http://plus.maths.org/content/richard-elwes

EXCERPT: [...] Do higher dimensions exist? Mathematics provides a surprisingly emphatic answer to this question. Just as a 2-dimensional plane can be described by pairs of coordinates such as (5,6) with reference to a pair of axes, so 3-dimensional space can be described by triples of numbers such as (5,6,3). Of course we can continue this line of thought: 4-dimensional space, for a mathematician, is identified with the sets of quadruples of real numbers, such as (5,6,3,2). This procedure extends to all higher dimensions. Of course this does not answer the physicist's question, of whether such dimensions have any objective physical existence. But mathematically, at least, as long as you believe in numbers, you don't have much choice but to believe in 4-dimensional space too.

Well that is fine, but how can such spaces be imagined? What does the lair of Yog-Sothoth actually look like? This is a much harder question to answer, since our brains are not wired to see in more dimensions than three. But again, mathematical techniques can help, firstly by allowing us to generalise the phenomena that we do see in more familiar spaces....

http://www.theguardian.com/science/life-...tunnelling

EXCERPT: Quantum tunnelling sounds like science fiction, and does indeed feature quite often in the genre. But it is real, and plays a role in nuclear fusion, chemical reactions and the fate of the universe. Here’s how it works... The recent claim from Stark Industries Lockeed Martin that a compact fusion reactor could be built soon is, if true, a breakthrough in engineering rather than basic physics. The basic physics of fusion has been known for some time, and a key element of understanding it is quantum tunnelling. Nuclei have a positive electric charge, and since like charges repel, there is an energy barrier to be overcome. Once the barrier is overcome, the strong nuclear force takes over. One way of overcoming the barrier is ‘quantum tunnelling’, and, weird though it sounds (and indeed is) the maths and physics of that is quite well understood....

http://www.theguardian.com/environment/c...inaccurate

EXCERPT: Abraham et al. show that a paper by ‘sceptics’ Spencer & Braswell is rife with unrealistic assumptions in an overly simple model... Well, again this year, I’ve wasted my time (and my colleagues’ time) by rebutting a 2014 paper published by the darling of the Dwindling Few, Roy Spencer. Dr. Spencer wrote a paper earlier this year that used a very simple ocean model to suggest that standard climate models overestimate the Earth’s sensitivity to carbon dioxide increases in the atmosphere. You can see his manuscript here although it is behind a paywall so you will have to shell out about $40 to read it. Dr. Spencer and his colleague Danny Braswell made a number of basic math and physics errors in the article that call into question their conclusions....

http://www.theguardian.com/science/the-h...of-science

EXCERPT: Today’s Google Doodle marks the birthday of Christopher Wren, the architect, but we should also remember him as an astronomer and founding figure for the Royal Society and Royal Observatory... If people have heard of Christopher Wren, they tend to know him as an architect. As the plaque in St Paul’s Cathedral says, “if you seek his monument – look around you”. It is unsurprising, then, that today’s Google Doodle celebrates him as the man behind that building and the city churches rebuilt after the great fire of London. He was, however, also a very significant figure for the history of science. He was central to all the groups that, come the end of the commonwealth and the restoration of the monarchy in 1660, formed the Royal Society of London. At Oxford he became part of the group around John Wilkins, he was key to the correspondence network known as the Invisible College, and in London he became professor of astronomy at Gresham College in 1657....

http://visitcryptoville.com/2014/10/16/c...than-good/

EXCERPT: Cryptozoology lovers are no doubt enjoying all the latest TV shows delving into the mysteries of monsters from all parts of the United States. Bigfoot, Swamp Beast, Saber Wolves and all the rest are fair game to these intrepid investigators. But is any of it real?

Like many of you I’ve been enjoying the latest rash of TV programs about the cryptids we love to think about. We have Destination America channel’s Mountain Monsters, Swamp Monsters, Alaska Monsters and the very popular Cryptid: Swamp Beast over on History Channel.

I’d like to share with you my thoughts about these shows and my perceived problems with them, then get into whether they help or hurt the cause for serious investigation into these creatures....

http://www.sciencedaily.com/releases/201...070138.htm

ARTICLE: Math describes and predicts the world all around us -- from the helical structure of DNA to the spirals of galaxies. But does this mean our world is inherently mathematical?

