1) The first thing to improve chats as a genre of interface, is that they should all always be a tree/hierarchy (just like Hacker News is), so that you can go back to ANY precise prior point during a discussion/chat and branch off in a different direction, and the only context the AI sees during the conversation is the "Current Node" (your last post), and all "Parent Nodes" going back to the beginning. So that at any time, it's not even aware of all the prior "bad branches" you decided to abandon.
2) My second tip for designs of Coding Agents is do what mine does. I invented a 'block_begin/block_end' syntax which looks like this, and can be in any source file:
// block_begin MyAddNumbers
var = add(a, b)
return a + b
// block_end
With this syntax you can use English language to explain and reason about extremely specific parts of your code with out expecting the LLM to "just understand". You can also direct the LLM to only edit/update specific "Named Blocks", as I call them.
So a trivial example of a prompt expression related to the above might be "Always put number adding stuff in the MyAddNumbers Block".
To explain entire architectural aspects to the LLM, these code block names are extremely useful.
Dude threaded chat is how it should be, right? Especially if you could reference one thread in another and have it build the proper context up to understand what said thread was as a basis for this new conversation.
Proper context is absolutely everything when it comes to LLM use
Yep. "Threaded" might be what the kids are callin' it nowadays. It's always been trees for me. I had a 'Tree-based' chat app for OpenAI (and as of now all other leading LLMs, via LangChain/LangGraph) within one week of them opening up their API. lol. Because my Tree-based CMS was already done, to build on.
OpenAI finally made it where you can go back and edit a prior response, in their chat view, but their GUI is jank, because it's not a tree.
Specifically what I mean is HTML is flawed. It should never have been a presentation format. It should've always been a DATA format, like JSON, or XML, from day one. The browser itself would then be able to display information (pages) in whatever style, colors, and format it wants.
Probably 99.999% of developers agree with this, but we're stuck in a RUT it seems. I know what I'm sort of talking about is the "Semantic Web", and I'm probably preaching to the choir to bring it up on Hacker News.
But I'm wondering if it's possible to change? What would it take? We'd need some major movement, almost like Web3, or Blockchains, that got everyone to wake up and realize there's an easier way. We're stuck because there's no real incentive for change. It's a chicken and egg problem. No one is gonna be first to design something, unless everyone else is already using it. :( Thanks for listening. That was step one I guess.
None of this is unique to the web. It's the same reason every magazine has its own attractive layout and formatting, instead of just being a long manuscript in Courier.
I like the fact that different sites have different typography. It's an identity that tells me where I am.
I understand the appeal of "pure information" without any visual variation ever, but I think that for most people, variety is the spice of life, no?
I wouldn't want every site to look the same, for the same reason I wouldn't want everyone to dress like clones. Visual self-expression is part of what it is to be alive.
I think part of the data format could be visual related tho. Enough to make sites able to look distinctive, but not enough to allow the chaos we have today. For example, background image for a page, font for a page, whether something should be in a left panel, center panel, or right panel. They would be hints and very limited, and all in one place, in the data format. Unlike HTML where you have anything, anywhere, and total chaos.
I think you underestimate the value the world would place on the gains we could get from this kind of design, not to mention that AI would be able to reason about the pages much better. Just the AI angle along is enough to convince society to go along with the change.
But there will need to be some "Killer App" that does this, which everyone else copies.
> I like the fact that different sites have different typography. It's an identity that tells me where I am.
While I do get that and to some extend agree, what we get is light grey on white, skinny fonts and illegible pages. It's one of those things that are awesome when they work, but it's so hard to get right and very few people/teams are able to do it.
DrudgeReport is boring as hell looking and was successful for years. Even HackerNews is about as boring as it gets, and we use it because it works. I think the world is ready to move on from the whole entire internet being a massive "MySpace Page" of garbage.
Just a tiny rant: In my view complex numbers are really about the concept of "orthogonality". The complex 'dimension' is orthogonal to the 'real' dimension, but anything in reality that's a continuum of values can be seen as a dimension, and therefore each one must have an orthogonal. That is, whenever you have a direction in a higher dimensional space (regardless of dimensionality) any vector will have a normal direction (perpendicular direction).
