Sosigenes

Stellar objects that are expected to look dark are the ones that are collapsing and, according to the outside observer, will continue to do so for infinite time without actually becoming a black hole. Of course, in the early stages of collapse, a star is expected to produce observable electromagnetic radiation. As the collapse progresses, the resulting strong gravity red shifts all electromagnetic radiation to a degree that makes them unobservable. Hence, paradoxically, dark stars should not be expected to be black holes while actual primordial black holes can appear to be not dark at all.

http://arxiv.org/abs/1006.4185

Filed under: Physics

Causality and backward causation

dimitrivan — Thu, 15 Oct 2009 07:47:16 +0000

An article in The New York Times caught my attention and it is based on another article posted on arXiv.org by Holger B. Nielsen and Masao Ninomiya, Search for Future Influence from L.H.C. The article “predicted” recurring “accidents” in the LHC ring, and explains the SSC cancellation using the same argument. The SSC in Texas was abandoned after a quarter of the tunnel was built, attributed to a remarkable piece of bad luck. Not according to the two authors.

Posted in Physics

The Pentagram

dimitrivan — Thu, 11 Jun 2009 12:46:25 +0000

The pentagram (πεντάγραμμον) is the simplest regular star polygon. The pentagram contains ten points (the five points of the star, and the five vertices of the inner pentagon) and fifteen line segments. It is represented by the Schläfli symbol {5/2}. Like a regular pentagon, and a regular pentagon with a pentagram constructed inside it, the regular pentagram has as its symmetry group the dihedral group of order 10.

The pentagram can be constructed by connecting alternate vertices of a pentagon; see details of the construction. It can also be constructed as a stellation of a pentagon, by extending the edges of a pentagon until the lines intersect.

A pentagram’s four lengths are in golden ratio to one another.

The golden ratio, , satisfying

plays an important role in regular pentagons and pentagrams. Each intersection of edges sections the edges in golden ratio: the ratio of the length of the edge to the longer segment is φ, as is the length of the longer segment to the shorter. Also, the ratio of the length of the shorter segment to the segment bounded by the 2 intersecting edges (a side of the pentagon in the pentagram’s center) is φ.

The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ. The acute triangles are golden triangles.

As a result, in an isosceles triangle with one or two angles of 36°, the longer of the two side lengths is φ times that of the shorter of the two, both in the case of the acute as in the case of the obtuse triangle.

Successive inferior conjunctions of Venus repeat very near a 13:8 orbital resonance (The Earth orbits 8 times for every 13 orbits of Venus), creating a pentagrammic precession sequence.

Posted in Mathematics