Related papers: Why Mathematics Works So Well
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…
Criteria for defining errors of a physical theory are formulated. It is shown that the Special Theory of Relativity (STR) has a solid mathematical basis. An enormous amount of experiments carried out in particle physics use beams of…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
Every physical measuring needs a finite, different from zero measurement time and provides information in form of the choice of a measurement result from all possible measurement results. If infinitely many (different) measurement results…
A definition of a {\it Realistic} Physics Theory is proposed based on the idea that, at all time, the set of physical properties possessed (at that time) by a system should unequivocally determine the probabilities of outcomes of all…
Physical laws are a set of rules in the relationship between observations made by the experimenter. All these observations are made through a mechanism that links the external world to the experimenter's awareness, a mechanism which is not…
We illustrate the concept of mathematical proof.
This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in…
The physical models of a successful unified theory about the Universe must operate in different phase of matter evolution and different fields of physics. The attempts to build such wide range theory as a bunch of theories developed for…
The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…
Astrophysical paradoxes are the paradoxes of physics. The main motivation of a formulated paradox is clearly recognized in the scientific environment because the phenomenon of a paradox itself has become interesting. There is an explanation…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of…
To better understand the deep significance of our best physical theories it could be interesting to compare our Universe with its models. It may happen that the differences between the model and reality can be made indistinguishable, to the…
There are reasons to doubt that making sense of the wave function (other than as a probability algorithm) will help with the project of making sense of quantum mechanics. The consistency of the quantum-mechanical correlation laws with the…
When a physicist says that a theory is fine-tuned, they mean that it must make a suspiciously precise assumption in order to explain a certain observation. This is evidence that the theory is deficient or incomplete. One particular case of…
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…