Bernhard Mueller

We usually assume an objective world exists "out there," independent of anyone looking at it. This book drops that assumption. It starts with something we do have access to: a perspective. Every observer holds a finite amount of information about the world. Where two observers' views overlap, their descriptions have to agree. That single requirement turns out to be enormously restrictive. The book works through the consequences one question at a time: why the Universe is hard to reverse engineer, why there is anything at all, why a universe would need anybody in it, and why two descriptions of the same thing ever agree. Each chapter is a question, and the answers build on each other.

Could the computation that makes a physical world and the computation that makes a mind be the same kind of process? We examine one candidate, local repair: components correct their disagreements with their neighbours until the whole agrees. Two running systems carry the test. Observer Patch Holography proposes that physics is what bounded observers can establish by comparing and repairing their records on overlapping patches, and runs as an executable observer. Cadence is a library of animal brains that perceive, choose and learn by settling reciprocal neural activity into one equilibrium. The two meet in exact results. The condition that makes a record a public fact in the physical model, that records separate the consistent states, is the condition under which a predictive model of perception settles on one interpretation; in the linear Gaussian case the surprisal of an observation is the disagreement no repair can remove, and what the observation teaches is the disagreement repair will remove. The agreement a repair reaches, and the disagreement it spends reaching it, are the same under every admissible law and order of repairs, while what a learner reads along the way is not: a world's public facts are independent of the path, and a brain is taught by it. Every elementary repair of the physical observer is exact Bayesian conditioning on what it sees, while the descent of disagreement it performs is no descent of improbability. Both systems keep records that decide what they do next and pass the same intervention test: the observer's next action follows its retained record, and a brain given a donor's memory carriers answers as the donor. The guarantee a law admits follows the structure of its interactions: at linear order a reciprocal law survives every change of local speeds, and a non-reciprocal one can be destabilised by a single change. Three obstructions say what a shared mechanism must survive: compatible states do not fix a law, a summary of the present can omit what an intervention reveals, and eliminating a mediator can destroy a pairwise description. On a measured fly connectome, the existence of an equilibrium, settling within a budget and useful responses come apart, and a code of meaning learned by local repair groups words by shared context where raw keys stay at chance. A comparison with Friston's free-energy principle locates where it and local repair coincide and where they part.

Why is there anything at all? An equation can describe a real structure, but consistency alone does not establish that it exists. Observer Patch Holography proposes a closed, self-referential history whose inhabitants recover the rules producing their records and realize those rules within that same history. Consistency has a local mechanism: finite observers compare overlapping records and repair disagreements. A fact is public when its record survives every authorized comparison and repair. We prove a canonical finite consensus theorem. On a twelve-port carrier, repair has exactly three slow directions; a faithful complete current implementing the carrier's rotations internally has the Standard Model gauge Lie type. A supplied complex algebra of states and effects yields quantum measurement identities. A specified finite source connects currents, localized modes and a mass operator; separate constructions give controlled free fields, interactions and a conditional route to the Einstein equation. The central proposal is that existence, objectivity, space, matter and gravity belong to one self-consistent process. Its identification with our universe requires a common interacting chiral 3 + 1-dimensional limit with the observed particle spectrum, responsive geometry and independent empirical agreement.

A robot that works among people needs a brain that learns while it acts and finds what it needs in its own past, as animal brains do. Most deployed machine learning does not: its networks are trained by backpropagation and then frozen, and a transformer attends over a cache that grows with the context. Cadence is an open-source library of biologically inspired neural networks that learn during life, in real time. This paper describes it as a whole, aiming to make such networks powerful and scalable. A Cadence brain is one continuing network of regions joined by reciprocal synapses. With its senses held fixed, its neurons repair their local disagreements until the network rests in one equilibrium, which is its answer. Learning compares two nearby equilibria: a small nudge on the motor neurons travels back over the reciprocal synapses, and each synapse changes from the activity at its two ends, with no backward pass. In a deep brain the top-down half of each pair lands on an apical compartment, bounded to a share of the bottom-up drive; where depth pays, each added region raises accuracy, and four regions reach 0.86 against 0.89 for a two-layer backpropagation network. A dopamine-like prediction error drives reward learning, and arousal from surprise and unmet need decides when the creature explores, learns and writes memory. Like every purely recurrent network, settled activity must compress its past, so Cadence adds synaptic memory read by learned attention. Beside a working trace and an episodic memory, a recall memory keeps its recent moments verbatim as slots, keyed by the observation or by a code of meaning learned by settling, each holding an event and its successor. Before each settle one or several heads form a query from the present and the previous interpretation, weigh the slots by a softmax over the match and a learned term for each slot's age, and hold the read while the brain settles. Queries, age terms and codes learn during life by local rules, and the memory's cost per moment does not grow with the life. Read with its successor, the memory is an induction head, and the age term makes order answerable: questions about first, last and how long ago reach 0.9 to 1.0 in sequence tasks, stories and a survival world where lessons teach them. Composing reads within one moment and learning where to look from reward alone are measured as missing. Proofs establish what settling guarantees in a plainly summed network.