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=== Development of related concepts ===

=== Development of related concepts ===

The theory of causal emergence seeks to answer the question of what emergence is from a phenomenological perspective,  employing a causal-based quantitative research methodology. Consequently, the development of causal emergence is closely tied to our understanding of the improvement of concepts such as emergence and causality.

The theory of causal emergence seeks to answer the question of what emergence is from a phenomenological perspective,  employing a causal-based quantitative research methodology. Consequently, the development of causal emergence is closely tied to our understanding of the improvement of concepts such as emergence and causality.

==== Emergence ====

==== Emergence ====

[[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 ([4])([6]), 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 ([4])([6]), 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 several 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.

 

* [[Strong emergence]] remains  highly controversial. It refers to macroscopic-level attributes that cannot, in principle, be reduced to microscopic-level attributes, including the interactions between individuals. Additionally, Jochen Fromm further interprets strong emergence as the [[causal effect]] of [[downward causation]] <ref>Fromm, J. Types and forms of emergence. arXiv 2005, arXiv:nlin/0506028</ref>. [[Downward causation]] refers to the [[causal force]] exerted from the macroscopic level to the microscopic level. However, the concept of [[downward causation]] itself is subject to significant debate <ref>Bedau, M.A.; Humphreys, P. Emergence: Contemporary Readings in Philosophy and Science; MIT Press: Cambridge, MA, USA, 2008. </ref><ref>Yurchenko, S.B. Can there be a synergistic core emerging in the brain hierarchy to control neural activity by downward causation? TechRxiv 2023. [CrossRef] </ref>.

* [[Strong emergence]] remains  highly controversial. It refers to macroscopic-level attributes that cannot, in principle, be reduced to microscopic-level attributes, including the interactions between individuals. Additionally, Jochen Fromm further interprets strong emergence as the [[causal effect]] of [[downward causation]] <ref>Fromm, J. Types and forms of emergence. arXiv 2005, arXiv:nlin/0506028</ref>. [[Downward causation]] refers to the [[causal force]] influence exerted from the macroscopic level to the microscopic level. However, the concept of [[downward causation]] itself is subject to significant debate <ref>Bedau, M.A.; Humphreys, P. Emergence: Contemporary Readings in Philosophy and Science; MIT Press: Cambridge, MA, USA, 2008. </ref><ref>Yurchenko, S.B. Can there be a synergistic core emerging in the brain hierarchy to control neural activity by downward causation? TechRxiv 2023. [CrossRef] </ref>.

 

These early studies reveal a deep and inherent connection between emergence and causality.

These early studies reveal a deep and inherent connection between emergence and causality.

==== Causality and its measurement ====

==== Causality and its measurement ====

With the further development of [[causal science]] in recent years, it is now possible to use a mathematical framework to quantify causality.[[Causality]] describes the [[causal effect]] of a dynamical process <ref name=":14">Pearl J. Causality[M]. Cambridge university press, 2009.</ref><ref>Granger C W. Investigating causal relations by econometric models and cross-spectral methods[J]. Econometrica: journal of the Econometric Society, 1969, 424-438.</ref><ref name=":8">Pearl J. Models, reasoning and inference[J]. Cambridge, UK: CambridgeUniversityPress, 2000, 19(2).</ref>. Judea Pearl <ref name=":8" /> uses [[probabilistic graphical models]] to describe causal interactions. Pearl uses different models to distinguish and quantify three layers of causality. Here we are more concerned with the second layer in the [[causal ladder]]: [[intervening]] in the input distribution. Quantifying the causal effect between two variables is challenging due to inherent uncertainty and ambiguity. Many independent historical studies have addressed the issue of measuring causal relationships. These measurement methods include [[Hume]]'s [[concept of constant connection]] <ref>Spirtes, P.; Glymour, C.; Scheines, R. Causation Prediction and Search, 2nd ed.; MIT Press: Cambridge, MA, USA, 2000.</ref> and value function-based methods <ref>Chickering, D.M. Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2002, 2, 445–498.</ref>, Eells and Suppes' probabilistic causal measures <ref>Eells, E. Probabilistic Causality; Cambridge University Press: Cambridge, UK, 1991; Volume 1</ref><ref>Suppes, P. A probabilistic theory of causality. Br. J. Philos. Sci. 1973, 24, 409–410.</ref>, and Judea Pearl's [[causal measure]] indicators among others. <ref name=":14" />.

