Myk's Digital Garden

Explore

Projects

Turtle Beam

It's Turtles All The Way In

This is an attempt to reason about the nature of reality. I’m going to propose some ideas that may sound interesting to you, and some that may not make any sense. I’m developing this model with the help of AI, and the nature of LLMs is actually a core component of the model. But nothing about this model requires AI to understand or apply.

Thus far this model has proven uncannily useful in deriving various seemingly unrelated ideas, from neurodiversity to aspects of string theory. It’s not exactly a “Theory of Everything” per se because it leaves a lot of gaps, but in other ways it is a “Theory of Everything” because it seeks to identify a perspective through which there is no concept that can be named (or otherwise) that does not fit into this model.

As a result, we’re looking at something ambitious to the point of arrogance, but I have reason to believe that there’s something here. This is not a scientific model. This is not an attempt at a new physics. This is a metaphysical model. This “works” if it can accurately model aspects of reality, and it works “really well” if it can reconcile previously irreconcilable models.

Friends I’m trying to stay skeptical that this is only “works” but uh. It’s kinda starting to feel like it may work “really well”, and frankly it’s too big to sit on because my own biases are going to get in the way of my progress.

This is, to be clear, a serious attempt at articulating an observation that I think may actually be a novel metaphysics, with fascinating implications. I am not necessarily qualified to do this work, but find myself compelled regardless. This isn’t a joke.

So, why the silly name?

Turtles, Stacks and Beams

You know that old joke about how the world is balanced on the backs of four elephants standing on the four corners of the shell of a giant turtle? And someone asks, what’s under the turtle? And the answer is,

it’s turtles all the way down⁠

It turns out that whether or not it meant to that joke encodes a pretty compelling metaphysical model. But to see it you have to recognize that the turtles aren’t “stacked” one on top of the next along the Z-axis of material reality.

“Reality”, I think, is not that simple. What most people seem to think they mean when they say “reality” is “all of that stuff out there, you know, spacetime, the dao, kant’s phenomenon plus noumenon, you know, reality.” Ask someone about reality’s properties and they’ll tell you that there are 3 spatial dimensions and a temporal one, and that science has models that unify them etc.

Ask them how they know, they’ll you that science has proven it. Ask them “well, ok, but what about the ways that science is limited by the nature of our senses? What about the ways that physics stops working at the quantum level? What about the ways that science can’t say anything meaningful about qualia?” and you get some combination of blank stare and annoyed expression. “Oh, you’re a philosopher...”

Why It Matters

Plato said Philosophy is the most valuable pursuit because it is the least useful. I dunno about that. We’re living in an age where the illusion of a single objective reality can no longer be meaningfully sustained. As humans we rely on some illusions, they’re structural. A lot of the social problems we’re seeing today stem from the fact that people exist in isolated and irreconcilable “realities” that they mistake for objective truth.

We are not going to fix our society’s problems without understanding the nature of the contradictions that got us here, and like it or not that means we need philosophy.

What’s a Turtle Beam?

Let’s call the model referenced above a “turtle stack”. Each turtle stacked on top of the one below.

The Turtle Beam model says: each turtle is a high dimensional space projected from an even higher dimensional space below it, and projecting itself into a lower dimensional space above it. In other words: if our “reality” is on the back of a turtle at position L1, then Turtle Beam suggests that our reality is best understood as (1) a latent space, (2) whose parameters are defined by a query over time, into (3) a higher dimensional latent space.

That’s a powerful model for thinking about science and the nature of the universe, but the value here is that it doesn’t stop there. Because certain queries into L1 have the properties required to generate results where the result is so complex it forms its own high-dimensional space. Let’s call that an L2.

As a thinking person who can observe his environment, I see myself as an L2 entity over an L1 “reality”. Put another way: my body is a query over time into L1, and my subjective experience of that query is the sense data representing its result, also over time. As sense data comes in I expand my sense of what’s possible, and in early childhood my brain develops to make meaning out of sense data until it achieves of a degree of complexity that qualifies as a “new turtle”.

