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Origin Gaps and the Eternal Sunshine of the Second-Order Pendulum
Abstract
The rich experiences of an intentional, goal-oriented life emerge, in an unpredictable fashion, from the basic laws of physics. Here I argue that this unpredictability is no mirage: there are true gaps between life and non-life, mind and mindlessness, and even between functional societies and groups of Hobbesian individuals. These gaps, I suggest, emerge from the mathematics of self-reference, and the logical barriers to prediction that self-referring systems present. Still, a mathematical truth does not imply a physical one: the universe need not have made self-reference possible. It did, and the question then is how. In the second half of this essay, I show how a basic move in physics, known as renormalization, transforms the "forgetful" second-order equations of fundamental physics into a rich, self-referential world that makes possible the major transitions we care so much about. While the universe runs in assembly code, the coarse-grained version runs in LISP, and it is from that the world of aim and intention grows.
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Downward causation is the controversial idea that ‘higher’ levels of organization can causally influence behaviour at ‘lower’ levels of organization. Here I propose that we can gain traction on downward causation by being operational and examining how adaptive systems identify regularities in evolutionary or learning time and use these regularities to guide behaviour. I suggest that in many adaptive systems components collectively compute their macroscopic worlds through coarse-graining. I further suggest we move from simple feedback to downward causation when components tune behaviour in response to estimates of collectively computed macroscopic properties. I introduce a weak and strong notion of downward causation and discuss the role the strong form plays in the origins of new organizational levels. I illustrate these points with examples from the study of biological and social systems and deep neural networks.
This article is part of the themed issue ‘Reconceptualizing the origins of life’.
Dominance hierarchies are group-level properties that emerge from the aggression of individuals. Although individuals can gain critical benefits from their position in a hierarchy, we do not understand how real-world hierarchies form. Nor do we understand what signals and decision-rules individuals use to construct and maintain hierarchies in the absence of simple cues such as size or spatial location. A study of conflict in two groups of captive monk parakeets (Myiopsitta monachus) found that a transition to large-scale order in aggression occurred in newly-formed groups after one week, with individuals thereafter preferring to direct aggression more frequently against those nearby in rank. We consider two cognitive mechanisms underlying the emergence of this order: inference based on overall levels of aggression, or on subsets of the aggression network. Both mechanisms were predictive of individual decisions to aggress, but observed patterns were better explained by rank inference through subsets of the aggression network. Based on these results, we present a new theory, of a feedback loop between knowledge of rank and consequent behavior. This loop explains the transition to strategic aggression and the formation and persistence of dominance hierarchies in groups capable of both social memory and inference.
In contrast to entropy, which increases monotonically, the "complexity" or
"interestingness" of closed systems seems intuitively to increase at first and
then decrease as equilibrium is approached. For example, our universe lacked
complex structures at the Big Bang and will also lack them after black holes
evaporate and particles are dispersed. This paper makes an initial attempt to
quantify this pattern. As a model system, we use a simple, two-dimensional
cellular automaton that simulates the mixing of two liquids ("coffee" and
"cream"). A plausible complexity measure is then the Kolmogorov complexity of a
coarse-grained approximation of the automaton's state, which we dub the
"apparent complexity." We study this complexity measure, and show analytically
that it never becomes large when the liquid particles are non-interacting. By
contrast, when the particles do interact, we give numerical evidence that the
complexity reaches a maximum comparable to the "coffee cup's" horizontal
dimension. We raise the problem of proving this behavior analytically.
Although it has been notoriously difficult to pin down precisely what is it that makes life so distinctive and remarkable, there is general agreement that its informational aspect is one key property, perhaps the key property. The unique informational narrative of living systems suggests that life may be characterized by context-dependent causal influences, and, in particular, that top-down (or downward) causation-where higher levels influence and constrain the dynamics of lower levels in organizational hierarchies-may be a major contributor to the hierarchal structure of living systems. Here, we propose that the emergence of life may correspond to a physical transition associated with a shift in the causal structure, where information gains direct and context-dependent causal efficacy over the matter in which it is instantiated. Such a transition may be akin to more traditional physical transitions (e.g. thermodynamic phase transitions), with the crucial distinction that determining which phase (non-life or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal architecture. We discuss some novel research directions based on this hypothesis, including potential measures of such a transition that may be amenable to laboratory study, and how the proposed mechanism corresponds to the onset of the unique mode of (algorithmic) information processing characteristic of living systems.
To build a theory of social complexity, we need to understand how aggregate social properties arise from individual interaction rules. Here, I review a body of work on the developmental dynamics of pigtailed macaque social organization and conflict management that provides insight into the mechanistic causes of multi-scale social systems. In this model system coarse-grained, statistical representations of collective dynamics are more predictive of the future state of the system than the constantly in-flux behavioural patterns at the individual level. The data suggest that individuals can perceive and use these representations for strategical decision-making. As an interaction history accumulates the coarse-grained representations consolidate. This constrains individual behaviour and provides the foundations for new levels of organization. The time-scales on which these representations change impact whether the consolidating higher-levels can be modified by individuals and collectively. The time-scales appear to be a function of the 'coarseness' of the representations and the character of the collective dynamics over which they are averages. The data suggest that an advantage of multiple timescales is that they allow social systems to balance tradeoffs between predictability and adaptability. I briefly discuss the implications of these findings for cognition, social niche construction and the evolution of new levels of organization in biological systems.
It is shown that the Hilbert-Bernays-Quine principle of identity of indiscernibles applies uniformly to all the contentious cases of symmetries in physics, including permutation symmetry in classical and quantum mechanics. It follows that there is no special problem with the notion of objecthood in physics. Leibniz's principle of sufficient reason is considered as well; this too applies uniformly. But given the new principle of identity, it no longer implies that space, or atoms, are unreal.
