The hundred-and-twenty-two-order disagreement I cannot resolve
A lattice budget and a holographic budget for the same horizon, differing by a hundred and twenty-two decades. One of them has to give.
computation
20 posts.
Why a monolithic machine cannot do this
Detecting novelty across N branches costs N log N with signatures rather than N squared with full states. The architecture is forced, not preferred.
How many facts fit in a causal past
One event per Planck four-volume gives a number with two hundred and forty-four digits, and it caps what a simulation can honestly render.
Identical universes are worthless
The harvesting theorem: a homogeneous multiverse returns O of log N bits regardless of how many branches you run. Heterogeneity is mandatory.
S_dS over pi squared replaced a number I made up
The derived capacity of the horizon, and the fraction of the holographic budget the old numerology was quietly using.
How many operations does the universe get?
Two times the energy times the time, divided by pi hbar. Applied to a horizon, with three independent bounds agreeing.
Varney's Law, derived rather than assumed
A logistic term from preferential attachment on a finite pool, a quadratic term from obsolescence, and a fixed point that matches a simulation to a tenth of a per cent.
Two ways past a plateau, and only two
Get a better theory, or get data from different physics. The second one is the entire justification for the machine.
The floor under the plateau
When the truth sits outside your model class the rate still dies, but at a level set by your framework rather than your effort.
The plateau theorem
If the truth is in your model class, discovery decays to zero and the total budget is finite. Stated, proved, and demonstrated.
Novelty is a compression measurement
Replacing a formula involving agents and rule-set complexity with something you can actually compute: a description length.
Minimum description length as a theory-selection principle
Prefer the theory that compresses the data and pays for its own parameters. It is Occam with an invoice.
Paper 17: the computational multiverse
The newest paper, and the one that stopped leaning on the topological sector. Seven derivations that hold whatever happens to the rest.
Paper 1: novelty as an exact resource theory
Making novelty a monotone rather than a slogan, so that no free operation can manufacture it.
Two-part MDL codes, concretely
Model cost plus residual cost, with a polynomial fit you can reproduce, because the whole plateau argument runs on this.
Kolmogorov complexity for people who write code
The shortest program that outputs your data. Uncomputable in general, measurable in practice, and the reason I reach for a compressor.
Lloyd, Bekenstein and Landauer agree
Three completely different arguments about how much a horizon can compute, landing on the same number. That is worth pausing on.
Novelty flux density: the quantity the whole thing is about
Every claim in this programme is ultimately a claim about one rate. Here is what it is, and here is where the original definition went wrong.
The Universe Complexity Spectrum, from Pong to cosmology
Seven classes of simulated environment, ordered by how much novelty they generate per unit of compute. The economics are counterintuitive.
The Forever Machine: what it would take to run one
A novelty-harvesting multiverse is an engineering specification, not a philosophy question. The specification has numbers in it.