Grand Challenges in Planetary Nebulae Studies: Binary Evolution and MHD

We review work on the evolution of planetary nebulae and proto-planetaries via magneto-rotational mechanisms showing that a dynamo generated magnetic field can produce the energy and momentum needed to drive pPN and PNe outflows. Angular momentum considerations lead to the conclusion that single stars may not be capable of supporting strong fields for long times. Thus we take the working hypothesis that most PN may form via binary stars. We propose that the grand challenge for PN studies is fully understanding the diverse physical processes at work in binary late stage evolution including the development of disks, fields and outflows.Comment: 4 pages. To be published in IAU Symposium #234, "Planetary Nebulae in Our Galaxy and Beyond" proceedings. Text with figures can be found at http://www.pas.rochester.edu/~afrank/frank_pne.pd

Earth as a Hybrid Planet - The Anthropocene in an Evolutionary Astrobiological Context

We develop a classification scheme for the evolutionary state of planets based on the non-equilibrium thermodynamics of their coupled systems, including the presence of a biosphere and the possibility of what we call an agency-dominated biosphere (i.e. an energy-intensive technological species). The premise is that Earths entry into the Anthropocene represents what might be from an astrobiological perspective a predictable planetary transition. We explore this problem from the perspective of the solar system and exoplanet studies. Our classification discriminates planets by the forms of free energy generation driven from stellar forcing. We then explore how timescales for global evolutionary processes on Earth might be synchronized with ecological transformations driven by increases in energy harvesting and its consequences (which might have reached a turning point with global urbanization). Finally, we describe quantitatively the classification scheme based on the maintenance of chemical disequilibrium in the past and current Earth systems and on other worlds in the solar system. In this perspective, the beginning of the Anthropocene can be seen as the onset of the hybridization of the planet - a transitional stage from one class of planetary systems interaction to another. For Earth, this stage occurs as the effects of human civilization yield not just new evolutionary pressures, but new selected directions for novel planetary ecosystem functions and their capacity to generate disequilibrium and enhance planetary dissipation.Comment: Accepted for publication in the journal Anthropocen

Bayesianism, Infinite Decisions, and Binding

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses

The Silurian Hypothesis: Would It Be Possible to Detect an Industrial Civilization in the Geological Record?

If an industrial civilization had existed on Earth many millions of years prior to ourown era, what traces would it have left and would they be detectable today? We summarize the likely geological fingerprint of the Anthropocene, and demonstrate that while clear, it will not differ greatly in many respects from other known events in the geological record. We then propose tests that could plausibly distinguish an industrial cause from an otherwise naturally occurring climate event

Bisector energy and few distinct distances

We introduce the bisector energy of an $n$-point set $P$ in $\mathbb{R}^2$, defined as the number of quadruples $(a,b,c,d)$ from $P$ such that $a$ and $b$ determine the same perpendicular bisector as $c$ and $d$. If no line or circle contains $M(n)$ points of $P$, then we prove that the bisector energy is $O(M(n)^{\frac{2}{5}}n^{\frac{12}{5}+\epsilon} + M(n)n^2).$. We also prove the lower bound $\Omega(M(n)n^2)$, which matches our upper bound when $M(n)$ is large. We use our upper bound on the bisector energy to obtain two rather different results: (i) If $P$ determines $O(n/\sqrt{\log n})$ distinct distances, then for any $0<\alpha\le 1/4$, either there exists a line or circle that contains $n^\alpha$ points of $P$, or there exist $\Omega(n^{8/5-12\alpha/5-\epsilon})$ distinct lines that contain $\Omega(\sqrt{\log n})$ points of $P$. This result provides new information on a conjecture of Erd\H{o}s regarding the structure of point sets with few distinct distances. (ii) If no line or circle contains $M(n)$ points of $P$, then the number of distinct perpendicular bisectors determined by $P$ is $\Omega(\min\{M(n)^{-2/5}n^{8/5-\epsilon}, M(n)^{-1} n^2\})$. This appears to be the first higher-dimensional example in a framework for studying the expansion properties of polynomials and rational functions over $\mathbb{R}$, initiated by Elekes and R\'onyai.Comment: 18 pages, 2 figure