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DouglasAHOrr (talk | contribs) Correct a detail in the first figure caption. Tags: Mobile edit Mobile web edit |
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'''Theorem.''' (Theorem 14.11.1<ref name=":1" />) <math>\log \frac{1}{P(x)} = K(x) + O(1)</math>
==Implications in biology==
In the context of biology to argue that the symmetries and modular arrangements observed in multiple species emerge from the tendency of evolution to prefer minimal Kolmogorov complexity <ref>{{Cite journal |last=Johnston |first=Iain G. |last2=Dingle |first2=Kamaludin |last3=Greenbury |first3=Sam F. |last4=Camargo |first4=Chico Q. |last5=Doye |first5=Jonathan P. K. |last6=Ahnert |first6=Sebastian E. |last7=Louis |first7=Ard A. |date=2022-03-15 |title=Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution |url=https://www.pnas.org/doi/full/10.1073/pnas.2113883119 |journal=Proceedings of the National Academy of Sciences |volume=119 |issue=11 |pages=e2113883119 |doi=10.1073/pnas.2113883119 |pmc=8931234 |pmid=35275794}}</ref>. Considering the genome as a program to create an that must solve a task or implement a series of functions, shorter programs would be preferred on the basis that they are easier to find by the mechanisms of evolution <ref>{{Cite journal |last=Alon |first=Uri |date=2007-03 |title=Simplicity in biology |url=https://www.nature.com/articles/446497a |journal=Nature |language=en |volume=446 |issue=7135 |pages=497–497 |doi=10.1038/446497a |issn=1476-4687}}</ref>. An example of this approach is the eight-fold symmetry of the compass circuit that is found across insect species, which correspond to the circuit that is both functional and requires the minimum Kolmogorov complexity to be generated from self-replicating units <ref>{{Cite journal |last=Vilimelis Aceituno |first=Pau |last2=Dall'Osto |first2=Dominic |last3=Pisokas |first3=Ioannis |date=2024-05-30 |editor-last=Colgin |editor-first=Laura L |editor2-last=Vafidis |editor2-first=Pantelis |title=Theoretical principles explain the structure of the insect head direction circuit |url=https://elifesciences.org/articles/91533 |journal=eLife |volume=13 |pages=e91533 |doi=10.7554/eLife.91533 |issn=2050-084X}}</ref>.
==Conditional versions==
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