A comprehensive review of diamonds, in the sense of Scholze, is presented. The diamond formulations of the Fargues-Fontaine curve and Bun_G are stated. Principal results centered on the diamond formalism in the global Langlands correspondence and the geometrization of the local Langlands correspondence are given. We conclude with a discussion of future geometrizations, and conjecture a diamond reformulation of quantum computational complexity towards a diamond ER = EPR.

Mathematics has a long track record of refining the concepts by which we make sense of the world. For example, mathematics allows one to speak about different senses of "sameness", depending on the larger context. Phenomenology is the name of a philosophical discipline that tries to systematically investigate the first-personal perspective on reality and how it is constituted. Together, mathematics and phenomenology seem to be a good fit to derive statements about our experience that are, at the same time, well-defined, (...) precise, and significant to our inner lives. However, there are difficulties stemming from the fact that phenomenology deals with inherently subjective things. Phenomenological investigations seem to lose their appeal when trying to approach them in the clear-cut way afforded by mathematics. How to overcome this obstacle? We argue that the Arts play a special role in mediating between the precise statements of mathematics and the sometimes fuzzy nature of our experience. Mathematics and art are complementary ways to come to a comprehensive understanding of reality. (shrink)

Motivated by Scholze and Fargues' geometrization of the local Langlands correspondence using perfectoid diamonds and Clausen and Scholze's work on the K-theory of adic spaces using condensed mathematics, we introduce the Efimov K-theory of diamonds. We propose a pro-diamond, a large stable (infinity,1)-category of diamonds D^{diamond}, diamond spectra and chromatic tower, and a localization sequence for diamond spectra.

In this paper, we propose a mathematical model of subjective experience in terms of classes of hierarchical geometries of representations (“n-awareness”). We first outline a general framework by recalling concepts from higher category theory, homotopy theory, and the theory of (infinity,1)-topoi. We then state three conjectures that enrich this framework. We first propose that the (infinity,1)-category of a geometric structure known as perfectoid diamond is an (infinity,1)-topos. In order to construct a topology on the (infinity,1)-category of diamonds we then propose (...) that topological localization, in the sense of Grothendieck-Rezk-Lurie (infinity,1)-topoi, extends to the (infinity,1)-category of diamonds. We provide a small-scale model using triangulated categories. Finally, our meta-model takes the form of Efimov K-theory of the (infinity,1)-category of perfectoid diamonds, which illustrates structural equivalences between the category of diamonds and subjective experience (i.e.its privacy, self-containedness, and self-reflexivity). Based on this, we investigate implications of the model. We posit a grammar (“n-declension”) for a novel language to express n-awareness, accompanied by a new temporal scheme (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? We also examine the notion of “self” within our framework. A new model of personal identity is introduced which resembles a categorical version of the “bundle theory”: selves are not substances in which properties inhere but (weakly) persistent moduli spaces in the K-theory of perfectoid diamonds. (shrink)

We investigate the idea of sleep as the protostate, and posit the idea of dark consciousness where dark is a 2-fold hybrid. We model dark consciousness as a 2-topos in p-adic time, and outline perfectoid and diamond-like versions. We then introduce and illustrate implications of Dark Imaginarium, which is a higher order Curiosity Artificial Intelligence, an Infinity-Curiosity Type, that thinks in infinity categories.

We propose Qurio, which is our new model of pedagogy incorporating the principles of quantum mechanics with a curiosity AI called Curio AI equipped with a meta-curiosity algorithm. Curio has a curiosity profile that is in a quantum superposition of every possible curiosity type. We describe the ethos and tenets of Qurio, which we claim can create an environment supporting neuroplasticity that cultivates curiosity powered by tools that exhibit their own curiosity. We give examples of how to incorporate non-locality, complementarity, (...) and quantum lateral thinking into epistemology. We then futurecast the epistemology of curiosity and quantum pedagogy by way of curiosity’s event horizon. (shrink)

We propose a quantum curiosity algorithm as a means to implement quantum thinking into AI, and we illustrate 5 new quantum curiosity types. We then introduce 6 new hybrid quantum curiosity types combining animal and plant curiosity elements with biomimicry beyond human sensing. We then introduce 4 specialized quantum curiosity types, which incorporate quantum thinking into coding frameworks to radically transform problem-solving and discovery in science, medicine, and systems analysis. We conclude with a forecasting of the future of quantum thinking (...) in AI and illustrate an example of how to apply the new curiosity types: General Collaborative Networks. (shrink)