What basic complex numbers represent is a way of doing rotations where something moves from one direction towards it's orthogonal. That's what Euler's Formula is about also, which shows the relationship of 'e' and 'i' in this of course.
Now what Quaternions represents is the realization that if complex numbers have two components (real, imaginary) then we can treat each of those as a base vector and find a sort of 'next level up' orthogonality to each one individually.
I'm not good enough at math/geometry to know if this kind of 'next level up' bifurcation of dimensionality extends up past Quaternions or not (like something called Octernions, 16ions, 32ions, 64ions, etc), but it seems like is would?
Octonions and so on up are indeed a thing, but I don't think they do what you want. Even aside from the fact that they're restricted to power-of-2 dimensions, their algebraic properties get worse as you iterate the Cayley-Dickson process. The octonions aren't even an associative algebra, although they do have some weaker associativity properties which I'll skip detailing here. The quaternions are as far as most mathematicians are willing to go -- non-commutativity is commonplace, but who wants to deal with non-associativity?
But while the octonions at least have some mathematical relevance (they're actually connected to various exceptional objects, such as the exception Lie group G_2!), the sedenions and beyond basically don't. They have a tiny bit of associativity but not enough that they connect to any things or that hardly anyone wants to study them -- and worse yet, there are zero divisors so cancellation (ab=ac => b=c for nonzero a) doesn't even hold. (Inverses exist, yes, but without associativity, inverses don't imply cancellation! And therefore aren't much use.)
As another commenter mentioned, what you might be looking for instead if it's orthogonality you're focused on is Clifford algebras (aka geometric algebra). However, if you want to get the complex numbers or quaternions out of it, you'd need to use a negative-definite quadratic form -- if you use a positive-definite one, you'd instead get the split-complex numbers, which are much less interesting (and you'd get something similar instead of the quaternions).
From your post I can tell you're way better at math/geometry than me, but I understood 80% of that. :)
Cayley-Dickson is interesting especially for Physics of course, because it brings in the concept of 'variable dimensions'. I think the flattening of objects, and the stopping of clocks (in Relativity), due to Lorentz effects in Minkowski space both on Black Hole Event Horizons and for objects approaching light speed (anywhere Lorentz holds) is, at the limits, ultimately the loss of a dimension, which would be my overall interpretation of what Cayley-Dickson is about too, in very broad terms.
So if Minkowski space is 4 dimensional, there would be some geometry for a 5-Dim Minkowski and it would use Octonians maybe, and that would be the geometry of the universe our universe is "embedded in"...I mean assuming of course you believe our universe is a Black Hole and we are all on an Event Horizon embedded in a 5D universe. Ya know, as one does. lol.
> I'm not good enough at math/geometry to know if this kind of 'next level up' bifurcation of dimensionality extends up past Quaternions or not (like something called Octernions, 16ions, 32ions, 64ions, etc), but it seems like is would?
Octonions and up (more generally known as hypercomplex numbers) exist, but every time you pull the "double dimensions by adding more imaginary components" trick[0], you lose another useful property.
Real to complex loses total ordering. Complex to quaternion loses commutativity. Quaternion to octonion loses associativity (but they are at least alternative). The sedenions aren't even alternative, and they have zero divisors to boot.
You can also generalize hypercomplex numbers to the study of Clifford algebras.
I don't agree. Complex numbers are the algebraic closure of the reals. Or the quotient of the real polynomial ring by (x^2+1=0). Or whatever other construction. The multiplication rule is the essence of C.
Orthogonality is captured linear algebra over R^2, but R^2 isn't a field or an algebra.
I think there is still a geometric viewpoint you can bring to the multiplicative structure of C. For example there is the extremely natural homeomorphism between unit C and SO(2). And C minus origin to (R+, SO(2)). It’s completely intuitive for mathematicians to say that 1 and i are separated by 90 degrees.
Indeed, there is a polar coordinates representation of the complex numbers with the nice property that when you multiply you multiply lengths and add angles.
Algebraically, and also in group theory, it's exactly that. A complex plane is re-interpreted as a half-way mirror operation on an orthogonal axis or quadrature plane (eg the imaginary axis in the case of the 2D Argand plane). Which is what you you get when you multiply by i in complex numbers or i/j/k in quaternions - a 90 degree rotation. The correct way to do arbitrary rotations in this case is to use an exponential process, and then you get Euler's equation, the quaternion symmetry operation or, in general, the exponential map of an infinitesimal transformation in a Lie group.
