Ultrametric spaces of branches on arborescent singularities

Let $S$ be a normal complex analytic surface singularity. We say that $S$ is arborescent if the dual graph of any resolution of it is a tree. Whenever $A,B$ are distinct branches on $S$, we denote by $A \cdot B$ their intersection number in the sense of Mumford. If $L$ is a fixed branch, we define $U_L(A,B)= (L \cdot A)(L \cdot B)(A \cdot B)^{-1}$ when $A \neq B$ and $U_L(A,A) =0$ otherwise. We generalize a theorem of P{\l}oski concerning smooth germs of surfaces, by proving that whenever $S$ is arborescent, then $U_L$ is an ultrametric on the set of branches of $S$ different from $L$. We compute the maximum of $U_L$, which gives an analog of a theorem of Teissier. We show that $U_L$ encodes topological information about the structure of the embedded resolutions of any finite set of branches. This generalizes a theorem of Favre and Jonsson concerning the case when both $S$ and $L$ are smooth. We generalize also from smooth germs to arbitrary arborescent ones their valuative interpretation of the dual trees of the resolutions of $S$. Our proofs are based in an essential way on a determinantal identity of Eisenbud and Neumann.Comment: 37 pages, 16 figures. Compared to the first version on Arxiv, il has a new section 4.3, accompanied by 2 new figures. Several passages were clarified and the typos discovered in the meantime were correcte

Future Contingents and the Logic of Temporal Omniscience

At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true that, looking backwards, it was the case that there would be a sea battle? This tension forms, in large part, what might be called the problem of future contingents. A dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition--including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et. al (2001) and MacFarlane (2003, 2014)--have argued that the apparent tension between the intuitions is in fact merely apparent. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions

‘Instead of fetching flowers, the youths brought in flakes of snow’: exploring extreme weather history through English parish registers

Parish registers provide organized, dated and located population data and as such, are routinely among the most frequently consulted documents within the holdings of county record offices and archives. Throughout history, extreme weather has had significant impacts on the church, its congregation, and local landscape. It is for these reasons that extreme weather events have been deemed worthy of official note by authors of many registers. Although isolated entries have been used as supporting evidence for the occurrence of a number of historic extreme weather events, the information that parish registers contain relating to weather history has not been studied in its own right. Parish register narratives add new events to existing chronologies of extreme weather events and contribute to our understanding of their impacts at the local level. As public and well used documents they also function to keep the memory of particular events alive. The examples in this paper cover a wide range of weather types, places, and time periods, also enabling recording practice to be explored. Finally, as the number of digitized registers increases, we highlight the risks of weather narratives being obscured, and reflect on how the weather history contained within might be systematically captured

Living God Pandeism: Evidential Support

Pandeism is the belief that God chose to wholly become our Universe, imposing principles at this Becoming that have fostered the lawful evolution of multifarious structures, including life and consciousness. This article describes and defends a particular form of pandeism: living God pandeism (LGP). On LGP, our Universe inherits all of God's unsurpassable attributes—reality, unity, consciousness, knowledge, intelligence, and effectiveness—and includes as much reality, conscious and unconscious, as is possible consistent with retaining those attributes. God and the Universe, together “God-and-Universe,” is also eternal into the future and the past. The article derives testable hypotheses from these claims and shows that the evidence to date confirms some of these while falsifying none. Theism cannot be tested in the same way

Many Labs 5: Testing Pre-Data-Collection Peer Review as an Intervention to Increase Replicability

