The computational multiverse
The newest results, which do not depend on the topology. 12 posts, best read in order.
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Novelty is a compression measurement
Replacing a formula involving agents and rule-set complexity with something you can actually compute: a description length.
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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.
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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.
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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.
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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.
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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.
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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.
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The instanton exponent was hiding in plain sight
A numerical coincidence I could not explain turns out to be the standard exponential suppression with the coupling pinned by the central charge.
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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.
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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.
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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.
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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.