ترغب بنشر مسار تعليمي؟ اضغط هنا

On the relationship of Mathematics to the real world

97   0   0.0 ( 0 )
 نشر من قبل Deepak Dhar
 تاريخ النشر 2017
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Deepak Dhar




اسأل ChatGPT حول البحث

In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $pi$ can not be said to have existed $100,000$ years ago, using the conventional meaning of the word `exist.

قيم البحث

اقرأ أيضاً

198 - Jian Zhou 2021
Motivated by fractional quantum Hall effects, we introduce a universal space of statistics interpolating Bose-Einstein statistics and Fermi-Dirac statistics. We connect the interpolating statistics to umbral calculus and use it as a bridge to study t he interpolation statistics by the principle maximum entropy by deformed entropy functions. On the one hand this connection makes it possible to relate fractional quantum Hall effects to many different mathematical objects, including formal group laws, complex bordism theory, complex genera, operads, counting trees, spectral curves in Eynard-Orantin topological recursions, etc. On the other hand, this also suggests to reexamine umbral calculus from the point of view of quantum mechanics and statistical mechanics.
A large number of complex systems, naturally emerging in various domains, are well described by directed networks, resulting in numerous interesting features that are absent from their undirected counterparts. Among these properties is a strong non-n ormality, inherited by a strong asymmetry that characterizes such systems and guides their underlying hierarchy. In this work, we consider an extensive collection of empirical networks and analyze their structural properties using information theoretic tools. A ubiquitous feature is observed amongst such systems as the level of non-normality increases. When the non-normality reaches a given threshold, highly directed substructures aiming towards terminal (sink or source) nodes, denoted here as leaders, spontaneously emerge. Furthermore, the relative number of leader nodes describe the level of anarchy that characterizes the networked systems. Based on the structural analysis, we develop a null model to capture features such as the aforementioned transition in the networks ensemble. We also demonstrate that the role of leader nodes at the pinnacle of the hierarchy is crucial in driving dynamical processes in these systems. This work paves the way for a deeper understanding of the architecture of empirical complex systems and the processes taking place on them.
78 - Russell OConnor 2010
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically supported by adding additional non-constructive axioms. However, there is another perspective that views constructive logic as an extension of classical logic. This paper will illustrate how classical reasoning can be supported in a practical manner inside dependent type theory without additional axioms. We will see several examples of how classical results can be applied to constructive mathematics. Finally, we will see how to extend this perspective from logic to mathematics by representing classical function spaces using a weak value monad.
A foundational model has been developed based on trends built from empirical data of space exploration and computing power through the first six plus decades of the Space Age which projects earliest possible launch dates for human-crewed missions fro m cis-lunar space to selected Solar System and interstellar destinations. The model uses computational power, expressed as transistors per microprocessor, as a key broadly limiting factor for deep space missions reach and complexity. The goal of this analysis is to provide a projected timeframe for humanity to become a multi-world species through off-world colonization, and in so doing all but guarantees the long-term survival of the human race from natural and human-caused calamities that could befall life on Earth. Be-ginning with the development and deployment of the first nuclear weapons near the end of World War II, humanity entered a Window of Peril which will not be safely closed until robust off-world colonies become a reality. Our findings suggest the first human-crewed missions to land on Mars, selected Asteroid Belt objects, and selected moons of Jupiter and Saturn can occur before the end of the 21st century. Launches of human-crewed interstellar missions to exoplanet destinations within roughly 40 lightyears of the Solar System are seen as possible during the 23rd century and launch of intragalactic missions by the end of the 24th century. An aggressive and sustained space exploration program, which includes colonization, is thus seen as critical to the long-term survival of the human race.
We consider the problem of transferring policies to the real world by training on a distribution of simulated scenarios. Rather than manually tuning the randomization of simulations, we adapt the simulation parameter distribution using a few real wor ld roll-outs interleaved with policy training. In doing so, we are able to change the distribution of simulations to improve the policy transfer by matching the policy behavior in simulation and the real world. We show that policies trained with our method are able to reliably transfer to different robots in two real world tasks: swing-peg-in-hole and opening a cabinet drawer. The video of our experiments can be found at https://sites.google.com/view/simopt
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا