Thursday, 21 November 2019

Inferential Systems and the Causal Revolution

John O. Campbell

This is an excerpt from the book: The Knowing Universe.

As we have seen, real-world inferential systems, such as genetically controlled metabolic pathways, are maestros of causal control. Their step-by-step instructions form causal cascades creating entities and regulating them within existence. ­­­But this description of inferential systems as causal agents is scientifically awkward. The concept of causation is taboo because data or evidence, on its own, can indicate correlations but not causal relationships. This problem of induction, first described by the philosopher David Hume (1711 – 1776) and since integrated into the scientific worldview, claims there is no logical basis for the notion of causation. As Wikipedia explains (1):

Hume argued that inductive reasoning and belief in causality cannot be justified rationally; instead, they result from custom and mental habit. We never actually perceive that one event causes another, but only experience the "constant conjunction" of events.

An oft-quoted example is that the rising sun and the crowing rooster are correlated, but the crowing does not cause the rising. Something beyond data or observations is required to establish causality.

A recent scientific innovation called the causal revolution, led by Judea Pearl (born 1936) (2; 3), clarifies the scientific understanding of causality and provides critical new understandings illuminating the autopoietic and algorithmic (AA) nature of inferential systems.  While the causal revolution provides new methods to science, these methods may have been previously discovered and implemented subconsciously during human evolution. Sometime about 70,000 years ago, a series of mutations in genes specifying our neural structures most probably resulted in a cognitive revolution powering our species’ cultural evolution and providing critical abilities enabling our (perhaps temporary) ascendancy over other biological forms. Some researchers, including Pearl, attribute this cognitive revolution to the emergence of unconscious abilities for causal reasoning, the same type of causal reasoning now brought to our conscious attention with Pearl’s causal revolution (4; 3; 5)

 Figure 1: Judea Pearl

Other researchers have noted that each generation of children inherits a genetic propensity for causal reasoning. As Allison Gopnik (born 1955) writes (6):

In much causal reasoning research participants learn how a particular set of pre-selected variables produce a particular effect. Here, we investigate 3–5-year-olds’ ability to select the relevant variable for intervention in a novel causal system. Results demonstrate that even young children can learn which variable is causally relevant from sparse evidence.

In this view, the current scientific revolution is a mere rediscovery, in conscious terms, of a fitness-enhancing process placed long ago in our unconscious brains by natural selection.

Unfortunately, the current scientific causal revolution only extends to technical methods for discerning causal relationships among data. But, below we will argue that causal reasoning is a vital component of inferential systems and all existing forms. Within the context of inferential systems, we may say that, in general, knowledge is the cause of existence, and it is this causal mechanism that has brought nature’s many domains of reality into existence (7; 8). Generalized genotypes cause generalized phenotypes; in all domains, existence requires a mastery of causal reasoning.

For example, an organism’s (epi) genotype causes its phenotype. Although a gene’s expression also depends on environmental factors, the causal relationship is unmistakable. For instance, a specific genetic abnormality in fruit flies predictably causes legs to grow from the developing insect’s head in place of antennae (9). These type of  dramatic genetic defects clearly illustrates the general causal relationship between genotypes and phenotypes.

The causal revolution is a recent scientific discovery of a general law of nature underlying the many existing forms composing our universe, operating since the beginning, long before our species' evolution. In that sense, the causal revolution provides powerful tools for our scientific understanding of inferential systems and the widespread role of causality within natural systems.

Contrary to traditional statistics and the big data movement's mantra, that data is everything, and everything is data[1], Pearl points out that this perspective severely constrains the scope of statistics. Traditional statistics only view data as describing correlations, but correlations are not causes, as illustrated by the cliche of the crowing rooster and the rising sun. Pearl demonstrates that descriptions of causal relationships require an ingredient beyond data; they also require models that hypothesize causal relationships. As Pearl describes it (3):

The model should depict, however qualitatively, the process that generates the data – in other words, the cause and effect forces that operate in the environment and shape the data generated.

The generative models described by Pearl link his description of causal models to those of inferential systems. A generative model comprises a competing family of hypotheses explaining the generation or cause of some observable data. Thus, effective causal models must model how existing entities and processes are generated or brought into existence.

Pearl’s preferred types of causal models are causal diagrams depicting the variables involved as points and the cause-and-effect relationships between them as directed arrows serving to hypothesize their cause-and-effect relationships. He is clear that these causal diagrams are hypotheses or best guesses as to the actual causal relationship and that they must be subject to the scrutiny of data or model evidence.

Pearl suggests that when the evidence does not fully support the hypothesis, we construct another, perhaps a more informed, hypothesis of the causal relationship and test its implications against the data. We should continue with these informed guesses until we discover a diagram consistent with all the data. As Pearl puts it (3):

If the data contradict this implication, then we need to revise our model.

