Related papers: The Variant-Rule, Another Logically Universal Rule
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
The main mystery of quantum mechanics is contained in Wheeler's delayed choice experiment, which shows that the past is determined by our choice of what quantum property to observe. This gives the observer a participatory role in deciding…
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…
We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution…
Languages and genes are both transmitted from generation to generation, with opportunity for differential reproduction and survivorship of forms. Here we apply a rigorous inference framework, drawn from population genetics, to distinguish…
Classical results for exchangeable systems of random variables are extended to multi-class systems satisfying a natural partial exchangeability assumption. It is proved that the conditional law of a finite multi-class system, given the…
We explore the relation between two natural symmetry properties of voting rules. The first is transitive-symmetry -- the property of invariance to a transitive permutation group -- while the second is the "unbiased" property of every voter…
We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
We suggest to simulate evolution of complex organisms constrained by the sole requirement of robustness in their expression patterns. This scenario is illustrated by evolving discrete logical networks with epigenetic properties. Evidence…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such…
Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the…
Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g.…
Following an early observation of Ignatowsky, we present a derivation of the transformation rules between inertial systems making no other assumptions than the existence of the latter, and show that generically these rules are characterized…
Despite the impressive performance in a variety of complex tasks, modern large language models (LLMs) still have trouble dealing with some math problems that are simple and intuitive for humans, such as addition. While we can easily learn…
This paper investigates the dynamics of nonholonomic mechanical systems, focusing on fundamental variational assumptions and the role of the transpositional rule. We analyze how the Cetaev condition and the first variation of constraints…
The automatic design of robots has existed for 30 years but has been constricted by serial non-differentiable design evaluations, premature convergence to simple bodies or clumsy behaviors, and a lack of sim2real transfer to physical…