We study the predictability of emergent phenomena in complex systems. Using nearest-neighbor, one-dimensional cellular automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details. Several CA that can be coarse-grained by this construction are known to be universal Turing machines; they can emulate any CA or other computing devices and are therefore undecidable. We thus show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description. The renormalization group flows that we construct induce a hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method. Finally we argue that the large-scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of the large-scale update rule, and moreover exhibits a novel scaling law. We show that because of this large-scale simplicity, the probability of finding a coarse-grained description of CA approaches unity as one goes to increasingly coarser scales. We interpret this large-scale simplicity as a pattern formation mechanism in which large-scale patterns are forced upon the system by the simplicity of the rules that govern the large-scale dynamics.
When does history begin? What characterizes it? This brilliant and beautifully written book dissolves the logic of a beginning based on writing, civilization, or historical consciousness and offers a model for a history that escapes the continuing grip of the Judeo-Christian time frame. Daniel Lord Smail argues that in the wake of the Decade of the Brain and the best-selling historical work of scientists like Jared Diamond, the time has come for fundamentally new ways of thinking about our past. He shows how recent work in evolution and paleohistory makes it possible to join the deep past with the recent past and abandon, once and for all, the idea of prehistory. Making an enormous literature accessible to the general reader, he lays out a bold new case for bringing neuroscience and neurobiology into the realm of history.
We present three major transitions that occur on the way to the elaborate and
diverse societies of the modern era. Our account links the worlds of social
animals such as pigtail macaques and monk parakeets to examples from human
history, including 18th Century London and the contemporary online phenomenon
of Wikipedia. From the first awareness and use of group-level social facts to
the emergence of norms and their self-assembly into normative bundles, each
transition represents a new relationship between the individual and the group.
At the center of this relationship is the use of coarse-grained information
gained via lossy compression. The role of top-down causation in the origin of
society parallels that conjectured to occur in the origin and evolution of life
itself.
Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action--collectively known as f(R) theories--have been studied in great detail. When considered as complete theories of gravity they can generate nonperturbative deviations from the general relativistic predictions in the solar system, and the simplest models show instabilities on cosmological scales. Here, we show that it is possible to treat f(R)=R{+-}/R gravity in a perturbative fashion such that it shows no instabilities on cosmological scales and, in the solar system, is consistent with measurements of the parametrized post-Newtonian parameters. We show that such a theory produces a spatially flat, accelerating universe, even in the absence of dark energy and when the matter density is too small to close the Universe in the general relativistic case.
One might think that, once we know something is computable, how efficiently
it can be computed is a practical question with little further philosophical
importance. In this essay, I offer a detailed case that one would be wrong. In
particular, I argue that computational complexity theory---the field that
studies the resources (such as time, space, and randomness) needed to solve
computational problems---leads to new perspectives on the nature of
mathematical knowledge, the strong AI debate, computationalism, the problem of
logical omniscience, Hume's problem of induction, Goodman's grue riddle, the
foundations of quantum mechanics, economic rationality, closed timelike curves,
and several other topics of philosophical interest. I end by discussing aspects
of complexity theory itself that could benefit from philosophical analysis.
Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational, and social systems makes the problem harder. Here, we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.
Marr's demonstrations that retinal receptive field geometry could be derived by Fourier transformation of spatial frequency sensitivity data, that edges and contours could be detected by finding zero crossings in the light gradient by taking the Laplacian or second directional derivative, that excitatory and inhibitory receptive fields could be constructed from "DOG" functions (the difference of two Gaussians), and that the visual system used a two-dimensional convolution integral with a Gaussian prefilter as an operator for bandwidth optimation on the retinal light distribution, were more powerful than anything that had been seen up to that time. It was as if vision research suddenly acquired its own Principia Mathematica, or perhaps General Relativity Theory, in terms of the new explanatory power Marr's theories provided. Truly an extraordinary book from an extraordinary thinker in the area of perception, vision, and the brain.
Major observational efforts in the coming decade are designed to probe the equation of state of dark energy. Measuring a deviation of the equation-of-state parameter w from -1 would indicate a dark energy that cannot be represented solely by a cosmological constant. While it is commonly assumed that any implied modification to the LambdaCDM model amounts to the addition of new dynamical fields, we propose here a framework for investigating whether or not such new fields are required when cosmological observations are combined with a set of minimal assumptions about the nature of gravitational physics. In our approach, we treat the additional degrees of freedom as perturbatively constrained and calculate a number of observable quantities, such as the Hubble expansion rate and the cosmic acceleration, for a homogeneous Universe. We show that current observations place our Universe within the perturbative validity of our framework and allow for the presence of non-dynamical gravitational degrees of freedom at cosmological scales.
Humanity in a creative universe
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The Origins of Political Order: From Prehuman Times to the French Revolution. Farrar, Straus and Giroux
- F Fukuyama
F. Fukuyama. The Origins of Political Order: From Prehuman Times to the French Revolution.
Farrar, Straus and Giroux, 2011.
An evolutionary approach to culture
- Merlin Donald
Merlin Donald. An evolutionary approach to culture. In Robert N Bellah and Hans Joas,
editors, The Axial Age and its consequences. Harvard University Press, 2012.
Debt: the first 5,000 years
- David Graeber
David Graeber. Debt: the first 5,000 years. Melville House, New York, NY, USA, 2014.
Updated and expanded.
- Richard P Woodard
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https://arxiv.org/abs/1506.02210.
The Undecidables, 2013
- John Bova
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- Paul Livingston
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Groups as eide? toward a Platonic response to Metaphysics M on unity, structure, and number
- John Bova
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and number, 2017. Unpublished manuscript.
Introduction to renormalization
- Simon Dedeo
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Institute. http://renorm.complexityexplorer.org.