Original title: Everything Is Logarithms
Article
The essay argues that standard logarithms can be viewed as coordinate-dependent evaluations of a deeper baseless logarithm, emphasizing 8 ext{ to }log base as a choice of unit conversion, much like expressing a vector in different bases. It then develops a parallel with differential geometry: logs behave like geometric vectors or differentials where division by a basis element extracts components, while lacking a true separate partial-derivative analogue unless structures like p-adic valuation are introduced to isolate prime-log coefficients. The author connects this to number theory, complex analysis, and linear algebra, interpreting -adic valuations, orders of vanishing, and dimension formulas as instances of the same projection-and-basis perspective. A further section reverses direction by treating vectors as logarithms of translation operators in differential geometry, and briefly notes a derivative-style definition of ln x as a local limit that fits the same theme. The essay also reframes dimension, tensor products, and set-based cardinality-like constructions as logarithmic behaviors, extending speculatively to finite and possibly infinite fields, “fractional” dimensions, and a tentative notion of logarithmic bases as basis objects. It closes by treating many mathematical constructions as coordinate changes between additive and multiplicative representations and suggests a broader search for covariant formulations that separate structure from units, while flagging this as mostly analogy and numerology rather than a finished theory. The conclusion is that many operations feel redundant because a handful of primitive ideas are expressed with incompatible notation across areas. The author requests future work to formalize the program rigorously.
Commenters acknowledged the broader open-LLM context by comparing Apertus to OLMo 3.1, MBZUAI K2 Think V2, and Nvidia Nemotron, noting Nemotron’s stronger benchmark profile despite partial proprietary data. A large portion of the thread is skeptical about Aptus’s competitive standing, arguing it appears slow, possibly behind current systems, and affected by issues such as a March 2024 knowledge cutoff and unreliable multilingual answers. Some participants argued that sovereignty goals remain constrained by centralization and by access policies, including concerns about major labs’ increasing friction for users and identity checks. Others framed the real battleground as local versus service-based AI usage, arguing that local models are available but hard for typical users to adopt because of poor UX. Several commenters questioned how opt-out and PII-removal claims are verified, and cited prior version concerns about copyright-law adherence. At least one view praised the project’s team continuity, suggesting repeated training could improve quality at lower cost and support broader ecosystem value. Users also contrasted this with operational pragmatism, reporting successful long-context RAG and workflow use with other open stacks such as Nemo while noting Apertus is not yet suitable for agentic workloads. The thread ends with mixed expectations: hope for sovereign infrastructure, but doubts about near-term parity at 70B scale and immediate readiness.