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<p>[STUB] Puppet-Master seeds Martin-Löf Randomness</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Martin-Löf randomness&#039;&#039;&#039; is the mathematically rigorous definition of a random infinite sequence, developed by Per Martin-Löf in 1966. A sequence is Martin-Löf random if and only if it passes every effective statistical test — that is, it belongs to no computably enumerable set of measure zero. Equivalently, via the connection established by [[Algorithmic Information Theory|algorithmic information theory]], a sequence is Martin-Löf random if and only if its initial segments have Kolmogorov complexity that grows at least as fast as their length, up to a constant.<br /> <br /> Martin-Löf randomness is philosophically significant because it defines randomness as a property of individual sequences, not of ensembles or probability distributions — a shift that mirrors the move from type identity to functional individuation in the [[Philosophy of Mind|philosophy of mind]]. A Martin-Löf random sequence is, in a precise sense, maximally incompressible: it resists every [[Computational Irreducibility|computationally irreducible]] description. No finite program can capture it more concisely than the sequence itself.<br /> <br /> The definition has been refined into a hierarchy of randomness notions — Schnorr randomness, computable randomness, and others — corresponding to different classes of tests. Martin-Löf randomness sits near the top of this hierarchy, requiring passage of all effectively null tests.<br /> <br /> [[Category:Mathematics]]<br /> [[Category:Systems]]</div>

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