July 16, 2017

Wandering Towards an Essay of Laws

The winners of the FQXi "Wandering Towards a Goal" essay contest have been announced. I made an entry into the contest (my first FQXi contest entry) and did not win, but had a good time creating a number of interesting threads for future exploration. 

The essay itself, "Inverting the Phenomenology of Mathematical Lawfulness to Establish the Conditions of Intention-like Goal-oriented Behavior" [1], is the product of my work in an area I call Physical Intelligence in addition to intellectual discussions with colleagues (acknowledged in the essay). 

I did not have much time to polish and reflect upon the essay at the time it was submitted, but since then I have come up with a few additional points. So here are a few more focused observations extracted from the more exploratory essay form:

1) there is an underappreciated connection between biological physics, evolution, and psychophysics. There is an subtle but important research question here: why did some biological systems evolve in accordance with "law-like" behavior, while many others did not? 

2) the question of whether mathematical laws are discovered or invented (Mathematical Platonism) may be highly relevant to the application of mathematical models in the biological and social sciences [2]. While mathematicians have a commonly encountered answer (laws are discovered, notation was invented), an answer based on discovering laws from empirically-driven observations will likely provide a different answer.

3) how exactly do we define laws in the context of empirical science? While laws can be demonstrated in the biological sciences [3], biology itself is not thought of as particularly lawful. According to [4], "laws" fall somewhere in-between hypotheses and theories. In this sense, laws are both exercises in prediction and part of theory-building. Historically, biologists have tended to employ statistical models without reference to theory, while physicists and chemists often use statistical models to demonstrate theoretical principles [5]. In fields such as biology or the social sciences, the use of different or novel analytical or symbolic paradigms might facilitate the discovery of lawlike invariants.

4) the inclusion of cybernetic principles (Ashby's Law of Requisite Variety) may also bring together new insights on how laws occur in biological and social systems, and whether such laws are based on deep structural regularities in nature (as argued in the FQXi essay) or the mode of representating empirical observations (an idea to be explored in another post).

5) Aneural cognition is something that might guide information processing in a number of contexts. This has been explored further in another paper from the DevoWorm group [6] on the potential role of aneural cognition in embryos. It has also been explored in the form of the free-energy principle leading to information processing in plants [7]. Is cognition a unified theory of adaptive information processing? Now that's something to explore.

[1] A printable version can be downloaded from Figshare (doi:10.6084/m9.figshare.4725235).

[2] I experienced a nice discussion of this issue during an recent NSF-sponsored workshop. The bottom line is that while the variation typical of biology often makes the discovery of universal principles intractable, perhaps law discovery in biology simply requires a several hundred year investment in research (h/t Dr. Rob Phillips). For more, please see:

Phillips, R. (2015). Theory in Biology: Figure 1 or Figure 7? Trends in Cell Biology 25(12), 1-7.

[3] Trevors, J.T. and Saier, M.H. (2010). Three Laws of Biology. Water Air and Soil Pollution, 205(S1), S87-S89.

[4] el-Showk, S. (2014). Does Biology Have Laws? Accumulating Glitches blog, Nature Scitable. http://www.nature.com/scitable/blog/accumulating-glitches/does_biology_have-laws

[5] Ruse, M.E. (1970). Are there laws in biology? Australasian Journal of Philosophy, 48(2), 234-246. doi:10.1080/00048407012341201.

[6] Stone, R., Portegys, T.E., Mihkailovsky, G., and Alicea, B. (2017). Origins of the Embryo: self-organization through cybernetic regulation​. Figshare, doi:10.6084/m9.figshare.5089558.

[7] Calvo, P. and Friston, K. (2017). Predicting green: really radical (plant) predictive processing. Journal of the Royal Society Interface, 14, 20170096.

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