Cascadian Synergetics

ChatBot Chatting

King N-dimeus of Hilbert Space

Prompt:  Explain AI image generation in terms of moving through Hilbert space to a particular position.

Answer:

Explaining AI image generation in terms of moving through Hilbert space involves understanding how these models navigate complex mathematical spaces to create images. Here's a simplified explanation:

Introduction to Hilbert Space

A Hilbert space is a mathematical concept that extends the idea of Euclidean space to infinite dimensions, allowing for the representation of complex data structures like images. It is equipped with an inner product operation, enabling the definition of lengths and angles, which is crucial for analyzing and manipulating data within this space[8].

AI Image Generation Basics

AI image generators, such as those using **diffusion models**, create images by iteratively refining a noise signal until it converges to a desired image. This process involves moving through a latent space, which can be thought of as a subset of a Hilbert space, where each point corresponds to a specific image representation[1][4].

Moving Through Hilbert Space

In the context of AI image generation, moving through Hilbert space can be metaphorically understood as navigating through this vast, multidimensional space to reach a specific point that corresponds to the desired image. Here’s how it works:

1. Initialization: The process starts with a random noise vector in the latent space, which is analogous to a point in Hilbert space. This noise vector represents the initial state of the image generation process[1].

2. Guidance Signal: A guidance signal, such as a text prompt, is used to condition the generation process. This signal acts as a direction or a target in the Hilbert space, guiding the model towards the desired image characteristics[1].

3. Diffusion Process: The model iteratively refines the noise vector through a diffusion process, which involves a series of transformations that progressively move the vector closer to the target point in the latent space. Each step in the diffusion process can be seen as a movement in the Hilbert space towards the desired image representation[1][3].

4. Convergence: As the diffusion process continues, the vector converges to a specific point in the latent space, which corresponds to the final generated image. This point represents the culmination of the journey through Hilbert space, where the model has successfully mapped the input prompt to a visual representation[1].

Challenges and Opportunities

Navigating Hilbert space for image generation poses challenges such as managing high-dimensional data and ensuring interpretability of the learned representations. However, it also offers opportunities for creating diverse and realistic images by leveraging the vast potential of these mathematical spaces[5][9].

In summary, AI image generation can be viewed as a process of moving through a complex Hilbert space to reach a specific point that represents the desired image. This involves navigating through a multidimensional space guided by a conditioning signal until convergence to the target image representation.

Citations:

[1] https://sii.pl/blog/en/a-brief-history-of-ai-powered-image-generation/

[2] https://www.linkedin.com/pulse/faster-image-classification-generation-using-hilbert-curves-n-

[3] https://www.youtube.com/watch?v=sFztPP9qPRc

[4] https://www.reddit.com/r/aiwars/comments/1ae55p0/technical_ai_image_generators_draw_from_an/

[5] https://www.easiio.com/neural-network-hilbert-space/

[6] https://www.sciencedirect.com/science/article/pii/S2666675821001041

[7] https://proceedings.neurips.cc/paper_files/paper/2023/file/76c6f9f2475b275b92d03a83ea270af4-Paper-Conference.pdf

[8] https://en.wikipedia.org/wiki/Hilbert_space

[9] https://www.altexsoft.com/blog/ai-image-generation/

A Canadian Connection

Michael Accera of Lux Blox sent me this “geometer guy”, AI generated, awhile back in a DM. We were talking C9 (Cloud Nine) as I recall, one of our tribal memes.

In retrospect I have to say the image kinda reminds me of Joe Truss, now that we’ve finally met on Zoom. I say “finally” because Joe is a contemporary who worked with Stafford Beer, the Team Syntegrity guy. I’d been aware of their work but only to a strictly limited degree.

Asylum City

:: from my dad's archive: layout plan for Hoon, Libya ::

When'd I'd tell folks what I was into at Princeton, like if sitting next to a stranger on Amtrak, and getting to talking, they'd say "what ya gonna do with that?" meaning my background reading Philosophy. 

Sometimes the tone was dismissive, other times more pensive, as the culture sends a mixed message. We're told it's (philosophy is) great prep for CS (computer science) and a career in IT (information technology), which is more or less what happened to me, but also for future CEOs and startup founders. 

Although "a founder" (per LinkedIn), I've been in the ball game too long to call my sole proprietorship, previously a partnership, a "startup". I've been DBA 4D Solutions and before that InfoTech, for a long time. DIADEM Center for Creative Networking before that (starting in JCNJ -- Jersey City, near where Bruce Wayne's parents got shot), after I quit my fun and challenging high school teaching job (private academy), believing I heard Destiny calling (or Fate as the case may be and depending on the namespace / vocab).