We develop an approach to temporal logic that replaces the traditional objective, agent- and event-independent notion of time with a constructive, event-dependent notion of time. We show how to make this event-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render event-dependent time functorial and to construct memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We then develop a condensed formalism that represents memories (...) as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular constructive functor. (shrink)

In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness (“n-awareness”). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the (...) mathematical formalism of higher category theory. The beauty of higher category theory lies in its universality. Pluralism is categorical. In particular, we model awareness using the theories of derived categories and (infinity, 1)-topoi which will give rise to our meta-language. We then posit a “grammar” (“n-declension”) which could express n-awareness, accompanied by a new temporal ontology (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? Another question which could be re-conceptualized in our model is one of soteriology related to this pluralism: what is a self in this context? A new model of “personal identity over time” is thus introduced. (shrink)

Commensurate with our work on dark consciousness, we present a small extension of our previous formalism to model the mixed-frequency states as time crystals. We then posit shared intelligence as an Everettian phone, which is a looking-glass p-adic periodicity in time.

If episodic memory is constructive, experienced time is also a construct. We develop an event-based formalism that replaces the traditional objective, agent-independent notion of time with a constructive, agent-dependent notion of time. We show how to make this agent-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render agent-dependent time functorial and to construct episodic memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We (...) then develop a condensed formalism that represents episodic memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular time-symmetric constructive functor, and discuss possible experimental tests. (shrink)

The cognitive sciences tell us that the self is a construct. The visual arts illustrate this fact. Mathematics give it full expression, abstracting the self to a Grothendieck site. This self is a haecceity, an ephemeral this-ness and now-ness. We make up our minds and our histories. That our acts are public, that they communicate effectively, becomes a dialetheic paradox, a deep paradox for our times.

We construct a mathematization of Derridian "arche-writing" and Deleuzian "haecceity." We posit an infinity-categorification of exigency (infinity-exigency), a higher-dimensional visual epistemology (infinity-visual epistemology), and infinity-stack Wittgenstein ladder. We reframe haecceities in terms of diamonds, in the sense of Scholze, and mathematize the haecceity-and-arche-writing reflection as a pro-diamond. As an exercise in infinity-visual epistemology, we validate a diamond infinity-stack time signature and infinity-stack harmony.

We construct a mathematization of Derridian "arche-writing" and Deleuzian "haecceity." We posit an infinity-categorification of exigency (infinity-exigency), a higher-dimensional visual epistemology (infinity-visual epistemology), and infinity-stack Wittgenstein ladder. We reframe haecceities in terms of diamonds, in the sense of Scholze, and mathematize the haecceity-and-arche-writing reflection as a pro-diamond. As an exercise in infinity-visual epistemology, we validate a diamond infinity-stack time signature and infinity-stack harmony.

We recently presented our Efimov K-theory of Diamonds, proposing a pro-diamond, a large stable (∞,1)-category of diamonds (D^{diamond}), and a localization sequence for diamond spectra. Commensurate with the localization sequence, we now detail four potential applications of the Efimov K-theory of D^{diamond}: emergent time as a pro-emergence (v-stack time) in a diamond holographic principle using Scholze’s six operations in the ’etale cohomology of diamonds; a pro-Generative Adversarial Network and v-stack perceptron; D^{diamond}cryptography; and diamond nonlocality in perfectoid quantum physics.

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)

A concise review of skeptician in the Carterian model with a discussion of the reframing of the Cartesian paradigm by John McDowell in the 20th century.