With the further development of [[causal science]] in recent years, it is now possible to use a mathematical framework to quantify causality. [[Causality]] describes the [[causal effect]] of a dynamical process <ref name=":14">Pearl J. Causality[M]. Cambridge university press, 2009.</ref><ref>Granger C W. Investigating causal relations by econometric models and cross-spectral methods[J]. Econometrica: journal of the Econometric Society, 1969, 424-438.</ref><ref name=":8">Pearl J. Models, reasoning and inference[J]. Cambridge, UK: CambridgeUniversityPress, 2000, 19(2).</ref>. Judea Pearl <ref name=":8" /> uses [[probabilistic graphical models]] to describe causal interactions. Pearl uses different models to distinguish and quantify three layers of causality. Here we are more concerned with the second layer in the [[causal ladder]]: [[intervening]] in the input distribution. Quantifying the causal effect between two variables is challenging due to inherent uncertainty and ambiguity. Many independent historical studies have addressed the issue of measuring causal relationships. These measurement methods include [[Hume]]'s [[concept of constant connection]] <ref>Spirtes, P.; Glymour, C.; Scheines, R. Causation Prediction and Search, 2nd ed.; MIT Press: Cambridge, MA, USA, 2000.</ref> and value function-based methods <ref>Chickering, D.M. Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2002, 2, 445–498.</ref>, Eells and Suppes' probabilistic causal measures <ref>Eells, E. Probabilistic Causality; Cambridge University Press: Cambridge, UK, 1991; Volume 1</ref><ref>Suppes, P. A probabilistic theory of causality. Br. J. Philos. Sci. 1973, 24, 409–410.</ref>, and Judea Pearl's [[causal measure]] indicators among others. <ref name=":14" />.

In 2013, [[Erik hoel|Erik Hoel]], an American theoretical neurobiologist, introduced causality into the measurement of emergence. He proposed the concept of causal emergence and used [[effective information]] (EI for short) to quantify the extent of causality in system dynamics <ref name=":0" /><ref name=":1" />. '''Causal emergence occurs when a system has a stronger causal effect on a macroscopic scale compared to its microscopic scale.''' Causal emergence effectively captures the differences and connections between the macroscopic and microscopic states of a system. At the same time, it combines the two core concepts - causality in [[artificial intelligence]] and emergence in complex systems. Causal emergence also provides scholars with a quantitative perspective to answer a series of philosophical questions. For example, the top-down causal characteristics in life systems or social systems are often analyzed using the causal emergence framework. The top-down causation here refers to [[downward causation]], which involves macroscopic-to-microscopic causal effects. For example, consider the phenomenon of a gecko breaking its tail, which illustrates how a macroscopic system influences its microscopic components. When encountering danger, the gecko directly breaks off its tail regardless of its condition. Here, the whole is the cause and the tail is the effect. Then there is a [[causal force]] from the whole pointing to the part.

In 2013, [[Erik hoel|Erik Hoel]], an American theoretical neurobiologist, introduced causality into the measurement of emergence. He proposed the concept of causal emergence and used [[effective information]] (EI for short) to quantify the extent of causality in system dynamics <ref name=":0" /><ref name=":1" />. '''Causal emergence occurs when a system has a stronger causal effect on a macroscopic scale compared to its microscopic scale.''' Causal emergence effectively captures the differences and connections between the macroscopic and microscopic states of a system. At the same time, it combines the two core concepts - causality in [[artificial intelligence]] and [[emergence]] in [[complex systems]]. Causal emergence also provides scholars with a quantitative perspective to answer a series of philosophical questions. For example, the top-down causation in life systems or social systems are often analyzed using the causal emergence framework. The top-down causation here refers to [[downward causation]], which involves macroscopic-to-microscopic causal effects. For example, consider the phenomenon of a gecko breaking its tail, which illustrates how a macroscopic system influences its microscopic components. When encountering danger, the gecko directly breaks off its tail regardless of its condition. Here, the whole is the cause and the tail is the effect. Then there is a [[causal force]] from the whole pointing to the part.

 

=== Early work on quantifying emergence ===

=== Early work on quantifying emergence ===