We might note Pearl’s reference above to ‘cause and effect forces’ described by causal models. As noted in previous sections, system regulators employ causal forces to overcome obstacles to existence posed by nature’s laws. In this sense, inferential systems' knowledge initiates a causal chain of forces forming and maintaining systems within existence. It is in this manner that inferential systems achieve their autopoietic abilities.

Pearl provides a lovely metaphorical definition of causation:

For the purpose of constructing the diagram, the definition of ‘causation’ is simple, if a little metaphorical: a variable X is a cause of Y if Y ‘listens’ to X and determines its value in response to what it hears.

Although Pearl’s description is clear and accurate, the term ‘listens to’ may be a little anthropomorphic when applied to natural processes in general. Perhaps a better term is ‘receives information from’ and then his definition of causation becomes:

A variable X is a cause of Y if Y receives information from X and determines its value or state in response to that information.

Pearl’s definition of causality describes its role in inferential systems. The regulatory model of an inferential system receives information and performs updates in response to that information. The system’s sensed information causes optimal actions, and the model accumulates knowledge as it updates and learns from its actions. This regulatory knowledge exercises direct causal control over the system’s actions; the system only takes actions directed by the model. The sum effect of these actions predicts the creation and maintenance of the system within existence. In this sense, the model of the generalized genotype causes the existence of the generalized phenotype. In terms of Pearl’s definition, the generalized phenotype is caused by what it hears from the generalized genotype.

But within inferential systems, causation is a two-way street. Not only do generalized genotypes update or cause generalized phenotypes. But also, the evidence generated by generalized phenotypes updates or causes the knowledge of generalized genotypes. We may view the evidence as having a causal effect on models - each hypothesis's probability updates to consistency with the received evidence, and we may describe this update or response as a causal force; a model’s hypotheses are forced to new values by the evidence (10). Thus, the force of evidence shapes the model, or in Pearl’s terms, we may say that the generative model listens to the evidence of the phenotype and determines its value in response to what it hears.

This analogy between causation and force is widely accepted. As Wikipedia tells us (11):

Causal relationships may be understood as a transfer of force. If A causes B, then A must transmit a force (or causal power) to B which results in the effect. 

Given the close analogy between causation, inference, and force, we may consider inferential systems a basic form of causation. Forces cause effects, and forces are always in terms of inferential systems’ updates. Steven Frank (born 1957) has demonstrated that inference may be considered the force of data applied to models (10). For example, fundamental physical forces occur when information carried by a gauge boson updates a quantum model. In Pearl’s terms, we might say that the quantum system listens to the gauge boson and determines or updates its value, such as the value of its momentum, in response to what it hears.

Although nature has always employed inferential systems as its primary engine of existence, the causal revolution rediscovers and adds this tool to the scientific toolkit. The causal revolution provides essential tools for describing autopoietic algorithmic (AA) aspects of inferential systems. In short, this new tool allows us to scientifically describe inferential systems as initiating a cascade of causes whose cumulative effects are existing systems. We can understand these orchestrated forces as forming regulated networks designed to overcome the many natural obstacles to existence.  

A breakthrough concept of the causal revolution is that a full scientific description of a causal process must include a causal model of the hypothesized causal cascade. Our understanding of inferential systems rests on this same concept that models must orchestrate or regulate existing systems as required by the good regulator theorem. In other words, the causal revolution has discovered that scientific descriptions of existing systems must include a causal model. Causal models are crucial components of existing systems; scientific explanations that do not include causal models can not account for their existence. For example, a scientific explanation of biology, not including the genetic model's role in initiating life’s causal cascade, could not accurately account for life's existence.

Another core component of the causal revolution’s understanding is that causation often involves interventions to the standard or spontaneous unfolding of events. A caused effect occurs when the normal range of possible outcomes is constrained to a few or a single caused outcome that without the imposed constraint might be very unlikely. We may view this imposed constraint as an intervention in the ordinary course of events (2). Evidence may cause AA models to predict or initiate a single outcome or effect; a sensed state regulates or causes a particular system response. The response is appropriate to the system's specific state and not one that would typically take place without regulation or constraints.

At the core of AA knowledge is its ability to cause outcomes, intervene in the spontaneous course of events and specify a single, otherwise improbable outcome. As a biological example, we might consider that knowledge in an organism’s genome causes specific outcomes or effects. A given gene may cause the production of an enzyme catalyzing a specific biochemical reaction, which is extremely unlikely to occur without the enzyme’s intervention. Genetic knowledge initiates causal cascades, resulting in specific effects under their AA models' strict causal control or regulation.

Pearl describes the causal revolution in terms of a ladder having three rungs describing causality. Correlations, described by the field of statistics, characterize the first rung. Interventions in the ordinary course of events characterize the second rung. And counterfactuals regarding what might be rather than what is, characterize the third. A dictionary example of a counterfactual hypothesis is (12):

If kangaroos had no tails, they would topple over.

Counterfactual hypotheses incorporated into generative models form the Peircean branch of logic called abduction, they provide inferential systems with evolutionary abilities because they generate novel experimental tests. Only counterfactual hypotheses can explore design space, searching for new forms of existence as only these hypotheses concern what does not yet exist.

