March 21, 2013

Plausibility and de navitus models of complex systems

What are the plausible configurations of a living system? Let us take animal phenotypes as an example [1]. The number of plausible configurations is somewhere between all forms known to have lived and all possible configurations allowable by genotype and environment. Given the appropriate model, we should be able to constrain this a bit more to produce a concrete set of plausible phenotypes (see Figure 1).

Figure 1. Example of defining plausible phenotypes from a developmental (e.g. epigenetic) landscape. In this case, "plausibility" is defined as the interaction between environmental influence and coherent physiological (e.g. normal and coherent disease) states. Image is from Figure 1 in [2].

Instead of an inferential or predictive model, we will instead turn to an agent-based approach. Each agent will produce a series of naive (or de navitus) models, and a consensus among these models can produce a result comparable to an informed synthesis [3]. Naive models are based on naive theories (see Figure 2), which people formulate as heuristics for interpreting the natural world. When the level of theoretical synthesis is weak or amount of observed data is limited, naive theories tend to dominate. In fact, the early stages of informed synthesis tend to resemble naive theories to some degree, as the ideal conditions for the development of theoretical synthesis are contingent upon both trial-and-error and a high degree of information [4].

Figure 2. Two popular naive theories from the 19th century. INSET: The canals of Mars as envisioned by Giovanni Schiaparelli. BELOW: Expanding earth theory, which predates the notion of tectonic activity. COURTESY: Smashing Lists.

In general, naive theories are clearly inferior to informed synthesis. Naive theories suffer not only from a lack of informational definition, but are susceptible to logical fallacies and cognitive biases (for an example, see Figure 3). Two such examples involve naive theories of evolutionary biology and macroeconomic processes that are based on false equivalence [5]. In the case of evolutionary biology, naive theories tend to confuse Lamarkian (e.g. the propagation of adaptations) with Darwinian (germ-line inheritance) mechanisms [6]. In the case of naive economic theory, the notion that governments should be run like a household involves confusing micro- and macro-economic principles [7].

Figure 3. The potential cognitive substrate (and cognitive biases) of naive theories, at work in the process of superstitious beliefs. COURTESY: screenshot from [8].

The selective nature of historical recall [9] is also strongly influenced by cognitive bias. This can lead to both intentional and unintentional logical inconsistencies, which can only be remedied through either conceptual blending and/or a logical fallacy called appeal to authority [10]. This might be remedied through the construction of an unbiased consensus that would at least approximate more formal models trained with loads of data. But how do we accomplish this? To arrive at an answer, a thought experiment is in order.

What if we could construct a population of agents that each had the capacity to construct novel models de navitus, but also with the capacity for logical consistency. Furthermore, the diversity of these de navitus models would be much higher than is found among human populations, so that popular but false memes never dominate a population. In most cases, a resulting consensus would yield a much more refined theory than would otherwise be the case. This also allows us to study the nature of event or ideonational contingency, and create opportunities for new historical contingencies to arise.

The quasi-evolutionary, agent-based conception works by deriving a consensus model state by sampling multiple agents in the population at the densest concentration of agents. As the collective state moves through a geometric space representing relative plausibility, information from agents within a certain radius is sampled, and this information is incorporated into the consensus (see Figure 4). The brains of each agent consist of two mechanisms: bottom-up and top-down. The bottom-up process allows for each agent to generate naive models based on a set of constant environmental inputs. This can accomplished through a cognitive architecture that allows for significant variation, but still results in model that are capable of logical reasoning [11]. The top-down mechanism selects for the least biased de navitus model based on conflicting features and cognitive biases. This does not ensure bias-free models, but the selection mechanism does learn over time, which favors some level of collective state convergence over time [12].

Figure 4. Example of an evolving de navitus model with contributions of individual agents using the historical model geometry elaborated on in Figure 5.

To better understand how naive models are related to formal theories, there are two components of the naive theory that make them both powerful and potentially misleading. The first is an intuitive sense of how the world works. Without knowledge of the mechanism itself, this can be make relatively simple processes highly ambiguous. We can see how this plays out by comparing two mechanisms: the movement of cars in and out of a tunnel, and the movement of toast in and out of a toaster. In both cases, the brain must infer movement relative to an internal mechanism. In one case, there is transformation, while in the other case there is disappearance into on opening and re-emergence through another. Intuition can provide an answer to this mental challenge, but with a high potential for creative but inaccurate solutions [13].

The second component is a bit more subtle, and involves the mechanism of induction itself. In the case of our cars and bread, the key to explanation and prediction in a naive model is figuring out what happens in the toaster or tunnel. If one has a good grasp of the internal process, then representing this in theoretical terms is not much of a problem. The problem arises when the internal mechanism is not well known by the thinker. This can be seen in human development among small children, who often make up fanciful stories for questions like "Why is the sky blue?" or "Why does the sun set?" [14].

