Dimension is really just a concept used to help describe things in a mathematical manner. The everyday world is conviently described with 3, or 4 if you include time, but I’ve heard that certain subatomic phenomena are more conviently described with 9 dimensions. All that really means is that the equations are easier to deal with in that manner. Linear Algebra (which is a lot harder than it sounds) is partly about dealing with multiple dimensions.
You can download Flatland at Project Gutenberg. They have a lot of old books that are no longer under copyright there.
Well for one BH’s are still not proven to exist, 2nd is no one knows what happens inside the event horizon. Some say that the thing clapses to a point where matter can’t be compressed further, some say that it does clapse to a point. Also space-time is warped so there might be more dimentions, might be less, perhaps time doesn’t apply to a BH but it exist in 3d space I don’t know and dont think anyone else knows.
Not really - as far as we know, we live in a space that really is three dimensional. Three-dimensional just refers to the number of coordinates you have to specify to locate a position in space, or to the number of degrees of freedom of points in that space, if you prefer to think of it that way. You can define any coordinate system you like (they don’t have to be orthogonal), and you still find that you need exactly three dimensions to locate points in space.
Thank you. That link made my week.
You’re welcome, nothamlet.
So, you are asking if there are any subspaces of our 3D space that have less than three dimensions. I read somewhere (Scientific American I think) about some quantum effects that are limited to one or two dimensions and I think even zero dimensions (a point).
Protesilaus That site is great. I looked at Flatland over there. They even translated the illustrations to ASCII. Fortunately, the illustrations are simple enough to be rendered successfully in ASCII.
Black holes are about as proven as anything else in astronomy: Pretty much any theory of gravity you can name, and particularly General Relativity, predicts that they should exist, and there are a large number of astronomical observations which cannot be satisfactorially explained without invoking a black hole. However, all that we can observe (and all that we can ever observe) of a black hole is the event horizon, which is the surface of a perfectly ordinary 3-dimensional sphere or oblate ellipsoid. The singularity may well be a perfect geometrical point, but if it is, it’s a moot one.
Speaking of black holes, electrons are presumably larger than about 10[sup]-56[/sup] cm, because otherwise they’d be naked singularities, which is a big no-no. However, that’s almost certainly too small to talk about such things, and everyone would be extremely surprised if gravity was even remotely close to being recognizable on those scales.
The event horizon is not a real object, it’s just where gravity is just strong enough that light can’t escape. (would this mean the escape velocity at the event horizon = c?) The real object in the clapsed star and all that was sucked in.
Thank you very much for posting that, Protesilaus. I was concerned about posting a link that gave an entire text of a book. I had no idea if it was possible to update, or “re-edit” a book in a way that it would still be covered by applicable copywright laws, and the Terms of Service for the Straight Dope that we all agree to is very strict in it’s wording as to copywrighting, and pasting. I simply didn’t wish to risk a rule infraction.
I’m assuming your link is okay, since a Mod has been along since you posted it. Again, thanks for doing that. The book’s well deserving of another read !
Cartooniverse