William Mitchell

When is it a good time to think about time? The answer provided by this essay is that there is no time like the present, especially the crazy, tense present of the year 2020. In this year four distinct scales of temporality have collided in a prolonged period of crisis and uncertainty: (1) the onset of a global pandemic that devastated the world economy and killed over a million people, the worst public health disaster since the Spanish flu of 1918; (2) a political crisis featuring the rise of authoritarian governments around the world that threatened to overturn two centuries of efforts to secure stable representative democracies, centered in the rise of a would-be tyrant and demagogue in the US; (3) an explosive social movement centered in the endemic condition of systemic racism in the US; (4) a global environmental crisis that threatens the stability of the planetary ecological system as a sustainable habitat for thousands of species, including the human. Quarantined in monkish isolation by the pandemic, the author has engaged in a set of reflections on these convergent time scales. Instead of the classic (and unanswerable) philosophical question “What is time?” this essay reflects on the ways we picture time in metaphors, figures, personifications, and diagrams. In an anachronistic gathering of images of time from ancient and modern sources, the essay attempts to replace the ontology of time with an iconology that may provide some useful tools for finding our way through this epochal crisis.

A tension between perspectives that emphasize deterministic versus stochastic processes has sparked controversy in ecology since pre-Darwinian times. The most recent manifestation of the contrasting perspectives arose with Hubbell’s proposed “neutral theory”, which hypothesizes a paramount role for stochasticity in ecological community composition. Here we shall refer to the deterministic and the stochastic perspectives as the niche-based and neutral-based research programs, respectively. Our goal is to represent these perspectives in the context of Lakatos’ notion of a scientific research program. We argue that the niche-based program exhibits all the characteristics of a robust, progressive research program, including the ability to deal with disconfirming data by generating new testable predictions within the program. In contrast, the neutral-based program succeeds as a mathematical tool to capture, as epiphenomena, broad-scale patterns of ecological communities but appears to handle disconfirming data by incorporating hypotheses and assumptions from outside the program, specifically, from the niche-based program. We conclude that the neutral research program fits the Lakatosian characterization of a degenerate research program.

We reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every $\nu \in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik. the iterated forcing $R_{\lambda +1}$ used in this paper has the property that if λ is a cardinal less then κ then $R_{\lambda + 1}$ can be factored in V as $R_{\kappa + 1} = R_{\lambda + 1} \times R_{\lambda + 1, \kappa}$ where $\mid R_{\lambda +1}\mid \leq \lambda^+$ and $R_{\lambda + 1, \kappa}$ does not add any new subsets of λ