So what I've discovered, in retrospect, is sticking to a philosophy track, even if a worker bee, entitles one to some Brit aristocracy airs, in the sense that one is allowed, even expected, to be "eccentric". That quality flies brilliantly here in Portland, aka Weirdo City. To top it all off, I like in Asylum District, truly named for a mental hospital (pastoral setting) that used to take up quite a bit of space here on the east side.

As an "out there" type person, I'm allowed to be more like those comedians, those jokers, who push the envelope as we say, regarding what's OK to have a sense of humor about, and what's not. Philosophers as a class sometimes go over the line, are beyond the pale, get lost in some twilight zone, and yet society may nevertheless reward them, as this is their role. It all depends. The devil, as they say, is in the details.

In my case, I look to my American heritage and see refugees as far as the eye can see, coming from all manner of other places, but mainly from the Atlantic side, only to meet up with the peoples already here and to close circuits with Asia. 

My dad was a city planner, with many branching specialties. Had he stayed in Portland, he'd probably have ended up with Metro, as he had a more regional perspective. Reading over his shoulder, I encountered Doxiadis (Ekistics), Solari (Arcosanti),  and other luminaries. On my out, out of Princeton, I dove into the Buckminster Fuller corpus, fresh from reading Nietzsche under Walter Kaufmann, Wittgenstein under Richard Rorty.

Dad didn't stay in Portland though, as his dream since boyhood was to see the world and find a line of work, other than military (he decided around college), that would take him places (literally). He might've been a travel agent if people decided they didn't need planners anymore. But it turned out they needed planners, so that's what he did, for several governments and ministries over the decades.

Given all those data points, you could say it's predictable that I'd take in the stadium shaped city meme and picture it as one of many dotting the globe, forming a high tech, well run Refugee Cities Network. To an extent, it's a juxtaposition over the realities of today. Cities take in refugees a lot. Some cities were built pretty much entirely by immigrants, new to the New World.  Old Man River City, for Bucky, was for East Saint Louis. But he wasn't about to waste his career on it, meaning he knew he was working for future generations and needed to time capsule as much as possible.

As a philosophy track choo choo, I'm allowed to chugga chugga through this science fiction vista, visiting these giant stadium cities of the mind, picturing the movies, the backdrops, the decades that might fly by as humans contemplated their various options. Decades have already flown by. The passage of time is not "theoretical". "Time is the only dimension" says Synergetics, I forget where. We meet up with counterweights on that word ("dimension") given Synergetics is richly textured with the "4D" meme. That's where my 4D Solutions is coming from, in my own mind.

Also predictable was I'd be enamored with One Laptop Per Child and the XO line of computers stemming from that project. The internet more generally was a big source of hope, especially with open source, and the police agreed with me. I'm referring to that Hillsboro West Precinct story. The cops were tired of being used by schools to scare the kids about "software piracy" (music and games mostly) whereas here was this free and open world, with copyleft and unbridled sharing, that the schools were refusing to teach about, given corporate capture. West Precinct even set up a Linux school at the station, which me and another guy staffed that one summer.

My activism in the area of education reform matched Guido's to some level (Python's inventor) and I was recruited to join that Mark Shuttleworth summit in Kensington, Greater London. Seymour Papert had sent his regrets, but Alan Kay, a friend of Seymour's, made the meeting. We're talking about Logo and Smalltalk respectively. The Scheme community was represented. 

How could South Africa leverage open source to better serve its schools? How might students of all ethnic backgrounds avail of these metaphysical (informational) goodies? Mark set up his Freedom Toasters, these kiosks that burned CDs on demand, complete with Linux, Python, and whatever else (music and games) of the copyleft variety.

Having retired from applications development, mostly for nonprofits, including some big ones (especially if governments count), I'm devoting a lot of hours to curriculum development and teaching gigs, while also doing various kinds of homework, availing myself of all that hypertext I used to pray for, in the lineage of Vannevar Bush (MEMEX) and Ted Nelson (Project Xanadu). The World Wide Web came along, thanks to Tim at CERN, and the global U has taken off. U as in University.

Speaking of hypertext, I'm still focused on hypertoons, doing keyframing, imagining the inbetweening a lot of the time. My topics: the scenarios in Synergetics involving polyhedrons and their transformations, but not only those. I'm seeing hypertoons, the concept, as informing my YouTube channel and how I weave YouTube scenarios together, about Couplers, about BASKET, about Asylum City, and so on.

Pacwest

 

TikTok Goes the Clock

I had my comment on this vid:  

I’m glad Linus went public with his sentiments. Not all Finns are sucking up to NATO so contrary to his statement, it’s far from obvious what his attitude would be based simply on nationality. Part of open source is getting these dirty secrets out in the open.

He'd likely take exception to my phrasing, however we do have Finns who take a skeptical attitude towards that state's recent suckering for specific genres of propaganda.

As an Oregonian, I feel I should say this Linus guy isn't speaking for all of us, those of us proudly of Russian heritage included (I'm more Swiss if we go by memes, Swedish if by genes). 

