August 31, 2014

Godel's Revenge: All-Encompassing Formalisms vs. Incomplete Formalisms

This content is cross-posted to Tumbld Thoughts. A loosely-formed story in two parts about the pros and cons of predicting the outcome of and otherwise controlling complex sociocultural systems. Kurt Godel is sitting in the afterlife cafe right now, scoffing but also watching with great interest.

I. It's an All-encompassing, Self-regulation, Charlie Brown!

Here is a video [1] by the complexity theorist Dirk Helbing about the possibility of a self-regulating society. Essentially, by combining big data with the principles of complexity would allow us to solve previously intractable problems [2]. This includes more effective management of everything from massively parallel collective behaviors to very-rare events.

But controlling how big data is used can keep us from getting into trouble as well. Writing at Gigaom blog, Derrick Harris argues that the potentially catastrophic effects of AI taking over society (the downside of the singularity) can be avoided by keeping key data away from such systems [3]. In this case, even hyper-complex AI systems based on deep learning can become positively self-regulating.


[2] For a cursory review of algorithmic regulation, please see: Morozov, E.   The rise of data and the death of politics. The Guardian, July 19 (2014).

For a discussion as to why governmental regulation is a wicked problem and how algorithmic approaches might be inherently unworkable, please see: McCormick, T.   A brief exchange with Tim O’Reilly about “algorithmic regulation”. Tim McCormick blog, February 15 (2014).

[3] Harris, D.   When data become dangerous: why Elon Musk is right and wrong about AI. Gigaom blog, August 4 (2014).

II. Arguing Past Each Other Using Mathematical Formalisms

Here are a few papers on argumentation, game theory, and culture. My notes are below each set of citations. A good reading list (short but dense) nonetheless.

Brandenburger, A. and Keisler, H.J.   An Impossibility Theorem on Beliefs in Games. Studia Logica, 84(2), 211-240 (2006).

* shows that any two-player game is embedded in a system of reflexive, meta-cognitive beliefs. Players not only model payoffs that maximize their utility, but also model the beliefs of the other player. The resulting "belief model" cannot be completely self-consistent: beliefs about beliefs have holes which serve as sources of logical incompleteness.

What is Russell's Paradox? Scientific American, August 17 (1998).

* intorduction to a logical paradox which can be resolved by distinguishing between sets and sets that describe sets using a hierarchical classification method. This paradox is the basis for the Brandenburger and Keisler paper.

Mercier, H. and Sperber, D.   Why do humans reason? Arguments for an argumentative theory. Behavioral and Brain Sciences, 34, 57-111 (2011).

Oaksford, M.   Normativity, interpretation, and Bayesian models. Frontiers in Psychology, 5, 332 (2014).

* a new-ish take on culture and cognition called argumentation theory. Rather than reasoning to maximize individual utility, reasoning is done to maximize argumentative context. This includes decision-making that optimizes ideonational consistency. This theory predicts phenomena such as epistemic closure, and might be thought of as a postmodern version of rational agent theory. 

There also seems to be an underlying connection between the "holes" is a culturally-specific argument and the phenomenon of conceptual blending, but that is a topic for a future post.

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