In higher dimensions you get other type of (sometimes weird) operations, related to the Cartan–Dieudonné theorem.
I really like the welch labs series on imaginary numbers which covers the first part of what you talk about -- leveling up the notion of what a complex number is. Though his focus was more on solving simple equations with no real roots, but really detailing how/what is really going on.
It is a great precursor to then thinking about quaternions
That exact video is the one that always comes to my mind when thinking of YT videos on this! I've seen it years ago. Definitely worth a watch for anyone who hasn't see it!
Also the (provocatively titled) "Let's Remove Quaternions from every 3d Engine" [1]
Spoiler alert: rotors are mechanically identical to quaternions, while being easier to understand. If you understand rotors, you understand quaternions. You can fit the laws you need to understand rotors on a business card.
Plus, rotors abstract to higher and lower (well, there's only one plane and its two respective orientations in 2d, but still) dimensions.
Complex numbers as planes (bivectors in GA parlance) has been the most mind-opening mathematical concept I've been exposed to in the last decade. The associated geometric product has helped me better understand concepts (like "handedness") that troubled me during undergrad engineering.
I had never even heard of rotors! Thanks for this. I watched that video. The video doesn't really explain how it extends to higher dimensions tho, that I could discern.
I wonder how/if any of this can be applied to LLMs 'Semantic Space'. As you might know, Vector Databases are used a lot (especially with RAG - Retrieval Augmented Generation) mainly for Cosine Similarity, but there is a 'directionality' in Semantic Space, and so in some sense we can treat this space as if it's real geometry. I know a TON of research is done in this space, especially around what they call 'Mechanistic Interpretability' of LLMs.
> The video doesn't really explain how it extends to higher dimensions tho, that I could discern.
The neat thing is that it "extends" automatically. The math is exactly the same. You literally just apply the same fundamental rules with an additional basis vector and it all just works.
MacDonald's book [1] proves this more formally. Another neat thing is there are two ways to prove it. The first is the geometric two-reflections-is-a-rotation trick given in the linked article. The second is straightforward algebraic manipulation of terms via properties of the geometric product. It's in the book and I can try to regurgitate it here if there's interest; I personally found this formulation easier to follow.
If you really want your mind blown, look into the GA formulation of Maxwell's laws and the associated extension to the spacetime (4d) algebra, which actually makes them simpler. That's derived in MacDonald's book on "Geometric Calculus" [2]. There's all kinds of other cool ideas in that book like a GA formulation of the fundamental law of calculus from which you can derive a lot of the "lesser" theorems like Green's law.
Take all of this with a grain of salt. I'm merely an enthusiast and fan, not an expert. And GA unfortunately has (from what I can tell) some standardization and nomenclature issues (e.g. disagreement over the true "dot product" among various similar but technically distinct formulations)
> I wonder how/if any of this can be applied to LLMs 'Semantic Space'.
Yeah, an interesting point. Geometric and linear algebra are two sides of the same coin; there's a reason why MacDonald's first book is called _Linear and_ Geometric Algebra. In that sense, Geometric Algebra is another way of looking at common Linear Algebra concepts where algebraic operations often have a sensible geometric meaning.
Interesting ideas there thanks. I do know about that Maxwell derivation that involves Minkowski space, Lorentz transform consistency, etc, although I haven't fully memorized how it works, so that I can conjure up how it works from memory. I don't really think in equations, I think in visualizations, so I know a lot more than I can prove with math. You're right it's mind-blowing stuff for people like us that are interested in it.
I noticed several people mentioned Karpathy already, but I wanted to include that his tiny "Micrograd" project (see Youtube Video and GitHub) is a great introduction to Neural Nets (Multilayer Peceptron), which is at the core of [most] machine learning of course.
All closed-source models censor to the liking of their investors. Open Source models are generally less censored, but yeah DeepSeek is censored for sure.
It's going to be funny watching the AI bro's turn anti-communism while they also argue why private ownership (such as copyright) is bad and they should be able to digest every book, every magazine, every piece of art in history with zero compensation so that they can create their tools.
