数学证明因为太长而无法被人类验证

如果人类无法检验一个定理的证明,这个证明还能被当成数学吗?这是计算机辅助证明的流行而引发的一个疑问。利物浦大学的 Alexei Lisitsa和同事Boris Konev使用计算机生成了一个13GB大小的证明,这可能是有史以来最长的证明了,它的大小使得人类不可能去检查证明是否无误。他们的证明与匈牙利犹太数学家Paul Erdős在1930年代提出的一个猜想有关。Erdős提出,一个只含有+1s和-1s的随机无穷序列(例如对于序列(x1, x2, x3, …),其中xi = (−1)i+1)是否包含内在模式, 一种测量方法是将无穷序列在特定点切割,创造出了一个有限的子序列。Erdős的猜想是:对于任意整数C,存在整数K和d,使得liJ3eW3GO7XjU-small。Lisitsa和Konev用计算机证明,一个无穷序列总有一个大于2的差。论文预印本发表在arXiv.org上。

Amherst Researchers Create Magnetic Monopoles

Nearly 85 years after pioneering theoretical physicist Paul Dirac predicted the possibility of their existence, an international collaboration led by Amherst College Physics Professor David S. Hall ’91 and Aalto University (Finland) Academy Research Fellow Mikko Möttönen has created, identified and photographed synthetic magnetic monopoles in Hall’s laboratory on the Amherst campus. The groundbreaking accomplishment paves the way for the detection of the particles in nature, which would be a revolutionary development comparable to the discovery of the electron.

CERN成功产生反氢原子束

CERN的ASACUSA(低速反质子原子光谱和碰撞)实验首次成功制造出反氢原子束,检测到了80个反氢原子。研究发表在《自然·通讯》上。为什么宇宙是由正物质而非反物质构成?有关亚原子世界的最优理论——粒子物理标准模型也无法给出答案。但科学家认为,物质和反物质属性之间的微小差异可能就是答案所在,而这种差异体现在违反CPT对称定理上。CPT对称指把粒子用反粒子替换,右手坐标系换成左手坐标系,以及所有粒子速度反向,物理定律不变。而反氢原子由一个反质子和一个正电子构成,这样简单的结构是测试CPT对称的最佳模型。CERN在实验中通过将反电子(正电子)和由反质子减速器产生的低能量反质子混合,产生大量反氢原子。正反粒子相遇会湮没,为了让正反粒子分离,实验利用了反氢原子的磁特性(类似于氢气的),并使用非常强的非均匀磁场诱捕反原子足够长的时间来研究。

The Mathematics of Gamification

The Foursquare blog has an interesting post about some of the math they use to evaluate and verify the massive amount of user-generated data that enters their database. They need to figure out the likelihood that any given datapoint accurately represents reality, so they’ve worked out a complicated formula that will minimize abuse. Quoting: ‘By choosing the points based on a user’s accuracy, we can intelligently accrue certainty about a proposed update and stop the voting process as soon as the math guarantees the required certainty. … The parameters are automatically trained and can adapt to changes in the behavior of the userbase. No more long meetings debating how many points to grant to a narrow use case. So far, we’ve taken a very user-centric view of p-sub-k (this is the accuracy of user k). But we can go well beyond that. For example, p-sub-k could be “the accuracy of user k’s vote given that they have been to the venue three times before and work nearby.” These clauses can be arbitrarily complicated and estimated from a (logistic) regression of the honeypot performance. The point is that these changes will be based on data and not subjective judgments of how many “points” a user or situation should get.

数值计算工具Octave终于有了GUI,还是用OpenGL的

from http://www.phoronix.com/scan.php?page=news_item&px=MTU1NDg

GNU Octave, the open-source high-level language for dealing with numerical computations and largely compatible with MATLAB, has a graphical user-interface with its new 3.8 releaseGNU Octave 3.8 hasn’t been officially announced at the time of publishing, but the source package was uploaded just a short time ago to the project’s GNU.org FTP server.

The big feature of Octave 3.8 is a graphical user-interface, which has long been requested by users of this open-source package looking towards it as a MATLAB alternative. While there’s now a GUI, it’s not yet polished now and will not become the default user-interface until the GNU Octave 4.0 release. GNU Octave 3.8 considers the GUI to be in a preview state.

Octave 3.8 also now uses OpenGL graphics by default in conjunction with FLTK widgets. GNUplot is still used in cases where OpenGL or FLTK support is not available for its graphical tool-kit.

Another change to GNU Octabe 3.8 is support for nested functions with scoping rules that are compatible with MATLAB, limited support for named exceptions, new regular expressions, a TeX parser for the FLTK tool-kit, overhauls to many of the m-files, function rewrites, and numerous other changes.

GNU Octave 3.8 also ships many bug-fixes and other improvements. While waiting on the official release announcement, more information on Octave can be learned from GNU.org.

模拟支持宇宙全息理论

一组物理学家提供了至今最明确的证据证明我们的宇宙可能只是一个巨大的投影。1997年,理论物理学家Juan Maldacena提出了一个大胆的宇宙模型去诠释现有的物理学理论。在这个模型中,引力源于无限小、薄且振动的弦,而弦则存在于九维空间和一维时间中,弦的世界很可能只是一个全息图,真正的行动则发生在一个简化平坦无引力的宇宙中。Maldacena的理论令物理学家非常兴奋,因为它提供一种方法将热门但未获证明的弦论奠定在一个坚实的基础上,同时解决了量子理论和爱因斯坦引力理论不一致的地方。Maldacena理论虽然已广为接受,但仍然没有经过严格证明。现在,日本茨城大学的百武良文和同事在预印本网站上发表了两篇 论文,提供了强有力的证据证明Maldacena的猜想是正确的。

费曼物理学讲义第三卷上线

加州理工和费曼物理学讲义网站正在整理HTML5版费曼物理学讲义,今年9月发布了第一卷,刚刚上线了第三卷。费曼物理学讲义网站的Mike Gottlieb宣布,他们发布了付费的PDF版,读者可以通过购买PDF电子书来支持他们的活动。《费曼物理学讲义》由理查德·费曼、罗伯·雷顿及马修·山德士合著,分为三卷。第一卷主要讲力学、光学、电磁辐射和热力学;第二卷主要讲电动力学和电磁学;第三卷主要讲量子力学。第二卷的HTML转换工作还没有完成。

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