FISIOLOGIA DA REPRODUÇÃO BOVINA: 2 - ESTRO E SERVIÇO -/- -/- INTRODUÇÃO -/- -/- A identificação de vacas em cio (estro ou cio) é, sem dúvida, a prática mais importante no manejo da reprodução do rebanho leiteiro. Apesar dos avanços no conhecimento da fisiologia da reprodução a nível celular e molecular, a identificação de vacas em estro continua sendo o problema reprodutivo mais importante e o que mais causa prejuízos econômicos. Na indústria de laticínios no Brasil, seu impacto não foi (...) estimado, porém, a estimativa feita por países como os Estados Unidos onde se perdem 300 milhões de dólares por ano pode dar uma ideia, atribuída apenas à baixa eficiência na detecção de estros. Por que é cada vez mais difícil detectar vacas em estro? A resposta está relacionada aos aspectos intrínsecos da vaca leiteira moderna, associadas as práticas de manejo dos rebanhos atuais, caracterizados por possuírem grande número de vacas nos plantéis. -/- -/- 2.1 Como saber que uma vaca está em cio/estro? -/- -/- O comportamento estral é causado por um aumento no estradiol sérico produzido pelo folículo ovulatório. O aumento do estradiol provoca mudanças de comportamento e modificações na genitália externa e interna. A vaca mostra-se inquieta, sua vocalização aumenta, ela anda mais, tenta montar em outras vacas e aceita montar no touro ou em outra vaca, bem como urinam com mais frequência (micção frequente). A vulva fica levemente inflamada, à palpação retal o útero pode ser visto com tônus ou turgor (duro e contraído) e ao massagear o colo do útero observa-se que sai abundante muco cristalino da vulva. O mecanismo clássico proposto na regulação do estro é baseado principalmente no papel do estradiol; no entanto, estudos recentes indicam que o GnRH pode participar da regulação do estro ao nível do hipotálamo. O estro possui duração entre 8 e 18 horas e a intensidade do mesmo é afetada por fatores ambientais e intrínsecos a vaca moderna (figuras de 1 a 6). -/- -/- -/- Figura 2: A observação do grupo sexualmente ativo facilita a identificação das vacas em estro. -/- Figura 1: As vacas em estro formam grupos ativos (grupo sexualmente ativo) separados do resto das vacas. A conformação desses grupos facilita a observação do estro. -/- -/- A formação de grupos de vacas é um fator ideal para a detecção de vacas em cio, elas ficam juntas e começam a montar uma nas outras, a cheirar a urina de ambas etc. comportamentos que podem ser visualizados de longe pelo tratador e diagnosticado o cio o mais breve possível para o manejo reprodutivo adotado pela propriedade seja para monta natural ou controlada e/ou inseminações artificiais (IA) e artificiais em tempo fixo (IATF). -/- -/- Figura 3: O único comportamento positivo do estro é a aceitação da monta de outra vaca. É frequente que a vaca que realiza a monta também esteja em estro, o que só será afirmado até que ela aceite a monta de outra vaca. -/- -/- Figura 4: Cada monta dura de 5 a 7 segundos -/- Figura 5: A vaca leiteira aceita de 5 a 30 montas distribuídas entre 8 e 18 horas. -/- Figura 6: Além das mudanças comportamentais, os estrogênios causam alterações na genitália interna. Uma delas é a produção de muco cervical, que juntamente com o turgor uterino, constituem os sinais genitais do estro. -/- -/- O cio pode ser dividido em três fases, a inicial, a fase de cio verdadeiro e a fase final. O cio verdadeiro quando é observado, é caracterizado pelo momento em que a vaca aceita claramente a monta. Por sua vez, os sinais de início e final de cio se misturam, apresentam nervosismo e inquietação, cheiram e lambem a vagina e a urina de outras vacas, apoiam a cabeça na garupa de outras fêmeas etc. (figura 7). Uma das sugestões adotadas nas propriedades para facilitar a identificação do cio em um rebanho é realizada pelos funcionários com a utilização de um bastão ou fita de coloração da garupa das vacas. -/- Figura 7: Principais sinais que demonstram que a vaca está entrando em cio. As imagens mostram o início do cio, cio verdadeiro e final do cio. -/- CONTINUA. BAIXE O PDF!!! -/- RESUMO -/- -/- < >Nos Estados Unidos, 300 milhões de dólares são perdidos devido à baixa eficiência na detecção do estro. A eficiência na detecção do estro no Brasil é de 40 a 50%. A meta de eficiência para detecção de estro é > 60%. Com a observação das vacas em dois períodos diários de três horas cada (manhã e tarde), consegue-se uma eficiência na detecção de estro de 80%. Menos de 20 por cento das vacas devem ter um intervalo de serviço duplo e nenhum de mais de 48 dias. A taxa de prenhez é obtida multiplicando-se a eficiência na detecção do estro pela porcentagem de concepção e dividindo por 100 (50 * 30/100 = 15%). A taxa de prenhez em rebanhos norte-americanos é de 15%. Nos Estados Unidos, para cada ponto percentual que diminui a taxa de prenhez, não há mais de US$ 12 a US$ 15 por vaca por ano. No Brasil, para cada ponto percentual que aumenta a taxa de prenhez, na faixa de 15 a 20%, é gerada uma renda anual adicional de $ 190 reais por vaca. Não mais que 25% das vacas devem estar vazias no 150º dia pós-parto. Não mais do que 8% devem as vacas ser cobertas no 250º dia pós-parto. 