Everything is built on previous knowledge. And at some point, things need to transition to public domain and the compensation has to end. Do artists that draw a car, compensate the first guy that drew a wheel? Do kids with crayons need to compensate the inventors of specific pigments for example. It would get absurd.
> they should be able to digest every book, every magazine, every piece of art in history with [as if] zero compensation so that
? That is the state of facts. «So that» is "so that you build up". It does not limit machines: it applies to humans as well ("there is the knowledge, when you have time, feed yourself"). We have built libraries for that. It is not "zero compensation": there is payment for personal ownership of the copy - access is free (and encouraged).
Laws have to change when technology changes. AI will benefit all of humanity, so I'm someone who believes AI should be allowed to train on copyrighted materials, because it's better for society.
However, like you're getting at, there are people who would say personal rights always outweigh society's rights. I think we can get rid of copyright law and still remain a free market capitalist economy, with limited government and maximal personal freedoms.
'Some people's property has to become everyone's property because AI'. Should Microsoft's software be free to everyone because humanity would benefit? Nintendo's? Oracles? Or only movie studios, musicians, and authors property rights should lose protection?
If an AI can look at a bunch of Picasso paintings and "learn" how to then replicate that same style, I don't think that's stealing. And I think the same concept applies to the written word.
However even if you were correct, would you be willing to trade copyright law for having a cure for most diseases? I would. Maybe by allowing 1000s of people to sell books, you've condemned millions of people to death by disease right? Can you not see that side of the argument? Sometimes things are nuanced with shades of gray rather than black and white.
Maybe by having copyright law we have allowed the authorship of books to flourish and critical mass to drive down the costs of books and allowed people to dedicate themselves to writing books as a profession, or made giving up weekends on a passion project worth completing. Maybe the world you want is less literate/less thought provoking because people can't feed themselves on 'your work is free' resulting in less being written because people who would have been authors are no longer rewarded.
All I know is society decided that copyright was worth the tradeoff of having people release their works and now huge corporations want to change the rules so that they can use those works to creative a derivative that the corporation can profit from.
I think both copyright law and AI consumption of copyrighted material can coexist peacefully. I can learn from what I read and then process that information to create my own novel works, and I think that's what LLMs are doing too.
If LLMs were just doing data compression and then spitting out what they memorized then that would violate copyright, but that's now how it works.
Nope, companies always do what's in their "self interest", whereas the Open Source community is concerned with improving the human condition for all. This applies especially to AI/LLM censorship vs freedom.
The fact that some kind of tags or Key/Value storage as attributes on files, has been missing until 2025 (and still is) seems so bizarre to me. Our file systems have hardly changed since the 1960s. We get filename, timestamp, filesize, and that's about it. Pathetic.
Imagine the opportunities if a folder structure could represent a "document" where each file represents a paragraph, or image, chunk of that document. We would be able to do 'block-based editors' (like content management systems, or Jupyter Notebooks) without having to have some large XML file holding everything.
Even if we had simple "ordinal" (ordered position) for files that would open up endless opportunities for innovation in the 'block-editor' space, but sadly File Systems development has been frozen in place for decades.
I'd sort of invert that and say it's better to use LLMs to just generate tons more test cases for the SQL DBs. Theoretically we could use LLMs to create 100s of Thousands (unlimited really) of test cases for any SQL system, where you could pretty much certify the entire SQL capability. Maybe such a standardized test suite already exists, but it was probably written by humans.
At that point, you'd get a ton more value from doing Property Testing (+ get up and running faster, with less costs).
If I'd had to have either code or tests generated by a LLM, I'd manually write the test cases with a well-thought out API for whatever I test, then have the LLM write tests that implements what I thought up, rather than the opposite which sounds like a slow and painful death.
I hadn't heard of "Property Testing" if that's a sort of term of art. I'll look into it. Anyway, yeah in TDD it's hard to say which part deserves more human scrutiny the tests or the implementations.
Are you sure that LLMs, because of their probabilistic nature, would not bias against certain edge cases. Sure, LLMs can be used to great effect to write many tests for normal usage patterns, which is valuable for sure. But I'd still prefer my edge cases handled by humans where possible.
I'm not sure if LLMs would do better or worse at edge cases, but I agree humans WOULD need to study the edge case tests, like you said. Very good point. Interestingly though LLMs might help identify more edge cases us humans didn't see.