The question has become a hot topic of debate as neuroscientists continue to uncover mathematical abilities we seem to be born with, and have pinpointed regions in the brain responsible for mathematical thinking. "[N]umbers are not properties of the universe, but rather they reflect the biological grounding for how people make sense of the world," says Rafael Núñez, professor of cognitive science at the University of California, San Diego and member of UCSD's Kavli Institute for Brain and Mind.

Says Brian Butterworth, emeritus professor of cognitive neuropsychology at the Institute of Cognitive Neuroscience at University College London, "Numbers are not necessarily a property of the universe, but rather a very powerful way of describing some aspects of the universe."

Núñez and Butterworth are among four scientists who recently grappled with this question at the invitation of The Kavli Foundation. Offering a different perspective: physicists Simeon Hellerman and Max Tegman. "I think many physicists, including myself, agree that there should be some complete description of the universe and the laws of nature," says Hellerman, associate professor at the Kavli Institute for Physics and Mathematics of the Universe at the University of Tokyo, Japan. "Implicit in that assumption is the universe is intrinsically mathematical."

"[N]ature is clearly giving us hints that the universe is mathematical," says Tegmark, professor of physics at the Massachusetts Institute of Technology, and member of MIT's Kavli Institute for Astrophysics and Space Research. According to Tegmark, many mathematicians even feel that they don't invent mathematical structures, "they just discover them -- that these mathematical structures exist independently of humans."

Tegman also points out this isn't just interesting as an academic idea; if correct, then mathematics has a special role for advancing human knowledge.

"If math is inherent out in the universe, then mathematics can give us hints for solving future problems in physics," Tegman says. "If we really believe that nature is fundamentally mathematical, then we should look for mathematical patterns and regularities when we come across phenomena that we don't understand. This problem-solving approach has been at the heart of physics' success for the past 500 years."

EXCERPT: First published Wed Mar 18, 2009; substantive revision Fri Oct 17, 2014

Thomas Reid held a direct realist theory of memory. Like his direct realism about perception, Reid developed his account as an alternative to the model of the mind that he called ‘the theory of ideas.’ On such a theory, mental operations such as perception and memory have mental states—ideas or impressions—as their direct objects. These mental states are understood as representations that encode information about their causes. The mind is directed towards and reads off from these representations, information about extra-mental items. By contrast, Reid holds that the direct objects of memory and perception are extra-mental. In the case of perception, the mind is directed to present material objects and properties; in the case of memory, the mind is directed towards past events to which the person was agent or witness. In other words, according to Reid, when we remember, we do not recall previous experiences. In memory, the mind is directed neither towards an idea experienced previously nor towards an idea of a previous experience. Rather, we recall events, experienced previously.

Reid is interested in the notion of memory not only for its own sake but also because of its conceptual connection to the notion of personal identity. Reid criticizes Locke's theory of personal identity for inferring a metaphysical hypothesis now called the Memory Theory from the conceptual connection between memory and personal identity. On this theory, personal identity consists in memory; sameness of memory is metaphysically necessary and sufficient for sameness of persons. According to Reid, memory is neither necessary nor sufficient for personal identity, metaphysically speaking. Indeed, Reid holds that it is impossible to account for personal identity in any terms other than itself. Personal identity is simple and unanalyzable. Though memory is not the metaphysical ground of personal identity, according to Reid, it provides first-personal evidence of personal identity. I know that I was present at my graduation because I remember being there. Memories do not make one the same person over time. Rather, memories allow one to know one's own past, immediately and directly....

http://plato.stanford.edu/entries/comte/

EXCERPT: First published Wed Oct 1, 2008; substantive revision Thu Oct 16, 2014

Auguste Comte (1798–1857) is the founder of positivism, a philosophical and political movement which enjoyed a very wide diffusion in the second half of the nineteenth century. It sank into an almost complete oblivion during the twentieth, when it was eclipsed by neopositivism. However, Comte's decision to develop successively a philosophy of mathematics, a philosophy of physics, a philosophy of chemistry and a philosophy of biology, makes him the first philosopher of science in the modern sense, and his constant attention to the social dimension of science resonates in many respects with current points of view. His political philosophy, on the other hand, is even less known, because it differs substantially from the classical political philosophy we have inherited....