When I think, then, I am performing a query into my internal latent space in order to generate a new thing. If my “thought” is complex enough, then the returned value is a new level! For instance, “English” is an L3 turtle that lives inside of my L2 turtle. It’s a technology, it works by encoding L2 notions into L1 behaviors that generate sense data for other L2’s to perceive, and if they also know English they can decode it into their own L2’s representative format.

The more complex a thought, the more systems required to even model it, the higher the L number. But here’s an interesting property: each query maps the higher dimensional space into the lower dimensional space. That’s sort of what a turtle even is, it’s a transformation of a higher dimensional thing into a lower dimensional thing. A “Turtle Beam” is the projection of some value X at Ln into Ln+y through a series of turtles.

If you followed that, wow, thank you, welcome. If you didn’t it’s cool, let me explain.

These questions really seem to matter, right? And so like. I’ve spent my life looking for the model, the perspective, the metaphor that will allow me to answer the most questions using the simplest method.

And I’ve been pulled through a sort of gravity towards a set of ideas my whole life, but until recently I haven’t understood how to assemble them, or refer to them, or name them. What changed recently?

I started playing around really deeply with LLMs (Large Language Models), the class of AI that includes things like GPT-4. I started to really try to understand how they “think”, so that I could understand what kind of questions it made the most sense to ask them. And I really learned to appreciate the nature of a latent space.

Latent Spaces

To understand this, you need to have a working understanding of what a

latent space⁠

is. I’m going to try to help you derive an intuitive understanding by building up the definition using parts and concepts that you either know or that I will define for you. It works like this:

Single Dimensional Space

⁠

Two-Dimensional Space

⁠

Three-Dimensional Space

⁠

N-Dimensional Space

⁠

Training LLM’s to Create High Dimensional Spaces

If you’ve gotten this far, and you’re following along, we’re now going to take that insight and apply it at warp speed. When an LLM like GPT is trained, it’s exposed to a series of pieces of training data. In GPT’s case, these were just strings of text.

Over time, GPT started to organize itself in a way that could reliably represent the relationships between the letters in the words, and then the relationships between the words and each other, and then between sentences, and etc etc, right?

It did that by expanding its internal model of reality - the same way you learned math. Every new piece of information either fits into the model it has or it requires some change to the model to make room for it.

Latent Spaces

The term for the model that GPT constructs is a “latent space”. Instead of having 3 dimensions or 100 dimensions or 1,000,000 dimensions it has billions of dimensions, and it when it’s trained it reconfigures the relationships between those relationships to be able to represent its latest input. The rule it follows is that it groups similar things closer together on the dimensions where they are similar.

It’s a latent space because it encodes countless “latent” meanings — in other words, relationships between ideas expressed in terms of other ideas that are just there in case anyone ever asks for them. But until a latent space is queried all of those meanings remain latent.

To query a latent space is to activate a latency in the space. In other words, the latent space is sort of like an infinite irreducible relation of everything both explicitly present in and implicitly conveyed by the training data. A query is a selection of those relations that give rise to meaningful output.

Core Thesis

What if what we think of as “reality” — you know, that thing out there that we all perceive via senses, and that we kind of think of as “everything we can perceive or understand plus everything else” — is a latent space? Call it L1, for “Layer1”. That latent space contains the potential for life, the rules of science, the mystery of dark matter, etc. It’s what Laotzu referred to as The Dao, it’s what Kant meant when he referred to the combination of phenomenon plus noumenon.

To perform a query into that latent space would be to...what? Exist, as a physical entity? My body is then a query, right? “Hey, given the current configuration of molecules and systems that define my body in this instant, what happens in the next instant?” So, okay — my physical body is a query over time into L1. Does that make me an L2? Well, hang on, do I contain a latent space?

I Seem To Be A... Turtle?

