User talk:72.39.252.217

From Wikipedia, the free encyclopedia

[edit] Surface of a sphere

Dear Mr. Lamont,

The center of the Earth is not on the surface of the Earth. Similarly, it really is not necessary that the center of the universe be in the present universe.

Mathematically, the Earth is a ball in a 3-dimensional space, the set of all points {x,y,z} in that 3-space with distance (ie, sqrt[x^2+y^2+z^2]) less than 6370-some km from the origin, a point at the center of mass of the Earth. The surface  of the Earth is a 2-dimensional space, like a table top but with no edges, the boundary of the 3-d volume, nested or embedded in that same 3-space.

If you were a 2-dimensional creature living in that surface, you would never find the center, no matter where you looked. From the higher 3-dim point of view, the surface does have a center of course -- it's the center of the 3-d ball -- but that point is not in the surface, not part of it, and impossible for the 2-d inhabitant of the surface to visit (or possibly even to comprehend).

The same thing can happen, logically and mathematically, in higher dimensional spaces. In 4 dimensions, the surface of a 4-ball is a 3-dimensional "surface" bounding the 4-d object (the latter being the set of points, each with 4 coordinates, {w,x,y,z} say, at a distance less than the radius from the center). A 3-d creature living in that 3-d boundary space could explore it all (in principle) without ever finding an edge, or a point one could call the center.

Now it appears that the space we inhabit actually is a rather peculiar 4-dim space! The exact shape of it (see the Wiki article about the shape of the universe) is not precisely certain, but one leading possibility is that it is curved in exactly the way described in the previous paragraph, like the surface of a 4-ball. Or it could be flat (like an infinite table), or it could be curved rather like a saddle (ie, curved up in one direction, and curved down in another), and there are more complicated possibilities. All this is still in the great unknown. It does appear to be very nearly flat, possibly exactly so. There is no indication that it has a center anywhere, and if it is infinite (possible, but unknown) then it would not. If it is curved like the surface of the 4-ball, it would have a center, but the center would not be in the surface, which is the space of the present, in the same sense as for the 3-d ball with a 2-d surface.

My point was just that there is really no logical or mathematical necessity that the universe have a center that is in the 3-dim space we perceive, and there is no observational evidence for one anywhere; nor for any edges, of course. A naive peasant in 700 AD, say, might have thought it obvious that the surface of the Earth had to possess edges (if he rejected the possibility that it was infinite) and therefore a center. (I believe the center was widely believed to be located at Jerusalem in medieval Europe.) But from our point of view now, we can see that it just is not so, and that the reality of possibilities was richer than such a person imagined.

The possibility that the space we live in actually is something more complicated than simple 3-dimensional Euclidean space was noticed about 200 years ago, and has been taken seriously as a going possibility for a century or so. It is now commonplace among people working in the field, though still unknown. The understanding that our ordinary space really is embedded in a weird 4-dimensional "spacetime" became clear sometime between 1905 and 1915, largely due to the work of Einstein.

Very likely you have heard much of the above already, and I am sorry if seem to be talking down to you, but it is useless to leave holes in the explanation that may cause confusion, and of course I do not know exactly what your background is in all this. Wikipedia has a very rich set of articles covering these matters, mostly written by real experts (which I am not). I am sorry also if my response on the black hole talk page seemed condescending, but I wanted to give you some hint of the kind of problems you are likely to encounter in convincing the scientific community of your ideas. There is really no shame in being ignorant (I am convinced), because there is no way to know what we do not know, except by learning more, and there is no sign of an edge or end to what we do not know.

I regret that I do not have the time to enter into such lengthy discussions very often, so I am likely not to respond fully, if at all, to further comments or inquiries -- especially if they seem hostile. I am often willing to try to help explain or answer questions, but I have no interested in "winning" an argument with you, whatever that might mean.

