God's Infinite Dimensional Space

How does reality appear to you?

Reality is too large to be experienced all at once, so organisms inherit a finite way of carving it up. A person then becomes a specific realized version of that inherited structure through language, history, memory, culture, and repeated events. For prediction, I do not need the whole ‘soul’ in some mystical sense, I just need a task-relevant approximation of the person: a slow representation of what they are generally like now, a fast representation of what is currently active in them, their present role and world-state, and a representation of the ‘proposition’ hitting them now. Then I model the interaction, predict the next task-relevant state (for the observer), decode visible outcomes from it, and update the system under error. The categorical part matters because a lot of what we observe about people is discrete, repeated, and role-dependent.

Actors embedded in environments express persistent structure and transient state through the traces they leave behind. Those traces can be used to estimate the features by which the actor understands and operates in the world. Once those features are approximated, a proposition can be introduced into the model and the actor’s next state and behavior can be forecast. Humans are the first research target. Sales is the first laboratory. Corporations come later as composite actors built out of people, institutional structure, facts, statistics, memory, and environment.

You can model your current mental interior, everything that you are experiencing now, as a small slice of reality that your genetic lineage allows you to experience, that can be traced by a series of state transitions up until this moment in time. The mind is an evolved, structured projection system that turns input into a lived state, and behavior is downstream of transitions in that state. Predicting what your next state will be is not an impossible task: in this work I am attempting to formalize a standard algebra to make this easier and tractable.

I’ll be blunt, this work is a monster, and it is, in essence, autobiographical of the mental state of the author who wrote it, representing the debauched & tortured way in which these ‘discoveries’ were made:

-As philosophy: this work is ambitious but undisciplined.

-As math: this work is mostly formal packaging around these undisciplined assumptions.

-As ML research propositions: this work is potentially worthwhile if you squint at it.

-As a finished research article: I fear it cannot be completed with a lifetime of work.

However, the goal is to examine this. First, external conditions are registered and restricted to what a lineage can access:

Then inherited structure becomes one realized actor, and the inaccessible ideal is connected to a finite predictive model:

The measurable system estimates a state from records available before the proposition, simulates a recursively closed next state, and separately predicts delayed outcomes:

That is a roadmap, not a claim that the external world, a Hilbert space, a person, and an outcome are literally the same mathematical type.

skip to the end if you are impatient and want a definition now

If you accept my starting assumptions, you can apply this framework to your own projects and start estimating task-relevant state transitions and outward behavior for ‘agent observers’ (people); the next phenomenal state remains the motivating ideal rather than a directly observed target. If you do not believe my assumptions this paper will be useless to you (but I swear to entertain, nonetheless).

Almost every serious attempt to formalize mind or behavior ends up either:

Waiting on neuroscience: “once we map the ‘connectome’ (or whatever the new limitation is) we’ll understand behavior,” a promise that has repeatedly been pushed into an indefinite future

Staying purely behavioral: black box input/output with no theory/framework of internal structure

Getting lost in phenomenology: Husserl, Heidegger, etc. philosophical but computationally intractable, thus mostly pointless.

This paper attempts a fourth path: take the structure of experience seriously as a mathematical object without needing to know its physical underpinnings. The machinery of the brain is deliberately abstracted away from the formalism. You could run the same formal program on an octopus, a human, a corporation, or a hypothetical silicon agent, but this does not mean these are all the same kind of object. A corporation is not an oversized person-vector. It is an amalgamation of people, institutional memory, incentives, facts, statistics, rules, and the environment it exists inside. Once that composite system has persistence and a characteristic way of taking propositions and producing responses, it can be treated as a higher-order actor. The outer grammar remains the same; the construction of the actor does not.

The closest intellectual ancestors are probably:

Friston’s free energy principle (I legitimately didn’t read this guy until well after part 2 was written, avoiding this line of thinking earlier would have been great): similar ambition of substrate-independence, but Friston goes deep into neuroscience anyway and the math becomes almost deliberately obscure; I could not extract the engineering program I wanted from the concept itself.

Marr’s levels of analysis: the idea that computational and algorithmic descriptions can be analyzed without reducing them immediately to the physical implementation, while the levels remain complementary

Early Dennett: intentional stance as a legitimate predictive state without committing to substrate

But this paper is more engineering-forward than any of those. It’s not asking “what is mind,” which at this point is a stupid question to ask, instead we ask: “assuming mind has structure, what’s the minimal formal system that lets us estimate its predictive state and forecast its outward behavior from observations alone.”

