A New Biology: A Modern Perspective on the Challenge of Closing the Gap between the Islands of Knowledge

This paper discusses the rebirth of the old quest for the principles of biology along the discourse line of machine-organism disanalogy and within the context of biocomputation from a modern perspective. It reviews some new attempts to revise the existing body of research and enhance it with new developments in some promising fields of mathematics and computation. The major challenge is that the latter are expected to also answer the need for a new framework, a new language and a new methodology capable of closing the existing gap between the different levels of complex system organization

Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.Comment: 30 pages, 18 figure

Nonlinear Time Series Analysis of Sunspot Data

This paper deals with the analysis of sunspot number time series using the Hurst exponent. We use the rescaled range (R/S) analysis to estimate the Hurst exponent for 259-year and 11360-year sunspot data. The results show a varying degree of persistence over shorter and longer time scales corresponding to distinct values of the Hurst exponent. We explain the presence of these multiple Hurst exponents by their resemblance to the deterministic chaotic attractors having multiple centers of rotation.Comment: 10 pages, 6 figures, accepted for publication in Solar Physics, journal style corrections done in this versio

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

A predictive model for life expectancy curves

Life expectancy curves have a characteristic ominous shape that has fascinated scientists for centuries. Medawar was the first to explain this shape, specifically the steeply rising proneness of an average individual to die as a function of age, in evolutionary terms. The idea was that the "selective value" of the individual decreases as it has triggered other individuals taking its place (and carrying its genes) into existence. We demonstrate that this idea can be turned into a quantitative model. The resulting 4-parameter function reproduces well two well-known life expectancy curves from the first half of this century. Moreover, the easily interpretable parameters (3 of the 4) seem intuitively reasonable