The International Commission on Stratigraphy’s official chronostratigraphic chart (2013/01 version shown here) is one of my favorite compendia of scientific knowledge.

Jeffrey Morton - 2006-01

Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding a combinatorial model for some mathematical entity is a particular instance of the process called “categorification”. Examples include the interpretation of N as the Burnside rig of the category of finite sets with product and coproduct, and the interpretation of N[x] as the category of combinatorial species. This has interesting applications to quantum mechanics, and in particular the quantum harmonic oscillator, via Joyal’s “species”, a new generalization called “stuff types”, and operators between these, which can be represented as rudimentary Feynman diagrams for the oscillator. In quantum mechanics, we want to represent states in an algebra over the complex numbers, and also want our Feynman diagrams to carry more structure than these “stuff operators” can do, and these turn out to be closely related. We will show how to construct a combinatorial model for the quantum harmonic oscillator in which the group of phases, U(1), plays a special role. We describe a general notion of “M-Stuff Types” for any monoid M, and see that the case M = U(1) provides an interpretation of time evolution in the combinatorial setting, as well as other quantum mechanical features of the harmonic oscillator.

Have you guys read Eliezer’s new paper, Intelligence Explosion Microeconomics? It’s pretty good. Anybody wanna talk about it?

Robert K. Niven - 2007-04

This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy functions, as simplified forms of the multinomial distribution subject to the Stirling approximation; (ii) an explanation for the need to maximize entropy (or minimize cross-entropy) to find the most probable realization of a system; and (iii) new, generalized definitions of entropy and cross-entropy - supersets of the Boltzmann principle - applicable to non-multinomial systems. The combinatorial basis is therefore of much broader scope, with far greater power of application, than the information-theoretic and axiomatic bases. The generalized definitions underpin a new discipline of “combinatorial information theory”, for the analysis of probabilistic systems of any type.

Jaynes’ generic formulation of statistical mechanics for multinomial systems is re-examined in light of the combinatorial approach, including the analysis of probability distributions, ensemble theory, Jaynes relations, fluctuation theory and the entropy concentration theorem. Several new concepts are outlined, including a generalized Clausius inequality, a generalized free energy (“free information”) function, and a generalized Gibbs-Duhem relation and phase rule. For nonmultinomial systems, the generalized approach provides a different framework for the reinterpretation of the many alternative entropy measures (e.g. Bose-Einstein, Fermi-Dirac, Rényi, Tsallis, Sharma-Mittal, Beck-Cohen, Kaniadakis) in terms of their combinatorial structure. A connection between the combinatorial and Bayesian approaches is also explored.

How well do you know the Solar System? This handy chart I made provides basic information about the sun, the 8 planets, the 5 known dwarf planets, and the asteroid belt separating the inner and outer planets.

Most of this data is straight from Wikipedia; the estimated mass of the asteroid belt is from this paper. Distances are in Astronomical Units; masses are in Earth Masses.

Notice that the dwarf planet masses are around 10^(-4) - 10^(-3), the inner planet masses are around 10^(-1) - 10^(0), and the outer planet masses are around 10^(1) - 10^(2).

2020:

Researchers from the Korea Advanced Institute of Science and Technology have managed to remotely control the movements of a turtle.

(via postmodernmarvel)

you guys I did it

I finished The Road to Reality

I started reading that book circa 2005

Dino J Levy and Paul W Glimcher - 2012-06

How do humans make choices between different types of rewards? Economists have long argued on theoretical grounds that humans typically make these choices as if the values of the options they consider have been mapped to a single common scale for comparison. Neuroimaging studies in humans have recently begun to suggest the existence of a small group of specific brain sites that appear to encode the subjective values of different types of rewards on a neural common scale, almost exactly as predicted by theory. We have conducted a meta analysis using data from thirteen different functional magnetic resonance imaging studies published in recent years and we show that the principle brain area associated with this common representation is a subregion of the ventromedial prefrontal cortex (vmPFC) / orbitofrontal cortex (OFC). The data available today suggest that this common valuation path is a core system that participates in day-to-day decision making suggesting both a neurobiological foundation for standard economic theory and a tool for measuring preferences neurobiologically. Perhaps even more exciting is the possibility that our emerging understanding of the neural mechanisms for valuation and choice may provide fundamental insights into pathological choice behaviors like addiction, obesity and gambling.

It bums me out that the school system is basically set up to tell kids who struggle with the technical aspects of math & science that they are bad at math & science.

Most of the important progress in math & science has come from conceptual, rather than technical, insight.

Most of the important products of math & science are primarily characterized by creativity rather than skill.

Can someone with a background in art comment on the degree to which the above comments also apply to art?

How and to what degree can the axiomatization of geometry (by Euclid, c.  300BC), the invention of the number zero (by various people independently at various times), and/or the invention of category theory (by Eilenberg & Mac Lane, c. 1945) be described by physics?

Can the techniques of information theory or the theory of computation be brought to bear on these questions? Can the relationships between these fields and physics then tell us something about these (ultimately physical) processes, or about what physics should be like given that they seem to have occurred?

Will an answer along these lines help us reproduce or, better yet, automate this kind of phenomenon?

Could it tell us more about the physics of minds in general?

colchrishadfield:

Geneva, Switzerland. Under that rock is the incredible CERN particle accelerator. Their AMS is mounted on Station.