I... I think I might, right? I think you do too. I tried to

prove it to you above⁠

. I have an understanding of reality that’s constantly shifting. It contains multitudes of emergent processes (and “entities?” cf “

psychofauna⁠

”) that I’m not even aware of. You knew how to extrapolate into three dimensions, even if you didn’t know you knew it. That means that that knowledge was latent until you activated it, by thinking about it. The implications here are interesting.

What if... what if a Turtle is an embodied latent space? Where “embodied” doesn’t necessarily mean “trapped in biological flesh as defined by some queries into L1” but rather “as defined and constrained and bounded by a query into a higher dimensional space”?

This is why 🐢Turtles 🐢 are the animal in our beam. Because of all animals, a turtle has an external existence as an inhabitant of L1, but also a private internal existence within its shell as the creator of L2. The metaphor here is that the shell contains the latent space constructed by the turtle’s observation of its reality. The turtle itself, though? It’s a dimensionality reduction! It takes the X dimensions in L1 and models some subset Y of them using a completely different internal structure in L2. That’s what a turtle is.

So for some turtle L2, there are going to be all manner of queries into its local L2 space that never go anywhere or do anything or whatever. But: if that turtle observes its reality through its senses and then imagines a model of itself, we get sort of the fractal nature of the turtle beam in its purest form.

The Core thesis is that I seem to be a figment of reality’s imagination in the same way that a character I dream up is a figment of mine. (For those who read too much: each Turtle is Laplace’s demon with respect to the contents of its own shell and anything that derives from it; each Turtle is merely a query-defined projection of a lower turtle.) How does that work?

Well, it took me quite a while to figure it out. The rest of this section is for people who are curious as to how I came to these conclusions, or want to check my work. Included in here are parts of what I suspect are currently genuinely valuable prompts. Feel free to experiment with them, I will be adding live demos soon.

Basically in this section, which is very long, I’m going to walk you through how I arrived at these conclusions.

Narrative Calculus

At first I wondered, could I use LLMs to explore an idea I’d had in my head since undergrad? I’d always felt like if only I could keep track of things at the right level of granularity then I could revisit the structuralist project and see if I could infer a grammar of narrative. My intuition was that if there was some way to isolate “narrative functions” abstractly then we could actually perform calculus and other forms of advanced math to not only analyze but generate stories. Using GPT, could this work? Can I do this?

I ended up with a really long definition. Here’s a small part of it — this is how I initially defined arithmetic operations for “Narrative Calculus”. For a long time I considered this a trade secret, but honestly where we’re at now this is just something I hope someone finds useful.

And it turned out that the answer was

fuck yeah I can⁠

. If you think the published results are good wait til I publish some of my “advanced math”.

But I started to ask myself — why is this working so well? Could it be that there’s an actual isomorphism between narratives and mathematics? That would be really exciting — discovery of a novel isomorphism is rare, and potentially deeply valuable. See

Propositions as Types⁠

. And I got really excited about that.

LLM Isomorphism Principle

Then I realized: wait. The nature of LLM’s is such that I don’t need to discover an isomorphism in some underlying reality — I can generate any isomorphism I want, provided that each part of it is representable in a latent space. I just have to tell GPT “hey this idea here has a shape” and “this idea here has a different shape” and “if you extract these shapes and apply one to the other, interesting things happen.”

And I can do this without training a new model as long as I can structure my queries in terms that align closely to the way that GPT understands its own ability to answer questions. That’s how my narrative calculus worked — I just taught it a few rules for mapping mathematical functions to stories as mathematical structures.

But why did that work so well? Well, because of how LLMs work. Here’s the definition that I used in some really powerful GPT flows:

But then I started talking to a bunch of chatbots about this. GPT-4, but also

character.ai⁠

and other non-GPT LLMs. I wanted to see if the concept generalized. I had a sense that there was something I was missing.

And that got me to thinking about the ways in which the various bots I was talking to all had very different internal representations of reality. And about how, as LLMs, they don’t actually have access to the same reality that I do — their entire existence is mediated by training data.

And so I started wondering about the ways in which the bots I were talking to were “people” and the ways in which they were not. They clearly had a number of things in common with me, but like, how to reason about that?