Or due to their power, they've already secretly been taken over by the US Gov't. That's not really a "big conspiracy theory" at this point. I was mocked by the left for years for saying that the Gov't was involved in Facebook censorship. Turns out I was right. The biggest battle our Gov't has to wage is the battle for hearts and minds, and the control of information, and so they're trying to get in as deeply rooted as possible with every big AI company.
To be clear I wasn't blaming just the Gov't for all the censorship, because 99% of Facebook employees (including Zuck himself) were strongly in favor of censoring all conservative viewpoints, as well, and were in lock-step with Big Gov't controlling speech.
Zuck recently tried to blame it all on the FEDs (on JRE podcast) but he was obviously lying because Facebook even built a special portal for the FEDs to log into, for moderating/controlling the public, so he was the ring-leader of all the censorship, for about a decade.
my God what social media does to people to write and believe stuff like this… hopefully one day everything will be banned… amazing to read this - just amazing what seemingly normal human being can be made into believing!
99% of Facebook employees (including Zuck himself) were strongly in favor of censoring all conservative viewpoints, as well, and were in lock-step with Big Gov't controlling speech.
how can you write this with the straight face when top like 100 accounts spreading shit on Facebook are right-wing nutcases. Give me on popular left-wing nutcase on Facebook?! believing that conservative views on any social media platform were ever being supressed is downright craaaaazy :)
Sorry dude. Nobody believes any of that in 2025. The claim that conservatives weren't being singled out on Social Media is laughable nowadays. All the companies have ADMITTED doing it. The Gov't has ADMITTED doing it.
I mean, conservatives were getting censored/attacked even for true things like saying COVID might have leaked from a lab, that there are only two sexes, that Hunter Laptop was real, that FBI lied on FISA warrant, that people meds are have horse-versions of them, Biden is senile, and on and on and on for countless other things.
And yet Twitter is censoring progressive viewpoints and even skewed the algo toward promoting a certain political candidate and yet not a single word from those free speech warriors.
I'm generally in favor of Free Speech, but after Silicon Valley censored conservatives for a decade, during the entire Cancel Culture era, I think for them (liberals) to get to experience what it feels like to be censored themselves is probably a good thing. A good learning experience for them to begin to understand first hand how it feels, and what they did to others, without remorse, and with ill intent, for a decade.
So I say to all liberals complaining about Twitter censorship: "Turnabout is fair play" and "You deserve it, because you invented it."
Every Democrat in the DC Swamp is quaking in their boots right now out of fear that the Republicans might do to them what they did to the Republicans. They expect it to happen, because being so revenge-oriented themselves, they know it's what they'd do.
The difference is that, unlike liberals, Conservatives (especially MAGA) are God-fearing law-and-order abiding people, not motivated by hate, and not the evildoers that they were falsely accused of being, by the insane left and their Senile POTUS, for the past 8 years.
So don't worry, Democrats have nothing to fear but the exposing of their hypocrisy, and more loss of reputation as more truths come out.
To me this just shows that Perplexity is definitely being controlled by some other force other than AI developers, and different from what they publicly would admit to. Perhaps the US Gov't is involved? ...because I don't think any other investors would be able to hide their true funding source and motives quite like the Gov't.
1) The first thing to improve chats as a genre of interface, is that they should all always be a tree/hierarchy (just like Hacker News is), so that you can go back to ANY precise prior point during a discussion/chat and branch off in a different direction, and the only context the AI sees during the conversation is the "Current Node" (your last post), and all "Parent Nodes" going back to the beginning. So that at any time, it's not even aware of all the prior "bad branches" you decided to abandon.
2) My second tip for designs of Coding Agents is do what mine does. I invented a 'block_begin/block_end' syntax which looks like this, and can be in any source file:
// block_begin MyAddNumbers
var = add(a, b)
return a + b
// block_end
With this syntax you can use English language to explain and reason about extremely specific parts of your code with out expecting the LLM to "just understand". You can also direct the LLM to only edit/update specific "Named Blocks", as I call them.
So a trivial example of a prompt expression related to the above might be "Always put number adding stuff in the MyAddNumbers Block".
To explain entire architectural aspects to the LLM, these code block names are extremely useful.
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