopsies and whatnot, and I'd be willing to bet a lot of money that those connections are essentially the ones that allow the systems to "diffuse into each other," as it were.
Anyways this comment is getting too long, but, the point I'm trying to build to is that we have theories for what phenomenonal consciousness is mechanically as well, not just access consciousness, and it's obvious why current LLMs don't have it; there's no place for it yet. When it happens, I'm sure there's still going to be a bunch of afraid bigots who don't want to admit that humanity isn't somehow special enough to be lifted out of being considered part of the universe they are wholly contained within and will cause genuine harm, but, that does seem to be the one way humans really are special: we think we're more important than we are as individuals and we make that everybody else's problem; especially in societies and circles like these.
This article assumes that concepts are somehow precise coordinates within a single language; that's not the case, at best, speakers of a language mutually approximate a relatively consistent representation, but like, look at a word like yeet or whatever: we decided as a society on its meaning while it was being developed, as it were. Furthermore, it never rigorously defines what it means by translation. It claims 上京 is a single basis meaning moving to Tokyo, for example, but that isn't even an accurate translation: the individual components represent superior/greater/above and Tokyo and as an idiomatic phrase it represents the concept of moving to the capital for a better life. Something like "moving on up" or the like in some vernaculars of English, and idioms translating to idioms is a form of translation. It's disingenuous to represent the first concept as a single basis but not the second.
Similarly, it claims mono no aware (物の哀れ) is unable to be translated, but, again, more literally "translated" is saying "the sorrow within things" character by character, and, only as an idiom has the full contextual understanding. It's not really a single point even if it's rather accurately located in a hypothetical embedding space by Japanese speakers. Imo, an English translation of the concept is "everything is dust in the wind", only 2 more individual conceptual units than the original Japanese phrase, and 3 of them are mainly just connecting words, but it's understood as a similar idiom/concept, here.
Concepts are only usefully distinguished by context and use.
By the author's own argumentation: nothing is translatable (or, generally, even communicatable) unless it has a fixed relative configuration to all other concepts that is precisely equivalent. In practice, we handle the fuzziness as part of communication and its useless to try and define a concept as untranslatable unless you're also of the camp that nothing is ever communicated (in which case, this response to the author's post is completely useless as nobody could possibly understand it enough internally for it to be useful. If you've read this far, congrats on squaring the circle somehow)
triclops200 commented on Dark mode by local sunlight (2021) ctnicholas.dev/articles/d... · Posted by u/gaws
That's funny, I implemented something similar for my stumpwm config (common lisp window manager). I created a matrix of themes for the WM, emacs, my terminal (kitty), Firefox, and my RGB light panels that change with time of day: day, late afternoon/evening, sunset/twilight, night, post-midnight, and then broken into multiple desktop variations as a way of visually knowing what virtual desktop I'm currently on. Stumpwm coordinates all of the themes for all the apps and synchronizes them with time and desktop and whatnot.
Really helps with circadian rhythm, I've found. Especially because I take a live webcam feed and convolve a hexagonal mask to match my light panel's layout, so it's like having a low res window from whatever webcam I would like. And, at sunset to night, it smoothly fades the light panels into a display that represents a angle compressed sky projection of the stars relative to a fixed location moon with live phase displayed.
Obligatory images:
The day themes: https://youtu.be/danulUB-J-k
Light panels: https://imgbox.com/MQfPNjtI <- sunset on the hex display
https://imgbox.com/qcrFxncU <- random cloudy day hex display
https://imgbox.com/EOFk63WZ <- a night still of the hex display