Imwashingmypirate wrote:Have you ever tried cutting along the middle of a mobius strip?
A long time ago when I was 10 or so. It becomes one bigger loop with a a twist or two in it as I recall.
Are you a Mathmetician?
No, I'm an engineer. However, I like math more than many of the engineers I know and I was pretty good at all my math classes. When I was 16-18 I even placed fairly high in state math competitions. I'm not MIT or Cal-Tech material though.
That's General Leo. He could be my friend if he weren't my enemy. eritis sicut dii I support NCMO
Imwashingmypirate wrote:I was thinking as these have infinate aspects one coult say dimensions might go to infinity.
I suppose they do have infinite aspects, but a Mobius strip can be embedded in 3 dimensional Euclidean space while a Klein bottle can be embedded in 4-dimensional space. Both topologies themselves are 2 dimensional objects.
I would say that a regular ring also has infinite aspects to it as does a torus. Neither one implies infinitey in my opinion, but I do think that dimensions could go to infinity. In fact I still think that dimensions is merely a convenient idea for trying to understand how we interact with the world. Sometimes it's convenient to think of other things as dimensions too. Take DNA for example. If you look at each pair in a gene as a separate dimension, then you have an object that you can represent as a dot in a a graph that has millions or billlions of dimensions. Take a double-pendulum for example. This is often explained in terms of a torus where one direction of the torus represents one pendulum's angle while the other direction represents the other one. Then at each point on the torus you can plot what forces there will be for each pendulum. This can also be a useful way to think of genes because you could plot different genes on that graph and ask which ones are closest to each other. You can also ask what the environment is and plot those forces in the graph and then ask yourself where the dots likely to drift after many generations.
I imagine there are applications where thinking of infinite dimensions is also useful. As to whether there are actually infinite spatial dimenstions is another matter. I suppose it's possible. I for one wonder what it would be like to exist in such a world. I also wonder if there would be a difference if it were countable infinite or uncountably infinite. Countable infinity is more like the number of integers while uncountably infinite is more continuous like the set of real numbers
That's General Leo. He could be my friend if he weren't my enemy. eritis sicut dii I support NCMO