In this sense, counterfactual hypotheses aren’t restricted to science inquiry but are part of nature’s toolkit for discovering new forms of existence. For example, Kangaroo genetics may pose counterfactual hypotheses in the form of mutations hypothesizing tailless kangaroos. These hypotheses predict that a kangaroo with no tail would be reproductively successful (it doesn’t always topple over). If the resulting tailless kangaroo achieved reproductive success, the counterfactual possibility would become actual, and tail-less kangaroos would come to exist in the actual world. In this sense evolution generates a succession of counterfactual hypotheses, some of which become established actualities, although many prove unable to achieve existence.

The causal revolution extends scientific understanding of causation beyond correlations to include causal models, interventions, and counterfactual hypotheses. We have examined examples illustrating how these extensions describe actual biological causal processes, and in Part III, we see that this understanding is also central to other domains of reality. In all domains, AA inferential systems cause themselves to exist.

However, the causal revolution's founders tend to view their revolution more as a revolution in scientific calculation than in understanding natural phenomena. Pearl, for example, champions the crucial understanding that causal models are essential to computing relationships between statistical variables. However, his revolution doesn’t extend to the existence of causal models in the natural world or their essential role in bringing actual phenomena into existence (3).

A common confusion when science first reveals new phenomena for which there is little direct observational evidence is to conclude that this new phenomenon doesn’t exist but is just a calculational shortcut. And this is quite reasonable when the discovery of the mathematical description precedes discovery of the physical phenomena. For example, in the late 1800s, many considered the controversial concept of atoms as shorthand for making scientific calculations rather than as actual phenomena. When Boltzmann tried to publish his work deriving thermodynamics from atomic theory, his journal editors insisted he refer to atoms as Bilder; merely as counterfactual models or pictures (13).

Again, in the early 1900s, with the rediscovery of Mendel’s concept of genes, most leading biologists regarded these not as physical entities but merely as a means of making calculations regarding phenotypic outcomes. As the philosopher of science David Hull (1935 – 2010) recounts (14):

As much as Bateson might disagree with Pearson and Weldon about the value of Mendelian genetics, he agreed with them that it was unscientific to postulate the existence of genes as material bodies. They were merely calculation devices.

As with atoms and genetics, we may be confident that the causal revolution’s new calculational methods describe actual physical reality, that nature also uses this same logical reasoning[2] to create and regulate existence. Nature is a masterful orchestrator of causal cascades bringing specified entities into existence. Science has merely rediscovered nature’s methods, but, after all, that is the proper role of science.


1. Wikipedia. David Hume. Wikipedia. [Online] [Cited: November 22, 2020.]

2. Causal inference in statistics: an overview. Pearl, Judea. s.l. : Statistics Surveys, 2009, Vols. Volume 3 (2009), 96-146.

3. Pearl, Judea and Mackenzie, Dana. The Book of Why: The New Science of Cause and Effect. s.l. : Basic Books, 2018. ISBN-10: 046509760X.

4. Harari, Yuval Noah. Sapiens: A brief history of humankind. s.l. : Harvill Secker, 2014.

5. Boyer, Pascal. Minds make societies: How Cognition Explains the World Humans Create. s.l. : Yale University Press, 2018.

6. Learning what to change: Young children use "difference-making" to identify causally relevant variables. Goddu MK, Gopnik A. s.l. : Dev Psychol. 2020 Feb, 2020, Vols. 56(2):275-284. doi: 10.1037/dev0000872..

7. Universal Darwinism as a process of Bayesian inference. Campbell, John O. s.l. : Front. Syst. Neurosci., 2016, System Neuroscience. doi: 10.3389/fnsys.2016.00049.

8. Campbell, John O. and Price, Michael E. Universal Darwinism and the Origins of Order. [book auth.] Smart J., Flores Martinez C., Price M. (eds) Georgiev G. Evolution, Development and Complexity. s.l. : Springer Proceedings in Complexity. Springer, Cham, 2019.

9. Wikipedia. Antennapedia. Wikipedia. [Online] [Cited: August 21, 2020.]

10. Simple unity among the fundamental equations of science. Frank, Steven A. s.l. : arXiv preprint, 2019.

11. Wikipedia. Causal reasoning. Wikipedia. [Online] [Cited: May 26, 2019.]

12. Google dictionary. Counterfactual. Google dictionary. [Online] [Cited: June 2, 2019.]

13. Wikipedia. Ludwig Boltzman. Wikipedia. [Online] [Cited: June 7, 2014.]

14. Hull, David L. Science as a Process: An Evolutionary Account of the Social and Conceptual Development of Science. Chicago and London : The University of Chicago Press, 1988.


[1] If in doubt as to the widespread use of this meme, try googling it.

[2] We are reminded of Peirce’s prescience in understanding the rules of logic describing ‘right reasoning' and insisting that all processes in the universe follow these same rules of thought.