This paper aims to formalize several disparate fields into a single, coherent whole. We’ll begin with the tragic story for this exploration (which has to do with Kant), then go down the rabbit hole of theory together and come out the other side with a fundamental theory of ‘reality’ that can be applied across some fields. First, we’ll discuss how the appearance of reality is constructed and how organisms parse out their version of reality. Next comes how organisms perceive state (state being the appearance of reality at that instant), and what the organism is biased to do next. Afterwards, we’ll discuss how to compute memory and learning, and apply this to our understanding of state and decompose the philosophical proposition into a register that can be understood by engineers. If the program works, we will be able to progressively estimate an individual’s task-relevant psychology with greater precision, test which inferred features transfer, and use those estimates to forecast behavior under propositions.

I am proposing that there is a universal way to decompose these questions through a single mathematical arena, and I will illustrate that proposal here. Let us take the measure of reality and examine God’s infinite dimensional space!

Lastly, here are the differences between GIDS and standard ML:

Standard ML: construct a model → optimize for task performance → latent representations are a byproduct. GIDS: construct a stable latent object over the observer → task performance is a probe that tells you if your latent object is good → the ontology is the product.

One dominant paradigm in modern machine learning is:

-Collect massive undifferentiated data -Train a general model on reconstruction or next-token prediction -Hope that task-relevant structure emerges in the latent space -Fine-tune or probe for specific applications afterward

This is one version of the GPT/BERT/foundation-model playbook. It works extraordinarily well for language and, in adapted forms, for vision. In many such systems, the latent geometry is largely a consequence of the training objective and scale rather than an explicitly specified ontology of the actor.

GIDS inverts this completely and deliberately. The latent space is the goal, this is the product we will define, the inputs and outputs are just discovery probes. Scale is just a mechanism to get there; GIDS is a research program on how to bootstrap itself.

Preface

First, we’re going to talk about Kant (German philosopher, hugely important), don’t worry about the exact details of his works, I’m just going over the first handful of sections in his main book, Critique of Pure Reason, and using that as a jumping off point to how your reality can be represented using embeddings and states. Next, we’ll use the embedding concept to examine and measure bias when an individual is interpreting reality. And finally, we’ll talk about applications using this technique. Apologies for using philosophy as a segue into math; however, the pill is easier to swallow if the source of all this is adequately explained. I’ve kept the terms restricted to what you can find in a modern dictionary, so don’t worry about converting from some esoteric nonsense to English.

I read Kant directly while going through the Western canon. Unfortunately, Kant is the worst person to represent his own ideas, so you’ll have to bear with my fundamental misunderstanding of the source material. This is good news, however, as my misunderstanding of Kant is more useful than getting a ‘correct’ interpretation from most commentators. If you want to save yourself a year of your life, you can skip The Critique – and ignore all of the requisite readings – and try ​​Wolff’s class (Link). Kant uses a lot of dated terminology and systems that are only relevant to the era he wrote in (a reason why you should always start with the Greeks). I prefer the first edition, but the first and second editions differ materially, and a serious reading should consult both rather than pretending one simply replaces the other. Also, just skip Kant’s stupid moral system and the categorical imperative altogether. The Critique of Pure Reason rips itself to shreds: Nietzsche was right, Kant became a coward before his God.

Table of Contents:

The canonical symbol definitions are in Canonical Notation and Mathematical Conventions.

Part 0: Background: “Kant From An Evolutionary Perspective” “A Fucking Table”

Part 1: Specifying the Area of Interest: “Vectors Are All You Need” “The Nature of Phenomenal Reality: What are we trying to measure?” “The Evolutionary Mechanism for Encoding Transcendental Embeddings”

Part 2: Deriving the Transcendental Embedding: “The Technical Scope (because otherwise I’ll accidentally lie to you)” “Behold; You! The Chimera” “Psychology and Factor Analysis” “Dimensionality Reduction, Attention, and Relevance” “The Notion of State” “Observable Predictive State” “Memory as a Series of Vectors” “Categorical Trace Pooling as an Operational Memory Estimator” “Minimality, Identifiability, and Slow/Fast Factorization” “Deriving the Transcendental Embedding”

Part 3: Application — Predicting How People Behave: “Towards a Universal State Transition Function” “God’s Infinite Dimensional Space: Making All Realities Composable” “Creating the World Model” “From Forecasting to Proposition Search”

Part 4: Benchmarking the World Model: “Operational Definition of State” “Event Time and Dataset Construction” “The Benchmark” “The Proposed Latent-State Model” “Training Objective, Update Loop, and Intervention” “Temporal Split, Evaluation, and Drift”

Appendix A: Study Guide / Cheat Sheet