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Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better
Joel Cohen offers a historical and prospective analysis of the relationship between mathematics and biolog
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Navigating the Turbulent Waters of School Reform Guided by Complexity Theory
The goal of this research study has been to develop, implement, and evaluate a school reform design experiment at a continuation high school with low-income, low-performing underrepresented minority students. The complexity sciences served as a theoretical framework for this design experiment. Treating an innovative college preparatory program as a nested complex adaptive system within a larger complex adaptive system, the school, we used features of complex adaptive systems (equilibrium, emergence, self-organization, and feedback loops) as a framework to design a strategy for school reform. The goal was to create an environment for change by pulling the school far from equilibrium using a strategy we call âpurposeful perturbationsâ to disrupt the stable state of the school in a purposeful way. Over the four years of the study, several tipping points were reached, and we developed agent-based simulation models that capture important dynamic properties of the reform at these points. The study draws upon complexity theory in multiple ways that have supported improved education for low-achieving students
Commutative deformations of general relativity: nonlocality, causality, and dark matter
Hopf algebra methods are applied to study Drinfeld twists of
(3+1)-diffeomorphisms and deformed general relativity on \emph{commutative}
manifolds. A classical nonlocality length scale is produced above which
microcausality emerges. Matter fields are utilized to generate self-consistent
Abelian Drinfeld twists in a background independent manner and their continuous
and discrete symmetries are examined. There is negligible experimental effect
on the standard model of particles. While baryonic twist producing matter would
begin to behave acausally for rest masses above TeV, other
possibilities are viable dark matter candidates or a right handed neutrino.
First order deformed Maxwell equations are derived and yield immeasurably small
cosmological dispersion and produce a propagation horizon only for photons at
or above Planck energies. This model incorporates dark matter without any
appeal to extra dimensions, supersymmetry, strings, grand unified theories,
mirror worlds, or modifications of Newtonian dynamics.Comment: 47 pages including references, 0 figures, 0 tables Various
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