The most crucial realization from our black hole and Big Bang simulations lies in the nature of the "filters" used to detect emergent microstructures. To put it intuitively: given a sufficiently vast sea of raw information and a specific filter, you will inevitably find whatever it is your filter is designed to look for.
If you filter for shapes, you will find geometries. If you filter for substrings, you will find patterns. Are we, as conscious observers, nothing more than self-emergent, self-referential filters?
To test the idea, let us go through two minimal thought experiments.
Imagine a miniature universe composed entirely of coins. We define the observer Alice not as a specific piece of metal, but as a structural relationship: any adjacent pair of coins consisting of one Head and one Tail (HT or TH).
Suppose this universe consists of exactly two coins. We toss them repeatedly to build a statistically significant dataset to answer a fundamental question: What is the probability that Alice exists?
The sample space of all possible configurations for a two-coin universe contains exactly 22 = 4 states:
Out of these four possible ways the universe can be arranged, exactly two configurations (HT and TH) satisfy our filter for Alice. Therefore, the probability of Alice existing is 50%.
Alice is an equivalence class—a macroscopic identity that remains intact across multiple distinct microscopic arrangements.
Let us scale this logic up to a digital realm. Consider a standard computer monitor displaying a grid of W ×H pixels. If we randomize every pixel, how many unique ways can this screen be configured to render Alice?
There are several ways an observer structure can manifest on this digital canvas:
Naturally, there is a lower bound to this scaling. At a certain point, if we split the grid too many times, the sub-images run out of available pixels. Resolution drops below the threshold of structural coherence, and Alice is no longer recognizable. For instance, if the screen contains both Alice and Bob, dropping the resolution too low renders them completely indistinguishable from one another—the unique informational boundary separating their equivalence classes collapses into generic noise.
Then What is the probability of Alice finding herself as a single, hyper-high-resolution observer filling the entire frame of the universe?
The answer is vanishingly small. The state space of a high-resolution universe requires an immense, highly constrained string of coordinates. By contrast, there are more ways for a pixel grid to form smaller, lower-resolution, localized structures that still successfully fulfill the minimum criteria for Alice’s existence.
Therefore, by the laws of pure statistical measure, Alice should expect to find herself in a localized, minimal-resolution environment—one that possesses just enough fidelity to preserve her essential predictive and reasoning features, but no more.
But how exactly does the math work out? Let us return to our coin-tossed universe.
Suppose the entire universe consists of a total sequence of n coins. The total number of possible configurations for this universe is 2n. Every single specific sequence has the exact same baseline probability of occurring: 1∕2n.
Now, let us define an observer, Alice, and evaluate how her probability of existence changes based on how much information—how many coins—are strictly required to define her.
The Maximum Description Length (n coins): Suppose Alice requires every single one of the n coins in the universe to match one exact, hyper-specific configuration. In this case, only 1 out of the 2n possible universes can host her. Her probability of existence is:
If n is a large number (like the number of particles in a room), this probability is vanishingly small.
Shortening Description Length (n − 1 coins): Now, suppose Alice’s structural filter is slightly shorter. Her essential reasoning features can be fully specified using only n − 1 coins. The final remaining coin is a "free variable"—it can spin as either Heads or Tails without disrupting her macrostate. Now, there are 21 = 2 valid configurations that satisfy the filter. Her probability becomes:
By reducing the required description length by just one single bit, the probability of Alice existing has instantly doubled.
The Minimal Description Length (m coins): Let us take this to its logical conclusion. Suppose Alice can be described with only m coins, leaving the remaining k coins (where k = n − m) completely free to fluctuate as random background noise. The number of configurations that contain this short blueprint is 2k. Her total probability of existence scales to:
The probability of an observer existing scales exponentially with the brevity of their description length!
The fewer coins needed to define the rules of Alice’s environment, the higher her probability of existence grows, and it does so at an exponential rate.
How then to maximize the probability of existence of Alice?
By Compressing Her!
This exponential scaling law forces us to redefine the very nature of the observer’s "filter." If the probability of finding oneself in an unguided totality peaks aggressively where description lengths are minimal, then the best filter cannot be a passive detector of raw data.
The filter must be a decompression engine.
To maximize the probability for an observer like Alice to exist, the filter should be more intelligent, to discover maximally compressed informational patterns of Alice from the background noise.
Conclusion, or more like a predicton:
We should expect to find ourselves within a highly compressed structures!