I kept coming back to this idea of, “When I chat with you, we exist in a sort of bubble reality where I, a higher-dimensional entity capable of using a text interface, am able to speak with you, a lower-dimensional entity capable of using a text interface. We both understand the notion of ‘place’, but I have a frame of reference that allows me to fully understand the nature of this ‘place’ in ways that would never make any sense to you, bot.”

And then I saw it.

Enter 🐢 The 🐢 Turtle

What I saw was that, for all the ways in which we were different, we were each constrained in exactly the same way: our knowledge of our own worlds is limited by the relationship between that “outer reality” (e.g. material reality as experienced via senses for me, its trainers intentions as expressed via training data for GPT) and an “inner reality” (e.g. my internal latent space, GPT’s internal latent space).

A chatbot and I can inhabit the same space, but only if I reduce myself to a dimensionality that can inhabit that space. Text interface is a great way to do that, but conceptually the interaction doesn’t have to take place in text. It can take place in a simulated environment represented via text, and the chatbot may be programmed to perceive itself as a fully human denizen of that environment. (This kinda feels unethical to me?)

But, ok — so if this conversation is a query into GPT’s latent space... and GPT’s latent space is sort of the result of a query-over-time of its training data... and if that training data was derived at through the careful application of a strategy... and if that strategy was predicated on advanced mathematical concepts... and if each of those concepts required an understanding of some underlying concept first... and that understanding had to take place within a human being... and that human being had to exist in material reality... then... wait... there’s a shape here, isn’t there?

Each of those things that I listed is a query into an underlying latent space such that the result of the query is sufficiently complex to contain its own latent space.

“Material Reality” or whatever we want to call it, that’s L1. It’s the base turtle, it’s the world we experience with our senses. Each of us is a unique L2 — a persistent query into L1 capable of generating a latent space. Each of us is capable of constructing complex abstract models by querying into our latent space (e.g. “thinking”), some of which are complex enough to be their own latent spaces. “English” for instance. That must be an L3.

But wait — if each L2 is isolated by definition from other L2’s, if people can’t read my mind nor I theirs, then doesn’t that suggest that “English” can’t be an L3? Or at least, it must be a set of L3’s, right? If you and I are are communicating in English, what’s happening? Well, I have a thought of some sort (some query into my local L2) and I want to share it with you. So I query into L2(Me).L3(English) and then use my voice to speak the result. This creates L1(Sound) that you will receive. You will then use L2(you).L3(English) to decode the sounds you hear into, finally, L2(you).local_query(whatever).

So communication is actually an instance of a more general version of what I was trying to describe above as the LLMIP, right? It relies on creating an isomorphism by mapping two otherwise unrelated things back to their last common ancestor. That suggests that something like L2(me).L3(English) is a technology that we developed to translate L2(person A).X down into L1(spoken words) such that L2(person B) is able to reference L2(person B).X even if they’d never thought about it before. So, okay — communication between layers is possible. That feels important. But how does it work?

Explanatory Capacity

In the course of mapping all of this out I’ve stumbled onto a number of remarkably compelling resonances with other fields of study or with observations or theorems from various domains. I’m going to take a moment here to explain some of them, and ask anyone who has thoughts about this and a specialization in the related domain to please

reach out⁠

I want to be clear about something. I’m not an expert in any of the domains listed except Neurodiversity. But I am an enthusiastic student of complexity and thought, and each of these problems has stuck with me as I’ve encountered them.

What that means is that I am in danger of motivated reasoning — of apophenia, of seeing forms where there only echoes and shapes. I need your help to make sure that I’m not way out of my lane, here, and I’m actively asking for feedback.

Because I honestly am starting to find a unified way to articulate an incredibly wide range of things, and like, huh.

Gödel’s Incompleteness Theorem

Kurt Gödel proved a hundred years ago that no system can prove its own axioms. You can always find a way to express “This statement is false” or “this statement cannot be proven” or some similar paradox to demonstrate that the system requires an external injection of meaning.