Replication studies in psychological science sometimes fail to reproduce prior findings. If these studies use methods that are unfaithful to the original study or ineffective in eliciting the phenomenon of interest, then a failure to replicate may be a failure of the protocol rather than a challenge to the original finding. Formal pre-data-collection peer review by experts may address shortcomings and increase replicability rates. We selected 10 replication studies from the Reproducibility Project: Psychology (RP:P; Open Science Collaboration, 2015) for which the original authors had expressed concerns about the replication designs before data collection; only one of these studies had yielded a statistically significant effect (p < .05). Commenters suggested that lack of adherence to expert review and low-powered tests were the reasons that most of these RP:P studies failed to replicate the original effects. We revised the replication protocols and received formal peer review prior to conducting new replication studies. We administered the RP:P and revised protocols in multiple laboratories (median number of laboratories per original study = 6.5, range = 3–9; median total sample = 1,279.5, range = 276–3,512) for high-powered tests of each original finding with both protocols. Overall, following the preregistered analysis plan, we found that the revised protocols produced effect sizes similar to those of the RP:P protocols (Δr = .002 or .014, depending on analytic approach). The median effect size for the revised protocols (r = .05) was similar to that of the RP:P protocols (r = .04) and the original RP:P replications (r = .11), and smaller than that of the original studies (r = .37). Analysis of the cumulative evidence across the original studies and the corresponding three replication attempts provided very precise estimates of the 10 tested effects and indicated that their effect sizes (median r = .07, range = .00–.15) were 78% smaller, on average, than the original effect sizes (median r = .37, range = .19–.50).Additional co-authors: Ivan Ropovik, Balazs Aczel, Lena F. Aeschbach, Luca Andrighetto, Jack D. Arnal, Holly Arrow, Peter Babincak, Bence E. Bakos, Gabriel Baník, Ernest Baskin, Radomir Belopavlovic, Michael H. Bernstein, Michał Białek, Nicholas G. Bloxsom, Bojana Bodroža, Diane B. V. Bonfiglio, Leanne Boucher, Florian Brühlmann, Claudia C. Brumbaugh, Erica Casini, Yiling Chen, Carlo Chiorri, William J. Chopik, Oliver Christ, Antonia M. Ciunci, Heather M. Claypool, Sean Coary, Marija V. Cˇolic, W. Matthew Collins, Paul G. Curran, Chris R. Day, Anna Dreber, John E. Edlund, Filipe Falcão, Anna Fedor, Lily Feinberg, Ian R. Ferguson, Máire Ford, Michael C. Frank, Emily Fryberger, Alexander Garinther, Katarzyna Gawryluk, Kayla Ashbaugh, Mauro Giacomantonio, Steffen R. Giessner, Jon E. Grahe, Rosanna E. Guadagno, Ewa Hałasa, Rias A. Hilliard, Joachim Hüffmeier, Sean Hughes, Katarzyna Idzikowska, Michael Inzlicht, Alan Jern, William Jiménez-Leal, Magnus Johannesson, Jennifer A. Joy-Gaba, Mathias Kauff, Danielle J. Kellier, Grecia Kessinger, Mallory C. Kidwell, Amanda M. Kimbrough, Josiah P. J. King, Vanessa S. Kolb, Sabina Kołodziej, Marton Kovacs, Karolina Krasuska, Sue Kraus, Lacy E. Krueger, Katarzyna Kuchno, Caio Ambrosio Lage, Eleanor V. Langford, Carmel A. Levitan, Tiago Jessé Souza de Lima, Hause Lin, Samuel Lins, Jia E. Loy, Dylan Manfredi, Łukasz Markiewicz, Madhavi Menon, Brett Mercier, Mitchell Metzger, Venus Meyet, Jeremy K. Miller, Andres Montealegre, Don A. Moore, Rafał Muda, Gideon Nave, Austin Lee Nichols, Sarah A. Novak, Christian Nunnally, Ana Orlic, Anna Palinkas, Angelo Panno, Kimberly P. Parks, Ivana Pedovic, Emilian Pekala, Matthew R. Penner, Sebastiaan Pessers, Boban Petrovic, Thomas Pfeiffer, Damian Pienkosz, Emanuele Preti, Danka Puric, Tiago Ramos, Jonathan Ravid, Timothy S. Razza, Katrin Rentzsch, Juliette Richetin, Sean C. Rife, Anna Dalla Rosa, Kaylis Hase Rudy, Janos Salamon, Blair Saunders, Przemysław Sawicki, Kathleen Schmidt, Kurt Schuepfer, Thomas Schultze, Stefan Schulz-Hardt, Astrid Schütz, Ani N. Shabazian, Rachel L. Shubella, Adam Siegel, Rúben Silva, Barbara Sioma, Lauren Skorb, Luana Elayne Cunha de Souza, Sara Steegen, L. A. R. Stein, R. Weylin Sternglanz, Darko Stojilovic, Daniel Storage, Gavin Brent Sullivan, Barnabas Szaszi, Peter Szecsi, Orsolya Szöke, Attila Szuts, Manuela Thomae, Natasha D. Tidwell, Carly Tocco, Ann-Kathrin Torka, Francis Tuerlinckx, Wolf Vanpaemel, Leigh Ann Vaughn, Michelangelo Vianello, Domenico Viganola, Maria Vlachou, Ryan J. Walker, Sophia C. Weissgerber, Aaron L. Wichman, Bradford J. Wiggins, Daniel Wolf, Michael J. Wood, David Zealley, Iris Žeželj, Mark Zrubka, and Brian A. Nose

Many Labs 5:Testing pre-data collection peer review as an intervention to increase replicability

Replication studies in psychological science sometimes fail to reproduce prior findings. If these studies use methods that are unfaithful to the original study or ineffective in eliciting the phenomenon of interest, then a failure to replicate may be a failure of the protocol rather than a challenge to the original finding. Formal pre-data-collection peer review by experts may address shortcomings and increase replicability rates. We selected 10 replication studies from the Reproducibility Project: Psychology (RP:P; Open Science Collaboration, 2015) for which the original authors had expressed concerns about the replication designs before data collection; only one of these studies had yielded a statistically significant effect (p < .05). Commenters suggested that lack of adherence to expert review and low-powered tests were the reasons that most of these RP:P studies failed to replicate the original effects. We revised the replication protocols and received formal peer review prior to conducting new replication studies. We administered the RP:P and revised protocols in multiple laboratories (median number of laboratories per original study = 6.5, range = 3?9; median total sample = 1,279.5, range = 276?3,512) for high-powered tests of each original finding with both protocols. Overall, following the preregistered analysis plan, we found that the revised protocols produced effect sizes similar to those of the RP:P protocols (?r = .002 or .014, depending on analytic approach). The median effect size for the revised protocols (r = .05) was similar to that of the RP:P protocols (r = .04) and the original RP:P replications (r = .11), and smaller than that of the original studies (r = .37). Analysis of the cumulative evidence across the original studies and the corresponding three replication attempts provided very precise estimates of the 10 tested effects and indicated that their effect sizes (median r = .07, range = .00?.15) were 78% smaller, on average, than the original effect sizes (median r = .37, range = .19?.50)