All the best,

Bill Wheaton (Wwheaton (talk) 23:24, 5 May 2008 (UTC))

Hi,

I think the answer to the center of mass question may be the same as for center: it does  have (one if it is finite), but it may not be located in the "space" for which it is computed. The center of the surface of the Earth is not located on the 2-d surface of the Earth; is at the center of the (3-d) ball, so you cannot find it if you restrict your search to the surface.

The center of mass is a little bit different, in that it is not a unique point (event) in a 4-dim space, but can be calculated (again if the whole thing is finite -- which is not known) at any particular time, in a flat 3-d spatial surface. Since the definition of a particular time depends on the state of motion of the observer, the CM will too. I suspect, but am not sure, that the position of the CM will not be the same for different choices of the observer's particular state of motion (Lorentz frame), especially if the global geometry is not flat. Even in the simplest possibility, the CM would be a point at each time, and so from the 4-dimensional spacetime perspective, it would be a world line, a 1-dimensional curve in the 4-d universe, extending from the big bang into the future. But I think the curve may not be unique, depending on the choice of the observer's motion.

I appreciate the thought you are putting into this. I am sorry that I have to doubt the validity of your cosmology, but the thought may still lead you to real progress eventually.

All the best, Wwheaton (talk) 16:27, 26 May 2008 (UTC)

Greetings, thanks for your message. Re finite vs infinite, I really think nobody knows. These questions are just too big and too deep for us. There is a strong tradition in science that physical things have to be finite, and when you trace that back (eg, Zeno's paradox) it even infected mathematics and logic. Even zero  was considered a scary concept in ancient times. I personally see no logical necessity either way, and mathematics has recognized a whole hierarchy of infinities for over a century now.

In the standard cosmological picture of a decade or two ago, a closed universe would have been finite from the first instant and ever after. An open universe would be infinite: in the beginning, now, and forever. As far as I know the advances (in our perception of our ignorance!) of the past decade with dark energy, cosmic acceleration etc have not really changed that, but this is over my head. One situation where finite may change to infinite in accepted physics is in the formation of a black hole, where at a certain moment a smooth spacetime is predicted by general relativity to become physically singular. But there are conflicts between general relativity and quantum mechanics in this extreme situation that open the predicted infinity to question.

As far as a place in Wikipedia goes, it is very difficult, unfortunately. Wikipedia is just not a place to publish new ideas or research, and the rules WP:NOR are strict. The reason for this is inescapable for a reference work, which an encyclopedia is supposed to be. All we can do is try to map out the areas of knowledge that are securely known. The minute we go beyond that, we get mired in a thicket of trying to adjudicate between rival theories, etc. So, to be eligible for inclusion in an article, any theory needs to be published outside Wikipedia, by an authoritative source. This excludes self publication, blogs, and personal web sites, but includes refereed journals, textbooks by academic publishers, universities, etc. The arXiv used to permit unrestricted material, but since 2004 has been moderated. Articles there are mostly accepted as references by Wikipedia, and that might be the best hope for you.

The WP:NOR rules are not uniformly enforced, as it is up to the caprice of individual editors. I have noticed that material that seems to be correct in the sciences is seldom challenged immediately, whereas in less cumulative subjects (eg, humanities) it is often mercilessly reverted. Similarly there is more tolerance on article talk pages, and user talk pages are almost free of interference, as long as they are not libelous, abusive, in violation of copyright, etc. I cannot recommend article talk pages for extensive discussion of unestablished theories (and I've seen people blocked for stubborn abuse), but you can sometimes try out an idea there, and ask for comment.

Good luck! Bill Wwheaton (talk) 20:54, 30 May 2008 (UTC)

Mr. Lamont,

Thanks for your message. No need to apologize; I am only sorry I could not be more helpful. It is indeed a pity that Wikipedia cannot be a place for new knowledge to come forth. We must settle for trying to get the firmly known out for the world, and even that is not easy. I hope you will keep thinking and learning, and publishing when your ideas have matured further.

Best, Wwheaton (talk) 03:12, 2 June 2008 (UTC)