We need only to look at the state of theory in neuroscience to see how what was once considered a good theory of brain function (e.g. phrenology) falls apart given more data. Figure 4 shows how theories from a variety of scientific fields can gain or lose acceptance over time given more data or informed theoretical synthesis work. We can construct a similar graph for naive theories and de navitus models. Figure 5 shows this as an evolutionary process that iteratively incorporates knowledge from agents exploring their worlds.

The future direction for this work is to refine the agent-based architecture and test performance of these computational models against human-derived naive theories and formal scientific theories. Hopefully, de navitas models will allow us to build sophisticated theories and machine learning tutors in situations of sparse sampling and limited opportunities for data acquisition.

Figure 5. The landscape of scientific theoretical synthesis. CENTER: widely accepted ideas. EDGES: ideas in obscurity or disrepute. COURTESY: Slide from [15].

NOTES:

[1] Kirschner, M. and Gerhart, J. (2005). Plausibility of Life. Yale University Press, New Haven.

[2] Grabiec, A.M. and Reedquist, K.A.   The ascent of acetylation in the epigenetics of rheumatoid arthritis. Nature Reviews Rheumatology, doi:10.1038/nrrheum.2013.17 (2013).

[3] An informed synthesis is a prediction or solution based on large amounts of data and theoretical synthesis by experts (e.g. academics, specialists).

For more information about model-based reasoning, please see: Magnani, L.   Abduction, Reason, and Science: process of discovery and explanation. Kluwer, New York (2001), Magnini, L., Nersessian, N.J., and Thagard, P.   Model-based Reasoning in Scientific Discovery. Kluwer, New York (1999), AND Gooding, D.   Creative Rationality: towards an abductive model of scientific change. Philsophica, 58, 73-102.

[4] "Naive" theories include 1) folk theories such as Groundhog Day, which is an intuitive set of predictions about the weather embedded in ritual, 2) early theoretical syntheses such as Greek natural philosophy, and 3) mental models that are consistent with observations of the world such as intuitive physics.

[5] My definition of false equivalence: the assumption of equivalence between A and B which is based on mischaracterized attributes or misleading conclusions.

[6] Shtulman, A.   Qualitative differences between naive and scientific theories of evolution. Cognitive Psychology, 52, 170-194 (2006). See also: Thagard, P.   Conceptual revolutions. Princeton University Press (1992).

[7] Krugman, P.   Running Government Like A Business or Family. Conscience of a Liberal blog, March 14. (2013)

[8] QualiaSoup.   Superstition. March 14, YouTube (2013).

[9] Clues to what this part of the architecture should look like might come from the concept of selective memory and social amnesia: Stickgold, R. and Walker, M.P.   Sleep-dependent memory triage: evolving generalization through selective processing. Nature Neuroscience, 16, 139-145 (2013) AND Ferguson, J.N., Young, L.J., Hearn, E.F., Matzuk, M.M., Insel, T.R., Winslow, J.T.   Social amnesia in mice lacking the oxytocin gene. Nature Genetics, 25(3), 284-288 (2000).

[10] My definition of argument from authority: induction based on the existence of an absolute or divine authority, similar in tone to the god of the gaps argument.

[11] Clues to what this part of the architecture should look like might also come from the concept of a "straw vulcan": Galef, J.   The Straw Vulcan: Hollywood's illogical approach to logical decisionmaking. Measure of Doubt blog. November 26 (2011).


[12] The assumption here is that forced diversity, either through a very high mutation rate or a very large conceptual universe, would lead us to richer descriptions. However, there are caveats to this assumption, including the production of nonsense theories and the lack of convergence to any one consensus over time.

[13] This can seen in terms of the creative license taken in conceptions of scientific processes in motion pictures (something I call movie science). Since these models are partially plausible, movie science requires one to suspend their disbelief. In this context, the depiction of a scientific process (e.g. genetic engineering in “Jurassic Park”) can be enjoyable, but perhaps not by experts in the topic.

See also the following classic paper about the use of "naive" models of physics among non-physicists: Chi et.al   Categorization and Representation of Physics Problems by Experts and Novices. Cognitive Science, 5, 121-125 (1981).

[14] Clues to what this part of the architecture should look like might also come from the study of creativity: Carlsson, I., Wendt, P.E., and Risberg, J.   On the neurobiology of creativity. Differences in frontal activity between high and low creative subjects. Neuropsychologia, 38(6), 873-885 (2000).

[15] Alicea, B.   If your results are unpredictable, does it make them any less true? HTDE 2013.1. doi:10.6084/m9.figshare.157087 (2013).

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