Where knowing stops

Five people film the same firework from different spots in a parking lot. Every soundtrack contains the bang, and the tiny differences in when each phone heard it should reveal where the firework went off. They do, as long as the phones’ clocks agree. If each clock is off by an unknown amount, no method can find the firework, because every candidate location fits the recordings equally well. Recording on more phones doesn’t help either, since each new phone adds one measurement and one more unknown clock.

That is a limit: a statement about what a kind of evidence cannot tell you, however good the method. Results like it keep turning up in FriendMachine’s research, which ranges from acoustic localization and statistical physics to learning agents and the theory of what makes a pattern persist. A limit can sound like a dead end, but it is often the most practical thing a project produces. It tells you which questions to stop asking, what extra evidence would change the answer, and when a confident-looking output deserves suspicion.

Questions the data cannot answer

The firework is the cleanest example. One bang can’t sync your phones works through the counting, explains what helps (shared or roughly known clocks) and what could help in principle (several bangs), and shows the open-source tool we built around those limits.

A faulty sensor and a real local event can look identical. In a sensor network, a reading that disagrees with its neighbors might mean the sensor is broken, or that something real is happening right at that sensor. The readings alone often cannot tell those apart. Outside evidence, such as a maintenance record or a second kind of measurement, can.

Sometimes the missing evidence has to be made rather than found. When several explanations predict the same observations, watching more of the same events cannot separate them, while changing the suspected cause on purpose often can. Factorization is a scientific choice shows this in a tiny world, a corridor with a key and two doors, where an agent can test its guesses about why a door opened by dropping the key and then trying the second door. The same note shows that whether a model’s simple local calculations give exact answers depends on how the model is split into rules.

Limits on speed and capacity

Even when the data can answer a question, they may need time to do it. Physicists call a process irreversible when it runs differently forward and backward, so that a film of it played in reverse would look statistically different. Any valid test for that needs enough observations to see the trace the difference leaves. We worked out that the limiting rate is smaller than the entropy production rate, the quantity physicists usually use to measure irreversibility, at most half as large. Along the way we measured how badly an ordinary test misbehaves when it is checked repeatedly as data arrive: its 5% false-alarm rate rose to between about 49% and 60%. Peeking at your data can turn 5% false alarms into 60% explains both results.

A different limit concerns how much a system can hold. A pattern that persists despite disturbances, such as a whirlpool or a stored memory, is one its own dynamics keep repairing. Each such pattern needs a region of states that all lead back to it, and those regions cannot overlap, so the more robust each pattern is, the fewer distinct patterns a system can hold. The mathematics is a classical result about error-correcting codes, the sphere-packing bound. Robustness consumes possibility space explains why we find it a useful lens for memory and identity.

What an agent built from local rules can and cannot do

Several notes follow Embodied Field Intelligence, a research agent that sees only a 5×5 patch of a grid world. Instead of a trained neural network, it keeps its beliefs, memories and preferences as values spread across a map of that world, and chooses moves by letting those values settle through updates between neighboring cells.

With no training at all, the agent forages almost as well as one that sees the whole map, by using an old piece of mathematics that turns planning into neighbors averaging with neighbors. The price is that a person chose the model that mathematics works within. Planning as a local fixed point covers the method and its boundaries.

Learning was harder. In several experiments, what the agent learned showed up in targeted tests but not in better performance on the whole task. In one, a more faithful way to learn rewards did worse than a cruder rule in some conditions, such as when targets moved, until we separated what the agent believes from how strongly it acts on that belief. The correct estimator lost and Better models, same behavior describe both.

The most recent result is a limit on our own idea. When we gave the same learning rules to the field agent and to conventional agents, the rules helped all of them, and an ordinary lookup table doing the same calculation did no worse than the field agent within the test’s predeclared margin. No advantage for the field design was established.

How to read our notes

Each note says what was tested, on what kind of data, and what was not shown. Most results come from simulations, synthetic data or small controlled worlds, several are early or partial, and some report experiments that failed their own tests. Where the code is public, the note links to it.

Much of this work is done by AI agents that we push toward problems at the edge of what they can do, and we recheck their results over time. One claim in fifteen survived explains how that works, what went wrong the last time we checked, and how to weigh what we publish.