Computational Mechanics: Pattern and Prediction, Structure and Simplicity
Open accessThe claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The proposed measures can be applied to abstract, biological, economic, social or technological systems.
“These can be abstract (e.g. Turing machines (Delahaye and Zenil, 2007, 2012), ϵ -machines (Shalizi and Crutchfield, 2001; G¨ ornerup and Crutchfield, 2008)), biological (ecosystems, organisms), economic, social or technological (Helbing, 2011).”
From Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis (2013) · cites this paper as Shalizi and Crutchfield, 2001
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486 · see citing works
Causality: Models, Reasoning, and Inference
Pearl, J. (2009) · doi:10.1017/cbo9780511803161 · Cited by 11,653 · see citing works
Detecting strange attractors in turbulence
Takens, F. (1981) · Lecture Notes in Mathematics · doi:10.1007/bfb0091924 · Cited by 10,459 · see citing works
Valiant, L. G. (1984) · Communications of the ACM · doi:10.1145/1968.1972 · Cited by 3,279 · see citing works
A formal theory of inductive inference. Part II
Solomonoff, R. J. (1964) · Information and Control · doi:10.1016/s0019-9958(64)90131-7 · Cited by 1,758 · see citing works
A formal theory of inductive inference. Part I
Solomonoff, R. J. (1964) · Information and Control · doi:10.1016/s0019-9958(64)90223-2 · Cited by 1,192 · see citing works
On the Length of Programs for Computing Finite Binary Sequences
Chaitin, G. J. (1966) · Journal of the ACM · doi:10.1145/321356.321363 · Cited by 913 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
An information integration theory of consciousness
Tononi, G. (2004) · BMC Neuroscience · doi:10.1186/1471-2202-5-42 · Cited by 1,757 · see citing works
“A related measure could be constructed using the formalism of ε-machines [63].”
MethodHow Efficiency Shapes Human Language
Gibson, E., Futrell, R., Piantadosi, S. P., Dautriche, I., Mahowald, K., Bergen, L., & Levy, R. (2019) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2019.02.003 · Cited by 485 · see citing works
Integrated information in discrete dynamical systems: motivation and theoretical framework
Balduzzi, D., & Tononi, G. (2008) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000091 · Cited by 419 · see citing works
Contextual emergence of mental states.
Atmanspacher, H. (2015) · Cognitive Processing · doi:10.1007/s10339-015-0658-0 · Cited by 13 · see citing works
Transformers Represent Belief State Geometry in their Residual Stream
Shai, A., Marzen, S., Teixeira, L., Oldenziel, A., & Riechers, P. (2024) · Advances in Neural Information Processing Systems 37 · doi:10.52202/079017-2387 · Cited by 4 · see citing works
Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis
Fernandez, N., Maldonado, C., & Gershenson, C. (2013) · arXiv · doi:10.48550/arxiv.1304.1842 · Cited by 1 · see citing works
“Turing machines (Delahaye and Zenil, 2007, 2012), -machines (Shalizi and Crutchfield, 2001; Görnerup and Crutchfield, 2008)), biological (ecosystems, organisms), economic, social or technological (Helbing, 2011).”
Background
- Authors
- Shalizi, C. R., & Crutchfield, J. P.
- Affiliations
- Santa Fe Institute (US)
- Venue
- Journal of Statistical Physics
- Published
- 2001-08
- Volume
- 104
- Issue
- 3-4
- Pages
- 817-879
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W1551871633
- Cited by
- 471
- References
- 7
- Citations by year
- 2026: 31 · 2025: 22 · 2024: 28 · 2023: 15 · 2022: 20 · 2021: 16 · 2020: 23 · 2019: 23 · 2018: 25 · 2017: 29 · 2016: 24 · 2015: 24 · 2014: 20 · 2013: 26 · 2012: 20
- FWCI
- 11.27
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Journal of Statistical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (9970158)
- Santa Fe Institute
- Science Foundation Ireland
- Defense Advanced Research Projects Agency
- Office of Naval Research (N00014-95-1-0975)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Keywords
- computational mechanics, causal states, structural complexity, prediction, minimal representation, randomness measures, ergodic theory, information theory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
