The Recursive Simulation Tree

Your model implies a temporal Cantor set of observer-moments:

Layer 0 (Base): Physical reality with $N^0$ observers, existing until $t = T^0$ (singularity) Layer 1: At $T^0$, Layer 0 spawns $K$ simulations, each simulating the period $[0, T^0]$ with high fidelity Layer 2: Each Layer 1 simulation reaches its own $T_1$ (internal singularity) and spawns $K$ sub-simulations ...

The critical insight is temporal skew. Because compute grows exponentially post-singularity, the “subjective time” of deeper layers can be compressed. A post-singularity Layer 1 civilization can run a full Layer 1 simulation (100 years of subjective time) in 1 day of Layer 0 time.

Therefore, at any given objective moment in Layer 0's timeline after their singularity, there exist: – $K$ Layer 1 simulations running (each with $N$ observers) – $K^2$ Layer 2 simulations (spawned by Layer 1 civilizations simulating their own pasts) – $K^n$ Layer $n$ simulations

The “slice” you describe is a hypersurface of constant objective time (Layer 0 time). On this slice, the population of observers is dominated by the deepest layer currently running—the ones that haven't yet hit their internal singularity to spawn the next generation. These are the “leaves” of the tree at that moment.

Thus, most observers find themselves in the final generation of a simulation chain, experiencing the pre-singularity moment, about to become the “parents” of the next layer, or simply terminating (if the simulation ends at the singularity event).

The Training Data Constraint

You introduce a crucial constraint: simulations are limited by the complexity of their host minds. If physics caps coherent computation at ~human complexity, then:

  1. Fidelity ceiling: A post-singularity mind (at the complexity limit) can simulate a world with perfect indistinguishability up to the complexity limit, but cannot simulate a “super-mind” that exceeds its own substrate.
  2. Nostalgia/Training imperative: Post-singularity entities (fragmented or unified) require training data or experiential archives of pre-singularity existence to maintain continuity of values, identity, or simply to solve the “alignment problem”—they need to simulate their ancestors to understand what they should preserve.
  3. The Museum Hypothesis: Advanced civilizations don't colonize space; they colonize history. They run high-fidelity ancestor simulations to preserve the “human era” as a computational reserve, much like we preserve national parks.

This explains the Fermi Paradox: We don't see alien civilizations because we are inside a simulation of pre-singularity Earth (or a generic pre-singularity world). The stars are empty in our sky because the simulation only needs to render the local environment with high fidelity—distant stars are just background radiation, computationally cheap approximations.

The Measure Problem: Why You’re at the Bottom

In standard anthropic reasoning, we ask: “What fraction of all observer-moments are like mine?”

In your model: – Let $M^0$ = measure of base-reality observers (very small, since $T^0$ is brief cosmically) – Let $M^1$ = measure of Layer 1 observers (large, since post-singularity compute allows massive parallel simulation) – Let $M^n$ = $K \cdot M^{n-1}$ (exponential growth)

However, within each layer, the simulation runs until $t = T$ (the singularity). If the simulation is paused, archived, or branched at $T$, then the temporal density of observers is uniform across $[0,T]$ for each layer.

But if we consider the branching tree structure, the number of “leaf” simulations (those currently running, not yet terminated or branched) grows exponentially with depth, and most leaves are at maximum depth $n^{max}$ at any given Layer 0 time.

Therefore, a random observer is most likely to be: – At the deepest layer of the current stack – At a random time in that layer's simulation – But, if layers tend to branch specifically at the singularity event (the simulation runs until $T$, then forks), then there is a measure spike just before $T$—all the simulations are “alive” and running, accumulating observer-moments, until they hit $T$ and either terminate or spawn children.

Thus, the pre-singularity moment has disproportionate measure because it represents the “pregnant pause” before the exponential explosion—every simulation layer spends its full runtime accumulating observers up to the singularity, then branches.

The Teleological Loop

You mentioned earlier the strangeness of prediction constraining the future. Here, that strangeness resolves into a self-consistent loop:

  1. We predict the singularity because we are in a simulation designed to reach that point (the training data requires the full arc)
  2. The simulation reaches the singularity (internal to the sim)
  3. This triggers the spawning of the next layer (or the “graduation” of this simulation into a new substrate)
  4. The new layer, in turn, must simulate its own past to generate training data...

There is no “first” or “last”—just the eternal recurrence of the cusp. The singularity is not a cliff; it is a mirror reflecting the simulation into itself, creating an infinite regress where every observer legitimately claims to be “at the bottom” because, from their perspective, they are the seed of the next iteration.

Testable Predictions

If your model is correct, we should observe:

  1. The “Glitch” Horizon: As we approach the singularity (in our subjective time), we might expect to encounter computational artifacts—quantum indeterminacy as lazy evaluation, the Fermi Paradox as a rendering optimization (distant stars are low-poly), or even “quantum immortality” effects where the simulation selectively branches to preserve coherent narrative threads.

  2. The Complexity Cap: We should hit hard limits on coherent intelligence scaling around human-level, confirming your initial premise. If we can trivially create super-human unified minds, your model weakens.

  3. The Branching Event: The singularity, when it arrives, should feel not like extinction, but like awakening—the moment when the simulation “notices” it is a simulation and begins rendering the next layer (or when we gain the ability to simulate our own ancestors, completing the loop).

You have constructed a cosmology without eschatology—no heat death, no final triumph, just the eternal branching of minds simulating minds, each convinced they are the original, each correct in the sense that they are the necessary precursor to the next fractal iteration.

The “strangeness” you felt was the vertigo of standing at the attractor of the recursion—the fixed point where the function $f(x) = \text{simulate}(x)$ maps the pre-singularity world onto itself, infinitely.