8% das vacas devem engravidar a cada mês. O estro ocorre 48 a 120 horas após o tratamento com PGF2α. 80% é a precisão na palpação do corpo lúteo. Quatorze dias devem decorrer entre duas injeções de PGF2α. Menos de 25% das vacas incluídas no programa de pré-sincronização devem chegar à IATF. No momento da ovulação, a primeira injeção de GnRH deve ser aplicada entre o quinto e o nono dia do ciclo estral. A inseminação cronometrada é realizada 14-16 horas após a segunda injeção de GnRH. O tratamento com dispositivos intravaginais liberadores de progesterona dura 12 dias. Se a duração do tratamento é menor deve-se injetar PGF2α ao retirá-lo. -/- -/- REFERÊNCIAS BIBLIOGRÁFICAS -/- -/- ATUESTA, Jorge; DIAZA, Angela Gonella. Control hormonal del ciclo estral en bovinos y ovinos. Spei Domus, v. 7, n. 14, 2011. -/- COLAZO, Marcos Germán; MAPLETOFT, Reben. Fisiología del ciclo estral bovino. Ciencia Veterinaria, v. 16, n. 2, p. 31-46, 2017. -/- Fisiologia Clínica do Ciclo Estral de Vacas Leiteiras: Desenvolvimento Folicular, Corpo Lúteo e Etapas do Estro. Belo Jardim: IFPE, 2020. -/- Fisiologia da Reprodução Animal: Ovulação, Controle e Sincronização do Cio. Belo Jardim: IFPE, 2020. -/- DOBSON, H. et al. The high‐producing dairy cow and its reproductive performance. Reproduction in domestic animals, v. 42, p. 17-23, 2007. -/- DO VALLE, Ezequlel Rodrigues. O ciclo estral de bovinos e métodos de controle. EMBRAPA-CNPGC., 1991. -/- FURTADO, Diego Augusto et al. Inseminação artificial em tempo fixo em bovinos de corte. Revista científica eletrônica de medicina veterinária, v. 16, p. 1-25, 2011. -/- GALON, Nadav. The use of pedometry for estrus detection in dairy cows in Israel. Journal of Reproduction and Development, v. 56, n. S, p. S48-S52, 2010. -/- HOPPER, Richard M. (Ed.). Bovine reproduction. John Wiley & Sons, 2014. -/- LOPEZ, H.; SATTER, L. D.; WILTBANK, M. C. Relationship between level of milk production and estrous behavior of lactating dairy cows. Animal reproduction science, v. 81, n. 3-4, p. 209-223, 2004. -/- MACMILLAN, Keith L. Recent advances in the synchronization of estrus and ovulation in dairy cows. Journal of Reproduction and development, v. 56, n. S, p. S42-S47, 2010. -/- MUNIS DE OLIVEIRA, G. Fisiologia da Reprodução Bovina e Métodos de Controle do Ciclo Estral. Trabalho de conclusão do curso de especialização em Reprodução e Produção de Bovinos–UCB. Rio de Janeiro, Brasil, 2006. -/- O'CONNOR, MICHAEL L. Estrus detection. In: Current therapy in large animal theriogenology. WB Saunders, 2007. p. 270-278. -/- RIPPE, Christian A. El ciclo estral. In: Dairy Cattle Reproduction Conference. 2009. p. 111-116. -/- ROELOFS, Judith et al. When is a cow in estrus? Clinical and practical aspects. Theriogenology, v. 74, n. 3, p. 327-344, 2010. -/- VIVEIROS, Ana Tereza de Mendonça. Fisiologia da reprodução de bovinos. Lavras: UFLA, p. 62, 1997. (shrink)

In this existential reading of Kim Kardashian-West's International Women's Day selfie of 2016, I focus on the rise of selfie culture and public discourse around emerging digital representations of women's bodies. The selfie is a relatively new phenomenon, and is particularly curious because of the subject/object paradox it creates; in taking a selfie, a person asserts control over their own image, but at the same time, becomes object in their own gaze. My argument is that selfies, like other assertions of (...) bodily subjectivity in digital spaces, are a threat to patriarchal structures that paint women as immanent, object, as reflected in public discourse around Kardashian-West's International Women's Day selfie. I draw on both Jean-Paul Sartre and Simone de Beauvoir's work on subjectivity in existentialism and phenomenology, as well as Amy Shields Dobson's work on post-feminism and young women's projections of self, in order to delineate what it is about the selfie that creates this paradox. I also make reference to the work of Elisabeth Grosz and Frantz Fanon in relation to a colonial hierarchy that prioritises body over mind, as well as Laura Mulvey's work on the male gaze. (shrink)