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[[Emergence]] has long been recognized as a key characteristic of [[complex systems]] and a central concept in discussions about system [[complexity]] and the relationship between macroscopic and microscopic levels <ref>Meehl P E, Sellars W. The concept of emergence[J]. Minnesota studies in the philosophy of science, 1956, 1239-252.</ref><ref name=":7">Holland J H. Emergence: From chaos to order[M]. OUP Oxford, 2000.</ref>. Emergence can be understood as the phenomenon where the whole is greater than the sum of its parts, meaning that  the whole exhibits new characteristics that the individual components  do not possess <ref>Anderson P W. More is different: broken symmetry and the nature of the hierarchical structure of science[J]. Science, 1972, 177(4047): 393-396.</ref>. While scholars have identified emergent phenomena across various fields <ref name=":7" /><ref>Holland, J.H. Hidden Order: How Adaptation Builds Complexity; Addison Wesley Longman Publishing Co., Inc.: Boston, MA, USA, 1996.</ref>, such as the [[collective flocking behavior]] of birds <ref>Reynolds, C.W. Flocks, herds and schools: A distributed behavioral model. In Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, Anaheim, CA, USA, 27–31 July 1987; pp. 25–34.</ref>, the formation of [[consciousness]] in the brain, and the [[emergent]] capabilities of large language models <ref>Wei, J.; Tay, Y.; Bommasani, R.; Raffel, C.; Zoph, B.; Borgeaud, S.; Yogatama, D.; Bosma, M.; Zhou, D.; Metzler, D.; et al. Emergent abilities of large language models. arXiv 2022, arXiv:2206.07682.</ref>, there is no universally accepted or unified understanding of this phenomenon. Earlier research on emergence has largely remained qualitative. For instance, Bedau et al. <ref name=":9">Bedau, M.A. Weak emergence. Philos. Perspect. 1997, 11, 375–399. [CrossRef] </ref><ref>Bedau, M. Downward causation and the autonomy of weak emergence. Principia Int. J. Epistemol. 2002, 6, 5–50. </ref> conducted a classified research of emergence, dividing it into [[nominal emergence]]  <ref name=":10">Harré, R. The Philosophies of Science; Oxford University Press: New York, NY, USA, 1985.</ref><ref name=":11">Baas, N.A. Emergence, hierarchies, and hyperstructures. In Artificial Life III, SFI Studies in the Science of Complexity, XVII; Routledge: Abingdon, UK, 1994; pp. 515–537.</ref>, [[weak emergence]] <ref name=":9" /><ref>Newman, D.V. Emergence and strange attractors. Philos. Sci. 1996, 63, 245–261. [CrossRef]</ref>, and [[strong emergence]] <ref name=":12">Kim, J. ‘Downward causation’ in emergentism and nonreductive physicalism. In Emergence or Reduction; Walter de Gruyter: Berlin, Germany, 1992; pp. 119–138. </ref><ref name=":13">O’Connor, T. Emergent properties. Am. Philos. Q. 1994, 31, 91–104</ref>.

[[Emergence]] has long been recognized as a key characteristic of [[complex systems]] and a central concept in discussions about system [[complexity]] and the relationship between macroscopic and microscopic levels <ref>Meehl P E, Sellars W. The concept of emergence[J]. Minnesota studies in the philosophy of science, 1956, 1239-252.</ref><ref name=":7">Holland J H. Emergence: From chaos to order[M]. OUP Oxford, 2000.</ref>. Emergence can be understood as the phenomenon where the whole is greater than the sum of its parts, meaning that  the whole exhibits new characteristics that the individual components  do not possess <ref>Anderson P W. More is different: broken symmetry and the nature of the hierarchical structure of science[J]. Science, 1972, 177(4047): 393-396.</ref>. While scholars have identified emergent phenomena across various fields <ref name=":7" /><ref>Holland, J.H. Hidden Order: How Adaptation Builds Complexity; Addison Wesley Longman Publishing Co., Inc.: Boston, MA, USA, 1996.</ref>, such as the [[collective flocking behavior]] of birds <ref>Reynolds, C.W. Flocks, herds and schools: A distributed behavioral model. In Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, Anaheim, CA, USA, 27–31 July 1987; pp. 25–34.</ref>, the formation of [[consciousness]] in the brain, and the [[emergent]] capabilities of large language models <ref>Wei, J.; Tay, Y.; Bommasani, R.; Raffel, C.; Zoph, B.; Borgeaud, S.; Yogatama, D.; Bosma, M.; Zhou, D.; Metzler, D.; et al. Emergent abilities of large language models. arXiv 2022, arXiv:2206.07682.</ref>, there is no universally accepted or unified understanding of this phenomenon. Earlier research on emergence has largely remained qualitative. For instance, Bedau et al. <ref name=":9">Bedau, M.A. Weak emergence. Philos. Perspect. 1997, 11, 375–399. [CrossRef] </ref><ref>Bedau, M. Downward causation and the autonomy of weak emergence. Principia Int. J. Epistemol. 2002, 6, 5–50. </ref> conducted a classified research of emergence, dividing it into [[nominal emergence]]  <ref name=":10">Harré, R. The Philosophies of Science; Oxford University Press: New York, NY, USA, 1985.</ref><ref name=":11">Baas, N.A. Emergence, hierarchies, and hyperstructures. In Artificial Life III, SFI Studies in the Science of Complexity, XVII; Routledge: Abingdon, UK, 1994; pp. 515–537.</ref>, [[weak emergence]] <ref name=":9" /><ref>Newman, D.V. Emergence and strange attractors. Philos. Sci. 1996, 63, 245–261. [CrossRef]</ref>, and [[strong emergence]] <ref name=":12">Kim, J. ‘Downward causation’ in emergentism and nonreductive physicalism. In Emergence or Reduction; Walter de Gruyter: Berlin, Germany, 1992; pp. 119–138. </ref><ref name=":13">O’Connor, T. Emergent properties. Am. Philos. Q. 1994, 31, 91–104</ref>.

* [[Nominal emergence]] refers to attributes and patterns that can exist at the macroscopic level but not at the microscopic level. For example, the shape of a circle formed by several pixels is an instance of nominal emergence <ref name=":10" /><ref name=":11" />.

* [[Nominal emergence]] refers to attributes and patterns that can exist at the macroscopic level but not at the microscopic level. For example, the shape of a circle formed by pixels is an instance of nominal emergence <ref name=":10" /><ref name=":11" />.

* [[Weak emergence]] refers to macroscopic attributes or processes that arise from complex interactions between individual components. It can also be understood as a characteristic that could, in principle, be simulated by a computer. Due to [[computational irreducibility]], even though weak emergence traits can be simulated, they cannot easily be reduced to microscopic-level attributes. In the case of weak emergence, the causes of pattern formation may stem from both microscopic and macroscopic levels <ref name=":12" /><ref name=":13" />. Therefore, the causal relationship underlying emergence may coexist with microscopic causal relationships.

* [[Weak emergence]] refers to macroscopic attributes or processes that arise from complex interactions between individual components. It can also be understood as a characteristic that could, in principle, be simulated by a computer. Due to [[computational irreducibility]], even though weak emergence traits can be simulated, they cannot easily be reduced to microscopic-level attributes. In the case of weak emergence, the causes of pattern formation may stem from both microscopic and macroscopic levels <ref name=":12" /><ref name=":13" />. Therefore, the causal relationship underlying emergence may coexist with microscopic causal relationships.