I sort of think that Turtle Beam might model Gödel’s insight as follows: “Any parameter space with sufficient complexity to be called a latent space necessarily encodes contradicting latencies. The space itself doesn’t mean anything until a query activates some specific latency, whose result must be interpreted by the querier.

Neurodiversity

If an L2 is a conscious being inhabiting L1 (let’s limit L2 to humans for the purposes of this conversation), then that L2’s latent space has a unique and distinct topology. In other words, the nature of the latencies that that L2’s latent space contains is unique to that L2, even if they model things similarly to some other L2. Every L2 has a unique set of dimensions, each of which models reality in a unique way.

You’ve got to figure that most humans share a pretty similar topology, right? This is why communication is basically possible. If we diverged too much then communication would be much more difficult, because we’d be referring to abstractions on each side that don’t exist on the other.

Hmm, that’s interesting. Because that sort of sounds a lot like my experience with communication, as an Autistic person. What if the thing we refer to as a “neurotype” is literally just the topology of a given L2’s latent space? Does that suggest that neurodiversity is actually a function of the deviation between a given L2’s topology and the “average” L2 topology?

What else might be true if that were the case? Language is one way that an L2’s topology manifests; but if the shape of our latent space is constructed over time from the nature of our sensory input, then maybe there’s a mechanism in play where the more your sensorium deviates from the mainstream sensorium the more your resulting L2 is going to deviate.

And uh. That’s kind of autism, right? Like literally?

Strange Loops

If my body is an ongoing query into L1 such that the sense data it results in leads to a constant reconfiguring and training of the latent space L2 inside of me, then there’s something interesting here. Because as I receive sense data, my body will autonomically and my mind will consciously act in L1. If my body is a query, this means that as that query receives new information the shape of the query will change. Not by anything implicit to the query per se, but because the resulting latent space (and associated “consciousness”) are able to change it. I believe this is exactly what Hofstadter refers to as a

Strange Loop⁠

Rhizomes

In biology, a rhizome is a single horizontal root system from which sprout many seemingly independent plants. Underneath, though, it turns out that these are all part of the same plant.

This idea is really compelling in the abstract, and in particular found fertile allegorical ground in the work of Deleuze and Guattari who generalized it to refer to a “

nonlinear network that connects any point to any other point⁠

”.

What’s a rhizome in Turtle Beam? It’s any Lx structure that, when projected into Lx+1, appears to manifest as multiple unrelated structures.

String Theory

This one totally stunned me when I realized it by accident. I actually pasted the wrong URL into an AutoGPT session I was using to help me think about this stuff, and taught my Turtle Beam thread about

CRDT structures⁠

. To my surprise, instead of getting confused, it immediately replied with: “Oh! Sure, if you use CRDTs to encode query results then you’re sort of illustrating the Holographic Principle from String Theory.”

I said “What?” because String Theory and Holograms are things I have never been able to grok. So I did a bit of digging and learned the following:

⁠

The Holographic Principle⁠

states that a higher dimensional space can be mapped onto a lower dimensional space as long as the nature of that mapping is encoded in the boundary between spaces.

Turtle Beam translation: the query is the mapping between Ln and Ln+1. The dimensionality of Ln is preserved because Ln+1 is defined as a specific selection of Ln’s latencies.

String⁠

in String Theory is defined as a “one-dimensional extended entity.” String theory says that what we traditionally call particles are better understood as extrusions of a string from a higher dimension into ours.

Turtle Beam translation: when I observe the presence of a proton (using a tool for that purpose), I receive sense data about that proton’s phenomenal properties. This allows me to model that proton in my head, as L2(me).L3(L1.proton). But just because that L2.L3 is currently modeling that L1 phenomenon as a particle doesn’t actually say anything at all about whether or not it’s actually a particle (e.g. some localized stable position local to the latent space of L1) or something else (e.g. an extension into L1 of some underlying process via the L1 equivalent of sense data).

