Red Hook Public Library

The concept of imaginary logical values was introduced by Spencer-Brown in Laws of Form, in analogy to the square root of -1 in the complex numbers. In this paper, we develop a new approach to representing imaginary values. The resulting system, which we call BF, is a four-valued generalization of Laws of Form. Imaginary values in BF act as cyclic four-valued operators. The central characteristic of BF is its capacity to portray imaginary values as both values and as operators. We show that the BF algebra is a stronger, axiomatically complete extension to Laws of Form capable of representing other four-valued systems, including the Kauffman/Varela Waveform Algebra and Belnap's Four-Valued Bilattice. We conclude by showing a representation of imaginary values based on the Artin braid group, a representation of the braid group and a braided representation of the quaternions in this form.

Urban agriculture is emerging across the United States (U.S.) as a distinct food production system that can help address food security and equity concerns of marginalized, urban communities. While urban farming is accelerating across the nation rapidly, the system of peer-to-peer learning that represents farmer education and training in the U.S. is based on rural agriculture. We describe the development of virtual reality (VR) platforms to support farmer knowledge transfer and innovation that transcend the physical constraints of traditional agricultural extension based on on-farm demonstrations. We feature a VR model representing an organic farm in New York City with details of farm operations, and opportunities to stack educational and training materials along with personal narratives, as part of the virtual farm demonstration. The potential for VR to accelerate innovations in food justice is a critical component of smart cities technologies and should be developed in parallel with modernization efforts with land grant universities and their cooperative extension networks of farmer-to-farmer education and training.

In this citizen science–aided, college laboratory–based microbiology research project, secondary school students collaborate with college research students on an investigation centered around bacterial species in the local watershed. This study specifically investigated the prevalence of violacein-producing bacterial isolates, as violacein has been demonstrated as a potential bioremediation treatment for outbreaks of the worldwide invasive chytrid, Batrachochytrium dendrobatidis (Bd). The impact of this invasion has been linked to widespread amphibian decline, and tracking of the spread of Bd is currently ongoing. Secondary school students participated in this research project by sterilely collecting water samples from a local watershed, documenting the samples, and completing the initial sample plating in a BSL1 environment. In the second phase of this project, trained college students working in courses and as research assistants in the academic year and summer term in a BSL2 laboratory facility were able to use physiological, biochemical, and molecular techniques to further identify individual isolates as well as characterize their properties. Collaboration between these learning spaces provides an increased interest in the community for environmentally relevant research projects and allows for an expansion of the research team to increase study robustness. Journal of Microbiology & Biology Education