Related papers: Some comments on "The Mathematical Universe"
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
The hard problem in consciousness is the problem of understanding how physical processes in the brain could give rise to subjective conscious experience. In this paper, I suggest that in order to understand the relationship between…
Speculations and theories about the existence of other worlds have a long history. In recent times, the arguments have shifted away from their typical philosophical and theological character to supposedly become more objective thanks to…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
We present the quantum measurement problem as a serious physics problem. Serious because without a resolution, quantum theory is not complete, as it does not tell how one should - in principle - perform measurements. It is physical in the…
The quantum world is fascinating. It presents a description of nature that defies our most rooted concepts about what reality is. For example, quantum objects possess \lq\lq spooky\rq\rq\ properties that allow them to be in multiple places…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
What is physics? What are the limits of what physics can say about the world? In seeking ever-broader theoretical `umbrellas' for physical phenomena, we are seeking unifying principles. Emergent phenomena have turned out to be some of the…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
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…
Czachor's recent proposal introduces a form of non-Newtonian calculus built by pulling back arithmetic operations through arbitrary bijections between continua. Although the idea is mathematically inventive, it runs into serious conceptual…
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
Many of the classic problems of particle physics appear in a very different light when viewed from the perspective of the multiverse. Most importantly the two great ``fine tuning'' problems that motivate the field are far less serious when…
Despite the success of modern physics in formulating mathematical theories that can predict the outcome of experiments, we have made remarkably little progress towards answering the most fundamental question of: why is there a universe at…
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…