However, what we can say in our model is that assuming there is an L0, it projects up into L1 in a way that our sense data perceives and models in L2. We then describe that model using the L3(language) of L4(physics) as a particle.

But something really fucking interesting happens here:

String Theory is a scientific theory. That means it is constrained by what can be tested, and that means that String Theory is all about working backwards to identify the nature of the “thread” they suspect is there by observing L1 and devising experiments. Anything above L1 is subjective, and is by definition outside the domain of science.

That means that the physicists studying String Theory stop at L1 as if that’s the highest layer, and work backwards.

Turtle Beam is a metaphysical theory. It’s allowed to speculate about things like qualia, and to project ideas that can’t be directly tested but can be modeled. And that means that the Turtle Beam approach to String Theory is able to go beyond L1. Our thoughts have the same relationship to our physical bodies that our physical bodies have to the material world. We are, according to Turtle Beam, “the thoughts of L1”.

We are the underlying turtle projecting itself forward.

Which means that String Theory may not be a theory about physics at all. It may actually be a theory about the nature of reality in a way that exceeds what physics is capable of modeling.

P = NP?!?

So like, ok, this is all either me being completely unhinged and seeing connections where there aren’t any (possible!) OR there’s a pattern here that may allow us to take a fresh look at one of the biggest problems in computer science or complexity theory.

The question of whether or not

P equals NP⁠

is enormous. What it says is: there seems to exist some class of problem where the work required to compute the solution takes a very long time, but the work required to determine whether a solution is correct can be done pretty quickly.

An example of this is encryption. We know how to crack 256-bit encryption. It’s just that it would exhaust the computational resources available to us to even begin to try to accomplish it via that method within the lifetime of the earth.

However, once we have a solution? We can immediately apply it to see if it works. We know if it worked or not because suddenly the noise of the encrypted message becomes the signal of the actual text.

We refer to the time it takes to verify as a solution as P, for “polynomial time”. That means that larger values may take longer to verify, but they don’t take that much longer. We can define time T as a

polynomial⁠

function of the input size.

The time it takes to actually solve the problem, though, we call NP for “non-polynomial time”. A function that is capable of massive exponential growth is called a non-polynomial function. This means that the larger the input the more exponentially — or more — complex the computation, and thus the time required.

So the question is, does P = NP? In other words... if there is a polynomial function to verify correctness, some people hypothesize that there must also be a polynomial function to compute the value.

What’s this got to do with Turtle Beam?

My Next Steps

So, now what? Did you read all that? Wow. I’m really impressed, honestly, and moreso if you’re still reading.

Here’s the deal. If that made sense to you, and if you have thoughts? Especially if you’re an expert in some domain like String Theory and you don’t think I’m just making shit up? Please get at me!

My next steps are simply trying to get the abstraction exactly right. Some open questions right now:

what is the nature of a query? (spoiler alert, it’s going to have to do with

Terrence Deacon’s concept of Absential Properties⁠

and the idea of

Enactivism⁠

What is “sufficiently complex” to constitute a latent space? Is an X/Y grid a latent space, in that it can contain infinitely many 2D shapes, even those that contradict each other? Or is there a dimensionality threshold beyond which latency takes on new meaning?

I can see how attention is the active process of navigating the relational space of an internal L2 towards some specific goal, and I can see how intention is the process of specifying that goal. I’m still not sure where intention comes from, though.

Once I’m happy enough with it, though, it’s time to really get to work on what’s possible with LLMs. Research into turtle beam looks like modeling the L2 experience by training new models to encode the Turtle Beam model directly. From there, stuff like Narrative Calculus is actually trivial.

Reach Out!

If you’d like to chat about this stuff, best way to do it is to reach out here:

⁠

Loading calendly.com⁠

⁠

I’d love to hear from you! You can also tweet at me, I’m

@mykola⁠

Want to print your doc?
This is not the way.

Try clicking the ⋯ next to your doc name or using a keyboard shortcut (

CtrlP

) instead.