X-Message-Number: 19211 From: Date: Thu, 6 Jun 2002 07:33:29 EDT Subject: Re: dimensions --part1_3f.c6f42fe.2a30a289_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit R. Ettinger said: > Again, if a hypothetical being that only perceives one dimension could live > on the perimeter of a circle, he would say what Yvan said. His universe > (like > Einstein's) is "finite but unbounded," and his single-coordinate system, > whether expressed as an angle or as a displacement from an origin, is > cyclic. > From our point of view the circle necessarily exists in two dimensions, and > > his "dimension" is curved in visible reality and not just as an inference > from cyclicality. > > Yvan does, however, appear to agree that there are problems with the > confused > use of terms such as dimensions, coordinates, and degrees of freedom. > A circle gives indeed an idea about a cyclic dimension, on the other hand, it has no curvature!! Curvature needs at least two dimensions. The surface of a sphere has a curvature, a cylinder has not because you can cut it and unfold it on a plane surface. In the same way, you can cut a circle and unfold it on a straight line. On way to look at curvature without using more d imensions is to look at triangles: If the sum of angles in a triangle is 180 degrees, there is no curvature, if we get a different value, there is a curvature. In 3-dim. space, you would test a tetraedron: 4 triangle to meter, if at least one has an angle sum different from 180 degrees, there is curvature. To do the test, you need not a fourth dimension nor think about it. Time is often taken as the fourth dimension, in fact it is simply a free parameter, not really a dimension. If you have a space with N curved dimensions, you can think of each dimension as a parameter and then add one more to look at the curvature from outside in a space with N+1 parameters, it is a bad habit to call them "dimensions". In any case, that language torsion will never add a real dimension to the real thing. We may be here somewhat far from cryonics, so some more words to get on track with the main subject on this list: In science and technology, you may use abusive words if you point to them in the first place as abusive. In the end you must take everything right. The opposite attitude is to use abusive words, don't mark them as such and then redefine reality as the words you use. This is faith, religion and so on. Thank to Robert, to put things on the good road. Cryonics must be on the science/ technology track and we must always think in this way, even on parallel subjects. Yvan Bozzonetti. --part1_3f.c6f42fe.2a30a289_boundary Content-Type: text/html; charset="US-ASCII" [ AUTOMATICALLY SKIPPING HTML ENCODING! ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=19211