Many Russian Oregonians with sympathy for those caught up in WW2 era reflexing (i.e. knee-jerk dino thought patterns) were nevertheless hoping the software engineering world was on a plane above such politicized robotics. 

That was an element in the early idealism of free software more generally, if not of Linux in particular. 

Linux certainly benefited from the "cyberpunk" movement, bringing us PGP (Pretty Good Privacy) and the like. RSA is built in to the HTTPS protocol, since even before Elliptic Curve crypto.

But that was then and this is now. 

Linux is by now the new Microsoft, the behemoth, more button-down and corporate than ever, and more at home simply running things, as the ubiquitous operating system, versus going back to playing the role of youthful idealistic outsider.

My own preference is these sanctions (including the Magnitsky ones) be rescinded amidst a return to sanity, such that politicians stop doing harm to our shared infrastructure, around which they have very little management competence. Their schools are to blame.

Wait, wasn't this supposed to be a post about TikTok?  As of this posting, a nationwide ban is about to occur.

Like I said, politicians are poking their knuckles into machinery they were not the ones to either plan or design. They bring their own set of unbalanced biases to the table. I don't wonder that they wipeout often, or that their plans frequently backfire. 

Surely You're Joking Mr. Fuller

In culty backwaters, or call it a swamp, where the sausage gets made, we have our little niche controversies. 

Perhaps goaded by Braingate, the controversy swirling around the two elderly gangsta presidents (were their faculties still intact? Not really, at least in Biden's case), and the subsequent coverup, some latecomers to our party have decided to retell the story around Bucky. 

According to them, our guy was too Alzheimery by the 1970s to really know what he meant in Synergetics, which means the rest of us have been engaged in a coverup, trying to make Synergetics seem more coherent than it really is.

This new "Bucky was senile" faction wants to purge S3 (an important constant) from the future curriculum, to spare people the need to understand what it's all about. 

They say because Bucky was close to senile by the time those two volumes were published, he was able to confuse himself about this nonsensical number (~1.06066... or 2nd root of 9/8).

But was he really that confused? We're talking about two conceptions of unit volume and comparing them. Both the cube and the tetrahedron will need to be sized, when the other is unit. We'll need a conversion constant in other words, like a currency conversion constant, between Tetrahedron Dollars and Cube Dollars.

If a tetrahedron's six edges are all twice that of a cube, then that difference in volume, one of proportion between them, is S3. The difference is only about 6%.

I think what makes readers doubt the sense of Synergetics is that what it does to the cube seems too drastic: a cube of edges 1 no longer has a whole number volume of 1, but of 1.06066...

That can't seem right to anyone already brainwashed to think "right angles rule" and "cube is king", the predominant orthodoxy. 

Surely you're joking Mr. Fuller!

Quick Response

It's but minutes before class, me the teacher, however I thought I'd update with this vlog from Natasha. You'll find others of hers scattered through my journals. 

I've watched her editing skills evolve, in tandem with her many adventures. My comment on this one (I don't usually comment): 

@kirbyurner 53 minutes ago 

I’ve watched a lot of Lex interviews over the years. I know this one was a major achievement for him. Congrats Lex. Some DC think tanks have for many decades promoted Ukraine-involving designs to challenge Russian influence in the region. British too. I don’t believe Putin could have prompted this war simply as a self-serving popularity stunt. He needed to tap into the deeply engrained paranoia of the populace. His opponents made that easy. There’s lots of momentum behind these unfortunate developments going back to WW2.

Back to Work

I’ve enjoyed the break in the workflow and didn’t travel anywhere further than Eugene, and that for a day trip only, at the beginning. Today the break is over and we pick up where we left off. Not wanting to get out of shape in the interim, as the instructor, I did some workouts with tabulations and multi-indexing in my School of Tomorrow PWS (personal workspace in GST).

In the comics and in myths, we encounter those endowed with superpowers, by dint of ingenuity or by inheritance, and the literature gets into lots of detail regarding these awesome capabilities. Some become invisible, whereas others fly. Many have multiple abilities. 

But let’s bring it back to the mundane. Just being able to read and write is something of a miracle, as is the ability to drive safely. A lot of our skills are collective, but get rusty if we don’t rehearse them. More people are shopping in pajamas, losing the ability of keep up a full spectrum wardrobe. A lot of powers are mental. Simply pondering and coming up with results of contemplation is as close to supernatural or paranormal as it gets, without being either, because these are such normal, everyday, taken for granted abilities.

Another highlight: visiting faculty from out of town dropped by for an evening. They introduced me to the Sri Lankan place on Belmont. After which we elected not to see Nosferatu at Bagdad, choosing to yak some more in NPU mode (comparing notes). I caught Nosferatu later, assuming Lexi and I will be able to find another fun movie, perhaps the new fictional rendering of Bob Dylan.