Related papers: Free Lunch
Beginning with the Bell theorem, cyclic systems of dichotomous random variables have been the object of many foundational findings in quantum mechanics. Here, we ask the question: if one chooses a cyclic system "at random" (uniformly within…
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of…
In this work we study a simple evolutionary model of bipartite networks which its evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary…
We show normalisation and decidability of convertibility for a type theory with a hierarchy of universes and a proof irrelevant type of propositions, close to the type system used in the proof assistant Lean. Contrary to previous arguments,…
The positive existential theories of the sets $M_n(\mathbb N)$ without parameters build an inclusion lattice isomorhic with the lattice of divisibility. All these sets are algorithmically undecidable. In further sections some easier…
Species coexistence is one of the central themes in modern ecology. Coexistence is a prerequisite of biological diversity. However, the question arises how biodiversity can be reconciled with the statement of competition theory, which…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
The set of natural integers is fundamental for at least two reasons: it is the free induction algebra over the empty set (and at such allows definitions of maps by primitive recursion) and it is the free monoid over a one-element set, the…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
In this second article, we show a simple use of the Ignorance as defined in "Jaynes & Shannon's Constrained Ignorance and Surprise". By giving an example about the journey of a person, we believe to show some simple, obvious but…
All living things exhibit adaptations that enable them to survive and reproduce in the natural environment that they inhabit. From a biological standpoint, it has long been understood that adaptation comes from natural selection, whereby…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
Today's science provides quite a lean picture of time as a mere geometric evolution parameter. I argue that time is much richer. In particular, I argue that besides the geometric time, there is creative time, when objective chance events…
Herbrand's Theorem is a fundamental result in mathematical logic which provides a reduction of first-order formulas satisfied by a universal class to formulas free of existential quantifiers. In this work, a simpler and self-contained…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula \[E(AB|a,b) = \int A(a,b,\lambda)B(a,b,\lambda)\rho(\lambda) d\lambda\] follows from the logic of plausible reasoning…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of $n$-dimensional Euclidean space has a convergent subsequence…
The splitting principle states that morphisms in a derived category do not "split" accidentally. This has been successsfully applied in several characterizations of rational, DB, and other singularities. In this article I prove a general…
The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced…